0.00/0.04 % Problem : theBenchmark.p : TPTP v0.0.0. Released v0.0.0. 0.00/0.04 % Command : tptp2X_and_run_prover9 %d %s 0.03/0.24 % Computer : n134.star.cs.uiowa.edu 0.03/0.24 % Model : x86_64 x86_64 0.03/0.24 % CPU : Intel(R) Xeon(R) CPU E5-2609 0 @ 2.40GHz 0.03/0.24 % Memory : 32218.625MB 0.03/0.24 % OS : Linux 3.10.0-693.2.2.el7.x86_64 0.03/0.24 % CPULimit : 300 0.03/0.24 % DateTime : Sat Jul 14 05:50:24 CDT 2018 0.03/0.24 % CPUTime : 10.52/10.51 ============================== Prover9 =============================== 10.52/10.51 Prover9 (32) version 2009-11A, November 2009. 10.52/10.51 Process 43659 was started by sandbox2 on n134.star.cs.uiowa.edu, 10.52/10.51 Sat Jul 14 05:50:34 2018 10.52/10.51 The command was "/export/starexec/sandbox2/solver/bin/prover9 -t 300 -f /tmp/Prover9_43457_n134.star.cs.uiowa.edu". 10.52/10.51 ============================== end of head =========================== 10.52/10.51 10.52/10.51 ============================== INPUT ================================= 10.52/10.51 10.52/10.51 % Reading from file /tmp/Prover9_43457_n134.star.cs.uiowa.edu 10.52/10.51 10.52/10.51 set(prolog_style_variables). 10.52/10.51 set(auto2). 10.52/10.51 % set(auto2) -> set(auto). 10.52/10.51 % set(auto) -> set(auto_inference). 10.52/10.51 % set(auto) -> set(auto_setup). 10.52/10.51 % set(auto_setup) -> set(predicate_elim). 10.52/10.51 % set(auto_setup) -> assign(eq_defs, unfold). 10.52/10.51 % set(auto) -> set(auto_limits). 10.52/10.51 % set(auto_limits) -> assign(max_weight, "100.000"). 10.52/10.51 % set(auto_limits) -> assign(sos_limit, 20000). 10.52/10.51 % set(auto) -> set(auto_denials). 10.52/10.51 % set(auto) -> set(auto_process). 10.52/10.51 % set(auto2) -> assign(new_constants, 1). 10.52/10.51 % set(auto2) -> assign(fold_denial_max, 3). 10.52/10.51 % set(auto2) -> assign(max_weight, "200.000"). 10.52/10.51 % set(auto2) -> assign(max_hours, 1). 10.52/10.51 % assign(max_hours, 1) -> assign(max_seconds, 3600). 10.52/10.51 % set(auto2) -> assign(max_seconds, 0). 10.52/10.51 % set(auto2) -> assign(max_minutes, 5). 10.52/10.51 % assign(max_minutes, 5) -> assign(max_seconds, 300). 10.52/10.51 % set(auto2) -> set(sort_initial_sos). 10.52/10.51 % set(auto2) -> assign(sos_limit, -1). 10.52/10.51 % set(auto2) -> assign(lrs_ticks, 3000). 10.52/10.51 % set(auto2) -> assign(max_megs, 400). 10.52/10.51 % set(auto2) -> assign(stats, some). 10.52/10.51 % set(auto2) -> clear(echo_input). 10.52/10.51 % set(auto2) -> set(quiet). 10.52/10.51 % set(auto2) -> clear(print_initial_clauses). 10.52/10.51 % set(auto2) -> clear(print_given). 10.52/10.51 assign(lrs_ticks,-1). 10.52/10.51 assign(sos_limit,10000). 10.52/10.51 assign(order,kbo). 10.52/10.51 set(lex_order_vars). 10.52/10.51 clear(print_given). 10.52/10.51 10.52/10.51 % formulas(sos). % not echoed (5740 formulas) 10.52/10.51 10.52/10.51 ============================== end of input ========================== 10.52/10.51 10.52/10.51 % From the command line: assign(max_seconds, 300). 10.52/10.51 10.52/10.51 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 10.52/10.51 10.52/10.51 % Formulas that are not ordinary clauses: 10.52/10.51 1 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_395_mult__less__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 2 (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),zero_zero(real)),X) = zero_zero(X_a)))) # label(fact_4709_scaleR__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 3 (all X_1 all N_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))))) # label(fact_1362_exp__mono__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 4 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),A_3) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 5 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hAPP(int,nat,nat_1,Y_1) = hAPP(int,nat,nat_1,X_1) <-> ti(int,X_1) = ti(int,Y_1))))) # label(fact_1105_transfer__nat__int__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 6 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1))),zero_zero(X_a))) <-> zero_zero(X_a) = ti(X_a,Y_1) & zero_zero(X_a) = ti(X_a,X_1))))) # label(fact_45_sum__squares__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 7 (all B all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A_1))),hAPP(complex,real,norm_norm(complex),B))),hAPP(complex,real,norm_norm(complex),A_1)))) # label(fact_1784_complex__mod__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 8 (all X_a (cancel_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_3_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 9 (all X_a (real_algebra_1(X_a) -> (all X all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(real,X_a,of_real(X_a),X)),N) = hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))))) # label(fact_2789_of__real__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 10 (all X_a (real_algebra(X_a) -> (all X all A_1 all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_4675_mult__scaleR__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 11 (all X_a (cancel_semigroup_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,C) = ti(X_a,B))))) # label(fact_768_add__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 12 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),K_4)),J_2)) # label(fact_742_diff__commute) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 13 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_2))))) # label(fact_3783_zero__less__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 14 (all B all B_5 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_5)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))))))) # label(fact_1017_zdiv__mono2__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 15 (all X_a (field_char_0(X_a) -> (all N_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)),field_char_0_Rats(X_a))))))) # label(fact_3697_Rats__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 16 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_394_mult__pos__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 17 (all X_c all X_a all X_b all Z all C_1 all P_4 ((all A_4 all B_4 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) = ti(product_prod(X_a,X_b),P_4) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z),hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_4),B_4))))) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),Z),hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4))))) # label(fact_4057_mem__splitI2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 18 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_1622_real__sqrt__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 19 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_2))))) # label(fact_982_neg__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 20 (all N N != hAPP(nat,nat,suc,N)) # label(fact_1216_Suc__n__not__n) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 21 (all I_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,abs_abs(int),I_1) = ti(int,I_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),zero_zero(int))) -> hAPP(int,int,uminus_uminus(int),I_1) = hAPP(int,int,abs_abs(int),I_1)))) # label(fact_2168_zabs__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 22 (all X_a (real_normed_field(X_a) & field_inverse_zero(X_a) -> (all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1783_norm__divide) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 23 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_1080_div__add1__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 24 (all X_a (division_ring(X_a) -> (all B_1 all A_2 all C_1 (zero_zero(X_a) != ti(X_a,C_1) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2) <-> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 25 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),int_gcd,X),Y)) # label(fact_3671_Nitpick_Oint__gcd__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 26 (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_1154_MultInv__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 27 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_2)),one_one(real))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),hAPP(real,int,archimedean_ceiling(real),X_1))))) # label(fact_3417_le__ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 28 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3812_bdd__int__set__l__le__finite) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 29 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,tan,X)) = hAPP(real,real,tan,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2252_tan__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 30 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3542_minus__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 31 (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]. 10.52/10.51 32 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_4010_summable__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 33 (all X_a (number_ring(X_a) -> (all V all C all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),hAPP(int,X_a,number_number_of(X_a),W))) = 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)))) # label(fact_2174_add__number__of__diff2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 34 (all X_a (real_algebra_1(X_a) -> (all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = hAPP(real,X_a,of_real(X_a),hAPP(int,real,ring_1_of_int(real),Z_1))))) # label(fact_3573_of__real__of__int__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.51 35 (all N_1 all X_1 exists T_4 (hAPP(real,real,exp(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4270_Maclaurin__exp__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 36 (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),F),A_3)))))) # label(fact_4305_transfer__nat__int__sum__prod__closure_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 37 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,tan,X)) # label(fact_2256_tan__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 38 (all X_a (linorder(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X))))))) # label(fact_4977_min__max_Osup__least) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 39 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))))) # label(fact_74_less__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 40 (all V_1 all N_1 (hAPP(nat,nat,suc,N_1) = hAPP(int,nat,number_number_of(nat),V_1) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> N_1 = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & -hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_3885_eq__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 41 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> Y = hAPP(real,real,cos,hAPP(real,real,arccos,Y))))) # label(fact_2263_cos__arccos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 42 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 43 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_1778_norm__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 44 (all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),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_2 exists D_3 ((all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_4),A_4)),D_3)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))))))) # label(fact_3205_lemma__BOLZANO) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 45 (all X_a (ord(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),ord_less_eq(X_a)) = ord_min(X_a))) # label(fact_4837_min__ord__min) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 46 (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_641_dvd_Oless__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 47 (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_1378_nat__0__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 48 (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_1878_abs__eq__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 49 (all X_a (monoid_mult(X_a) -> (all A_1 all M all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))))) # label(fact_349_power__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 50 (all X all Y hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y))) # label(fact_2978_Im_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 51 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)) -> (hAPP(nat,nat,suc,I_1) != K_4 -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> K_4 != hAPP(nat,nat,suc,J_1)))))) # label(fact_1542_lessE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 52 (all A_2 all D_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),plus_plus(nat),A_2)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))),D_1))))) # label(fact_4322_arith__series__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 53 (all X_b all X_a all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),B_2),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2))))) # label(fact_3642_finite__surj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 54 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),hAPP(int,int,uminus_uminus(int),J_2)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3443_zgcd__zminus2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 55 (all X_a hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),one_one(int))) = one_frac(X_a)) # label(fact_3684_Nitpick_Oone__frac__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 56 (all X_a (linordered_idom(X_a) -> (all X all Y all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))))) # label(fact_2440_power__mono__even) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 57 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1979_ln__add__one__self__le__self2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 58 (all Z_1 hAPP(complex,real,norm_norm(complex),Z_1) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,Z_1))) # label(fact_2941_complex__mod__cnj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 59 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1705_frac__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 60 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))))))) # label(fact_2574_inverse__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 61 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,inverse_inverse(real),X))) # label(fact_2623_real__inv__sqrt__pow2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 62 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),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_4),X))))) # label(fact_4693_of__real_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 63 (all X_a (real_vector(X_a) -> (all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(int,real,number_number_of(real),min_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_4724_scaleR__minus1__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 64 (all X_a all X_b (comm_monoid_mult(X_b) -> (all Y_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),Y_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),Y_1)),A_3))))) # label(fact_3959_setprod__constant) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 65 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 66 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_71_rel__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 67 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),X)) # label(fact_4673_real__scaleR__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 68 (all X_a (number_ring(X_a) -> (all V all W all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),C)))) # label(fact_507_add__number__of__diff1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 69 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B))))) # label(fact_3117_mod__neg__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 70 (all Y all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y)))))) # label(fact_278_zpower__zdvd__prop2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 71 (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_3334_real__of__int__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 72 (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]. 10.52/10.52 73 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),hAPP(int,int,uminus_uminus(int),W))) # label(fact_2162_diff__int__def__symmetric) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 74 (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(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) & (-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))))))) # label(fact_902_negDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 75 (all X_a all X_b all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_3))),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_3636_image__Pow__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 76 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists K_2 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_2352_lemma__NBseq__def2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 77 (all X_b all X_c all X_a all F all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3993_split__conv) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 78 (all X_b all X_c all X_a all F1 all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_rec(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3155_prod_Orecs) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 79 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) & real_algebra_1(X_b) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4613_of__real_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 80 (all X_b all X_a all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))))) # label(fact_3638_imageI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 81 (all D all I_1 (zero_zero(int) != ti(int,I_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),I_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),D)),hAPP(int,int,abs_abs(int),I_1)))))) # label(fact_1940_dvd__imp__le__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 82 (all X_a all X_1 all Y_1 all F (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(X_a,nat),fun(product_prod(X_a,X_a),bool),measure(X_a),F))))) # label(fact_3319_in__measure) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 83 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_1677_divide__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 84 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),min_1)),B))) # label(fact_1064_zmod__minus1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 85 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),zero_zero(real))))) # label(fact_4917_isCont__root__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 86 (all A_1 all C all D all B (zero_zero(int) != ti(int,B) -> (zero_zero(int) != ti(int,D) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))))) # label(fact_3786_diff__rat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 87 (all X_a (real_normed_algebra(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_1788_norm__mult__ineq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 88 (all X_a (linordered_idom(X_a) -> (all A_1 all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(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))))) # label(fact_2084_abs__power__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 89 (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]. 10.52/10.52 90 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y ((all Z_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_2),X)),Y))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1523_field__le__mult__one__interval) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 91 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) # label(fact_521_nat__add__commute) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 92 (all X_a (real_normed_vector(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3317_CauchyI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 93 (all X_1 X_1 = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X_1)))) # label(fact_3867_card__bdd__nat__set__l) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 94 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4077_of__real_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 95 (all X_a (field(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2558_field__divide__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 96 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_1843_abs__ge__self) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 97 (all X_a (real_normed_vector(X_a) -> (all X_1 all A_2 hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1)),hAPP(real,filter(real),at(real),A_2)))))) # label(fact_4733_scaleR__left_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 98 (all X_a (ring_1(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_2117_ring__1__class_Opower__minus__even) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 99 (all X_a (real_algebra_1(X_a) -> (all F all X_2 hAPP(real,X_a,of_real(X_a),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),F),X_2)) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),F)),X_2)))) # label(fact_4111_diffs__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 100 (all X_a (linordered_field(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_2613_inv__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 101 (all X_a (real_normed_algebra(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_875_mult_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 102 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1466_even__sum__div__2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 103 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1)) # label(fact_230_nat__mult__2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 104 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_4986_le__maxI1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 105 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),hAPP(complex,complex,uminus_uminus(complex),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y)) # label(fact_2153_complex__diff__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 106 (all K_4 all L_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),z3mod,K_4),L_4)))) # label(fact_2728_z3mod__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 107 (all X_a all F all A_3 all N_1 (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) = hAPP(nat,nat,suc,N_1) -> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))))) # label(fact_4301_setsum__SucD) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 108 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (exists B_4 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3)))))) # label(fact_2727_psubset__imp__ex__mem) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 109 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_780_add__le__imp__le__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 110 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3906_DERIV__cos__cos__mult3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 111 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_3999_mult__right_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 112 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),N))) # label(fact_1086_Divides_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 113 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),X_1),Y_1)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1))))) # label(fact_3678_image__uminus__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 114 (all X_a all X_b (metric_space(X_a) & real_n2089651433ebra_1(X_b) -> (all A_2 all K all L_2 (ti(X_a,L_2) != ti(X_a,K) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),L_2),hAPP(X_b,filter(X_b),at(X_b),A_2))))))) # label(fact_4559_LIM__const__not__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 115 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2536_inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 116 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially)))))) # label(fact_4515_summable__Leibniz_H_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 117 (all X_b all X_a (topological_space(X_a) & real_n1866405975lgebra(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (zero_zero(X_b) != hAPP(X_a,X_b,F,A_2) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),A_2))))))) # label(fact_4912_isCont__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 118 (all X_a (plus(X_a) & dvd(X_a) & linorder(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]. 10.52/10.52 119 (all A_1 all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1))))) # label(fact_3058_prime__dvd__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 120 (all X_1 all N_1 all Y_1 (Y_1 = X_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))) # label(fact_1254_exp__mono__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 121 (all X_a (linordered_field(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1717_divide__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 122 (all X_1 all Y_1 (hAPP(complex,complex,cnj,Y_1) = hAPP(complex,complex,cnj,X_1) <-> X_1 = Y_1)) # label(fact_2937_complex__cnj__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 123 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)) = ti(X_a,A_1)))) # label(fact_915_mod__div__equality) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 124 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))) # label(fact_828_wset__mem__inv__mem) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 125 (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]. 10.52/10.52 126 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) # label(fact_3263_gcd__add__mult__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 127 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_1284_of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 128 (all K_4 hAPP(int,int,bit0,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),K_4)) # label(fact_133_Bit0__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 129 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_2)) -> (N_1 = Ma <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),Ma)))))) # label(fact_413_power__inject__exp) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 130 (all X_b all X_a (topological_space(X_a) & real_normed_field(X_b) -> (all Y_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4586_divide_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 131 (all X_a (ring_char_0(X_a) -> (all Z (ti(int,Z) = zero_zero(int) <-> hAPP(int,X_a,ring_1_of_int(X_a),Z) = zero_zero(X_a))))) # label(fact_3578_of__int__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 132 (all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))) -> A_1 = one_one(nat))) # label(fact_897_gcd__lcm__complete__lattice__nat_Ole__bot) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 133 (all Ma all N_1 ((exists K_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1) = N_1) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_571_le__iff__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 134 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_2422_odd__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 135 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))))) # label(fact_687_less__diff__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 136 (all V all W hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) # label(fact_25_times__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 137 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_2073_comm__ring__1__class_Onormalizing__ring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 138 (all X_a (ring_char_0(X_a) -> (all Z (ti(int,Z) = zero_zero(int) <-> hAPP(int,X_a,ring_1_of_int(X_a),Z) = zero_zero(X_a))))) # label(fact_3579_of__int__0__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 139 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 140 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)))) # label(fact_904_pos__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 141 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_1282_of__nat__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 142 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))))))) # label(fact_3612_floor__correct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 143 (all R_4 all P_5 all Q_3 (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) = hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3726_normalize__denom__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 144 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),pi)) & hAPP(real,real,cos,X_2) = Y & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),pi)) & hAPP(real,real,cos,Y_2) = Y -> Y_2 = X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2))))))) # label(fact_2248_cos__total) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 145 (all X_a (linordered_idom(X_a) -> (all N hAPP(nat,X_a,semiring_1_of_nat(X_a),N) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_1849_abs__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 146 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(int,int,number_number_of(int),V) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(int,X_a,number_number_of(X_a),V))))) # label(fact_2872_floor__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 147 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5))))) # label(fact_4717_scaleR_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 148 (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)) -> (B != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,B)),hAPP(real,real,ln,A_1))),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X))))))) # label(fact_2651_log__eq__div__ln__mult__log) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 149 (all X_a (ord(X_a) -> ord_atLeastLessThan(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_atLeastLessThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OatLeastLessThan_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 150 (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_1)),Z_1)))) # label(fact_2101_mult__minus1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 151 (all M all N -(all Q_4 all R_2 -hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_4),R_2))))) # label(fact_3104_divmod__nat__rel__ex) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 152 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,one_one(int)),hAPP(int,int,number_number_of(int),K_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3733_Fract__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 153 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3))))) # label(fact_1310_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 154 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)),X)))))))) # label(fact_437_mult__left__le__one__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 155 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),X) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X)))) # label(fact_2615_sqrt__divide__self__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 156 (all R_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_4)) -> -(all S_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),S_1)) -> (all T_4 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),T_4)) -> hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),S_1),T_4) != R_4)))))) # label(fact_3731_obtain__pos__sum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 157 (all X_a (banach(X_a) -> (all F all N_4 all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C_1),one_one(real))) -> ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_4054_ratio__test) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 158 (all X_a (real_vector(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),one_one(real)),X)))) # label(fact_4706_real__vector_Oscale__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 159 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))))) # label(fact_152_add__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 160 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))))))) # label(fact_2879_floor__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 161 (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]. 10.52/10.52 162 (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_3459_zgcd__non__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 163 (all X hAPP(real,real,abs_abs(real),X) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X))) # label(fact_1872_real__sqrt__abs2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 164 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),X))) # label(fact_4346_gcd__dvd1__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.52 165 (all X hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,tan,X)) # label(fact_2266_tan__periodic) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 166 (all X_b all X_a (real_algebra_1(X_b) & real_normed_vector(X_b) & topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4595_LIM__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 167 (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]. 10.52/10.53 168 (all X_a (metric_space(X_a) -> (all Y all Z_1 all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1))))))) # label(fact_3507_dist__triangle__alt) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 169 (all W hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),W)) = hAPP(int,nat,number_number_of(nat),W)) # label(fact_1113_nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 170 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)) = hAPP(complex,complex,cnj,hAPP(fun(nat,complex),complex,suminf(complex),X_3)))) # label(fact_4041_cnj_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 171 (all X_a (linord581940658strict(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))))))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 172 (all X_a (field(X_a) & number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1733_divide__numeral__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 173 (all X_a all X_b all A_2 all B_1 all A_8 all B_7 all R_1 all Sa (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),A_2),A_8)),R_1)) | ti(X_a,A_8) = ti(X_a,A_2) & hBOOL(hAPP(fun(product_prod(X_b,X_b),bool),bool,hAPP(product_prod(X_b,X_b),fun(fun(product_prod(X_b,X_b),bool),bool),member(product_prod(X_b,X_b)),hAPP(X_b,product_prod(X_b,X_b),hAPP(X_b,fun(X_b,product_prod(X_b,X_b)),product_Pair(X_b,X_b),B_1),B_7)),Sa)) <-> hBOOL(hAPP(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool,hAPP(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),fun(fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),bool),member(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),hAPP(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(product_prod(X_a,X_b),fun(product_prod(X_a,X_b),product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b))),product_Pair(product_prod(X_a,X_b),product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_8),B_7))),hAPP(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool),hAPP(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool)),lex_prod(X_a,X_b),R_1),Sa))))) # label(fact_3487_in__lex__prod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 174 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),A_3)))) # label(fact_3652_transfer__nat__int__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 175 (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]. 10.52/10.53 176 (all X_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1)),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1161_StandardRes__SRStar__prop4) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 177 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1993_arctan__ubound) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 178 (all X_a (real_normed_vector(X_a) -> (all Y all S_3 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),S_3)))))))) # label(fact_1792_norm__add__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 179 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))),one_one(X_a)))))))) # label(fact_1404_power__Suc__less__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 180 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),zero_zero(nat))) # label(fact_4112_nat__case__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 181 (all X_b all X_a (real_normed_algebra(X_b) & metric_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4577_LIM__mult__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 182 (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),A_1),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X) -> A_1 = B))))) # label(fact_4705_scaleR__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 183 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1434_mod2__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 184 (all A_3 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))))) -> ((exists X_2 ((exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_3)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xa),X_2))))) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & hBOOL(hAPP(int,bool,P_2,X_2)))) <-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))))) # label(fact_4875_cppi) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 185 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1644_real__sqrt__sum__squares__ge2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 186 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2339_cos__diff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 187 (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]. 10.52/10.53 188 (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),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))) & 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_365_split__mult__neg__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 189 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))) # label(fact_1689_mult__divide__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 190 (all Ma all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))))) # label(fact_597_mult__less__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 191 (all N all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_261_Nat__Transfer_Otransfer__nat__int__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 192 (all B all X all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)))))) # label(fact_3235_gcd__semilattice__nat_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 193 (all B all A_1 all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),C)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C))) # label(fact_4364_gcd__int_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 194 (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),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))) = 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_215_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 195 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all Ma all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),L),Ma)),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4566_LIM__diff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 196 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),P_4)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),P_4)) = hAPP(int,nat,nat_1,A_2)))) # label(fact_3204_Bnor__prime) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 197 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4599_cnj_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 198 (all X_a (ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (ti(X_a,C_1) = ti(X_a,D_1) <-> ti(X_a,A_2) = ti(X_a,B_1)))))) # label(fact_773_diff__eq__diff__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 199 (all D_1 hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(fun(int,bool),fun(int,bool)),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combb(fun(int,bool),fun(int,bool),int),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int)))) = hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than2,D_1)) # label(fact_4075_int__ge__less__than2__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 200 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = Y -> X = zero_zero(real))) # label(fact_1646_real__sqrt__sum__squares__eq__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 201 (all K_4 hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,real,number_number_of(real),K_4)) # label(fact_3763_Ratreal__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 202 (all I all P_1 all K (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_2843_int__induct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 203 (all X_b all X_a (metric_space(X_a) & topological_space(X_b) -> (all L all F all G all A_2 all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),R_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4652_metric__LIM__equal2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 204 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y))))))) # label(fact_2705_real__root__less__mono__lemma) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 205 (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 -> Y = hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))) # label(fact_2710_real__root__pos__unique) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 206 (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]. 10.52/10.53 207 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),X))))) # label(fact_4829_min__max_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 208 (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_2551_nonzero__inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 209 (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)) -> 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),quadRes,P_5),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5) = hAPP(int,int,number_number_of(int),min_1))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5)))) # label(fact_607_Legendre__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 210 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,abs_abs(int),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))) # label(fact_4379_gcd__proj2__if__dvd__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 211 (all X_a (metric_space(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E)))))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3522_Cauchy__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 212 (all P_1 all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))) <-> (all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))))) # label(fact_4536_all__nat__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 213 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,X_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(X_a))))) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 214 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(real))))) # label(fact_1906_less__one__imp__sqr__less__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 215 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,cos,X))) # label(fact_2220_cos__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 216 (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),div_mod(nat),M),N)),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))) # label(fact_1093_mod__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 217 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),zero_zero(nat)),N) = N) # label(fact_4961_max__0L) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 218 (all X_b all X_c all X_a all F1 all A_2 all B_1 hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),F1,A_2),B_1) = hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1))) # label(fact_3992_Product__Type_Oprod_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 219 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3))))))) # label(fact_4006_of__real_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 220 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,A_1) = ti(X_a,B) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_1553_ord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 221 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4855_SetInterval_Otransfer__int__nat__set__function__closures) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 222 (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_3285_ceiling__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.53 223 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 224 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_791_add__less__cancel__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 225 (all P_1 all P_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P_2,X_2)))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_2),X_2)) -> (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P_2,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2845_plusinfinity) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 226 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2060_less__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 227 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3914_DERIV__cos__realpow2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 228 (all R_4 all P_5 all Q_3 (hAPP(rat,product_prod(int,int),quotient_of,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int))) # label(fact_4403_quotient__of__coprime) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 229 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),min_1))))) # label(fact_2605_nonzero__number__of__Min) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 230 (all X all Y all M (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),M) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),M) = one_one(nat))) # label(fact_3292_invertible__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 231 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z)))))) # label(fact_4830_min__le__iff__disj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 232 (all S_3 all T_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),S_3),T_5)) -> S_3 != T_5)) # label(fact_519_less__not__refl3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 233 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4019_summable__rabs) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 234 (all A_1 all B all C all D hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))) # label(fact_2745_complex__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 235 (all X_a all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_3)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3))) # label(fact_4862_transfer__int__nat__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 236 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all N_1 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> zero_zero(X_a) = hAPP(nat,X_a,F,M_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))))))) # label(fact_4291_series__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 237 (all N hAPP(nat,complex,semiring_1_of_nat(complex),N) = hAPP(complex,complex,cnj,hAPP(nat,complex,semiring_1_of_nat(complex),N))) # label(fact_2940_complex__cnj__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 238 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,A_2))))) # label(fact_4115_Im_Osums) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 239 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4580_LIM__offset__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 240 (all N hAPP(int,nat,number_number_of(nat),N) = hAPP(real,nat,natfloor,hAPP(int,real,number_number_of(real),N))) # label(fact_1876_natfloor__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 241 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b)))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),P_1)) # label(fact_4781_split__paired__Eps) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 242 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_1658_divide__zero__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 243 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2))),X)))))))) # label(fact_2719_ex__inverse__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 244 (all X_b all X_a (order(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,B_1)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),A_2)))))))) # label(fact_2835_xt4) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 245 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1152_div__2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 246 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3540_times__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 247 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,real_1(int),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)))) # label(fact_3384_real__of__int__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 248 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_711_real__mult__order) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 249 (all F all A_2 all B_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))),B_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,A_2)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2))),A_2))) # label(fact_1800_lemma__MVT) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 250 (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_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)))) & 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))))))) # label(fact_3124_conjI__realizer) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 251 (all I all J hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),suc),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J)) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,I)),hAPP(nat,nat,suc,J))) # label(fact_4539_image__Suc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 252 (all X_a (linorder(X_a) -> (all Y all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))))) # label(fact_4985_le__maxI2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 253 (all Ma all K all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K) <-> N_1 = Ma)) # label(fact_525_nat__add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 254 (all X_a (division_ring(X_a) -> (all N all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),N) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))) # label(fact_2553_nonzero__power__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 255 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_1301_zle__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 256 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all Ma all F all L all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L),hAPP(X_b,X_b,uminus_uminus(X_b),Ma))),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4587_LIM__add__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 257 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K))) <-> (zero_zero(int) = ti(int,K) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),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,N_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) -> hBOOL(hAPP(int,bool,P_1,I_2))))))) # label(fact_1055_split__zdiv) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 258 (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_1036_zmod__zdvd__zmod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 259 (all X_a (comm_ring_1(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N))))) # label(fact_2424_Parity_Opower__minus__even) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 260 (all N_1 all Ma (hAPP(nat,real,real_1(nat),Ma) = hAPP(nat,real,real_1(nat),N_1) <-> N_1 = Ma)) # label(fact_2292_real__of__nat__inject) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 261 (all N_1 all X_1 (X_1 != one_one(real) -> hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1)),one_one(real))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real))))) # label(fact_4206_sumr__geometric) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 262 (all X_1 (X_1 = zero_zero(real) <-> hAPP(real,real,exp(real),X_1) = one_one(real))) # label(fact_2569_exp__eq__one__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 263 (all X_a all One all Times all A_2 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),Times,A_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),N_1)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),hAPP(nat,nat,suc,N_1))) # label(fact_2841_power_Opower_Opower__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 264 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,W_1)),zero_zero(int))))) # label(fact_157_bin__less__0__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 265 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B_5)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),B_5))))) # label(fact_880_mult_Oadd__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 266 (all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_1817_finite__Diff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 267 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2))))))) # label(fact_3669_transfer__int__nat__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 268 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3493_Cauchy__Bseq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 269 (all X all Y all Xa_1 all Ya hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1648_real__sqrt__sum__squares__mult__squared__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 270 (all X_a (linorder(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),C),D)))))))) # label(fact_4976_min__max_Osup__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 271 (all X_a (group_add(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,uminus_uminus(X_a),zero_zero(X_a)))) # label(fact_2025_minus__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 272 (all E_1 all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),E_1)))))) # label(fact_2856_coprime__divisors) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 273 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),zero_zero(X_a))))))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 274 (all A_1 all B hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,abs_abs(int),A_1)),hAPP(int,int,abs_abs(int),B))) # label(fact_3757_abs__rat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 275 (all W ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),W)),hAPP(int,nat,number_number_of(nat),W)))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W))) -> zero_zero(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W))))) # label(fact_3890_nat__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 276 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),zero_zero(int)),X) = hAPP(int,int,abs_abs(int),X)) # label(fact_4387_gcd__0__left__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 277 (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]. 10.52/10.54 278 (all Real1_1 all Real2_1 hAPP(complex,nat,size_size(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1)) = zero_zero(nat)) # label(fact_2754_complex_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 279 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2197_ComplE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 280 (all V (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V))) -> hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat))))) # label(fact_1432_expand__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 281 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),hAPP(int,int,succ,L_4))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_1532_add__Bit1__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 282 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_1659_times__divide__eq__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 283 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_3)))))) # label(fact_3803_finite__Collect__subsets) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 284 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_1583_linorder__not__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 285 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_681_zero__less__diff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 286 (all X_b (number(X_b) & monoid_mult(X_b) -> (all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),W)),hAPP(int,X_b,number_number_of(X_b),W))))) # label(fact_168_power2__eq__square__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 287 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),D_2))))))) # label(fact_3863_DERIV__cmult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 288 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,sin,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,cos,X))) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_2322_sin__diff2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 289 (all A_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))))) # label(fact_2177_power3__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 290 (all X_a (metric_space(X_a) -> (all X_3 hAPP(fun(nat,X_a),X_a,lim(X_a),X_3) = hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(filter(nat),fun(X_a,bool),hAPP(fun(X_a,fun(filter(nat),bool)),fun(filter(nat),fun(X_a,bool)),combc(X_a,filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3)),sequentially))))) # label(fact_4495_lim__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 291 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N))))) # label(fact_579_add__leE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 292 (all X_a all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3)) # label(fact_3942_int__setprod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 293 (all X_b all X_a (real_normed_algebra(X_a) -> (all X_1 all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4191_mult__right_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 294 (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)) <-> X_1 != Y_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_622_dvd_Oless__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 295 (all Q_2 all P_1 ((all A_4 all B_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) = one_one(int) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4)))))) -> hBOOL(hAPP(rat,bool,P_1,Q_2)))) # label(fact_4413_Rat__induct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 296 (all X_1 all Y_1 all P_1 ((-hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),Y_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))) & (hBOOL(P_1) -> hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),P_1),X_1),Y_1))))) # label(fact_1484_int__if__cong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 297 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_412_one__le__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 298 (all K_4 all L_4 (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))) # label(fact_2159_zmod__zminus2__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 299 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)))) # label(fact_1957_equalityD2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 300 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))))) # label(fact_2788_of__real__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 301 (all X_a (semiring_div(X_a) -> div_mod(X_a) = ti(fun(X_a,fun(X_a,X_a)),div_mod(X_a)))) # label(tsy_c_Divides_Odiv__class_Omod_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 302 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))))))) # label(fact_785_add__le__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 303 (all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) <-> (exists X_2 ((all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_3)) -> (ti(X_a,Xa) != ti(X_a,X_2) -> hAPP(X_a,nat,F,Xa) = zero_zero(nat)))) & hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(X_a,nat,F,X_2) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3))))))) # label(fact_4256_setsum__eq__Suc0__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 304 (all X_a (real_normed_vector(X_a) -> (all X_3 all K (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3826_Bseq__offset) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 305 (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_2921_nat_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 306 (all X_c all X_a all X_b all F all A_2 all B_1 all A_3 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),A_3)) -> hBOOL(hAPP(fun(X_c,bool),bool,hAPP(X_c,fun(fun(X_c,bool),bool),member(X_c),hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,A_2),B_1)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_c,bool),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(product_prod(X_a,X_b),bool),fun(X_c,bool)),image(product_prod(X_a,X_b),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F)),A_3))))) # label(fact_3981_pair__imageI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 307 -(all T_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),T_4)) # label(fact_18__096_B_Bthesis_O_A_I_B_Bt_O_As_A_094_A2_A_L_A1_A_061_A_I4_A_K_Am_A_L_A1_) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 308 (all X_a (semiring_div(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)),A_1))))) # label(fact_1001_dvd__div__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 309 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1034_pos__mod__sign) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 310 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)))))) # label(fact_4455_tendsto__norm__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 311 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,X_a,number_number_of(X_a),V) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V))))))) # label(fact_1514_of__nat__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 312 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))))))) # label(fact_2026_le__minus__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 313 (all B all D all A_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat) -> (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))))) # label(fact_3269_coprime__mult__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 314 (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_3358_powr__divide2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 315 (all P_1 all Y_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),Y_1))))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y_1),zero_zero(int))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X_1)),hAPP(int,int,uminus_uminus(int),Y_1)))))) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X_1),Y_1)))))))) # label(fact_4394_gcd__cases__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 316 (all X_a (ring_1(X_a) -> (all K ((zero_zero(int) = ti(int,K) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = zero_zero(X_a)) & (zero_zero(int) != ti(int,K) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),K))) = hAPP(int,X_a,ring_1_of_int(X_a),K)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K) = hAPP(product_prod(int,int),X_a,hAPP(fun(int,fun(int,X_a)),fun(product_prod(int,int),X_a),product_prod_case(int,int,X_a),hAPP(fun(int,X_a),fun(int,fun(int,X_a)),hAPP(fun(int,fun(X_a,fun(int,X_a))),fun(fun(int,X_a),fun(int,fun(int,X_a))),combs(int,X_a,fun(int,X_a)),hAPP(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a))),hAPP(fun(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a))),fun(fun(int,fun(int,fun(X_a,X_a))),fun(int,fun(X_a,fun(int,X_a)))),combb(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),int),combc(int,X_a,X_a)),hAPP(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a))),hAPP(fun(X_a,fun(int,fun(X_a,X_a))),fun(fun(int,X_a),fun(int,fun(int,fun(X_a,X_a)))),combb(X_a,fun(int,fun(X_a,X_a)),int),hAPP(fun(int,fun(X_a,fun(X_a,X_a))),fun(X_a,fun(int,fun(X_a,X_a))),combc(int,X_a,fun(X_a,X_a)),hAPP(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a))),hAPP(fun(bool,fun(X_a,fun(X_a,X_a))),fun(fun(int,bool),fun(int,fun(X_a,fun(X_a,X_a)))),combb(bool,fun(X_a,fun(X_a,X_a)),int),if(X_a)),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a))))),hAPP(X_a,fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(X_a,fun(int,X_a)),combc(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),hAPP(fun(int,X_a),fun(int,X_a),hAPP(fun(int,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,X_a)),combs(int,X_a,X_a),hAPP(fun(int,X_a),fun(int,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(int,X_a),fun(int,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),int),plus_plus(X_a)),ring_1_of_int(X_a))),ring_1_of_int(X_a)))),one_one(X_a)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3978_of__int__num) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 317 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),zero_zero(int))) -> (exists N_2 ti(int,X) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_2186_negD) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 318 (all Ma all N_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_4538_SetInterval_Otransfer__nat__int__set__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 319 (all X_a (ring_1(X_a) -> one_one(X_a) = hAPP(int,X_a,ring_1_of_int(X_a),one_one(int)))) # label(fact_3585_of__int__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 320 (all X hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),X)) = hAPP(complex,complex,uminus_uminus(complex),X)) # label(fact_2763_complex__i__mult__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 321 (all X_a (number_ring(X_a) & linord1117847801e_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1768_half) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 322 (all X_a (real_field(X_a) -> (all N_1 all X_1 all Y_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1)),N_1))))) # label(fact_4664_exp__series__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 323 (all X_1 hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),ord_lessThan(real),X_1)) = X_1) # label(fact_4327_Sup__lessThan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 324 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_2059_neg__0__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 325 (all X hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_450_four__x__squared) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 326 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3590_of__int__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 327 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))) # label(fact_332_dvd__triv__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 328 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_823_add__le__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 329 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4))))))) # label(fact_1058_zmult2__lemma__aux1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 330 (all X_a (real_normed_algebra(X_a) -> (all X_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4552_mult__right_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 331 (all N hAPP(real,nat,natfloor,hAPP(nat,real,real_1(nat),N)) = N) # label(fact_2294_natfloor__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.54 332 (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_366_split__mult__pos__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 333 (all X_a (semiring_1(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),one_one(X_a))))) # label(fact_2562_not__iszero__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 334 (all Y_1 all X_1 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1163_SRStar__mult__prop1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 335 (all M one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),one_one(int))) # label(fact_3433_zgcd__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 336 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)))))))) # label(fact_1672_divide__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 337 (all A_1 all B hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))) # label(fact_3777_quotient__of__Fract) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 338 (all X_a (real_normed_algebra(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),A_1)),B)))) # label(fact_4678_mult_OscaleR__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 339 (all M all R_4 all S_3 all T_5 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_3),T_5)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) = ti(int,R_4)))) # label(fact_3082_xzgcd__linear) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 340 (all X_a (comm_semiring_1(X_a) -> (all N all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N))))))) # label(fact_343_dvd__power__same) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 341 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> zero_zero(nat) = hAPP(real,nat,natfloor,X))) # label(fact_1895_natfloor__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 342 (all X_a all F all X_1 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(X_a,nat,F,I_2)),X_1) = 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_3)),X_1) = one_one(nat))) # label(fact_4128_setprod__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 343 (all X_a (real_normed_field(X_a) -> (all Y_3 all F all X_1 all X_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),X_3)) -> (ti(X_a,Y_3) = ti(X_a,X_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Y_3))))))) # label(fact_2634_DERIV__cong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 344 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_1774_norm__minus__commute) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 345 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) # label(fact_3119_mod__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 346 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (exists N_2 hAPP(nat,int,semiring_1_of_nat(int),N_2) = ti(int,K_4)))) # label(fact_1490_zero__le__imp__eq__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 347 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(int,bool),nat,finite_card(int),A_3) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))) # label(fact_3668_Nat__Transfer_Otransfer__int__nat__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 348 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),one_one(X_a)),A_1))))) # label(fact_342_one__dvd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 349 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),F),X_1)))))) # label(fact_4886_DERIV__isCont) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 350 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_930_mod__mult__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 351 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = hAPP(fun(X_a,bool),X_a,the(X_a),hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F))))) # label(fact_4135_suminf__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 352 (all X_a (real_normed_vector(X_a) -> (all G all F all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially))))))) # label(fact_4447_LIMSEQ__diff__approach__zero2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 353 (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),plus_plus(int),Z1),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))) # label(fact_69_zadd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 354 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),A_2)))))) # label(fact_2063_neg__less__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 355 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archim2085082626_floor(real),X) = ti(int,N)))) # label(fact_3398_floor__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 356 (all R_4 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> hAPP(real,real,uminus_uminus(real),R_4) = hAPP(real,real,abs_abs(real),R_4)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> R_4 = hAPP(real,real,abs_abs(real),R_4)))) # label(fact_2111_real__abs__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 357 (all X_a (real_normed_vector(X_a) -> (exists K_2 all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))) # label(fact_4759_scaleR_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 358 (all Y all X (hAPP(real,real,cos,X) != zero_zero(real) -> (hAPP(real,real,cos,Y) != zero_zero(real) -> (hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) != 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_2268_tan__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 359 (all K all L hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L))))) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),L)) # label(fact_3465_zgcd__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 360 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_1545_le__funE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 361 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> -hBOOL(hAPP(nat,bool,even_odd_even(nat),P_5)) | P_5 = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_3079_prime__odd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 362 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_1634_le__real__sqrt__sumsq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 363 (all X_b all X_a (real_normed_field(X_a) -> (all G all A_3 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),G)),Y_1)),A_3)))) # label(fact_4184_divide_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 364 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),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_3960_setprod__mono__one__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 365 (all X_a (ordered_ab_group_add(X_a) -> ord_gr676655987ssThan(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_2_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 366 (all X all Y all Xa_1 all Ya hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Xa_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Ya),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1606_real__sqrt__sum__squares__mult__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 367 (all A_2 all B_1 all C_1 (C_1 != zero_zero(real) -> (A_2 = B_1 <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_1),C_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_2),C_1)))) # label(fact_708_real__mult__right__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 368 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) # label(fact_2092_minus__real__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 369 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))),B)))))) # label(fact_1731_gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 370 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),U))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)))) # label(fact_2087_real__minus__mult__self__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 371 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Aq),Ar))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Bq),Br))) -> (zero_zero(int) != ti(int,C) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Aq),Bq)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ar),Br)),C)))))))) # label(fact_1196_zadd1__lemma) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 372 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2493_fact__ge__one__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 373 (all X all Y all M (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),M))) # label(fact_4349_invertible__coprime__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 374 (all W all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))))) # label(fact_1069_negDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 375 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),G)),H)),A_3))))) # label(fact_4219_setsum_Odistrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 376 (all X_b all X_a (minus(X_a) -> (all A_3 all B_2 all X_1 hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),minus_minus(fun(X_b,X_a)),A_3),B_2),X_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_b,X_a,A_3,X_1)),hAPP(X_b,X_a,B_2,X_1))))) # label(fact_2964_minus__apply) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 377 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)))) # label(fact_158_rel__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 378 (all R all S_5 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R),hAPP(real,real,inverse_inverse(real),S_5)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),R),S_5)) # label(fact_2564_real__divide__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 379 (all X_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_1),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),X_1)),A_2),P_4)))))))) # label(fact_3933_SetS__setprod__prop) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 380 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))) # label(fact_3339_real__of__int__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 381 (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]. 10.52/10.55 382 (all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,B) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = ti(int,Q_3)))) # label(fact_1191_divmod__int__rel__div) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 383 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = ti(X_a,B_1))))) # label(fact_2042_equation__minus__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 384 (all X_a finite_finite_1(X_a) = ti(fun(fun(X_a,bool),bool),finite_finite_1(X_a))) # label(tsy_c_Finite__Set_Ofinite_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 385 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),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_4294_setsum__mono__zero__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 386 (all K all F all N_1 all Ma ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,Ma)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (ti(int,K) = hAPP(nat,int,F,I_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),I_2))))))))) # label(fact_2128_nat__intermed__int__val) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 387 (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_807_inv__distinct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 388 (all Z_1 hAPP(complex,complex,cnj,hAPP(complex,complex,cnj,Z_1)) = Z_1) # label(fact_2938_complex__cnj__cnj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 389 (all P_5 all R_4 all S_3 all Q_3 (zero_zero(int) != ti(int,Q_3) -> (zero_zero(int) != ti(int,S_3) -> (hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),R_4),S_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),Q_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),P_5),S_3))))) # label(fact_3728_normalize__crossproduct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 390 (all X_a all P hAPP(X_a,X_a,combi(X_a),P) = ti(X_a,P)) # label(help_COMBI_1_1_U) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 391 (all X_a (group_add(X_a) -> (all A_2 all B_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) <-> ti(X_a,B_1) = ti(X_a,A_2))))) # label(fact_793_right__minus__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 392 (all X all Q_3 all N all R_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_3),N)),R_4) = X -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),X)))))) # label(fact_732_divides__div__not) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 393 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1972_psubsetD) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 394 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) # label(fact_179_one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 395 (all X_a finite_psubset(X_a) = hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),collect(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),product_prod_case(fun(X_a,bool),fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),ord_less(fun(X_a,bool))))),finite_finite_1(X_a))))) # label(fact_4050_finite__psubset__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 396 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,real_1(int),A_2))))) # label(fact_3361_floor__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 397 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))))) # label(fact_1652_Union__SetS__finite) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 398 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X)))))) # label(fact_3409_real__of__int__div2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 399 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X))))) # label(fact_2595_exp__gt__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 400 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_938_mod__add__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 401 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),U_1),one_one(int)))) # label(fact_4572_atLeastLessThanPlusOne__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 402 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X))))),X))))) # label(fact_2006_best__division__abs) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 403 (all Z1 all Z2 all W hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z1),Z2)),W)) # label(fact_481_zdiff__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 404 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4140_mono__SucI2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 405 (all I all K (hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K) = zero_zero(int) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) | 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)) | zero_zero(int) = ti(int,K))) # label(fact_1026_zdiv__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 406 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all G all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),T_3)))))))) # label(fact_4416_setsum__mono__zero__cong__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 407 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) = hAPP(real,real,cos,X)) # label(fact_2391_cos__sin__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 408 (all X_a all X_b (uminus(X_b) -> (all A_3 all X_2 hAPP(X_b,X_b,uminus_uminus(X_b),hAPP(X_a,X_b,A_3,X_2)) = hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),uminus_uminus(fun(X_a,X_b)),A_3),X_2)))) # label(fact_2965_fun__Compl__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 409 (all X_a (linordered_idom(X_a) -> (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3570_of__int__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 410 (all X all 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)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y))) # label(fact_1305_Nat__Transfer_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 411 (all X_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,real_1(int),X_1)),ring_1_Ints(real)))) # label(fact_3853_Ints__real__of__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 412 (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_1347_diff__Suc__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 413 (all A_1 all B hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,B),A_1)) # label(fact_3750_inverse__rat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 414 (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,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))) = 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_2611_inverse__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 415 (all X_a (banach(X_a) -> (all F ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),M_2)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),M_2),N_2)))),E))))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4287_summable__Cauchy) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 416 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z))))) # label(fact_1125_zless__nat__conj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 417 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),A_1))))) # label(fact_311_dvd__refl) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 418 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,ti(fun(X_a,X_c),B_1_1),B_2_1) = hAPP(X_a,X_c,B_1_1,B_2_1)) # label(tsy_c_hAPP_arg1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 419 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4518_LIMSEQ__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 420 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (C = B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_631_dvd_Oord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 421 (all X_a (semiring_div(X_a) -> (all Y all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Z_1)))))) # label(fact_1005_div__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 422 (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_3551_euclid__bound) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 423 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3273_gcd__diff2__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 424 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),K)))) # label(fact_159_rel__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 425 (all L_4 min_1 != hAPP(int,int,bit0,L_4)) # label(fact_291_rel__simps_I42_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 426 (all N hAPP(real,nat,natceiling,hAPP(nat,real,real_1(nat),N)) = N) # label(fact_2295_natceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 427 (all X_a (real_n2089651433ebra_1(X_a) & number_ring(X_a) -> (all W hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),W))))) # label(fact_1892_norm__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 428 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all C_1 all W_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_1747_divide__less__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 429 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_1),A_3)))) # label(fact_3649_transfer__nat__int__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 430 (all X_a (real_n2089651433ebra_1(X_a) -> (all N hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,real,semiring_1_of_nat(real),N)))) # label(fact_1775_norm__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 431 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)) <-> hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat))) # label(fact_39_eq__number__of__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 432 (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_1379_zless__nat__eq__int__zless) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 433 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_988_pos__mod__bound) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 434 (all Z_1 all W hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),Z_1)),W)) # label(fact_2140_zmult__zminus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 435 (all Ma all N_1 (zero_zero(nat) = N_1 & Ma = zero_zero(nat) <-> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))) # label(fact_3255_gcd__zero__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 436 (all Z1 all Z2 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),W)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),W)) # label(fact_68_zadd__zmult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 437 (all A_1 -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),one_one(nat))))) # label(fact_893_gcd__lcm__complete__lattice__nat_Onot__less__bot) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 438 (all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),R_4)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4)) # label(fact_2814_i__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 439 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) | ti(X_a,Y) = ti(X_a,X))))) # label(fact_1596_order__le__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 440 (all X_a all C_1 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,int),fun(X_a,int),hAPP(fun(int,int),fun(fun(X_a,int),fun(X_a,int)),combb(int,int,X_a),hAPP(int,fun(int,int),times_times(int),C_1)),F)),A_3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3)))) # label(fact_4252_setsum__const__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 441 (all M_5 all D_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_5),D_4) = zero_zero(nat) -> (exists Q_4 M_5 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_4),Q_4)))) # label(fact_1184_mod__eq__0D) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 442 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),R_4))),hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),S_3))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_3))) # label(fact_3780_Ratreal__number__of__quotient) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 443 (all P_1 all X_1 all Y_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> hBOOL(P_1)))) # label(fact_644_dvd_Oless__imp__triv) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 444 (all X_a (semiring_div(X_a) -> (all D_1 all B_1 all C_1 all A_2 (ti(X_a,A_2) != zero_zero(X_a) -> (ti(X_a,C_1) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C_1),D_1)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),D_1),C_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))))))) # label(fact_1043_dvd__div__div__eq__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 445 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ta),one_one(int))),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (ti(int,Ta) = ti(int,X_2) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2) = ti(int,Ta))))))) # label(fact_4637_bset_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 446 (all N hAPP(nat,nat,fact_fact(nat),N) != zero_zero(nat)) # label(fact_2483_fact__nonzero__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 447 (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]. 10.52/10.55 448 (all X_a (linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)))))))) # label(fact_4820_min__max_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 449 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2779_Pow__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 450 (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))) -> N = M))) # label(fact_1235_less__antisym) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 451 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M)))))) # label(fact_662_diff__less__mono2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 452 (all X_b all X_a all A_1 all B hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),A_1),B)) = ti(X_a,B)) # label(fact_3138_snd__conv) # label(axiom) # label(non_clause). [assumption]. 10.52/10.55 453 (all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P_1,X_2)))) -> ((exists X1 hBOOL(hAPP(int,bool,P_1,X1))) <-> (exists X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_1))))))))) # label(fact_4643_periodic__finite__ex) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 454 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all F_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> 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) = one_one(X_b))))) # label(fact_4772_setprod__1_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 455 (all F all N_1 all R_1 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),R_1)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) # label(fact_4176_sumr__diff__mult__const) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 456 (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]. 10.52/10.56 457 (all B all A_1 all A_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_6)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_6),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))))) # label(fact_1014_zdiv__mono1__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 458 (all X all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))))),one_one(int)),P_5))))) # label(fact_1151_Little__Fermat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 459 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_788_add__strict__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 460 (all X_a (semiring_div(X_a) -> (all B all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B)))) # label(fact_941_mod__add__self1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 461 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_2894_floor__le__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 462 (all X hAPP(rat,real,ratreal,hAPP(rat,rat,inverse_inverse(rat),X)) = hAPP(real,real,inverse_inverse(real),hAPP(rat,real,ratreal,X))) # label(fact_3772_real__inverse__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 463 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),Y)))) # label(fact_3346_powr__ge__pzero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 464 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3768_real__minus__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 465 (all X_a (archim1804426504_field(X_a) -> (all X exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),X_2)),X)) & (all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Y_2)),X)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Y_2),one_one(int))))) -> ti(int,Y_2) = ti(int,X_2))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),one_one(int))))))))) # label(fact_3617_floor__exists1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 466 (all Z_1 hAPP(int,real,ring_1_of_int(real),Z_1) = hAPP(complex,real,re,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3571_complex__Re__of__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 467 (all X_a one_frac(X_a) = ti(X_a,one_frac(X_a))) # label(tsy_c_Nitpick_Oone__frac_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 468 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1275_even__odd__disj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 469 (all A_2 all B_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd))))) # label(fact_1367_even__plus__odd__prop2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 470 (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_1621_real__sqrt__eq__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 471 (all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))) -> X = hAPP(nat,nat,suc,zero_zero(nat)) | zero_zero(nat) = X)) # label(fact_1319_nat__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 472 (all X_a all X_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4336_predicate1D) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 473 (all X hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),zero_zero(nat)) = X) # label(fact_3254_gcd__0__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 474 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M))))) # label(fact_486_nat__dvd__not__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 475 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_393_mult__pos__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 476 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(X_a,int,archim2085082626_floor(X_a),R_4) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archim2085082626_floor(X_a),R_4)))))) # label(fact_3357_ceiling__floor) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 477 (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_3531_code__numeral_Osimps_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 478 (all A_1 hAPP(real,real,sin,A_1) = hAPP(complex,real,im,hAPP(real,complex,cis,A_1))) # label(fact_3027_Im__cis) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 479 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1616_real__sqrt__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 480 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = ti(X_a,Y))))) # label(fact_4822_min__max_Oinf__absorb2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 481 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4753_scaleR__left_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 482 (all Ma all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X_1) = zero_zero(int))) # label(fact_1011_StandardRes__eq__zcong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 483 (all N_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),hAPP(bool,fun(real,fun(real,real)),if(real),hAPP(nat,bool,even_odd_even(nat),N_1)),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1)) = zero_zero(real)) # label(fact_2471_lemma__STAR__sin) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 484 (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,sgn_sgn(real),A_1) = hAPP(real,real,uminus_uminus(real),one_one(real))) & (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> one_one(real) = hAPP(real,real,sgn_sgn(real),A_1))) & (A_1 = zero_zero(real) -> hAPP(real,real,sgn_sgn(real),A_1) = zero_zero(real)))) # label(fact_2228_sgn__real__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 485 (all S ((all M_2 exists N_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)))) <-> -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_3657_infinite__nat__iff__unbounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 486 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))))))) # label(fact_380_zero__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 487 (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)),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_3077_prime__divprod__pow) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 488 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_2461_even__nat__div__two__times__two) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 489 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1582_linorder__not__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 490 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3498_BseqD) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 491 (all X_a all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(X_a,int,F,X_2))))) -> hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),hAPP(fun(X_a,int),fun(X_a,nat),hAPP(fun(int,nat),fun(fun(X_a,int),fun(X_a,nat)),combb(int,nat,X_a),nat_1),F)),A_3)))) # label(fact_4861_transfer__int__nat__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 492 (all X_a all X_c all B_1_1 all B_2_1 hAPP(X_a,X_c,B_1_1,B_2_1) = hAPP(X_a,X_c,B_1_1,ti(X_a,B_2_1))) # label(tsy_c_hAPP_arg2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 493 (all I_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),I_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,nat,nat_1,I_1))),one_one(nat)) = hAPP(list(int),nat,size_size(list(int)),hAPP(int,list(int),quickc666637781d_zero,I_1)))) # label(fact_3203_length__around__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 494 (all X_a (real_algebra_1(X_a) -> one_one(X_a) = hAPP(real,X_a,of_real(X_a),one_one(real)))) # label(fact_2786_of__real__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 495 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all D_3 all I_2 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),lazy_small_lazy_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),D_3),I_2))) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),D_3),I_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,D_3),I_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3556_small__lazy_H_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 496 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1085_mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 497 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4582_LIM__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 498 (all X_b (minus(X_b) -> ti(fun(X_b,fun(X_b,X_b)),minus_minus(X_b)) = minus_minus(X_b))) # label(tsy_c_Groups_Ominus__class_Ominus_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 499 (all A_1 all J_2 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5))))) # label(fact_844_MultInv__zcong__prop1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 500 (all I_1 hAPP(quickcheck_code_int,nat,quickcheck_nat_of,I_1) = hAPP(int,nat,nat_1,hAPP(quickcheck_code_int,int,quickcheck_int_of,I_1))) # label(fact_3176_nat__of__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 501 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1744_divide__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 502 (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,uminus_uminus(rat),one_one(rat)) = hAPP(rat,rat,sgn_sgn(rat),Q_3)) & (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),Q_3)) -> hAPP(rat,rat,sgn_sgn(rat),Q_3) = one_one(rat))) & (zero_zero(rat) = Q_3 -> zero_zero(rat) = hAPP(rat,rat,sgn_sgn(rat),Q_3)))) # label(fact_3716_sgn__rat__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 503 (all A_2 all B_1 all C_1 all D_1 all X_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1)),C_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D_1),hAPP(int,nat,nat_1,X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_1),C_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_1),A_2) = one_one(int) -> (exists K_1 exists L_3 exists M_2 (ti(int,C_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),M_2),hAPP(int,nat,nat_1,X_1)) & ti(int,B_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),L_3),hAPP(int,nat,nat_1,X_1)) & ti(int,A_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1))))))))))) # label(fact_3481_int__triple__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 504 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 ti(int,Z_1) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3564_ceiling__of__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 505 (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_4809_min__max_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 506 (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_3874_card__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 507 (all X_a (linordered_idom(X_a) -> (all X_1 all A_2 all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),R_1)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),R_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),A_2))),R_1)))))) # label(fact_1883_abs__diff__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 508 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),one_one(nat)) = hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))))) # label(fact_1911_natceiling__add__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 509 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact,M)),hAPP(nat,nat,fact,N))))) # label(fact_3539_fact__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 510 (all X_a (ring_div(X_a) -> (all A_1 all B all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_6)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B))))) # label(fact_2011_mod__minus__cong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 511 (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_2544_inverse__positive__imp__positive) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 512 (all X_a all X_b (topological_space(X_b) -> (all K all A_3 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),A_3))))) # label(fact_4460_tendsto__const) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 513 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,X_1)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),X_1))),D_2),hAPP(X_a,filter(X_a),at(X_a),X_1))))))) # label(fact_4601_DERIV__iff2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 514 (all X_a hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) = zero_frac(X_a)) # label(fact_3680_Nitpick_Ozero__frac__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 515 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),Ma))))) # label(fact_2304_real__of__nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 516 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4))) # label(fact_691_diff__add__assoc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 517 (all A_1 hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1))) = one_one(real)) # label(fact_2749_cmod__unit__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 518 (all X_a (linordered_semidom(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_105_power2__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 519 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archim2085082626_floor(X_a),X))),X))))) # label(fact_3567_of__int__floor__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 520 (all X_b all X_a all P_5 ti(product_prod(X_a,X_b),P_5) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_5)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_5))) # label(fact_3130_pair__collapse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 521 (all X zero_zero(real) != hAPP(real,real,cos,hAPP(real,real,arctan,X))) # label(fact_2210_cos__arctan__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 522 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_816_add__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 523 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) | N = M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_567_less__or__eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 524 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2428_Parity_Otransfer__int__nat__relations) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 525 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),W),Z_1))))) # label(fact_3589_of__int__diff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 526 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> A_3 = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))) # label(fact_3666_transfer__nat__int__set__return__embed) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 527 (all A_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_2)) <-> A_2 = zero_zero(nat))) # label(fact_891_gcd__lcm__complete__lattice__nat_Otop__unique) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 528 (all V all W hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))) # label(fact_2169_minus__numeral__code_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 529 (all X_a (real_normed_field(X_a) -> (all C_1 all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),X_1),C_1))))) # label(fact_2636_DERIV__cmult__Id) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 530 (all X_a all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),B_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2188_subsetI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 531 (all X_a all X_b all F all G all P_4 hAPP(product_prod(X_a,X_b),nat,hAPP(fun(X_b,nat),fun(product_prod(X_a,X_b),nat),hAPP(fun(X_a,nat),fun(fun(X_b,nat),fun(product_prod(X_a,X_b),nat)),product_prod_size(X_a,X_b),F),G),P_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(X_a,nat,F,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4))),hAPP(X_b,nat,G,hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),P_4)))),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_3122_prod__size__simp) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 532 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X)))) # label(fact_2120_aux5) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 533 (all A_1 all B all C (ti(int,C) != zero_zero(int) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3752_mult__rat__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 534 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))))))) # label(fact_2883_floor__less__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 535 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,hAPP(int,fun(int,int),plus_plus(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),plus_plus(X_a),X),one_one(X_a)))))) # label(fact_3305_ceiling__add__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 536 (all X_a all X_b product_snd(X_a,X_b) = ti(fun(product_prod(X_a,X_b),X_b),product_snd(X_a,X_b))) # label(tsy_c_Product__Type_Osnd_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 537 (all X_a all X_b all C_1 all P_4 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),P_4)) -> -(all X_2 all Y_2 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) -> -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,X_2),Y_2)))))) # label(fact_4062_splitE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 538 (all R_4 all S_3 all T_5 all R_5 all S_4 all M all T_6 all N (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) = ti(int,R_5) -> (ti(int,R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_3))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_6),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_5))),N)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4)))) # label(fact_968_xzgcda__linear__aux2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 539 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 540 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)))) # label(fact_976_zmod__zmult2__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 541 (all C all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),B),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Q_3),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_3),C))),R_4)))))))) # label(fact_3096_divmod__nat__rel__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 542 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_400_zero__le__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 543 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),Xa_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1))))) # label(fact_4713_scaleR__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 544 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma))) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1239_not__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 545 (all X hAPP(complex,complex,cnj,hAPP(real,complex,of_real(complex),X)) = hAPP(real,complex,of_real(complex),X)) # label(fact_2945_complex__cnj__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 546 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_2),B_1)),A_3))))))) # label(fact_4726_scaleR_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 547 (all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B),C),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),C),M))))) # label(fact_316_zcong__trans) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 548 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3037_termination__basic__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 549 (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_2146_uminus__dvd__conv_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 550 (all X_1 hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(rat,fun(int,bool),hAPP(fun(int,fun(rat,bool)),fun(rat,fun(int,bool)),combc(int,rat,bool),hAPP(fun(int,rat),fun(int,fun(rat,bool)),hAPP(fun(rat,fun(rat,bool)),fun(fun(int,rat),fun(int,fun(rat,bool))),combb(rat,fun(rat,bool),int),ord_less_eq(rat)),ring_1_of_int(rat))),X_1))),hAPP(fun(int,rat),fun(int,bool),hAPP(fun(rat,bool),fun(fun(int,rat),fun(int,bool)),combb(rat,bool,int),hAPP(rat,fun(rat,bool),ord_less(rat),X_1)),hAPP(fun(int,int),fun(int,rat),hAPP(fun(int,rat),fun(fun(int,int),fun(int,rat)),combb(int,rat,int),ring_1_of_int(rat)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int)))))) = hAPP(rat,int,archim2085082626_floor(rat),X_1)) # label(fact_4147_floor__rat__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 551 (all M all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N) = one_one(int) -> ti(int,M) = one_one(int) | ti(int,M) = hAPP(int,int,number_number_of(int),min_1))) # label(fact_309_pos__zmult__eq__1__iff__lemma) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 552 (all X_a all X_b all X_c all X_d all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_4),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3)))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),bool,P_1,X_1)))) # label(fact_3154_prod__induct4) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 553 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(real,real,ln,X)) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X))) # label(fact_2630_log__base__10__eq1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 554 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4824_min__max_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 555 (all X_a (comple44059174attice(X_a) -> (all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),B_2))))))) # label(fact_1764_Sup__subset__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 556 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) <-> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2194_Compl__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 557 (all R_4 all A_1 hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))) # label(fact_3170_Im__rcis) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 558 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Z all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z))))))))) # label(fact_4024_powser__inside) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 559 (all X_a (archim1727834104eiling(X_a) -> (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))) # label(fact_2875_floor__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 560 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),sequentially))))))) # label(fact_4444_LIMSEQ__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 561 (all A_2 all B_1 ((all D_3 (hAPP(nat,nat,suc,zero_zero(nat)) = D_3 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = one_one(nat))) # label(fact_3296_coprime__Suc__0__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 562 (all X_a (number_ring(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),ring_1_Ints(X_a)))))) # label(fact_3843_Ints__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 563 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all F all X_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),X_1)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4920_isCont__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 564 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zEven)))) # label(fact_1269_even__times__either) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 565 (all C_1 all X_1 all Ta all A_2 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),D_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),D_1))),Ta)))))) # label(fact_208_zdvd__period) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 566 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),one_one(nat)) = ti(X_a,X)))) # label(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 567 (all X_a (linordered_idom(X_a) -> (all A_2 (hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),A_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2230_sgn__1__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 568 (all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4073_suminf__0__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 569 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)))))))) # label(fact_4489_Bseq__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 570 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all X_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4746_scaleR__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 571 (all B all A_1 (A_1 != zero_zero(nat) | B != zero_zero(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))) = one_one(nat))) # label(fact_3291_div__gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 572 (all X_a (comm_semiring_1(X_a) -> (all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),semiring_1_of_nat(X_a)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),one_one(X_a)))))) # label(fact_4617_gauss__sum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 573 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K))))) # label(fact_3820_DERIV__sin__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 574 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4567_cnj_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 575 (all X_c all X_a all X_b all R_3 all A_2 all B_1 all C_1 (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),R_3),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1)),C_1)) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),R_3,A_2),B_1),C_1)))) # label(fact_4042_splitD_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 576 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))))))) # label(fact_2865_floor__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 577 (all C all A_1 all B (A_1 = B -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),B)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_636_dvd_Oord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 578 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_614_two__realpow__ge__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 579 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_971_odd__mult__odd__prop) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 580 (all N all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,Z_1)),N))) # label(fact_1146_nat__power__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 581 (all X_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2450_even__nat__equiv__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 582 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | N_1 = Ma)) # label(fact_564_le__eq__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 583 (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_43_arith__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 584 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 585 (all X_a (semiring_div(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),zero_zero(X_a))))) # label(fact_964_div__by__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 586 (all X_a (linordered_semidom(X_a) -> (all N all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N)))))))) # label(fact_404_power__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 587 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1334_le__imp__less__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 588 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)) = zero_zero(X_a)))) # label(fact_2065_right__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.56 589 (all X_a all F1 all Real1 all 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)) = hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2)) # label(fact_2759_complex_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 590 (all X_a all F all A_3 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_3)) # label(fact_4250_real__of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 591 (all X_a (ring_1(X_a) -> (all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Q_2),ring_1_Ints(X_a))) -> -(all Z_2 hAPP(int,X_a,ring_1_of_int(X_a),Z_2) != ti(X_a,Q_2)))))) # label(fact_4345_Ints__cases) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 592 (all X_a (real_vector(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a))))) # label(fact_4702_scaleR__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 593 (all X all N hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi))) = hAPP(real,real,tan,X)) # label(fact_2347_tan__periodic__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 594 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_4803_min__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 595 (all X hAPP(real,real,ln,hAPP(real,real,exp(real),X)) = X) # label(fact_2509_ln__exp) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 596 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,bit1,pls))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))))) # label(fact_16_add__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 597 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4029_summable__exp) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 598 (all N 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)) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat)))) # label(fact_2498_fact__plus__one__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 599 (all X all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X)),M))) # label(fact_972_StandardRes__prop1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 600 (all X_a (semiring_div(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Z_1),W)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),W)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),W),Z_1))))))) # label(fact_1000_div__mult__div__if__dvd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 601 (all X_b all X_a all P_1 all P_4 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),P_4))) -> -(all X_2 all Y_2 -hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2))))) # label(fact_3146_exE__realizer_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 602 (all M all N all R_5 all S_4 all S_3 all T_6 all T_5 all Rn all Sn_1 all Tn_1 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),Rn),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn_1),Tn_1)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_6),N)) = ti(int,R_5) -> (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),S_3),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),T_5),N)) = ti(int,R_4) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Sn_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Tn_1),N)) = ti(int,Rn)))))) # label(fact_3085_xzgcda__linear) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 603 (all N hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),N))) = hAPP(int,int,uminus_uminus(int),N)) # label(fact_3373_floor__minus__real__of__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 604 (all X_a (ring_1(X_a) & real_normed_vector(X_a) -> (all C_1 all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),C_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))))) # label(fact_4107_diffs__equiv) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 605 (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_1770_real__average__minus__second) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 606 (all D_1 hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),collect(product_prod(int,int)),hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,bool))),combs(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(bool,bool),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(bool,bool)),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),int),combb(bool,bool,int)),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),D_1)))),ord_less(int)))) = hAPP(int,fun(product_prod(int,int),bool),int_ge_less_than,D_1)) # label(fact_4074_int__ge__less__than__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 607 (all X_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2449_odd__nat__equiv__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 608 (all X_a (semiri456707255roduct(X_a) -> (all C_1 all D_1 all A_2 all B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),D_1)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),D_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1)) <-> ti(X_a,C_1) != ti(X_a,D_1) & ti(X_a,A_2) != ti(X_a,B_1))))) # label(fact_241_crossproduct__noteq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 609 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),tan),X_1)))) # label(fact_4885_isCont__tan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 610 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))))) # label(fact_635_dvd__diff__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 611 (all X_a complex_case(X_a) = ti(fun(fun(real,fun(real,X_a)),fun(complex,X_a)),complex_case(X_a))) # label(tsy_c_Complex_Ocomplex_Ocomplex__case_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 612 (all P (fFalse = ti(bool,P) | fTrue = ti(bool,P))) # label(help_fFalse_1_1_T) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 613 (all X_1 all A_3 all Ma (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),A_3)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))))) # label(fact_3900_RsetR__zmult__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 614 (all M all N hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)),N))) # label(fact_922_zmod__zdiv__equality_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 615 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)))))) # label(fact_3234_gcd__semilattice__nat_Oinf__greatest) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 616 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),Y) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),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))))))) # label(fact_3114_bezw__non__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 617 (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_4015_split__comp__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 618 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_4758_scaleR__left_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 619 (all X_a all Q_1 all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4867_someI2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 620 (all X_1 all Y_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))))) # label(fact_3759_real__less__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 621 (all Ma (hAPP(nat,nat,suc,zero_zero(nat)) = Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_1323_dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 622 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4))) # label(fact_512_diff__bin__simps_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 623 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2403_arcsin) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 624 (all X_a (ring_1(X_a) -> (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,X_a,ring_1_of_int(X_a),Z_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,Z_1)))))) # label(fact_3604_of__nat__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 625 (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_4711_real__vector_Oscale__left__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 626 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_2225_cos__monotone__minus__pi__0_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 627 (all N (zero_zero(nat) != N -> 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(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)))))))) # label(fact_1459_lemma__Suc__Suc__4n__diff__2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 628 (all K_4 all 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))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4)) # label(fact_2722_pdivmod__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 629 (all X_a (semiring_1(X_a) -> (all M all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))))) # label(fact_1287_of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 630 (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_3576_floor__of__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 631 (all X_a (semiring_div(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B))))) # label(fact_997_div__mult__self2__is__id) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 632 (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]. 10.52/10.57 633 (all Ma hAPP(int,fun(int,bool),norRRset,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)) # label(fact_3560_norRRset__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 634 (all N_1 all X_1 exists T_4 (hAPP(real,real,cos,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))) # label(fact_4242_Maclaurin__cos__expansion) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 635 (all D_1 all A_2 all B_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1)) = one_one(int) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),B_1) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D_1),A_2) = one_one(int))) # label(fact_4386_coprime__mul__eq__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 636 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_576_add__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 637 (all X_b all X_a all F all A_3 all B_2 (hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3) = ti(fun(X_a,bool),B_2) -> hAPP(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_b,bool),fun(X_a,bool)),fun(fun(fun(X_b,bool),bool),fun(fun(X_a,bool),bool)),image(fun(X_b,bool),fun(X_a,bool)),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F)),hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),pow(X_b),A_3)) = hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) # label(fact_3640_image__Pow__surj) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 638 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),zero_zero(real))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)))))) # label(fact_3528_DERIV__nonpos__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 639 (all A_3 hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = A_3) # label(fact_3650_transfer__int__nat__set__return__embed) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 640 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3297_zero__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 641 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> (exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2) = X_1))) # label(fact_2442_even__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 642 (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)))))) # label(fact_4018_summable__rabs__comparison__test) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 643 (all Y all X (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X)) -> (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,Y)) -> hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_211_is__mult__sum2sq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 644 (all X all Y all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),R_4)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),R_4)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4))) # label(fact_2808_Complex__mult__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 645 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),Y_1)))))))) # label(fact_443_power__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 646 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),A_2)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(real,int,archimedean_ceiling(real),X_1))))) # label(fact_3366_less__ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 647 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3)))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3499_BseqI2_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 648 (all A_2 all B_1 all C_1 (zero_zero(real) != C_1 -> (A_2 = B_1 <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),A_2) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),B_1)))) # label(fact_709_real__mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 649 (all K_4 zero_zero(rat) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),K_4)) # label(fact_3739_rat__number__collapse_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 650 (all P_5 all M ((zero_zero(nat) != 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)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M)) & (M = zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),M) = one_one(nat)))) # label(fact_720_power__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 651 (all N_1 all N_7 all F ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_7)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,N_7))) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_7)),hAPP(nat,nat,F,N_1)))))) # label(fact_1492_dvd_Olift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 652 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_2888_floor__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 653 (all X_a (ring_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a)))))) # label(fact_3886_Ints__double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 654 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,fact_fact(nat),N)),hAPP(nat,nat,fact_fact(nat),M))))) # label(fact_2492_fact__dvd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 655 (all X_a (field_inverse_zero(X_a) -> (all B_1 all C_1 all A_2 ((ti(X_a,C_1) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_2)) & (zero_zero(X_a) != ti(X_a,C_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1) = ti(X_a,B_1)) <-> ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))) # label(fact_1686_divide__eq__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 656 (all X_2 ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,cos_coeff,X_2) = zero_zero(real)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,cos_coeff,X_2) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2)))))) # label(fact_2480_cos__coeff__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 657 (all N -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),zero_zero(real)))) # label(fact_2303_not__real__of__nat__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 658 (all P (-hBOOL(P) | -hBOOL(hAPP(bool,bool,fNot,P)))) # label(help_fNot_1_1_U) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 659 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2095_abs__of__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 660 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)))) # label(fact_3677_finite__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 661 (all K_4 pls != hAPP(int,int,bit1,K_4)) # label(fact_116_rel__simps_I46_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 662 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)))) # label(fact_3681_finite__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 663 (all A_1 all B all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3239_gcd__semilattice__nat_Ole__infI2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 664 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_1249_Suc__leD) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 665 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)),A_1)) # label(fact_3327_powr__powr__swap) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 666 (all X_b all X_a all P_4 hAPP(product_prod(X_b,X_a),X_a,hAPP(fun(X_b,fun(X_a,X_a)),fun(product_prod(X_b,X_a),X_a),product_prod_case(X_b,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_b,fun(X_a,X_a)),combk(fun(X_a,X_a),X_b),combi(X_a))),P_4) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)) # label(fact_4003_snd__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 667 (all X_a (field_inverse_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2525_field__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 668 (all X_b all X_a (real_normed_algebra(X_a) -> (all G all A_3 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3)),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),G)),Y_1)),A_3)))) # label(fact_4190_mult__left_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 669 (all Ma all K all N_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),N_1) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1)))))) # label(fact_4392_coprime__dvd__mult__iff__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 670 (all X_a (number_ring(X_a) -> (all V all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W))),Z_1)))) # label(fact_42_mult__number__of__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 671 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all L all Ma all F all G all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,B_1) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (ti(X_b,L) = ti(X_b,Ma) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),hAPP(X_a,filter(X_a),at(X_a),B_1))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))))) # label(fact_4762_LIM__cong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 672 (all X_a (real_normed_field(X_a) -> (all X_1 (zero_zero(X_a) != ti(X_a,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),inverse_inverse(X_a)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_3888_DERIV__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 673 (all X_a (ordere236663937imp_le(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_784_add__le__cancel__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 674 (all M all X hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)) # label(fact_911_StandardRes__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 675 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),A_2))))))) # label(fact_4896_isCont__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 676 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sqrt,X) != zero_zero(real))) # label(fact_1626_real__sqrt__not__eq__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 677 (all A_1 all N all B hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N))) # label(fact_4362_gcd__exp__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 678 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),X)))))))) # label(fact_438_mult__right__le__one__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 679 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1)))) # label(fact_4164_finite__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 680 (all X_a (real_normed_vector(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),L),hAPP(nat,X_a,F,zero_zero(nat))))))))) # label(fact_4095_sums__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 681 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_5)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1158_Int2_Oaux__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 682 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1)))) # label(fact_4884_isCont__real__root) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 683 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)))))))) # label(fact_2713_real__root__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 684 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X))) # label(fact_617_dvd_Oorder__refl) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 685 (all X_b all X_a (ring_1(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co302546470etprod(X_b,int),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_3)))) # label(fact_3929_of__int__setprod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 686 (all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),ii)) # label(fact_2767_Complex__mult__i) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 687 (all X_a (ring_1(X_a) -> (all Z_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,uminus_uminus(int),Z_1))))) # label(fact_3568_of__int__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 688 (all D_1 all K all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> ((exists I_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),I_2) = D_1 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),K)))))) # label(fact_3068_divides__primepow) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 689 (all K (hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),K))) <-> hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),K))))) # label(fact_3690_iszero__rat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 690 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = M)) # label(fact_693_le__add__diff__inverse2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 691 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_4046_Re_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 692 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arctan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2654_DERIV__arctan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 693 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2)))))) # label(fact_867_d22set__mem) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 694 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))))))) # label(fact_1059_zmult2__lemma__aux4) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 695 (all A_1 all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1))))) # label(fact_199_zprime__zdvd__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 696 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,Ma)),N_1))))))) # label(fact_4598_setsum__head__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 697 (all X_a (monoid_mult(X_a) & comm_semiring_0(X_a) -> (all X_1 all Y_1 all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N_1))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))))))) # label(fact_4174_lemma__realpow__diff__sumr) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 698 (all X_a (ord(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_1574_ord__eq__less__trans) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 699 (all R_4 all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,cis,A_1))) # label(fact_3173_rcis__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 700 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),zero_zero(X_a)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),zero_zero(real)),sequentially)))))) # label(fact_4450_LIMSEQ__norm__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 701 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X)))))) # label(fact_2357_real__of__nat__div2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 702 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2))))))) # label(fact_4081_mult__right_Osums) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 703 (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),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)) = ti(int,X))) # label(fact_1201_two__times__odd__div__two__plus__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.57 704 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all K hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))))) # label(fact_4182_sumr__offset3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 705 (all X_1 (zero_zero(real) != hAPP(real,real,cos,X_1) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),tan),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2653_DERIV__tan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 706 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),one_one(int))) <-> one_one(int) = hAPP(int,int,abs_abs(int),X_1))) # label(fact_1931_zdvd1__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 707 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X)) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X))))))) # label(fact_4975_min__max_Ole__supE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 708 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,suc,zero_zero(nat))),A_1))) # label(fact_2861_coprime__Suc0_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 709 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(real,X_a,of_real(X_a),hAPP(real,real,sgn_sgn(real),R_4)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(real,X_a,of_real(X_a),R_4))))) # label(fact_2801_sgn__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 710 (all N_1 all Ma (hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),N_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))))) # label(fact_3160_less__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 711 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_388_mult__neg__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 712 (all Z hAPP(complex,real,arg,Z) = hAPP(fun(real,bool),real,hilbert_Eps(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z)))),cos))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(fun(real,real),fun(real,bool),hAPP(fun(real,bool),fun(fun(real,real),fun(real,bool)),combb(real,bool,real),hAPP(real,fun(real,bool),fequal(real),hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z)))),sin))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),pi)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi)))))) # label(fact_3926_arg__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 713 (all X_2 hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),X_2)) # label(fact_4119_exp__fdiffs) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 714 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1600_xt1_I7_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 715 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_565_less__imp__le__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 716 (all J_2 all K_4 all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),A_1)),P_5)))) # label(fact_836_aux______3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 717 (all X_a (ring_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),A_2)),A_2) != zero_zero(X_a))))) # label(fact_3907_Ints__odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 718 (all A_2 all B_1 ((all D_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)) <-> D_3 = one_one(nat))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1) = one_one(nat))) # label(fact_3265_coprime__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 719 (all B_1 hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1) = hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combs(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(fun(int,int),fun(int,bool),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),B_1))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(int))))),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),minus_minus(int)),B_1))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_4035_adjust__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 720 (all X hAPP(real,int,archim2085082626_floor(real),hAPP(rat,real,ratreal,X)) = hAPP(rat,int,archim2085082626_floor(rat),X)) # label(fact_3748_real__floor__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 721 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))))))) # label(fact_1793_norm__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 722 (all X 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),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)))))) # label(fact_2400_sin__cos__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 723 (all X_b all X_c all X_a (semiring_0(X_a) -> (all F all A_3 all G all B_2 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),hAPP(fun(X_c,X_a),fun(X_b,fun(X_c,X_a)),hAPP(fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_c,X_a),fun(X_b,fun(X_c,X_a))),combc(X_b,fun(X_c,X_a),fun(X_c,X_a)),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a))),hAPP(fun(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a))),fun(fun(X_b,fun(X_a,X_a)),fun(X_b,fun(fun(X_c,X_a),fun(X_c,X_a)))),combb(fun(X_a,X_a),fun(fun(X_c,X_a),fun(X_c,X_a)),X_b),combb(X_a,X_a,X_c)),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F))),G))),B_2)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),G),B_2))))) # label(fact_4209_setsum__product) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 724 (all X_b all X_a all R_3 all X_1 all Y_1 (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)),R_3)) <-> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),in_rel(X_a,X_b),R_3),X_1),Y_1)))) # label(fact_3043_in__rel__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 725 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4611_LIM__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 726 (all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,R_4),zero_zero(real)) = hAPP(real,complex,of_real(complex),R_4)) # label(fact_2791_complex__of__real__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 727 (all X_a (archim1804426504_field(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,N_2)))),X))))))) # label(fact_2723_ex__inverse__of__nat__Suc__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 728 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)))) # label(fact_577_add__leD2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 729 (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,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)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),zero_zero(int)),P_5)))))) # label(fact_280_zcong__zprime__prod__zero__contra) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 730 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all Y_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4576_mult__left_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 731 (all X_b all X_a (field(X_a) -> (all F all A_3 all R_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),inverse_divide(X_a)),F)),R_1)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),R_1)))) # label(fact_4218_setsum__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 732 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all C_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))))))) # label(fact_1754_divide__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 733 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_937_zmod__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 734 (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_4686_scaleR__minus__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 735 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3)) -> ti(X_a,E_3) = ti(X_a,D_2)))))) # label(fact_2633_DERIV__unique) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 736 (all X_a all Y_3 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),combi(X_a)),Y_3) = ti(fun(X_a,bool),Y_3)) # label(fact_3845_image__ident) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 737 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1))))))) # label(fact_1675_zero__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 738 (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),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))) & (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),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)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))))) # label(fact_899_zmod__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 739 (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_3482_zgcd__ex__linear) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 740 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_2885_floor__less__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 741 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),of_real(X_a)),A_2))))) # label(fact_4903_of__real_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 742 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,A_2))))) # label(fact_4109_cnj_Osums) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 743 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_180_less__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 744 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)))))) # label(fact_2435_zero__le__power__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 745 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)))) # label(fact_3445_zgcd__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 746 (all X_a (topological_space(X_a) -> (all F all K all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)))))) # label(fact_4443_LIMSEQ__offset) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 747 (all X_b all X_a (real_normed_vector(X_a) & topological_space(X_b) -> (all F all A_2 all L_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),L_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4581_LIM__offset__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 748 (all P_1 all N_1 all K ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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)) & 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,N_1) -> hBOOL(hAPP(int,bool,P_1,J_1))))) & (zero_zero(int) = ti(int,K) -> hBOOL(hAPP(int,bool,P_1,N_1))) <-> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K))))) # label(fact_1061_split__zmod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 749 (all K_4 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),K_4)),M)))) # label(fact_358_zcong__scalar) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 750 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3))))))) # label(fact_4151_setprod__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 751 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (zero_zero(X_a) != ti(X_a,Y) -> (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z_1))))))) # label(fact_1722_add__frac__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 752 (all X_a (monoid_mult(X_a) & linordered_ring(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_2433_zero__le__even__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 753 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),hAPP(real,real,F,X_1))))))) # label(fact_4927_isCont__inv__fun) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 754 (all X_a (field_char_0(X_a) & number_ring(X_a) -> (all W_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),field_char_0_Rats(X_a)))))) # label(fact_3694_Rats__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 755 (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_3447_zgcd__zadd__zmult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 756 (all X_a (comm_semiring_1(X_a) -> (all X hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)))) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 757 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1))))))) # label(fact_4666_scaleR__left_Osums) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 758 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_825_le__iff__diff__le__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 759 (all X_a (linord1117847801e_zero(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),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_1848_abs__divide) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 760 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z)))))) # label(fact_3595_ceiling__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 761 (all K_4 ((zero_zero(quickcheck_code_int) != K_4 -> (hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) & (zero_zero(quickcheck_code_int) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),K_4),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(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)))) & (K_4 = zero_zero(quickcheck_code_int) -> hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4) = zero_zero(int)))) # label(fact_3157_Quickcheck__Narrowing_Oint__of__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 762 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),pls)),A_1) = ti(X_a,A_1)))) # label(fact_148_add__numeral__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 763 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_962_zdvd__zmod__imp__zdvd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 764 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)))))) # label(fact_2850_coprime__mul) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 765 (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),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2052_minus__diff__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 766 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),plus_plus(rat)),X_3)),Y_3)))))) # label(fact_4842_vanishes__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 767 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,cos,X_1)))) # label(fact_4097_cos__converges) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 768 (all X_a all P_1 all A_2 (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> ti(X_a,A_2) = ti(X_a,X_2))) -> ti(X_a,A_2) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))) # label(fact_4789_some__equality) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 769 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2610_one__le__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 770 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_3185_finite__Plus__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 771 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit0,K))))) # label(fact_55_rel__simps_I21_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 772 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),A_1) = hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))))) # label(fact_2364_natceiling__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 773 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_4),B_4)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_1181_posDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 774 (all N all A_1 all B all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),A_1)))))) # label(fact_3069_prime__power__dvd__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 775 (all Z_1 hAPP(complex,real,re,hAPP(real,complex,of_real(complex),Z_1)) = Z_1) # label(fact_2994_Re__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 776 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),N)),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),N))) -> hAPP(real,int,archimedean_ceiling(real),X) = ti(int,N)))) # label(fact_3415_ceiling__eq3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 777 (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 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_1) != ti(X_a,A_1)))))) # label(fact_2772_dvdE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 778 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(real,X_a,of_real(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)))))) # label(fact_4020_of__real_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 779 (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]. 10.52/10.58 780 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2652_DERIV__real__sqrt) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 781 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) -> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2))))) # label(fact_1828_card__seteq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 782 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))) # label(fact_4964_min__max_Osup__assoc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 783 (all X_a all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4784_someI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 784 (all P (hBOOL(hAPP(bool,bool,fNot,P)) | hBOOL(P))) # label(help_fNot_2_1_U) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 785 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_2549_inverse__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 786 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),hAPP(int,int,bit1,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),K)))) # label(fact_51_rel__simps_I22_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 787 (all N_1 all S (hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) -> ((all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),S)) -> N_1 = hAPP(fun(int,bool),nat,finite_card(int),X_2))) -> hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),hAPP(nat,fun(fun(int,bool),nat),combk(nat,fun(int,bool)),N_1)),S) = hAPP(fun(fun(int,bool),bool),nat,hAPP(fun(fun(int,bool),nat),fun(fun(fun(int,bool),bool),nat),big_co1399186613setsum(fun(int,bool),nat),finite_card(int)),S))))) # label(fact_4418_card__setsum__aux) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 788 (all X_a (linorder(X_a) -> (all X all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))) -> -(hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B))))))) # label(fact_4818_min__max_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 789 (all X_a (order(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_1597_order__le__neq__trans) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 790 (all X_a (real_n1866405975lgebra(X_a) & divisi14063676e_zero(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_2510_norm__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 791 (all X_a (real_normed_field(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4564_divide_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 792 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_569_le__add2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 793 (all X_a all X_b (real_normed_algebra(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),B_1)),A_3))))))) # label(fact_4474_mult_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 794 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2247_cos__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 795 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y))) # label(fact_3257_gcd__red__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 796 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_260_Nat__Transfer_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 797 (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_3053_prime__divprod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 798 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> X = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))))) # label(fact_2708_real__root__pos2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 799 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1716_divide__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 800 (all X_a (linord1278240602ring_1(X_a) -> (all V all U all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_457_convex__bound__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 801 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))),hAPP(nat,X_a,X_3,N_2)))) | (all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_3922_monoseq__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 802 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),zero_zero(int))))))) # label(fact_2882_floor__le__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 803 (all X_a (real_normed_vector(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B))))) # label(fact_4695_scaleR_OscaleR__right) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 804 (all X_a all A_3 all B_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),B_2)) # label(fact_1963_Diff__idemp) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 805 (all X_a (field_inverse_zero(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1)),N)))) # label(fact_1698_power__one__over) # label(axiom) # label(non_clause). [assumption]. 10.52/10.58 806 (all Diff all F all N_1 all H (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & (all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H)) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)))))) # label(fact_4279_Maclaurin__objl) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 807 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2880_zero__le__floor) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 808 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))))) # label(fact_78_rel__simps_I15_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 809 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4))))))))) # label(fact_4284_Maclaurin) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 810 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zOdd))))) # label(fact_970_EvenOdd_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 811 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = one_one(X_a))))) # label(fact_2223_sgn__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 812 (all M all N all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),I_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_347_nat__power__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 813 (all Q all P (-hBOOL(P) | hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)) | -hBOOL(Q))) # label(help_fconj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 814 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4663_LIM__I) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 815 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)))))) # label(fact_4669_scaleR__right_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 816 (all A_1 all B all C all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> (exists K_1 hAPP(int,int,abs_abs(int),A_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),N)))))) # label(fact_3476_int__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 817 (all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),N)))) # label(fact_3061_prime__coprime__strong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 818 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X_1)))))) # label(fact_3608_less__floor__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 819 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_375_mult__nonpos__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 820 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all G all A_3 all B_2 (B_2 = A_3 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,F,X_2) = hAPP(int,X_a,G,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),G),B_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_3))))))) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 821 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2547_less__imp__inverse__less__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 822 (all X_b all X_a (real_normed_vector(X_a) -> (all F all A_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),hAPP(fun(X_b,X_a),fun(X_b,real),hAPP(fun(X_a,real),fun(fun(X_b,X_a),fun(X_b,real)),combb(X_a,real,X_b),norm_norm(X_a)),F)),A_3)))))) # label(fact_4177_norm__setsum) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 823 (all X_a (number_semiring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z_1)))) # label(fact_139_semiring__mult__2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 824 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X)))) # label(fact_2598_exp__ge__add__one__self) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 825 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))))) # label(fact_4178_setsum__shift__bounds__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 826 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X))))))) # label(fact_2390_sin__monotone__2pi_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 827 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),X))) # label(fact_3246_gcd__semilattice__nat_Oinf__le1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 828 (all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_4),M)),K_4)))) # label(fact_1463_int__power__div__base) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 829 (all K_4 ((K_4 = zero_zero(code_code_numeral) -> zero_zero(int) = hAPP(code_code_numeral,int,code_int_of,K_4)) & (K_4 != zero_zero(code_code_numeral) -> (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int))) & (hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(code_code_numeral) -> hAPP(code_code_numeral,int,code_int_of,K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(code_code_numeral,int,code_int_of,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),K_4),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1202_Code__Numeral_Oint__of__code) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 830 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_1294_zero__zle__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 831 (all X_1 (hAPP(real,real,cos,X_1) != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),sin)),cos)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_3915_lemma__DERIV__tan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 832 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (X_1 = one_one(real) <-> zero_zero(real) = hAPP(real,real,ln,X_1)))) # label(fact_1948_ln__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 833 (all X_a (order(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Least) = ti(X_a,Least))))) # label(fact_4835_min__leastR) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 834 (all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,M),zero_zero(int)),M))) # label(fact_352_zcong__id) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 835 (all X_1 all N_1 all Diff all F (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X_1 != zero_zero(real) -> ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1)))))))) # label(fact_4276_Maclaurin__all__lt) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 836 (all N_1 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_1)) -> (exists K_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_1)) & (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,P_1,K_1))))))) # label(fact_859_ex__least__nat__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 837 (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_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_2)))) -> ((exists D_3 ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),D_3)) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,A_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4923_metric__isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 838 (all K all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),I),J))) # label(fact_4223_image__add__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 839 (all X_a (real_normed_field(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))))) # label(fact_4231_sums__group) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 840 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2780_PowD) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 841 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all B_1 all C_1 all W_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> (ti(X_a,C_1) = zero_zero(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),W_1)) & (ti(X_a,C_1) != 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),W_1)),C_1) = ti(X_a,B_1)))))) # label(fact_1725_divide__eq__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 842 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1)),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),power_power(X_a)))),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))))))) # label(fact_4124_termdiffs) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 843 (all M all K_4 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_664_diff__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 844 (all X_b all X_a all F all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_2),B_1)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))))) # label(fact_4040_splitI) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 845 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_1317_Nat__Transfer_Otransfer__int__nat__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 846 (all X_a (real_normed_vector(X_a) -> hAPP(X_a,real,norm_norm(X_a),zero_zero(X_a)) = zero_zero(real))) # label(fact_1776_norm__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 847 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real)))))) # label(fact_2695_real__root__lt__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 848 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_2550_inverse__less__imp__less__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 849 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_1420_Nat__Transfer_Otransfer__nat__int__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 850 (all X_a (comm_semiring_1(X_a) -> (all X one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),zero_zero(nat))))) # label(fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 851 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_3396_real__of__int__floor__add__one__ge) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 852 (all R_4 all X all Y hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),X)),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2811_complex__of__real__add__Complex) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 853 (all U all V all X all Y (Y = X -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),U)),V)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),U)),Y))),V))))) # label(fact_1894_sin__bound__lemma) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 854 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1898_norm__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 855 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),P_4)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N_1),P_4))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),P_4))))))) # label(fact_4201_setsum__add__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 856 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),hAPP(nat,nat,suc,zero_zero(nat))))) # label(fact_2862_coprime__Suc0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 857 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,A_2)),sequentially)))) # label(fact_4511_Re_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 858 (all X_a (real_field(X_a) -> (all X all Y (zero_zero(real) != Y -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y)))))) # label(fact_2805_nonzero__of__real__divide) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 859 (all F all K all A_2 all B_1 (B_1 != A_2 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)) = K))) # label(fact_2666_DERIV__const__ratio__const2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 860 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)))))) # label(fact_2505_aux4) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 861 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_1241_add__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 862 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))))) # label(fact_2039_arith__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 863 (all X_a (preorder(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)))))) # label(fact_1572_order__less__asym_H) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 864 (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_1380_zdiff__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 865 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),one_one(nat))) # label(fact_1346_diff__Suc__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 866 (all A_2 (A_2 != zero_zero(nat) <-> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),zero_zero(nat))))) # label(fact_890_gcd__lcm__complete__lattice__nat_Oless__top) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 867 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3249_gcd__mult__distrib__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 868 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) <-> (all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E)))))))))))) # label(fact_3316_Cauchy__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 869 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_3118_mod__pos__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 870 (all N all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_1267_odd__pow) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 871 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4616_Im_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 872 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) | ti(int,Z) = ti(int,W_1))) # label(fact_167_zless__add1__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 873 (all X_a all One all Times all A_2 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),One),Times),A_2),zero_zero(nat)) = ti(X_a,One)) # label(fact_2840_power_Opower_Opower__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 874 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),hAPP(int,int,bit0,K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)))) # label(fact_298_rel__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 875 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(int,int,number_number_of(int),min_1)))) # label(fact_1063_div__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 876 (all X_1 all Y_1 (Y_1 = X_1 <-> hAPP(real,real,sqrt,Y_1) = hAPP(real,real,sqrt,X_1))) # label(fact_1610_real__sqrt__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 877 (all X_a (number_ring(X_a) -> (all X ((hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = one_one(X_a)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = hAPP(int,X_a,number_number_of(X_a),min_1)))))) # label(fact_2458_neg__one__even__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 878 (all X_a (divisi14063676e_zero(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),A_2))))) # label(fact_2527_inverse__nonzero__iff__nonzero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 879 (all X_a all X_b all Z all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) <-> (exists X_2 (ti(X_a,Z) = hAPP(X_b,X_a,F,X_2) & hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))))) # label(fact_3637_image__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 880 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_1039_div__mult__self1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 881 (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_1771_real__sum__of__halves) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 882 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),hAPP(real,nat,natceiling,X))))) # label(fact_2312_real__natceiling__ge) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 883 (all X ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> zero_zero(int) = hAPP(int,int,fact_fact(int),X)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),hAPP(int,nat,nat_1,X))) = hAPP(int,int,fact_fact(int),X)))) # label(fact_3178_fact__int__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 884 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_6),B_5)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))))) # label(fact_935_mod__add__cong) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 885 (all X_a (linorder(X_a) -> (all C_1 all D_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> (ti(X_a,C_1) = ti(X_a,A_2) & ti(X_a,D_1) = ti(X_a,B_1) <-> hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))))))) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 886 (all F all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) = zero_zero(real)) # label(fact_4192_sumr__one__lb__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 887 (all X_b all X_a (comm_monoid_add(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,zero_zero(X_a)),zero_zero(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),S)))))))))) # label(fact_4795_setsum_Orelated) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 888 (all N all M_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),M_4)) -> (exists M_2 M_4 = hAPP(nat,nat,suc,M_2)))) # label(fact_1524_Suc__le__D) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 889 (all V_3 all K_4 all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))))) # label(fact_232_nat__number__of__mult__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 890 (all K all L (K = L <-> hAPP(quickcheck_code_int,int,quickcheck_int_of,L) = hAPP(quickcheck_code_int,int,quickcheck_int_of,K))) # label(fact_3162_Quickcheck__Narrowing_Oint__of__inject) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 891 (all X_a (real_normed_algebra(X_a) -> (all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),B) = zero_zero(X_a)))) # label(fact_876_mult_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 892 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2576_one__less__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 893 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4823_min__max_Oinf__absorb1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 894 (all Ma all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),combi(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1))) # label(fact_4123_diff__Suc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 895 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),L)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_496_less__bin__lemma) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 896 (all X_b all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)))))) # label(fact_3184_finite__Plus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 897 (all A_2 all B_1 all N_1 (zero_zero(nat) != N_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),B_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_2),N_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_1),N_1)))))) # label(fact_871_pow__divides__eq__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 898 (all X_a (real_div_algebra(X_a) -> (all X (X != zero_zero(real) -> hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X)))))) # label(fact_2807_nonzero__of__real__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 899 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = one_one(X_a) -> ti(X_a,B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2552_inverse__unique) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 900 (all X_a (archim1727834104eiling(X_a) -> (all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X)))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))),one_one(X_a))),X)))))) # label(fact_3607_ceiling__correct) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 901 (all X_a (real_normed_vector(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X_1)),zero_zero(real))))))) # label(fact_1786_norm__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 902 (all X_a (real_n1866405975lgebra(X_a) -> (all X all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N) = hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_1782_norm__power) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 903 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4))) # label(fact_695_add__diff__assoc) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 904 (all V hAPP(int,nat,number_number_of(nat),V) = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V))) # label(fact_1112_nat__number__of__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 905 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),field_char_0_Rats(X_a))))) # label(fact_3695_Rats__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 906 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,inverse_inverse(real),X_1))))) # label(fact_2641_DERIV__ln) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 907 (all L all U_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),L) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),U_1))) # label(fact_4202_card__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 908 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),hAPP(real,real,inverse_inverse(real),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),U),hAPP(real,real,inverse_inverse(real),X1_1)))))))) # label(fact_2591_real__mult__inverse__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 909 (all X_b all X_a (semiring_0(X_a) -> (all R_1 all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1)),F)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_1),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))))) # label(fact_4211_setsum__right__distrib) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 910 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_721_diff__square) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 911 (all A_2 all P_4 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))) # label(fact_1669_wset__fin) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 912 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(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)))))) # label(fact_1167_posDivAlg__eqn) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 913 (all X_a (real_normed_vector(X_a) -> (all K all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4169_suminf__split__initial__segment) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 914 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N),M)) # label(fact_3533_mod__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 915 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) # label(fact_2987_Im_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 916 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> (exists K_1 N_1 = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K_1))))) # label(fact_1327_less__iff__Suc__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.59 917 (all X_1 (zero_zero(real) = hAPP(real,real,cos,X_1) <-> (exists N_2 (X_1 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))) | (exists N_2 (X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))))) # label(fact_2412_cos__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 918 (all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)),M)))) # label(fact_362_zcong__shift) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 919 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1645_real__sqrt__sum__squares__ge1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 920 (all V all W hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,V))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W)))) # label(fact_986_zdiv__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 921 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) # label(fact_1318_zdvd__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 922 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))))))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 923 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists K_1 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,X_3,N_3))))),K_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3490_Bseq__iff3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 924 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1868_abs__triangle__ineq3) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 925 (all X_a all X_1 hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)) = ti(X_a,X_1)) # label(fact_4788_some__sym__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 926 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_618_real__le__eq__diff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 927 (all X_a (semiring_0(X_a) & dvd(X_a) -> (all P_1 all L ((exists X_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),L),X_2)))) <-> (exists X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),zero_zero(X_a)))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))))))) # label(fact_602_unity__coeff__ex) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 928 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)))))) # label(fact_740_nat__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 929 (all X_b all X_a all X_c all F all G all A_3 hAPP(fun(X_c,bool),fun(X_a,bool),hAPP(fun(X_c,X_a),fun(fun(X_c,bool),fun(X_a,bool)),image(X_c,X_a),hAPP(fun(X_c,X_b),fun(X_c,X_a),hAPP(fun(X_b,X_a),fun(fun(X_c,X_b),fun(X_c,X_a)),combb(X_b,X_a,X_c),F),G)),A_3) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_c,bool),fun(X_b,bool),hAPP(fun(X_c,X_b),fun(fun(X_c,bool),fun(X_b,bool)),image(X_c,X_b),G),A_3))) # label(fact_3844_image__image) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 930 (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_1845_dvd__abs__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 931 (all R_4 all A_1 hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),R_4)),hAPP(real,real,uminus_uminus(real),A_1))) # label(fact_3174_rcis__inverse) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 932 (all X_a hilbert_Eps(X_a) = ti(fun(fun(X_a,bool),X_a),hilbert_Eps(X_a))) # label(tsy_c_Hilbert__Choice_OEps_res) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 933 (all N all P_5 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),M)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)))))) # label(fact_279_zprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 934 (all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls)) <-> hAPP(int,nat,number_number_of(nat),V_1) = zero_zero(nat))) # label(fact_40_eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 935 (all X_a (linordered_idom(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_1853_abs__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 936 (all I_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,I_1)),N) = hAPP(nat,nat,hAPP(int,fun(nat,nat),nat_aux,I_1),N)) # label(fact_1170_nat__aux__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 937 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_403_not__one__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 938 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(nat,real,F,N_2))),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G))) & hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4070_summable__le2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 939 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3120_mod__pos__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 940 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))))))) # label(fact_41_semiring__mult__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 941 (all A_1 all B all C all D all N (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),D),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),C) = one_one(int) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C),A_1) -> (exists K_1 exists L_3 exists M_2 (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),C) = 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),K_1),N) = hAPP(int,int,abs_abs(int),A_1))))))))) # label(fact_3483_int__triple__relprime__power__divisors) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 942 (all A_2 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_1))))) # label(fact_4433_LIMSEQ__le__const) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 943 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2061_neg__0__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 944 -(all S_1 -(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),S_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),S_1)))) # label(fact_196__096_B_Bthesis_O_A_I_B_Bs_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 945 (all X_a (archim1727834104eiling(X_a) -> (all R_4 hAPP(X_a,int,archimedean_ceiling(X_a),R_4) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),hAPP(X_a,int,archimedean_ceiling(X_a),R_4)))))) # label(fact_3355_floor__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 946 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = zero_zero(nat) -> (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M) -> N = M))) # label(fact_658_diffs0__imp__equal) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 947 (all X_a all X_b all X_1 all Y_1 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1))))) # label(fact_4780_Eps__split__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 948 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,fact_fact(nat),Ma)),hAPP(nat,nat,fact_fact(nat),N_1)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),Ma)))) # label(fact_4612_fact__div__fact) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 949 (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_184_zadd__power2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 950 (all X_a all A_3 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_1826_card__ge__0__finite) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 951 (all X_a (semiring_char_0(X_a) -> (all Ma all N_1 (hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1) = hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma) <-> N_1 = Ma)))) # label(fact_1214_of__nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 952 (all K_4 all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,pred,K_4)),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_2909_diff__bin__simps_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 953 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,N_1)),one_one(nat)))) # label(fact_3882_card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 954 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1684_divide__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 955 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> Y_1 != X_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_655_real__less__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 956 (all Ma all N_1 (hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) <-> Ma = zero_zero(nat) & hAPP(nat,nat,suc,zero_zero(nat)) = N_1 | N_1 = zero_zero(nat) & Ma = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1325_one__is__add) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 957 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X))))) # label(fact_3293_floor__minus) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 958 (all M all K_4 all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M))))) # label(fact_3290_coprime__dvd__mult__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 959 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> -(all K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1)),one_one(int)) != ti(int,X_1)))) # label(fact_1072_zOddE) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 960 (all X 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,X),M) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,phi,M))),one_one(int)),M))))) # label(fact_3427_Euler__Fermat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 961 (all X_1 all N_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,sin,X_1)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),X_1)),N_1))))) # label(fact_4162_Maclaurin__sin__bound) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 962 (all X_a (archim1727834104eiling(X_a) -> one_one(int) = hAPP(X_a,int,archimedean_ceiling(X_a),one_one(X_a)))) # label(fact_3282_ceiling__one) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 963 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) <-> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) & hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),A_3))) # label(fact_3627_is__RRset__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 964 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1)))) # label(fact_4959_max__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 965 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3) = zero_zero(X_b))))) # label(fact_4207_setsum_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 966 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3908_DERIV__sin__circle__all__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 967 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> hAPP(real,nat,natceiling,X) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))))) # label(fact_2383_natceiling__eq) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 968 (all Y exists X_2 (hAPP(real,real,tan,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)))) # label(fact_2284_lemma__tan__total1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 969 (all X_5 all N_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_6)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_6),X_5)))))) # label(fact_2704_real__root__pos__pos) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 970 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1))))))) # label(fact_4082_mult__left_Osums) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 971 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1)))) # label(fact_4534_finite__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 972 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)))))) # label(fact_839_wset__g__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 973 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),S)) -> ((all X_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),S)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_2)))) -> ((all T1 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T1),S)) -> (all T2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),T2),S)) -> (ti(fun(X_a,bool),T2) != ti(fun(X_a,bool),T1) -> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),T2)) -> hAPP(X_a,X_b,F,X_2) = zero_zero(X_b))))))))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),S)) = hAPP(fun(fun(X_a,bool),bool),X_b,hAPP(fun(fun(X_a,bool),X_b),fun(fun(fun(X_a,bool),bool),X_b),big_co1399186613setsum(fun(X_a,bool),X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F)),S))))))) # label(fact_4310_setsum__UNION__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 974 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)) = hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_1815_card__Diff__subset) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 975 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,norm_norm(complex),X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2094_complex__mod__minus__le__complex__mod) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 976 (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 (X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2) & Y = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),J_1)))))) # label(fact_3426_prime__power__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 977 (all Y all X all P_5 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y))))) # label(fact_272_Euler_Oaux____1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 978 (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_2329_tan__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 979 (all X_a (power(X_a) -> (all A_1 one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),zero_zero(nat))))) # label(fact_415_power__0) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 980 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_805_inv__not__p__minus__1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 981 (all X_a all C_1 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_1) -> hBOOL(hAPP(X_a,bool,P_1,C_1))))) # label(fact_4778_exE__some) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 982 (all Ma all N_1 (N_1 = one_one(nat) & one_one(nat) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = one_one(nat))) # label(fact_590_nat__mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 983 (all X_b (number(X_b) & ord(X_b) -> (all U all V ((-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),V)) & (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(int,X_b,number_number_of(X_b),U) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_min(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))))))) # label(fact_4831_min__number__of) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 984 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y))),X)))) # label(fact_1045_zdiv__leq__prop) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 985 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)))) # label(fact_1266_even__difference) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 986 (all B all D all A_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int)))) # label(fact_4384_coprime__mult__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 987 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2466_nat__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 988 (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_3034_cis__real__of__nat__Suc__mult) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 989 (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_3191_fact__nonzero__int) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 990 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))))) # label(fact_2818_of__real_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 991 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B) = zero_zero(int)) # label(fact_907_zmod__zdiv__trivial) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 992 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2989_Im_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 993 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),hAPP(real,real,inverse_inverse(real),Y))) # label(fact_2563_divide__real__def) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 994 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_1570_order__less__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 995 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),M))))) # label(fact_1121_div__less__dividend) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 996 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))) # label(fact_1858_abs__minus__commute) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 997 (all W hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),W),W))) # label(fact_657_real__le__refl) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 998 (all X_a (real_vector(X_a) -> (all A_2 all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),Y_1) <-> zero_zero(real) = A_2 | ti(X_a,Y_1) = ti(X_a,X_1))))) # label(fact_4700_scaleR__cancel__left) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 999 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_1544_linorder__le__cases) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1000 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hAPP(real,real,sgn_sgn(real),X) = hAPP(int,real,number_number_of(real),min_1))) # label(fact_2226_real__sgn__neg) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1001 (all X_a (linord219039673up_add(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))) # label(fact_2021_neg__equal__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1002 (all X_a (topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,G,X_2))))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,G,X_2)),hAPP(X_a,real,F,X_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4776_real__LIM__sandwich__zero) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1003 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(complex,real,im,hAPP(fun(nat,complex),complex,suminf(complex),X_3)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)))) # label(fact_4049_Im_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1004 (all X_b all X_a all X_c (comm_monoid_add(X_c) -> (all F all R_3 all T_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3)) -> hAPP(fun(X_b,bool),X_c,hAPP(fun(X_b,X_c),fun(fun(X_b,bool),X_c),big_co1399186613setsum(X_b,X_c),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,X_c)),combs(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),collect(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3))))),T_3) = hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,X_c),hAPP(fun(X_a,fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,X_c)),combs(X_a,fun(X_b,bool),X_c),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c)),hAPP(fun(fun(X_b,X_c),fun(fun(X_b,bool),X_c)),fun(fun(X_a,fun(X_b,X_c)),fun(X_a,fun(fun(X_b,bool),X_c))),combb(fun(X_b,X_c),fun(fun(X_b,bool),X_c),X_a),big_co1399186613setsum(X_b,X_c)),F)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_3)))),S)))))) # label(fact_4188_setsum__setsum__restrict) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1005 (all M all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N)) # label(fact_2310_power__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1006 (all X_a (real_normed_algebra(X_a) & power(X_a) -> (all Ma all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(nat,fun(nat,X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),combc(nat,nat,X_a),hAPP(fun(nat,X_a),fun(nat,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(nat,X_a),fun(nat,fun(nat,X_a))),combb(X_a,fun(nat,X_a),nat),power_power(X_a)),X_3)),Ma)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),Ma)),sequentially)))))) # label(fact_4467_LIMSEQ__pow) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1007 (all B_5 all Q_5 all R_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),zero_zero(int))))))) # label(fact_265_q__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1008 (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)))) # label(fact_640_dvd_Oless__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1009 (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_1)),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) # label(fact_1066_negDivAlg__minus1) # label(axiom) # label(non_clause). [assumption]. 10.52/10.60 1010 (all X_a (metric_space(X_a) -> (all X all Y -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),zero_zero(real)))))) # label(fact_3515_dist__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1011 (all X_a (linordered_field(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N)))))))) # label(fact_2612_inv__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1012 (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_638_dvd_Oless__imp__neq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1013 (all X_a (real_normed_vector(X_a) -> (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X)))))) # label(fact_1779_norm__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1014 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),zero_zero(real)))))) # label(fact_1949_ln__less__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1015 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_2),Ma) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_1),Ma)))) # label(fact_1035_zcong__zmod__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1016 (all X_2 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2))) = hAPP(real,real,cos,X_2)) # label(fact_3971_lemma__cos__ext) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1017 (all Z_1 hAPP(int,complex,ring_1_of_int(complex),Z_1) = hAPP(complex,complex,cnj,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3572_complex__cnj__of__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1018 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,suc,N))) # label(fact_1240_add__Suc__shift) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1019 (all Y_1 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),Y_1)))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),hAPP(real,real,cos,Y_1)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),hAPP(real,real,sin,Y_1)))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3916_lemma__DERIV__sin__cos__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1020 (all Z_1 Z_1 = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(complex,real,im,Z_1))) # label(fact_3000_complex__surj) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1021 (all X_a (ab_semigroup_add(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_771_ab__semigroup__add__class_Oadd__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1022 (all Y all X all Z_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3040_termination__basic__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1023 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),S_3) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),hAPP(real,real,uminus_uminus(real),S_3))) # label(fact_2091_real__diff__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1024 (all X_b all X_a (comm_monoid_add(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),plus_plus(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4220_setsum__addf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1025 (all B all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),M) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B),M))))) # label(fact_3468_zgcd__zcong__zgcd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1026 (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),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_696_le__add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1027 (all X_a (zero_neq_one(X_a) & no_zero_divisors(X_a) & mult_zero(X_a) & power(X_a) -> (all A_2 all N_1 (zero_zero(X_a) = ti(X_a,A_2) & zero_zero(nat) != N_1 <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1) = zero_zero(X_a))))) # label(fact_414_power__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1028 (all X_a all X_b (ab_group_add(X_b) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))))) # label(fact_4233_setsum__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1029 (all X_a (linordered_semidom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))))))) # label(fact_408_less__add__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1030 (all X_a all X_c all X_b all F all X_1 all G (hAPP(X_c,X_b,G,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) = hAPP(X_c,X_b,F,hAPP(product_prod(X_a,X_c),X_c,product_snd(X_a,X_c),X_1)) <-> hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),G),X_1) = hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1))) # label(fact_4066_apsnd__eq__conv) # label(axiom) # label(non_clause). [assumption]. 10.61/10.60 1031 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,A_2)),A_3)))) # label(fact_4508_Im_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1032 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,int,number_number_of(int),min_1)),P_5)))) # label(fact_756_Wilson__Russ) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1033 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int)) = hAPP(nat,rat,semiring_1_of_nat(rat),K_4)) # label(fact_3742_of__nat__rat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1034 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> (exists M_2 N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_2)))) # label(fact_2467_even__mult__two__ex) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1035 (all X_1 all Y_1 (hAPP(int,real,real_1(int),Y_1) = hAPP(int,real,real_1(int),X_1) <-> ti(int,Y_1) = ti(int,X_1))) # label(fact_3328_real__of__int__inject) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1036 (all B all A_1 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A_1))))) # label(fact_350_Euler_Oaux2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1037 (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_1475_Suc__mult__two__diff__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1038 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4635_aset_I7_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1039 (all A_1 all B hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B))) # label(fact_1358_zmod__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1040 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_15_add__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1041 (all X_a all R_1 ((all X_2 hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_2),X_2)),R_1))) <-> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,refl(X_a),R_1)))) # label(fact_3554_Nitpick_Orefl_H__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1042 (all X_a (real_normed_field(X_a) -> (all G all E_2 all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_2)) -> (hAPP(X_a,X_a,G,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_1),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_2),hAPP(X_a,X_a,F,X_1)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))))))) # label(fact_3899_DERIV__quotient) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1043 (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]. 10.61/10.61 1044 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) | ti(X_a,Y) = ti(X_a,X) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1563_linorder__less__linear) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1045 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))),zero_zero(int)))) # label(fact_2175_negative__zless__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1046 (all X_a (dense_linorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ((all W_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),W_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W_2),Z_1))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1))))))) # label(fact_2826_dense__le__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1047 (all X_a all B_2 all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),B_2),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))))) # label(fact_1750_Union__upper) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1048 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))))) # label(fact_1338_Suc__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1049 (all K (ti(int,K) = min_1 <-> min_1 = hAPP(int,int,bit1,K))) # label(fact_285_rel__simps_I47_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1050 (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_2142_zminus__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1051 (all I all J (zero_zero(int) = ti(int,I) & ti(int,J) = zero_zero(int) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I),J) = zero_zero(int))) # label(fact_3435_zgcd0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1052 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1))) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) & -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)))) # label(fact_1265_even__sum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1053 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(product_prod(int,int),product_prod(int,int)),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combb(product_prod(int,int),product_prod(int,int),int)),hAPP(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int)))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combs(int,int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(int,product_prod(int,int)))),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),int),combc(int,int,product_prod(int,int))),hAPP(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int)))),hAPP(fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),fun(fun(int,fun(int,int)),fun(int,fun(int,fun(int,product_prod(int,int))))),combb(fun(int,int),fun(int,fun(int,product_prod(int,int))),int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),times_times(int)),sgn_sgn(int))))),abs_abs(int)))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,inverse_inverse(rat),P_4))) # label(fact_4033_rat__inverse__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1054 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_1615_real__sqrt__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1055 (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]. 10.61/10.61 1056 (all X all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))))) # label(fact_3369_ceiling__le__real) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1057 (all X_a (ring_1(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),ring_1_Ints(X_a))))))) # label(fact_3858_Ints__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1058 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (N_1 = Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma)))))) # label(fact_1332_le__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1059 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_990_Divides_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1060 (all X_a (linordered_field(X_a) -> (all X all Z_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))))) # label(fact_1739_mult__imp__div__pos__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1061 (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]. 10.61/10.61 1062 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_3089_divmod__nat__step) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1063 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4668_scaleR__right_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1064 (all X_a all X_b (linordered_semidom(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3))))))) # label(fact_4149_setprod__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1065 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(real,real,sin,X_1)))) # label(fact_4076_sin__paired) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1066 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all A_2 ((all S_2 ((all N_2 A_2 != hAPP(nat,real,S_2,N_2)) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))) -> hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),A_2))))))) # label(fact_4661_LIMSEQ__SEQ__conv2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1067 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all A_2 all B_1 all W_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1068 (all X_a (semiri456707255roduct(X_a) -> (all W_1 all Y_1 all X_1 all Z (ti(X_a,X_1) = ti(X_a,W_1) | ti(X_a,Y_1) = ti(X_a,Z) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Z)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Y_1)))))) # label(fact_244_crossproduct__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1069 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)))))))) # label(fact_4821_min__max_Ole__infI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1070 (all X_a (metric_space(X_a) -> ti(fun(fun(X_a,bool),X_a),the(X_a)) = the(X_a))) # label(tsy_c_HOL_OThe_0_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1071 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 all C_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1708_less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1072 (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))) -> (zero_zero(int) = hAPP(product_prod(int,int),int,product_snd(int,int),P_5) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5)) & (hAPP(product_prod(int,int),int,product_snd(int,int),P_5) != zero_zero(int) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,P_5) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(int,int,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))))))) & (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_4344_normalize__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1073 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1))))) = ti(int,N_1))) # label(fact_3808_int__card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1074 (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_7)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,N_7)))))) # label(fact_1482_dvd_Olift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1075 (all A_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,number_number_of(int),min_1))) # label(fact_1037_zmod__minus1__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1076 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),one_one(real))))) # label(fact_1630_real__sqrt__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1077 (all X_a (linordered_semidom(X_a) -> (all X all Y (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> ti(X_a,Y) = ti(X_a,X))))))) # label(fact_102_power2__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1078 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (zero_zero(real) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_3517_dist__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1079 (all X_a all X_b all P_1 ((all X1 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,X1))) <-> (all A_4 all B_4 hBOOL(hAPP(product_prod(X_a,X_b),bool,P_1,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4)))))) # label(fact_3135_split__paired__All) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1080 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,sin,X))),one_one(real)))) # label(fact_2319_abs__sin__le__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1081 (all X_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> (exists Y_2 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),Y_2)) = X_1))) # label(fact_2441_odd__nat__equiv__def2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1082 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2019_minus__divide__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1083 (all X_a all X_b all X_c all X_d all X_e all X_f all Y -(all A_4 all B_4 all C_4 all D_3 all E all F_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),Y) != hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_4),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3))))))) # label(fact_3151_prod__cases6) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1084 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2626_exp__bound) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1085 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_233_power__even__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1086 (all P_4 hAPP(rat,int,archim2085082626_floor(rat),P_4) = hAPP(product_prod(int,int),int,hAPP(fun(int,fun(int,int)),fun(product_prod(int,int),int),product_prod_case(int,int,int),div_div(int)),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4027_rat__floor__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1087 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_405_zero__le__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1088 (all A_1 all B ((zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),B)) & (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),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)))) # label(fact_2171_zmod__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1089 (all X (zero_zero(real) != X -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),X) = one_one(real))) # label(fact_2592_real__mult__inverse__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1090 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat)))) # label(fact_889_gcd__lcm__complete__lattice__nat_Otop__greatest) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1091 (all X_a (ab_group_add(X_a) -> (all F all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))) # label(fact_4180_sumr__offset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1092 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_1915_lemma__interval__lt) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1093 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,real,real_1(int),X) = hAPP(nat,real,real_1(nat),hAPP(int,nat,nat_1,X)))) # label(fact_3394_real__nat__eq__real) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1094 (all P_1 ((exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))) <-> (exists X1 hBOOL(hAPP(nat,bool,P_1,X1))))) # label(fact_1107_ex__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1095 (all X_a (preorder(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),X))))) # label(fact_1541_order__refl) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1096 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))))) # label(fact_558_trans__less__add2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1097 (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_642_dvd_Oless__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1098 (all X_a all A_2 all F all V_1 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),A_2),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4157_nat__rec__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1099 (all X_a (linordered_ring(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),zero_zero(X_a)))))) # label(fact_398_not__square__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1100 (all X_a (comm_semiring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_327_comm__semiring__class_Odistrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1101 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),B_1)),sequentially))))))) # label(fact_4739_scaleR_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1102 (all X_a (semiring_div(X_a) -> (all N all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))) # label(fact_1006_div__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1103 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))))) # label(fact_804_inv__g__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1104 (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_3221_gcd__semilattice__nat_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1105 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_814_add__increasing) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1106 (all X_a (linordered_field(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1713_mult__imp__less__div__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1107 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(int,int,number_number_of(int),min_1)),P_5))))))) # label(fact_1076_Euler__part1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1108 (all X_b all X_a (comm_monoid_mult(X_a) -> (all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),one_one(X_a))),A_3) = one_one(X_a)))) # label(fact_3947_setprod__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1109 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) # label(fact_679_diff__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1110 (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))) -> one_one(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),hAPP(int,int,bit1,W)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))))))) # label(fact_3898_power__number__of__odd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1111 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = one_one(nat)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),one_one(nat)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))))) # label(fact_1535_nat__number__of__add__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1112 (all K_4 hAPP(int,int,uminus_uminus(int),K_4) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),min_1),K_4)) # label(fact_2160_mult__Min) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1113 (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_452_zcong__zless__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1114 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4072_suminf__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1115 (all X_b all X_a (comm_monoid_add(X_b) & ord(X_a) -> (all F all G all B_1 all D_1 all A_2 all C_1 (ti(X_a,A_2) = ti(X_a,C_1) -> (ti(X_a,D_1) = ti(X_a,B_1) -> ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),D_1)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2)))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1)))))))) # label(fact_4302_setsum__ivl__cong) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1116 (all X_a all G all A_3 hAPP(complex,real,re,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),A_3)) # label(fact_4249_Re_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1117 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_144_even__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1118 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)))))) # label(fact_1382_n__less__n__mult__m) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1119 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Q_3),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)) = hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,uminus_uminus(int),P_5)),hAPP(int,int,uminus_uminus(int),Q_3))))) # label(fact_3718_normalize__negative) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1120 (all X hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),pi)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2326_sin__periodic__pi) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1121 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) -> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))))) # label(fact_4325_finite__nat__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1122 (all X_a (archim1727834104eiling(X_a) -> zero_zero(int) = hAPP(X_a,int,archim2085082626_floor(X_a),zero_zero(X_a)))) # label(fact_2863_floor__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1123 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,cnj,X))) # label(fact_2935_cnj_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1124 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(code_code_numeral,X_a,hAPP(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a),hAPP(X_a,fun(fun(code_code_numeral,X_a),fun(code_code_numeral,X_a)),code_c600343653l_case(X_a),F1),F2),zero_zero(code_code_numeral))) # label(fact_3549_code__numeral_Osimps_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1125 (all N all M -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),N)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),M))))) # label(fact_2156_not__int__zless__negative) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1126 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),A_2),B_1)),A_3))))))) # label(fact_4440_tendsto__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1127 (all X_c all X_b all X_a (topological_space(X_c) & topological_space(X_b) & metric_space(X_a) -> (all G all C_1 all F all B_1 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),B_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),B_1))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),D_3)) -> ti(X_b,B_1) != hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),C_1),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4602_metric__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1128 (all A_3 all B_2 (A_3 = B_2 <-> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) # label(fact_3648_transfer__nat__int__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1129 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_4853_Nat__Transfer_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1130 (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_873_mult__left__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1131 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Z_1))))))) # label(fact_1548_order__trans) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1132 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))) # label(fact_946_mod__diff__right__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.61 1133 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),one_one(X_b))),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(X_a,X_b,B_1,A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),one_one(X_b))),S)))))) # label(fact_3956_setprod__delta) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1134 (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_1304_zmult__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1135 (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]. 10.61/10.62 1136 (all X_a (ring_1(X_a) -> ti(fun(int,X_a),ring_1_of_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]. 10.61/10.62 1137 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real)))))) # label(fact_2698_real__root__le__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1138 (all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> one_one(nat) = N | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),N)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N)))) # label(fact_3071_prime__coprime) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1139 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_1),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),C)))))) # label(fact_688_diff__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1140 (all A_1 hAPP(real,complex,cis,A_1) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,one_one(real)),A_1)) # label(fact_3167_cis__rcis__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1141 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1))))))) # label(fact_503_less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1142 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1704_frac__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1143 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),B)),A_1)) # label(fact_2768_i__mult__Complex) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1144 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3547_fact__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1145 (all X_a all X_b all C_1 all P_4 ((all A_4 all B_4 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),C_1,A_4),B_4)))) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),C_1),P_4)))) # label(fact_4061_splitI2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1146 (all X_a (comm_semiring_1(X_a) -> (all X all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)))))) # label(fact_1457_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1147 (all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((exists X1 hBOOL(hAPP(nat,bool,P_1,X1))) -> (exists N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) & -hBOOL(hAPP(nat,bool,P_1,N_2))))))) # label(fact_2738_exists__least__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1148 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4865_vanishesI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1149 (all X_a (linorder(X_a) -> ord_min(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))))) # label(fact_4834_dual__max) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1150 (all X_a (ring_1(X_a) -> (all P_1 all Q_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Q_2),ring_1_Ints(X_a))) -> ((all Z_2 hBOOL(hAPP(X_a,bool,P_1,hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))) -> hBOOL(hAPP(X_a,bool,P_1,Q_2))))))) # label(fact_4415_Ints__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1151 (all A_1 all B all C (ti(int,C) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) = ti(int,A_1))) # label(fact_483_Int2_Oaux1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1152 (all A_2 all B_1 all N_1 (zero_zero(nat) != N_1 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_2),B_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),N_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_1),N_1)))))) # label(fact_869_pow__divides__eq__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1153 (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 & hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_5),B_3) = one_one(nat) & 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_3312_gcd__coprime__exists__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1154 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z),one_one(int)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_509_zle__diff1__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1155 (all Z_1 hAPP(complex,real,im,hAPP(real,complex,of_real(complex),Z_1)) = zero_zero(real)) # label(fact_2974_Im__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1156 (all X_a all X_b (comm_ring_1(X_b) & real_normed_algebra(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co302546470etprod(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4657_LIMSEQ__setprod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1157 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1097_Divides_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1158 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) <-> Ma = N_1))) # label(fact_746_nat__mult__eq__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1159 (all X_a (finite_finite(X_a) -> (all A_3 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1819_finite) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1160 (all P (fFalse = ti(bool,P) | ti(bool,P) = fTrue)) # label(help_fTrue_1_1_T) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1161 (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_270_quartic__square__square) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1162 (all X_a (ring_1(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))) # label(fact_2097_power__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1163 (all N_1 all Ma (zero_zero(nat) = N_1 & Ma = zero_zero(nat) <-> hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)) = hAPP(nat,int,semiring_1_of_nat(int),Ma))) # label(fact_2155_negative__eq__positive) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1164 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> X_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1))) # label(fact_3244_gcd__semilattice__nat_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1165 (all X all Y (hAPP(complex,real,re,Y) = hAPP(complex,real,re,X) -> (hAPP(complex,real,im,X) = hAPP(complex,real,im,Y) -> X = Y))) # label(fact_2997_complex__eqI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1166 (all A_1 all B ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))) # label(fact_918_zmod__zdiv__equality) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1167 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),M)))) # label(fact_420_zdvd__bounds) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1168 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)))) # label(fact_3041_termination__basic__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1169 (all X_a all X_b (metric_space(X_b) -> (all G all Ma all F all L all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),Ma),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_a,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,real)),combs(X_a,X_b,real),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,real)),hAPP(fun(X_b,fun(X_b,real)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,real))),combb(X_b,fun(X_b,real),X_a),dist_dist(X_b)),F)),G)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),L),Ma)),A_3))))))) # label(fact_4457_tendsto__dist) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1170 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),X))))))) # label(fact_4978_min__max_Ole__supI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1171 (all X_a all F all A_3 hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,nat),fun(X_a,real),hAPP(fun(nat,real),fun(fun(X_a,nat),fun(X_a,real)),combb(nat,real,X_a),real_1(nat)),F)),A_3)) # label(fact_3941_real__of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1172 (all X_a (number_ring(X_a) -> (all V all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))))) # label(fact_153_number__of__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1173 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natfloor,X)))) # label(fact_1874_zero__le__natfloor) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1174 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1)))) # label(fact_3597_ceiling__add__of__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1175 (all A_1 all B 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) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1769_real__average__minus__first) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1176 (all K all L (ti(int,K) = ti(int,L) <-> hAPP(int,int,bit1,L) = hAPP(int,int,bit1,K))) # label(fact_91_rel__simps_I51_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1177 (all X_a (real_normed_vector(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(X_a,real,norm_norm(X_a),Y))))))) # label(fact_1791_norm__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1178 (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]. 10.61/10.62 1179 (all N all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),N))))) # label(fact_718_divides__exp) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1180 (all X all K_4 hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),K_4) = hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),K_4))) # label(fact_1618_real__sqrt__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1181 (all Diff all N_1 all X_1 (zero_zero(real) = X_1 -> (zero_zero(nat) != N_1 -> hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(nat,fun(real,real),Diff,zero_zero(nat)),zero_zero(real))))) # label(fact_4230_Maclaurin__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1182 (all X_a (real_normed_vector(X_a) -> (all R_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4732_scaleR__right_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1183 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),A_2)),sequentially)))))) # label(fact_4468_of__real_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1184 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))))) # label(fact_3990_suminf__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1185 (all X_a (real_normed_vector(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2)))),E_2))))))))))) # label(fact_3315_CauchyD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1186 (all K all F all N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)) & ti(int,K) = hAPP(nat,int,F,I_2))))))) # label(fact_2008_int__val__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1187 (all X_a (comm_semiring_1(X_a) -> (all A_2 all D_1 all N_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),D_1)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2)),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)))))) # label(fact_4324_arith__series__general) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1188 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))) # label(fact_3274_gcd__diff1__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1189 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))))) # label(fact_2506_exp__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1190 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit1,K2))))) # label(fact_32_less__eq__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1191 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,real_1(nat),A_2)))))) # label(fact_2345_natceiling__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1192 (all Z_1 ((all N_2 ti(int,Z_1) != hAPP(nat,int,semiring_1_of_nat(int),N_2)) -> -(all N_2 ti(int,Z_1) != hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) # label(fact_3526_int__cases) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1193 (all X all Y hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,Y)))) # label(fact_2340_cos__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1194 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_514_less__not__refl) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1195 (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]. 10.61/10.62 1196 (all A_2 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),A_2)) -> (exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),A_2),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),N_2))))),R_1))))))) # label(fact_4056_suminf__exist__split) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1197 (all X_a (real_normed_field(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_4083_sums__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1198 (all X_a (metric_space(X_a) -> (all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> hAPP(fun(nat,X_a),X_a,lim(X_a),X_3) = ti(X_a,L_2))))) # label(fact_4494_limI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1199 (all X_a (linordered_idom(X_a) -> (all A_1 all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))))) # label(fact_251_zero__le__even__power_H) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1200 (all X_a all X_b all X_c (topological_space(X_c) & topological_space(X_a) & topological_space(X_b) -> (all F all A_2 all G all L (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),L)) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),A_2))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),A_2)))))))) # label(fact_4881_isCont__LIM__compose) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1201 (all X_b all X_c all X_a all P_1 all Z hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z) = hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,hAPP(product_prod(X_b,X_c),X_b,product_fst(X_b,X_c),Z)),hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),Z))) # label(fact_4016_split__beta) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1202 (all X_1 all N_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) & zero_zero(nat) != N_1 <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1))))) # label(fact_1363_even__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1203 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1900_abs__power2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1204 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)))) # label(fact_1094_nat__div__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1205 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2030_minus__mult__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1206 (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),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls))),A_1) = ti(X_a,A_1)))) # label(fact_110_mult__numeral__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1207 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)))) # label(fact_1628_real__sqrt__gt__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1208 (all X_a (semiring_div(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),C_1),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B_1),C_1)))))))) # label(fact_967_div__dvd__div) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1209 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1258_even__times__anything) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1210 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),pls)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)))))) # label(fact_1430_Suc__diff__eq__diff__pred) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1211 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = zero_zero(X_b))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)))))) # label(fact_4307_setsum_Oneutral) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1212 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 ((ti(X_a,X_1) = zero_zero(X_a) & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1))) & zero_zero(nat) != N_1 <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),zero_zero(X_a))))))) # label(fact_2453_power__le__zero__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1213 (all X_a all X_b all X_c all X_d all Y -(all A_4 all B_4 all C_4 all D_3 ti(product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),Y) != hAPP(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,X_d)),product_prod(X_a,product_prod(X_b,product_prod(X_c,X_d)))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,X_d))),A_4),hAPP(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d)),hAPP(X_b,fun(product_prod(X_c,X_d),product_prod(X_b,product_prod(X_c,X_d))),product_Pair(X_b,product_prod(X_c,X_d)),B_4),hAPP(X_d,product_prod(X_c,X_d),hAPP(X_c,fun(X_d,product_prod(X_c,X_d)),product_Pair(X_c,X_d),C_4),D_3))))) # label(fact_3149_prod__cases4) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1214 (all X_a all X_b all X_c all Z all C_1 all P_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),P_4))) -> -(all X_2 all Y_2 (hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) = ti(product_prod(X_b,X_c),P_4) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,X_2),Y_2))))))) # label(fact_4059_mem__splitE) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1215 (all X_a (number_semiring(X_a) -> (all X all Y hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))))) # label(fact_169_power2__sum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1216 (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]. 10.61/10.62 1217 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),hAPP(int,fun(int,bool),norRRset,Ma))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma))))),Ma)))))) # label(fact_4156_aux__some) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1218 (all M all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1439_Suc__mod__eq__add3__mod__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1219 (all X_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),X_1))))) # label(fact_4290_suminf__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1220 (all X_a (ring_div(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Y),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y)))))) # label(fact_2086_dvd__div__neg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1221 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)))) # label(fact_2479_even__square) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1222 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_458_power__Suc__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1223 (all A_2 all C_1 all D_1 all B_1 (ti(int,B_1) != zero_zero(int) -> (ti(int,D_1) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))))))) # label(fact_3784_le__rat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1224 (all B all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_702_divides__add__revr) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1225 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F))))))) # label(fact_3997_summable__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1226 (all K all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)))) # label(fact_3436_zgcd__greatest__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1227 (all F all X_1 all F_2 all N_1 all Ma ((all R_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),R_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),F,R_2)),X_1),hAPP(real,real,hAPP(nat,fun(real,real),F_2,R_2),X_1))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),X_1),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),F_2),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)))))) # label(fact_4289_DERIV__sumr) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1228 (all P_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,P_1,J)) -> ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J)) -> (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,I_2))) -> hBOOL(hAPP(nat,bool,P_1,I_2))))) -> hBOOL(hAPP(nat,bool,P_1,I)))))) # label(fact_1483_inc__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1229 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))))) # label(fact_2514_exp__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1230 (all N_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),zero_zero(real))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),zero_zero(int))))) # label(fact_3383_real__of__int__lt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1231 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_181_less__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1232 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)))))) # label(fact_333_dvd__triv__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1233 (all X all Y all Z_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))) # label(fact_31_zpower__zadd__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1234 (all X_2 hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,X_2)) = hAPP(nat,fun(nat,bool),ord_less(nat),X_2)) # label(fact_3815_less__eq__Suc__le__raw) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1235 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_2),one_one(nat)))),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),N_2))))))) # label(fact_2406_reals__Archimedean6) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1236 (all X all M all Y (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)))) # label(fact_959_Residues_Oaux) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1237 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),zero_zero(X_b))),S) = zero_zero(X_b)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),zero_zero(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)))))) # label(fact_4216_setsum__delta_H) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1238 (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(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,hAPP(int,int,number_number_of(int),V)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,number_number_of(int),V)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,number_number_of(int),W)),hAPP(int,int,number_number_of(int),V))))) # label(fact_1168_posDivAlg__eqn__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1239 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1262_odd__plus__even) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1240 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),A_3)) = ti(fun(X_a,bool),A_3)))) # label(fact_1997_double__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1241 (all X_a all X_b (ordere779506340up_add(X_b) & semiring_1(X_b) -> (all F all K_3 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),K_3)))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,semiring_1_of_nat(X_b),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))),K_3))))))) # label(fact_4296_setsum__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1242 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all B_2 all F all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (B_2 = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),Sa) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I)),B_2))))))))) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1243 (all X_a all X_b all X_1 all Y_1 all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4340_predicate2D) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1244 (all Y_1 all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) -> (Y_1 = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1))))) # label(fact_627_dvd_Oantisym__conv) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1245 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)))))) # label(fact_1381_one__less__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1246 (all A_1 all B all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))),K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),K_4)) # label(fact_921_zdiv__zmod__equality2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1247 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2793_of__real__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1248 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),K_4))) # label(fact_3456_zgcd__zmult__eq__self2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1249 (all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) # label(fact_3432_zgcd__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1250 (all Y all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> Y = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),Y))))) # label(fact_3407_log__powr__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1251 (all X_a (linordered_idom(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),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))) # label(fact_1854_abs__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1252 (all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) # label(fact_4840_is__nat__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1253 (all X_a (divisi14063676e_zero(X_a) & real_div_algebra(X_a) -> (all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,inverse_inverse(real),X))))) # label(fact_2798_of__real__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.62 1254 (all K all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all D_3 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)))),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),D_3)),one_one(nat)))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4271_sumr__pos__lt__pair) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1255 (all X_a all A_3 all B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),A_3))) # label(fact_1995_Diff__subset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1256 (all X_a (field(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1))))) # label(fact_2580_field__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1257 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)) & hAPP(real,real,tan,X_2) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2282_tan__total__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1258 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)))))) # label(fact_677_dvd__diffD1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1259 (all X_a (linorder(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),X)))) # label(fact_4802_Min_Oidem) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1260 (all B_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)))))) # label(fact_1023_nonneg1__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1261 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4764_metric__LIM__I) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1262 (all M all N all R_5 all R_4 all S_4 all S_3 all T_6 all T_5 all K_4 ((exists Sn exists Tn hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4)))) # label(fact_3477_xzgcd__correct__aux2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1263 (all W_1 all Z ((exists N_2 ti(int,Z) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))) # label(fact_1220_zless__iff__Suc__zadd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1264 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))),hAPP(int,int,number_number_of(int),min_1))) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))) # label(fact_468__096_126_AQuadRes_A_I4_A_K_Am_A_L_A1_J_A_N1_A_061_061_062_ALegendre_A_N) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1265 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),V)) = hAPP(int,X_a,number_number_of(X_a),V)))) # label(fact_3565_of__int__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1266 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),A_2)),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a)))))))) # label(fact_3799_Ints__odd__less__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1267 (all M all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),hAPP(nat,nat,suc,J_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4))))) # label(fact_1392_diff__Suc__diff__eq1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1268 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(nat,real),real,suminf(real),X_3)),X_1))))) # label(fact_4741_scaleR__left_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1269 (all X all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),X))))) # label(fact_3057_prime__divexp) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1270 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F all Sa (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),Sa),sequentially)) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)))))) # label(fact_4496_sums__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1271 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)) = hAPP(complex,real,re,hAPP(fun(nat,complex),complex,suminf(complex),X_3)))) # label(fact_4048_Re_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1272 (all B all A_1 (ti(int,B) != zero_zero(int) | zero_zero(int) != ti(int,A_1) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B))) = one_one(int))) # label(fact_3458_div__zgcd__relprime) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1273 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_2968_cnj_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1274 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),A_1))) # label(fact_2360_natfloor__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1275 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3626_ex__le__of__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1276 (all A_1 all B all C all D hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D))) # label(fact_3756_mult__rat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1277 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2567_exp__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1278 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2136_Compl__anti__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1279 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)))) # label(fact_36_rel__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1280 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z),X_1)))))) # label(fact_4987_le__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1281 (all X_a (linordered_semiring(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_430_mult__right__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1282 (all X_b (number(X_b) & monoid_mult(X_b) -> (all V all W hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3872_power__number__of__even__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1283 (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_2587_inverse__numeral__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1284 (all X_a (real_n1866405975lgebra(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,sgn_sgn(X_a),Y)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))))) # label(fact_2204_sgn__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1285 (all X_a (order(X_a) -> (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),N_7)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,N_7)))))))) # label(fact_1496_lift__Suc__mono__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1286 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),N)))) # label(fact_1122_mod__le__divisor) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1287 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X_1)),one_one(X_a))))))) # label(fact_2609_inverse__less__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1288 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),zero_zero(nat)) = zero_zero(nat)) # label(fact_550_mult__0__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1289 (all N one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,suc,N)),N)) # label(fact_3262_coprime__Suc__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1290 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),X))))))) # label(fact_1546_xt1_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1291 (all X_a all X_b all X_c all F all X_1 hAPP(product_prod(X_a,X_c),X_a,product_fst(X_a,X_c),X_1) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),X_1))) # label(fact_4065_fst__apsnd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1292 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_431_mult__le__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1293 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,M))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_2452_fact__diff__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1294 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X_1),Y_1)))))) # label(fact_1143_transfer__nat__int__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1295 (all X_a (linorder(X_a) -> (all Ma all N_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Ma)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),N_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Ma),N_1)))))) # label(fact_4320_lessThan__strict__subset__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1296 (all X_1 all Y_1 (Y_1 = X_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)))) # label(fact_624_divides__antisym) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1297 (all K all Xa_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),plus_plus(real)),K))),Xa_2),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Xa_2),K)))))) # label(fact_3814_DERIV__cos__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1298 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit1,L_4))) # label(fact_494_diff__bin__simps_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1299 (all X_a all X_c all X_b all F all X_1 all Y_1 hAPP(product_prod(X_a,X_c),product_prod(X_a,X_b),hAPP(fun(X_c,X_b),fun(product_prod(X_a,X_c),product_prod(X_a,X_b)),product_apsnd(X_c,X_b,X_a),F),hAPP(X_c,product_prod(X_a,X_c),hAPP(X_a,fun(X_c,product_prod(X_a,X_c)),product_Pair(X_a,X_c),X_1),Y_1)) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),hAPP(X_c,X_b,F,Y_1))) # label(fact_4064_apsnd__conv) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1300 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),one_one(real)))),suc))) = hAPP(real,real,ln,X_1)))) # label(fact_3977_ln__series) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1301 (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))) -> 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)))) & (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)))))) # label(fact_3902_zpower__number__of__odd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1302 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int)) = hAPP(int,rat,ring_1_of_int(rat),K_4)) # label(fact_3745_Fract__of__int__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1303 (all A_1 all C all B all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1643_real__sqrt__sum__squares__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1304 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,number_number_of(int),min_1)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),one_one(int)),P_5))))) # label(fact_317_zcong__neg__1__impl__ne__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1305 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),X)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),ii),hAPP(real,complex,of_real(complex),Y))))) # label(fact_2771_complex__inverse__complex__split) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1306 (all X_a (monoid_mult(X_a) -> (all N one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),N)))) # label(fact_341_power__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1307 (all Z all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1137_nat__less__eq__zless) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1308 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_1592_xt1_I12_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1309 (all N all X (hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X)) = X -> hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(real,int,archim2085082626_floor(real),X)),N))) # label(fact_3370_floor__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1310 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))),B))))) # label(fact_1040_div__mult__self2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1311 (all A_1 hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1981_abs__power2__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1312 (all X_a (metric_space(X_a) -> (all X all Y hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))) # label(fact_3518_dist__commute) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1313 (all M all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,real_1(nat),M)),N) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N))) # label(fact_2311_real__of__nat__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1314 (all X_a (ring_1(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2115_power2__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1315 (all X_a (real_normed_algebra(X_a) -> (all X_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),A_2))))) # label(fact_4907_mult__right_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1316 (all X_a all P_1 (hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))) <-> (exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))))) # label(fact_4786_some__eq__ex) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1317 (all M all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),K_4)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M))),K_4))) # label(fact_1418_Suc__times__mod__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1318 (all X_a all A_3 hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)) = ti(fun(X_a,bool),A_3)) # label(fact_2775_Union__Pow__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1319 (all A_1 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Y_2)),one_one(nat)))))) # label(fact_3090_bezout__prime) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1320 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K)))) # label(fact_4313_finite__lessThan) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1321 (all X_a (field(X_a) -> (all X all W all Z_1 all Y (zero_zero(X_a) != ti(X_a,Y) -> (ti(X_a,Z_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W),Y))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Z_1))))))) # label(fact_1727_diff__frac__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1322 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1758_real__less__half__sum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1323 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A_1))) # label(fact_905_pos__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1324 (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,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,abs_abs(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))) -> ti(X_a,A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2098_abs__if) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1325 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))) # label(fact_1071_neg__zdiv__mult__2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1326 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,D_1) = ti(X_a,B_1))))))) # label(fact_4195_atLeastLessThan__inj_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1327 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C))))) # label(fact_4812_min__max_Oinf_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1328 (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_728_divides__exp2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1329 (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]. 10.61/10.63 1330 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),one_one(nat))) # label(fact_589_nat__mult__1__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1331 (all X_a (linordered_idom(X_a) -> (all W_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W_1)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)))))) # label(fact_3569_of__int__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1332 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,sgn_sgn(real),X) = one_one(real))) # label(fact_2221_real__sgn__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1333 (all X_a ti(X_a,undefined(X_a)) = undefined(X_a)) # label(tsy_c_HOL_Oundefined_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1334 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),one_one(real))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,Y)),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),X)))))) # label(fact_2619_ln__x__over__x__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1335 (all X hAPP(real,real,abs_abs(real),hAPP(real,real,exp(real),X)) = hAPP(real,real,exp(real),X)) # label(fact_2532_abs__exp__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1336 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)))) # label(fact_1345_Suc__diff__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1337 (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_274_prime__g__5) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1338 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),one_one(real)) = one_one(real))) # label(fact_2685_real__root__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1339 (all N ti(int,N) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,real_1(int),N))) # label(fact_3324_floor__real__of__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1340 (all K_4 hAPP(int,int,bit0,K_4) != min_1) # label(fact_290_rel__simps_I45_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1341 (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_778_add__0__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1342 (all X_a (real_algebra_1(X_a) -> (all R_4 hAPP(real,X_a,of_real(X_a),R_4) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),one_one(X_a))))) # label(fact_4699_of__real__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1343 (all K all I all J hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J),K)) = hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,nat),fun(fun(nat,bool),fun(nat,bool)),image(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),I),J))) # label(fact_4540_image__add__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1344 (all P_5 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)))))) = 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))))))) # label(fact_1160_Euler_Oaux____2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1345 (all X_b all X_a (real_normed_vector(X_b) & metric_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4584_LIM__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1346 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_2)),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),hAPP(real,nat,natfloor,X_1)))))) # label(fact_2343_le__natfloor__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1347 (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_651_real__le__antisym) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1348 (all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),one_one(nat))) <-> one_one(nat) = Ma)) # label(fact_477_nat__dvd__1__iff__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1349 (all R_4 all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),Y))) # label(fact_2809_complex__of__real__mult__Complex) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1350 (all X_a (order(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)) <-> (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_2))))) | (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))))))))) # label(fact_3923_monoseq__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1351 (all X_a (number_ring(X_a) -> (all Y_1 (one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_2504_eq__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1352 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_383_mult__strict__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1353 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))))) # label(fact_739_nat__less__add__iff2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1354 (all B_1 all C_1 all A_2 all D_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),D_1) = one_one(nat) -> (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B_1),C_1) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),D_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),C_1) <-> B_1 = A_2 & C_1 = D_1)))) # label(fact_3270_coprime__crossproduct__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1355 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))))))) # label(fact_2233_cos__monotone__minus__pi__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1356 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y_1),Z))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)))))) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1357 (all X_a (ring_1(X_a) -> (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_1371_of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1358 (all R_4 all P_5 all Q_3 (hAPP(rat,product_prod(int,int),quotient_of,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)))) # label(fact_3724_quotient__of__denom__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1359 (all X_a (division_ring(X_a) -> (all B all A_1 all 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),A_1),C) = ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C) = ti(X_a,A_1)))))) # label(fact_1692_divide__eq__imp) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1360 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> zero_zero(nat) = N | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_872_divides__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1361 (all X_a (ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (ti(X_a,C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1))))) # label(fact_489_eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1362 (all X_a all X_b (topological_space(X_b) -> ti(fun(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool))),tendsto(X_a,X_b)) = tendsto(X_a,X_b))) # label(tsy_c_Limits_Otendsto_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1363 (all X_a (linordered_idom(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)),hAPP(X_a,X_a,abs_abs(X_a),X))))) # label(fact_2215_mult__sgn__abs) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1364 (all X_a (linordered_idom(X_a) -> (all A_2 (zero_zero(X_a) != ti(X_a,A_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_11_zero__less__power2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1365 (all X_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),N_1)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_1)),X_1)))))) # label(fact_1912_le__natfloor__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1366 (all X_a (division_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),one_one(X_a))))) # label(fact_1663_divide__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1367 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2419_even__product__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1368 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4007_summable__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1369 (all X_a all R_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),R_3),S)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),R_3)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))))) # label(fact_4339_pred__subset__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1370 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_981_div__neg__pos__less0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1371 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B)),C)))) # label(fact_4965_min__max_Osup_Oassoc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1372 (all A_2 all N_1 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_2),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B_1),hAPP(nat,nat,suc,N_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2874_coprime__exp2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1373 (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_1233_Suc__lessI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1374 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sin),X_1),hAPP(real,real,cos,X_1)))) # label(fact_2637_DERIV__sin) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1375 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)))))) # label(fact_2027_minus__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1376 (all X_a (semiring_div(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),C)))) # label(fact_916_div__mod__equality2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1377 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_3182_finite__PlusD_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1378 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hAPP(real,real,ln,X_1) = hAPP(real,real,ln,Y_1) <-> X_1 = Y_1)))) # label(fact_1934_ln__inj__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1379 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))))) # label(fact_3461_zgcd__zmult__zdvd__zgcd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1380 (all X_a all G all A_3 hAPP(complex,real,im,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),A_3)) # label(fact_4248_Im_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1381 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N)))) # label(fact_2709_real__root__pow__pos2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1382 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> hAPP(X_a,X_b,F,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),S))))))) # label(fact_3961_setprod__mono__one__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1383 (all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_1608_zero__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.63 1384 (all A_2 all B_1 ((exists X_2 exists Y_2 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),Y_2)) = one_one(nat) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),X_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_1),Y_2)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2896_coprime__bezout) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1385 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))) # label(fact_4396_gcd__ge__0__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1386 (all X_b all X_a all Q_1 all P_1 ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_2),Y_2)))) -> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)))) # label(fact_4342_predicate2I) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1387 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3226_gcd__assoc__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1388 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))))))) # label(fact_436_mult__le__cancel__left__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1389 (all X_a all A_3 all B_2 (hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3) <-> ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3))) # label(fact_2195_Compl__eq__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1390 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4620_DERIV__D) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1391 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)))) # label(fact_752_nat__eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1392 (all X_a all X_b (field_inverse_zero(X_b) -> (all F all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),A_3) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)))))) # label(fact_3957_setprod__dividef) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1393 (all X hAPP(real,real,sin,X) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X))) # label(fact_2392_sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1394 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1821_rev__finite__subset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1395 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4951_min__max_Oless__supI1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1396 (all X_a all X_b all B_1 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> -(all X_2 (hAPP(X_b,X_a,F,X_2) = ti(X_a,B_1) -> -hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),A_3)))))) # label(fact_3964_imageE) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1397 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_906_mod__mod__trivial) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1398 (all X_a all X_b all F all A_3 all B_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),B_2))),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,bool),fun(fun(X_b,bool),fun(X_b,bool)),minus_minus(fun(X_b,bool)),A_3),B_2))))) # label(fact_3641_image__diff__subset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1399 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all I all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,I)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)))))))) # label(fact_3953_dvd__setprod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1400 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3912_DERIV__cos__realpow2a) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1401 (all X_b all X_a (ab_group_add(X_a) -> (all F all A_3 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),uminus_uminus(X_a)),F)),A_3)))) # label(fact_4213_setsum__negf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1402 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),M))))) # label(fact_360_zcong__zmult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1403 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C))))))) # label(fact_312_dvd__trans) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1404 (all X_a (topological_space(X_a) -> (all L all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),X_1),sequentially)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),L)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),L))),X_1),sequentially))))))) # label(fact_4480_LIMSEQ__linear) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1405 (all X_a (power(X_a) & semiring_0(X_a) -> (all W ((zero_zero(nat) != hAPP(int,nat,number_number_of(nat),W) -> zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),W))) & (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),W) -> 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))))))) # label(fact_262_power__0__left__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1406 (all X_a (field_inverse_zero(X_a) & number(X_a) -> (all B_1 all W_1 all A_2 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,A_2) <-> (hAPP(int,X_a,number_number_of(X_a),W_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1)) = ti(X_a,B_1)) & (hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_2)))))) # label(fact_1726_divide__eq__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1407 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Z_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1)),X)))) # label(fact_4938_min__max_Osup__inf__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1408 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),im),A_2))) # label(fact_4893_Im_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1409 (all X_1 all Y_1 all Z (hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Z)) = X_1 <-> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),Y_1),Z))) # label(fact_1772_eq__divide__2__times__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1410 (all N all B all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),B)))))) # label(fact_202_zprime__power__zdvd__cancel__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1411 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),S))))))) # label(fact_4295_setsum__mono__zero__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1412 (all X hAPP(real,nat,natceiling,X) = hAPP(int,nat,nat_1,hAPP(real,int,archimedean_ceiling(real),X))) # label(fact_3284_natceiling__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1413 (all K_4 all L_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3711_Frct__code__post_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1414 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1)),hAPP(int,fun(int,bool),sRStar,P_4))) <-> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4))))) # label(fact_1162_StandardRes__SRStar__prop1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1415 (all M hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),zero_zero(nat))) # label(fact_3092_divmod__nat__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1416 (all N_1 all Ma hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_1)),Ma) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_min(nat),N_1))),Ma)) # label(fact_4833_min__Suc1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1417 (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_2206_sgn__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1418 (all X_a all X_b all X all Y all A_1 (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),X),Y)) -> ti(X_a,A_1) = ti(X_a,X))) # label(fact_3141_fst__eqD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1419 (all N hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_2173_neg__zminus__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1420 (all X_a all X_1 ti(X_a,X_1) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),X_1))) # label(fact_4787_some__eq__trivial) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1421 (all X_a all X_b (dvd(X_b) & comm_monoid_mult(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),B_2)))))))) # label(fact_3958_setprod__dvd__setprod__subset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1422 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_759_add__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1423 (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,bit1,K)),hAPP(int,int,bit1,L))))) # label(fact_33_rel__simps_I34_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1424 (all X_1 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),X_1)),A_2)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),A_2)),one_one(real)))))) # label(fact_3416_ceiling__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1425 (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)) -> (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))) & (ti(int,A_1) != zero_zero(int) -> hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> 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))))) # label(fact_3045_divmod__int__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1426 (all Code_numeral_4 zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_4)) # label(fact_2946_code__numeral_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1427 (all B_1 all A_2 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)))) # label(fact_3207_Bnor__mem__zle) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1428 (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_4314_lessThan__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1429 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),N_1)))) # label(fact_1335_Suc__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1430 (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_1) = ti(X_a,A_6) -> ti(X_b,B) != ti(X_b,B_5)))) # label(fact_3137_Pair__inject) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1431 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_a,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),product_prod(fun(X_a,bool),fun(X_a,bool))),product_Pair(fun(X_a,bool),fun(X_a,bool)),A_3),B_2)),finite_psubset(X_a))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))) # label(fact_3179_in__finite__psubset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1432 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,J_2),I_1) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)) # label(fact_3440_zgcd__commute) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1433 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1)))))))))))) # label(fact_2665_DERIV__pos__inc__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1434 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1578_order__less__trans) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1435 (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)) -> Y = hAPP(real,real,sqrt,X)))) # label(fact_1639_real__sqrt__unique) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1436 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M))))) # label(fact_204_zdvd__not__zless) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1437 (all X hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(real,real,exp(real),one_one(real))),X) = hAPP(real,real,ln,X)) # label(fact_2644_log__ln) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1438 (all D all A_1 all B (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),B))) # label(fact_3272_coprime__rmult__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1439 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_786_add__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1440 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3)),hAPP(complex,complex,cnj,A_2)),sequentially)))) # label(fact_4506_cnj_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1441 (all X_a trivial_limit(X_a) = ti(fun(filter(X_a),bool),trivial_limit(X_a))) # label(tsy_c_Limits_Otrivial__limit_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1442 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_1612_real__sqrt__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1443 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) -> hAPP(nat,nat,suc,zero_zero(nat)) = N))) # label(fact_1384_mn__eq__m__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1444 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),hAPP(int,int,fact_fact(int),N)))))) # label(fact_3197_dvd__fact__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1445 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),K_4))))) # label(fact_697_le__add__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1446 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2472_lemma__not__even__div2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1447 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists E ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_2),hAPP(real,real,F,X_1)))),E)) -> Y_2 = hAPP(real,real,F,hAPP(real,real,G,Y_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)))))))) # label(fact_4931_isCont__inv__fun__inv) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1448 (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]. 10.61/10.64 1449 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),A_1))))) # label(fact_2581_left__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1450 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_757_add__pos__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1451 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3920_monoseq__arctan__series) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1452 (all Ma all N_1 all P_1 ((all M_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),zero_zero(nat)))) -> ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M_2),N_2))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,M_2),N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Ma),N_1))))) # label(fact_3530_gcd__nat__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1453 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> N = hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_2892_floor__eq4) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1454 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1)))))) # label(fact_3913_DERIV__cos__realpow2b) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1455 (all K_4 K_4 = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,K_4))) # label(fact_3536_of__int__int__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1456 (all X_a (comple1803745165norder(X_a) -> (all A_2 all S (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),S))) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),X_2)))))))) # label(fact_1767_less__Sup__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1457 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)))))) # label(fact_3300_one__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1458 (all X_a (linorder(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),C)))) # label(fact_4810_min__max_Oinf_Oassoc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1459 (all X_a all N_1 all F all C_1 all H ((all N_2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2) = hAPP(nat,X_a,F,N_2)) -> hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1)) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),H,N_1),hAPP(nat,X_a,F,N_1)))) # label(fact_4330_def__nat__rec__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1460 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = M) # label(fact_1350_div__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1461 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_183_zadd__power3) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1462 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2))))) # label(fact_585_mult__le__mono2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1463 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,tan,X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_2286_tan__half) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1464 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),one_one(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))))),R_1),sequentially))) # label(fact_4498_LIMSEQ__inverse__real__of__nat__add__minus__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1465 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (ti(int,Ta) != ti(int,X_2) -> ti(int,Ta) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))))) # label(fact_4639_aset_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1466 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),No)))))) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4517_LIMSEQ__iff__nz) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1467 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,ring_1_of_int(X_a),Z))))))) # label(fact_3592_floor__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1468 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natfloor,X)),A_1) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))))) # label(fact_2348_natfloor__subtract) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1469 (all X_a all A_3 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2))) -> -(all X_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),X_4)) -> -hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),C_2)))))) # label(fact_1832_UnionE) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1470 (all X_a (idom(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) | ti(X_a,C_1) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))))) # label(fact_410_dvd__mult__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1471 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2717_DERIV__real__root) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1472 (all J all I all P_1 all P_4 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),P_4)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),P_4)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J),P_4)) -> hBOOL(hAPP(nat,bool,P_1,J))))))) # label(fact_1481_mod__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1473 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V))))) # label(fact_3306_ceiling__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1474 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,abs_abs(real),X)))) # label(fact_2689_real__root__abs) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1475 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sqrt),X_1))) # label(fact_4889_isCont__real__sqrt) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1476 (all X_a (ordere236663937imp_le(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_787_add__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1477 (all X_a (real_normed_vector(X_a) -> (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),zero_zero(real)))))) # label(fact_1780_norm__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1478 (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_2690_real__root__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1479 (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)))) # label(fact_656_real__le__linear) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1480 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,pred,W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2910_number__of__pred) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1481 (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]. 10.61/10.64 1482 (all N_1 one_one(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))) # label(fact_4240_sumr__cos__zero__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1483 (all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Z_1),Z_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_229_nat__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1484 (all X_a (comple44059174attice(X_a) -> (all Z all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),Z)))))) # label(fact_2734_complete__lattice__class_OSup__least) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1485 (all X_a (real_normed_vector(X_a) -> (all R_4 all A_1 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),A_1)),B)))) # label(fact_4697_scaleR_OscaleR__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1486 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_2967_cnj_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1487 (all X_a all P_1 hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),P_1))) # label(fact_3857_Collect__neg__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1488 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_762_add__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1489 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X_1))),hAPP(int,fun(int,bool),sRStar,P_4))))))) # label(fact_1165_StandardRes__SRStar__prop2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1490 (all X_a all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) <-> hBOOL(hAPP(X_a,bool,A_3,X_1)))) # label(fact_76_mem__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1491 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4573_LIM__mult__right__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1492 (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,F,X_2))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),F),A_3)))))) # label(fact_3937_transfer__nat__int__sum__prod__closure_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1493 (all X_a (real_normed_field(X_a) -> (all K all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),combk(X_a,X_a),K)),X_1),zero_zero(X_a)))))) # label(fact_3840_DERIV__const) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1494 (all X_1 all Y_1 (hAPP(nat,int,semiring_1_of_nat(int),X_1) = hAPP(nat,int,semiring_1_of_nat(int),Y_1) <-> X_1 = Y_1)) # label(fact_1485_Nat__Transfer_Otransfer__int__nat__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1495 (all M all K_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) != M -> (M != hAPP(nat,nat,suc,zero_zero(nat)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M))))) # label(fact_1387_one__less__m) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1496 (all Y all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1909_real__sqrt__ge__abs2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1497 (all X_a all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),S),T_3)))))) # label(fact_3036_Diff__infinite__finite) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1498 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),one_one(real))))) # label(fact_3397_real__of__int__floor__add__one__gt) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1499 (all A_1 all X hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,A_1))) # label(fact_2639_Log_Olog__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1500 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1142_nat__add__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1501 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_2002_psubset__subset__trans) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1502 (all I_1 all J_2 hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,uminus_uminus(int),I_1)),J_2)) # label(fact_3442_zgcd__zminus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1503 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_1945_ln__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1504 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1)),zero_zero(real))))))) # label(fact_3511_dist__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1505 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) | hBOOL(hAPP(int,bool,even_odd_even(int),Y_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1))))) # label(fact_1257_Parity_Oeven__product) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1506 (all X_a (linordered_ring(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))))))) # label(fact_46_sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1507 (all X_a (real_n1866405975lgebra(X_a) -> (all R_4 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(X_a,real,norm_norm(X_a),X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),X))),hAPP(real,real,inverse_inverse(real),R_4)))))))) # label(fact_2538_Bseq__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1508 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))))) # label(fact_1206_Suc__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.64 1509 (all N_1 all X_1 all Diff all F ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & X_1 != zero_zero(real) & hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,F,X_1) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))))))) # label(fact_4277_Maclaurin__all__lt__objl) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1510 (all X_a (preorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_1586_less__le__not__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1511 (all X_a (division_ring(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) != zero_zero(X_a) -> (ti(X_a,B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1) = one_one(X_a)))))) # label(fact_1696_right__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1512 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) # label(fact_3247_gcd__add2__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1513 (all X_a all X_b (ord(X_b) -> (all X_1 all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_1)),hAPP(X_a,X_b,G,X_1))))))) # label(fact_1555_le__funD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1514 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z)),Z)),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))))) # label(fact_175_odd__less__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1515 (all X_a (real_normed_vector(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4754_scaleR_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1516 (all X all Y hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),X),Y)) # label(fact_3519_dist__real__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1517 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1642_real__sqrt__pow2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1518 (all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1351_mod__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1519 (all V_3 ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3)))))) # label(fact_1498_one__mod__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1520 (all Q_2 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (Q_2 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),N_1) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_2)),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,suc,Q_2))))))) # label(fact_1442_split__div__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1521 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4609_LIM__norm__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1522 (all Z_1 all W hAPP(real,real,hAPP(real,fun(real,real),times_times(real),W),Z_1) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),W)) # label(fact_704_real__mult__commute) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1523 (all N_1 (zero_zero(nat) = N_1 <-> hAPP(nat,real,real_1(nat),N_1) = zero_zero(real))) # label(fact_2301_real__of__nat__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1524 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1525 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_132_add__Bit0__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1526 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),hAPP(int,nat,number_number_of(nat),N)) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N)))))) # label(fact_1841_natfloor__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1527 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),B_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))))) # label(fact_829_wset__inv__mem__mem) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1528 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_820_add__pos__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1529 (all Z_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,Z_1)),one_one(nat))),N)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_1),hAPP(nat,real,real_1(nat),N))))) # label(fact_2362_ge__natfloor__plus__one__imp__gt) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1530 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),A_1)))) # label(fact_1307_power__Suc2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1531 (all X_a all X_b (comm_monoid_add(X_b) -> big_co1399186613setsum(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),big_co1399186613setsum(X_a,X_b)))) # label(tsy_c_Big__Operators_Ocomm__monoid__add__class_Osetsum_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1532 (all U_1 all F ((all N_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_2),hAPP(nat,nat,F,N_2)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less_eq(nat)),F)),U_1)))))) # label(fact_4163_finite__less__ub) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1533 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),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),A_1),N)),A_1)))) # label(fact_331_power__commutes) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1534 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),M))))) # label(fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1535 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),zero_zero(real)))))) # label(fact_2692_real__root__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1536 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_856_int__gr__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1537 (all I_1 ((ti(int,I_1) != zero_zero(int) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> hAPP(int,int,uminus_uminus(int),one_one(int)) = hAPP(int,int,sgn_sgn(int),I_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),I_1)) -> one_one(int) = hAPP(int,int,sgn_sgn(int),I_1))) & (zero_zero(int) = ti(int,I_1) -> zero_zero(int) = hAPP(int,int,sgn_sgn(int),I_1)))) # label(fact_2258_zsgn__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1538 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (L != zero_zero(real) -> (exists R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) & X_2 != C_1 -> zero_zero(real) != hAPP(real,real,F,X_2)))))))) # label(fact_4627_LIM__fun__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1539 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_4760_scaleR__right_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1540 (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),sequentially)))) # label(fact_4471_LIMSEQ__imp__rabs) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1541 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) | ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_1587_order__le__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1542 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_2)))))) # label(fact_2829_pinf_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1543 (all B zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),B)) # label(fact_951_zdiv__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1544 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zEven))))) # label(fact_1364_IntNatAux_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1545 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1))))) # label(fact_2697_real__root__ge__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1546 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3509_dist__triangle__lt) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1547 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_2961_compl__less__swap1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1548 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_35_less__eq__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1549 (all P_4 hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),abs_abs(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,abs_abs(rat),P_4))) # label(fact_4030_rat__abs__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1550 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_1958_equalityD1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1551 (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_4355_gcd__add2__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1552 (all X hAPP(int,int,succ,hAPP(int,int,pred,X)) = ti(int,X)) # label(fact_2899_succ__pred) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1553 (all X_a (topological_space(X_a) -> ti(fun(X_a,filter(X_a)),at(X_a)) = at(X_a))) # label(tsy_c_Limits_Oat_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1554 (all X_b (monoid_mult(X_b) & number(X_b) -> (all V all W ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> one_one(X_b) = hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,W)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(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))) = 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)))))))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1555 (all L all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L))) # label(fact_4259_card__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1556 (all X_1 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),field_char_0_Rats(real))) -> -(all M_2 all N_2 (zero_zero(nat) != N_2 -> (hAPP(real,real,abs_abs(real),X_1) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),M_2)),hAPP(nat,real,real_1(nat),N_2)) -> one_one(nat) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M_2),N_2)))))) # label(fact_3679_Rats__abs__nat__div__natE) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1557 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1869_abs__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1558 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2274_arccos__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1559 (all X_b all X_a all A_3 all B_2 hAPP(fun(X_b,bool),fun(product_prod(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(product_prod(X_a,X_b),bool)),prod(X_a,X_b),A_3),B_2) = hAPP(fun(product_prod(X_a,X_b),bool),fun(product_prod(X_a,X_b),bool),collect(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3)))),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),B_2))))) # label(fact_4159_Nitpick_Oprod__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1560 (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_2620_DERIV__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1561 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,uminus_uminus(X_a),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),zero_zero(X_a)),A_1)))) # label(fact_2070_diff__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1562 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_2981_Im_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1563 (all X_a (linordered_semidom(X_a) -> (all M hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)))))) # label(fact_1278_zero__le__imp__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1564 (all X_a (linordered_field(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),C),B))))))))) # label(fact_1743_divide__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1565 (all X_a all A_3 all B_2 (-hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),B_2),A_3)) & hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_3),B_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less(filter(X_a)),A_3),B_2)))) # label(fact_4510_less__filter__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1566 (all X_a all X_b all X_c all X_d all X_e all X_f all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 all E all F_3 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),A_4),hAPP(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),B_4),hAPP(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))),hAPP(X_c,fun(product_prod(X_d,product_prod(X_e,X_f)),product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f)))),product_Pair(X_c,product_prod(X_d,product_prod(X_e,X_f))),C_4),hAPP(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f)),hAPP(X_d,fun(product_prod(X_e,X_f),product_prod(X_d,product_prod(X_e,X_f))),product_Pair(X_d,product_prod(X_e,X_f)),D_3),hAPP(X_f,product_prod(X_e,X_f),hAPP(X_e,fun(X_f,product_prod(X_e,X_f)),product_Pair(X_e,X_f),E),F_3)))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,product_prod(X_e,X_f))))),bool,P_1,X_1)))) # label(fact_3150_prod__induct6) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1567 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1682_divide__neg__neg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1568 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2079_abs__ge__minus__self) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1569 (all A_2 all D_1 all N_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),hAPP(int,fun(int,int),plus_plus(int),A_2)),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),semiring_1_of_nat(int))),D_1))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat)))),D_1))))) # label(fact_4311_arith__series__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1570 (all N (hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2473_lemma__odd__mod__4__div__2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1571 (all X_a (number_semiring(X_a) -> (all V_3 all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V_3)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),V_3))))))) # label(fact_86_semiring__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1572 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),X_3)),hAPP(X_a,real,norm_norm(X_a),A_2)),sequentially)))))) # label(fact_4466_LIMSEQ__norm) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1573 (all P_4 (hBOOL(hAPP(int,bool,zprime,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))))) = 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))) # label(fact_858_d22set__eq__wset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1574 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),D_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))))))) # label(fact_4529_atLeastAtMost__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1575 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1))))))) # label(fact_3686_Rats__dense__in__nn__real) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1576 (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) # label(fact_3022_Re_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1577 (all M all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),N)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) # label(fact_4354_gcd__add1__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1578 (all Q_2 all P_1 ((all A_4 all B_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> hBOOL(hAPP(rat,bool,P_1,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4))))) -> hBOOL(hAPP(rat,bool,P_1,Q_2)))) # label(fact_3795_Rat__induct__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1579 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4))) # label(fact_532_nat__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1580 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))) # label(fact_4943_minus__max__eq__min) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1581 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3))))) # label(fact_3850_Re_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1582 (all X_a (ab_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_2_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1583 (all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),I),K))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I))))) # label(fact_1024_pos__imp__zdiv__pos__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1584 (all X_a (real_normed_vector(X_a) -> (all B_1 all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),sequentially)))))) # label(fact_4441_LIMSEQ__diff__const) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1585 (all X_a all F1 all F2 all Nat hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),F1),F2),hAPP(nat,nat,suc,Nat)) = hAPP(nat,X_a,F2,Nat)) # label(fact_4110_nat__case__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1586 (all X_a (linorder(X_a) -> (all B all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),C))))) # label(fact_4967_min__max_Osup_Oleft__commute) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1587 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_472_less__zeroE) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1588 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)))),P_5)))))) # label(fact_848_Int2_Oaux____1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1589 (all X_a all X_b (real_normed_vector(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),A_2),B_1)),A_3))))))) # label(fact_4439_tendsto__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1590 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1114_le__mod__geq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1591 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_4034_exp__tail__after__first__two__terms__summable) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1592 (all X X = hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,suc,zero_zero(nat))),X)) # label(fact_2671_real__root__Suc__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1593 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a)))))) # label(fact_3980_summable__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1594 (all X all Y X = hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2993_Re) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1595 (all N all D all A_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N))))) # label(fact_2858_coprime__exp) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1596 (all X_a all X_b ti(fun(fun(product_prod(X_a,X_a),bool),fun(fun(product_prod(X_b,X_b),bool),fun(product_prod(product_prod(X_a,X_b),product_prod(X_a,X_b)),bool))),lex_prod(X_a,X_b)) = lex_prod(X_a,X_b)) # label(tsy_c_Wellfounded_Olex__prod_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1597 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ma),hAPP(int,int,number_number_of(int),N_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),Ma)),hAPP(int,real,number_number_of(real),N_1))))) # label(fact_3387_number__of__less__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1598 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y))))) # label(fact_881_mult__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1599 (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_2446_even__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1600 (all X_a ti(fun(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool))),mlex_prod(X_a)) = mlex_prod(X_a)) # label(tsy_c_Wellfounded_Omlex__prod_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1601 (all X hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,suc,X)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,X)),hAPP(nat,nat,fact_fact(nat),X))) # label(fact_2491_Fact_Ofact__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1602 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1156_Suc__n__div__2__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1603 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))))))) # label(fact_379_mult__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1604 (all K all Ma all N_1 (N_1 = Ma | K = zero_zero(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_744_nat__mult__eq__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1605 (all Y_3 all X_3 ((exists A_4 ((all N_2 hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),A_4))) & hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A_4)))) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),X_3)),Y_3)))))) # label(fact_4838_vanishes__mult__bounded) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1606 (all X all N hAPP(complex,complex,cnj,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),X),N)) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,cnj,X)),N)) # label(fact_2943_complex__cnj__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1607 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)) = 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)))) # label(fact_1665_diff__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1608 (all N all M ((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))) & (zero_zero(nat) = M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = zero_zero(nat)))) # label(fact_719_mult__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1609 (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_3418_log__powr) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1610 (all X_1 all R_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),R_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),R_1)),X_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),R_1)))) # label(fact_2090_abs__le__interval__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1611 (all Ta all A_3 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4647_aset_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1612 (all A_1 one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),powr,one_one(real)),A_1)) # label(fact_3323_powr__one__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1613 (all X hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_188_power2__ge__self) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1614 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1822_finite__subset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1615 (all B all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) = one_one(int) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),N)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),B),N)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Y_2)),B),N)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),N)) -> ti(int,Y_2) = ti(int,X_2)))))))) # label(fact_3478_zcong__lineq__unique) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1616 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)))),X),P_5)))))) # label(fact_849_Int2_Oaux____2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1617 (all Z_1 Z_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),Z_1)) # label(fact_703_real__mult__1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1618 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)))) # label(fact_623_dvd_Oless__le__not__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1619 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_1534_semiring__1__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1620 (all A_1 (hBOOL(hAPP(nat,bool,prime,A_1)) -> hBOOL(hAPP(int,bool,zprime,hAPP(nat,int,semiring_1_of_nat(int),A_1))))) # label(fact_3063_prime__impl__zprime__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1621 (all X_a all G all A_3 hAPP(complex,complex,cnj,hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),G),A_3)) = hAPP(fun(X_a,bool),complex,hAPP(fun(X_a,complex),fun(fun(X_a,bool),complex),big_co1399186613setsum(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),A_3)) # label(fact_4247_cnj_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1622 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),cos),X_1))) # label(fact_4887_isCont__cos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1623 (all A_2 all C_1 all D_1 all B_1 (ti(int,B_1) != zero_zero(int) -> (zero_zero(int) != ti(int,D_1) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1) <-> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))))) # label(fact_3753_eq__rat_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1624 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),P_5)))) # label(fact_3064_prime__g__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1625 (all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),K_4)),M)))) # label(fact_989_zmod__le__nonneg__dividend) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1626 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B))))) # label(fact_3354_powr__less__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1627 (all X_a all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3))))) # label(fact_3038_infinite__super) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1628 (all A_2 all B_1 all Ma (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,B_1),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))))) # label(fact_3473_Bnor__mem__if) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1629 (all X_a (number_ring(X_a) -> (all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W))),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))),Z_1)))) # label(fact_2045_minus__number__of__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1630 (all X all Y all L_4 all M hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),L_4)),hAPP(real,real,uminus_uminus(real),M))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),L_4)))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),M))))))) # label(fact_2112_abs__sum__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1631 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),min_1)))) # label(fact_304_rel__simps_I28_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1632 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,exp(real),X_1))))) # label(fact_2593_one__le__exp__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.65 1633 (all V hAPP(int,real,number_number_of(real),V) = hAPP(int,real,real_1(int),hAPP(int,int,number_number_of(int),V))) # label(fact_3337_real__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1634 (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_3746_Fract__of__int__quotient) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1635 -(all S1 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),S1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int))))) # label(fact_283__096_B_Bthesis_O_A_I_B_Bs1_O_A_091s1_A_094_A2_A_061_A_N1_093_A_Imod_A4_) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1636 (all X_a (linorder(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),C),D)))))))) # label(fact_4819_min__max_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1637 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))))) # label(fact_573_trans__le__add1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1638 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))))))) # label(fact_3514_dist__nz) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1639 (all B all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),B),C))) # label(fact_3224_gcd__left__commute__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1640 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))))) # label(fact_715_divides__mul__l) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1641 (all X_a all F all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_3) = hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),A_3))) # label(fact_4251_real__of__int__setsum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1642 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),hAPP(int,int,bit1,K))))) # label(fact_300_rel__simps_I26_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1643 (all X_a (semiring(X_a) -> (all A_1 all E_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),E_1)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),E_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),E_1)),C))))) # label(fact_326_combine__common__factor) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1644 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),Y_1),X_1)) = X_1)) # label(fact_4525_Sup__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1645 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,suc,N)))) # label(fact_1207_lessI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1646 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,Z_2)),hAPP(real,real,F,X_1))))))))) # label(fact_4932_lemma__isCont__inj2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1647 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))))))) # label(fact_4530_greaterThanLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1648 (all X_c all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> hAPP(fun(X_c,bool),X_b,hAPP(fun(X_c,X_b),fun(fun(X_c,bool),X_b),big_co1399186613setsum(X_c,X_b),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,X_b),hAPP(fun(fun(X_a,bool),X_b),fun(fun(X_c,fun(X_a,bool)),fun(X_c,X_b)),combb(fun(X_a,bool),X_b,X_c),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),collect(X_a)),hAPP(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_c,fun(X_a,bool)),fun(X_c,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_c),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S)))),hAPP(fun(X_a,fun(X_c,bool)),fun(X_c,fun(X_a,bool)),combc(X_a,X_c,bool),hAPP(fun(X_a,X_c),fun(X_a,fun(X_c,bool)),hAPP(fun(X_c,fun(X_c,bool)),fun(fun(X_a,X_c),fun(X_a,fun(X_c,bool))),combb(X_c,fun(X_c,bool),X_a),fequal(X_c)),F)))))),hAPP(fun(X_a,bool),fun(X_c,bool),hAPP(fun(X_a,X_c),fun(fun(X_a,bool),fun(X_c,bool)),image(X_a,X_c),F),S)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S))))) # label(fact_4224_setsum__image__gen) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1649 (all X_a (ordere216010020id_add(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y_1)) -> (ti(X_a,X_1) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,Y_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) = zero_zero(X_a))))))) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1650 (all X_a all X_b (ord(X_b) -> (all F all G (hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> (all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))))))) # label(fact_1559_le__fun__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1651 (all X_a all X_b all P_1 all Q_1 all X_2 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),Q_1),X_2)) & hBOOL(P_1) <-> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),combb(bool,bool,X_b),hAPP(bool,fun(bool,bool),fconj,P_1))),Q_1)),X_2)))) # label(fact_4044_split__part) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1652 (all X_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(int) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != zero_zero(int))) # label(fact_1062_neq__one__mod__two) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1653 (all X_a (group_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2041_minus__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1654 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arcsin),X_1))))) # label(fact_4922_isCont__arcsin) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1655 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> zero_zero(X_a) != hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))) # label(fact_2528_nonzero__imp__inverse__nonzero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1656 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int)))) = hAPP(int,int,fact_fact(int),N))) # label(fact_3202_fact__reduce__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1657 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> suminf(X_a) = ti(fun(fun(nat,X_a),X_a),suminf(X_a)))) # label(tsy_c_Series_Osuminf_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1658 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Y_1))))) # label(fact_2451_even__power__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1659 (all X all Y ((zero_zero(nat) = Y -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int)) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),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)))) # label(fact_3113_bezw_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1660 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2075_ab__diff__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1661 (all X_a (linorder(X_a) & dvd(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_862_pinf_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1662 (all X all Y (hAPP(nat,nat,suc,Y) = hAPP(nat,nat,suc,X) -> X = Y)) # label(fact_1213_Suc__inject) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1663 (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_3631_Nitpick_Oint__lcm__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1664 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),R_4),one_one(real))))) # label(fact_3402_real__of__int__ceiling__le__add__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1665 (all M hAPP(int,int,abs_abs(int),M) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),M)) # label(fact_3451_zgcd__0__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1666 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2702_real__root__strict__decreasing) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1667 (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_1252_Suc__diff__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1668 (all X_a (number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),pls))))) <-> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),X_1))))) # label(fact_2625_eq__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1669 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1))))) # label(fact_1947_ln__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1670 (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_3294_ceiling__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1671 (all A_1 -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),zero_zero(nat))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A_1)))) # label(fact_888_gcd__lcm__complete__lattice__nat_Onot__top__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1672 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) & power(X_b) -> (all N_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N_1)),A_2)))))) # label(fact_4902_isCont__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1673 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),B_2)))) # label(fact_3646_transfer__nat__int__set__relations_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1674 (all X_a (linordered_semidom(X_a) -> (all M -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),zero_zero(X_a)))))) # label(fact_1280_of__nat__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1675 (all X all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M))),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),X)),M)) # label(fact_2151_zminus__zmod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1676 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3350_powr__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1677 (all N_1 all Ma (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Ma) <-> one_one(nat) = Ma & one_one(nat) = N_1)) # label(fact_725_nat__mult__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1678 (all N_1 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)))))))) # label(fact_4516_summable__Leibniz_H_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1679 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all Y_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4549_mult__left_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1680 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),sequentially))))))) # label(fact_4442_LIMSEQ__diff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1681 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))) # label(fact_3318_ceiling__eq2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1682 (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_796_diff__0__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1683 (all X_a all X_b bijR(X_a,X_b) = ti(fun(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool)),bijR(X_a,X_b))) # label(tsy_c_BijectionRel_ObijR_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1684 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))))))) # label(fact_840_wset__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1685 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all R_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4734_scaleR__right_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1686 (all Nat_4 zero_zero(nat) != hAPP(nat,nat,suc,Nat_4)) # label(fact_1224_nat_Osimps_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1687 (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]. 10.61/10.66 1688 (all X_a (ab_group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) = zero_zero(X_a))))) # label(fact_794_eq__iff__diff__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1689 (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_205_zdvd__antisym__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1690 (all Z all 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)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z),hAPP(nat,int,semiring_1_of_nat(int),Ma))))) # label(fact_1970_dvd__int__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1691 (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]. 10.61/10.66 1692 (all Z (hAPP(complex,complex,cnj,Z) = zero_zero(complex) <-> Z = zero_zero(complex))) # label(fact_2930_complex__cnj__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1693 (all M all N ((hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) != N -> hAPP(nat,nat,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)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N) = zero_zero(nat)))) # label(fact_1352_mod__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1694 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))))) # label(fact_774_add_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1695 (all X_a (real_normed_field(X_a) -> (all F all X_1 all L (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),L)) <-> (exists G_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),G_1),X_1)) & ti(X_a,L) = hAPP(X_a,X_a,G_1,X_1) & (all Z_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G_1,Z_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Z_2),X_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,F,Z_2)),hAPP(X_a,X_a,F,X_1))))))))) # label(fact_4882_CARAT__DERIV) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1696 (all X_a all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1954_set__mp) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1697 (all X_a (linord1117847801e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_2534_abs__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1698 (all N all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))))))) # label(fact_3460_zcong__zgcd__zmult__zmod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1699 (all Z (ti(int,Z) = hAPP(int,int,number_number_of(int),min_1) | ti(int,Z) = one_one(int) <-> hAPP(int,int,abs_abs(int),Z) = one_one(int))) # label(fact_1943_abs__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1700 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),X)))) # label(fact_2190_ln__bound) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1701 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X))) # label(fact_2397_minus__sin__cos__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1702 (all A_1 all B all M hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),M)))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),M))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) # label(fact_969_zcong__zmod__aux) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1703 (all U all M all N all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),I_1)),U)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N)))) # label(fact_750_nat__diff__add__eq2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1704 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all K all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),K))),L_2),hAPP(X_a,filter(X_a),at(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),K)))))))) # label(fact_4585_LIM__offset) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1705 (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_328_field__power__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1706 (all X_a all X_b all X_c all Y -(all A_4 all B_4 all C_4 ti(product_prod(X_a,product_prod(X_b,X_c)),Y) != hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4)))) # label(fact_3147_prod__cases3) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1707 (all X_a (real_normed_vector(X_a) -> (all R_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),A_2))))) # label(fact_4914_scaleR__right_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1708 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1)),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))))) # label(fact_504_less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1709 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2010_abs__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1710 (all X_a (real_algebra_1(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),R_4)),X)))) # label(fact_4680_scaleR__conv__of__real) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1711 (all X_5 all Y_4 hAPP(real,real,cos,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2251_cos__arccos__lemma1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1712 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))))) # label(fact_3362_le__floor) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1713 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A0),A1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(fun(product_prod(nat,nat),fun(product_prod(nat,nat),bool)),fun(product_prod(nat,nat),bool),accp(product_prod(nat,nat)),nat_gcd_rel),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),X_2),Y_2))) -> ((Y_2 != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,Y_2),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_2),Y_2)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,X_2),Y_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,A0),A1))))) # label(fact_3672_nat__gcd_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1714 (all Z_1 (-hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1)) = ti(int,Z_1))) # label(fact_1509_not__neg__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1715 (all K_4 all L_4 hAPP(int,int,bit1,K_4) != hAPP(int,int,bit0,L_4)) # label(fact_118_rel__simps_I50_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1716 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)),A_1) = ti(X_a,B))))) # label(fact_1002_dvd__div__mult__self) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1717 (all L all K ((zero_zero(int) = ti(int,K) -> 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)) & (zero_zero(int) != ti(int,K) -> (zero_zero(int) = ti(int,L) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K)) & (ti(int,L) != zero_zero(int) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),hAPP(int,int,sgn_sgn(int),K)),hAPP(int,int,sgn_sgn(int),L))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L))))) # label(fact_4069_divmod__int__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1718 (all X_a (ord(X_a) -> (all I all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),K)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),K))))))) # label(fact_4988_atMost__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1719 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4520_LIMSEQ__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1720 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N)),N))) # label(fact_1243_Suc__n__not__le__n) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1721 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_1),Y_1)))) # label(fact_1302_Nat__Transfer_Otransfer__int__nat__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1722 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),one_one(real))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),Z_2)) & 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))))))) & X = hAPP(real,real,tan,Z_2))))) # label(fact_2281_tan__total__pi4) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1723 (all U all X (X = hAPP(real,real,exp(real),U) -> hAPP(real,real,ln,X) = U)) # label(fact_2508_exp__ln__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1724 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_1445_of__nat__less__two__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1725 (all M all N hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) # label(fact_3126_mod__nat__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1726 (all K_4 hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),K_4)) = hAPP(int,int,number_number_of(int),K_4)) # label(fact_3163_int__of__number) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1727 (all B_1_1 (hBOOL(ti(bool,B_1_1)) <-> hBOOL(B_1_1))) # label(tsy_c_hBOOL_arg1) # label(hypothesis) # label(non_clause). [assumption]. 10.61/10.66 1728 (all X_a (number_ring(X_a) -> (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X))))) # label(fact_2443_Parity_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1729 (all Ma all N_1 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1) <-> ti(int,N_1) = one_one(int) & ti(int,Ma) = one_one(int) | ti(int,N_1) = hAPP(int,int,number_number_of(int),min_1) & hAPP(int,int,number_number_of(int),min_1) = ti(int,Ma))) # label(fact_308_zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1730 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))))))) # label(fact_2212_sgn__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1731 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,pred,K)),L)))) # label(fact_2902_le__iff__pred__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1732 (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]. 10.61/10.66 1733 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_372_mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1734 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))),one_one(int)),P_4)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),P_4)))) # label(fact_513_inv__not__p__minus__1__aux) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1735 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),hAPP(int,int,uminus_uminus(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_2144_zcong__zminus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1736 (all N_1 all X_1 (zero_zero(real) != X_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,exp(real),X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),T_4)))))))) # label(fact_4269_Maclaurin__exp__lt) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1737 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> 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))))) # label(fact_2703_real__root__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1738 (all P_2 all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> (hBOOL(hAPP(int,bool,P_1,X_2)) <-> hBOOL(hAPP(int,bool,P_2,X_2))))) -> hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_2)))) # label(fact_4334_transfer__nat__int__set__cong) # label(axiom) # label(non_clause). [assumption]. 10.61/10.66 1739 (all X_b all X_a all F1 all A_2 all B_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F1,A_2),B_1)) -> hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F1),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))))) # label(fact_4039_prod__caseI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1740 (all A_2 (A_2 = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),one_one(nat))))) # label(fact_896_gcd__lcm__complete__lattice__nat_Obot__unique) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1741 (all U_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),U_1)) -> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(int,nat,nat_1,U_1))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1))) # label(fact_4323_image__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1742 (all N (N != one_one(nat) -> (exists P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),N)) & hBOOL(hAPP(nat,bool,prime,P_6)))))) # label(fact_3088_prime__factor) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1743 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_378_mult__nonneg__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1744 (all N (-hBOOL(hAPP(nat,bool,prime,N)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),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))),K_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M_2),K_1) = N & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M_2)))))) # label(fact_3091_not__prime__ex__mk) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1745 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)))))) # label(fact_676_dvd__diffD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1746 (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]. 10.61/10.67 1747 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4793_dvd_OmonoD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1748 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))))) # label(fact_710_real__mult__less__iff1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1749 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_leq)))) # label(fact_3489_pair__leqI1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1750 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Z_1))))))) # label(fact_4946_min__max_Odistrib__sup__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1751 (all X_a (field(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2578_inverse__add) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1752 (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))) -> Y = hAPP(real,real,cos,hAPP(real,real,arccos,Y)))) # label(fact_2260_cos__arccos__abs) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1753 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1222_Suc__neq__Zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1754 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> Y_1 = X_1)) # label(fact_620_dvd_Oeq__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1755 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))))) # label(fact_680_diff__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1756 (all C_2 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C_2)))) # label(fact_3663_Nat__Transfer_Otransfer__int__nat__set__function__closures_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1757 (all X_2 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_2))) = hAPP(real,real,sin,X_2)) # label(fact_3969_lemma__sin__ext) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1758 (all X_a (real_normed_algebra(X_a) -> (all Y all S_3 all X all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Y)),S_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),S_3)))))))) # label(fact_1789_norm__mult__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1759 (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N))) # label(fact_2675_odd__real__root__pow) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1760 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all I_2 all J_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),upto_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),I_2),J_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))),J_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3555_upto_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1761 (all X_a (field_char_0(X_a) -> (all N_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),field_char_0_Rats(X_a)))))) # label(fact_3700_Rats__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1762 (all N all M all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N) = one_one(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),R_4)))))) # label(fact_3288_divides__mult__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1763 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all W_1 all B_1 all C_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1746_less__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1764 (all K_4 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_485_zdvd__zdiffD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1765 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,number_number_of(int),min_1)))) # label(fact_1150_EvenOdd_Oneg__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1766 (all A_1 all B all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)))) # label(fact_1028_zdiv__zmult2__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1767 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_1588_leI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1768 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2)))))) # label(fact_101_zmult__zless__mono2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1769 (all S (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)) <-> (exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_atMost(nat),K_1)))))) # label(fact_4974_finite__nat__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1770 (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_1566_less__imp__neq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1771 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),zero_zero(int))) <-> ti(int,A_2) = ti(int,B_1))) # label(fact_353_IntPrimes_Ozcong__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1772 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))),one_one(int)),P_5)))))) # label(fact_811_inv__is__inv) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1773 (all X_a (number_ring(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) = one_one(X_a)))) # label(fact_364_power__m1__even) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1774 (all X all Y (hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = X -> Y = zero_zero(real))) # label(fact_1647_real__sqrt__sum__squares__eq__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1775 (all N_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,M_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4274_series__pos__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1776 (all X hAPP(rat,real,ratreal,hAPP(rat,rat,uminus_uminus(rat),X)) = hAPP(real,real,uminus_uminus(real),hAPP(rat,real,ratreal,X))) # label(fact_3769_real__uminus__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1777 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4026_summable__geometric) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1778 (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]. 10.61/10.67 1779 (all X X = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(quickcheck_code_int,int,quickcheck_int_of,X))) # label(fact_3535_int__of__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1780 (all X_a (number_ring(X_a) -> (all N hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))) = hAPP(int,X_a,number_number_of(X_a),min_1)))) # label(fact_1474_power__m1__odd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1781 (all X_a (real_normed_algebra(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y)))) # label(fact_4679_mult__left_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1782 (all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi))) # label(fact_2373_cos__npi) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1783 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N))) # label(fact_1098_div__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1784 (all R_4 exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))) # label(fact_3424_real__lb__ub__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1785 (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)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),P_5))))) # label(fact_3469_zless__zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1786 (all X_b all X_a all B_1 all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> (hAPP(X_a,X_b,F,X_1) = ti(X_b,B_1) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),B_1),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)))))) # label(fact_3639_rev__image__eqI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1787 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4745_scaleR_OLIM__prod__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1788 (all A_1 (one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) -> one_one(int) = hAPP(int,int,abs_abs(int),A_1))) # label(fact_1985_power2__eq1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1789 (all A_2 all B_1 all Q_2 all R_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_2),B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_1))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_2)),B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),hAPP(int,int,uminus_uminus(int),Q_2)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),Q_2)),one_one(int)))),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),R_1),zero_zero(int))),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B_1),R_1))))))) # label(fact_2183_zminus1__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1790 (all B all Q_3 all R_4 all B_5 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))))) # label(fact_267_zdiv__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1791 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),cos),X_1),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))))) # label(fact_2640_DERIV__cos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1792 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2616_inv__real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1793 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N_1))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_2668_DERIV__even__real__root) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1794 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)))))))) # label(fact_4631_aset_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1795 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),Y))))))) # label(fact_2648_log__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1796 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)))) # label(fact_1965_DiffD2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1797 (all X_a (topological_space(X_a) -> (all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),combi(X_a)),A_2))))) # label(fact_4899_isCont__ident) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1798 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),hAPP(int,int,number_number_of(int),K_4))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3712_Frct__code__post_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1799 (all V (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,number_number_of(nat),V) = zero_zero(nat))) # label(fact_1510_neg__imp__number__of__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1800 (all X_a (real_n2089651433ebra_1(X_a) -> (all X all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(X_a,real,norm_norm(X_a),X)),N)))))) # label(fact_1794_norm__power__ineq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1801 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X))),one_one(real)))) # label(fact_2218_abs__cos__le__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1802 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)),A_1)))) # label(fact_3380_powr__divide) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1803 (all R_4 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_4)),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_4)) # label(fact_2816_cmod__complex__polar) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1804 (all V hAPP(complex,real,im,hAPP(int,complex,number_number_of(complex),V)) = zero_zero(real)) # label(fact_2979_complex__Im__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1805 (all X_a (semiring_div(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),A_1) = one_one(X_a))))) # label(fact_999_div__self) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1806 (all X_a (field(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))) # label(fact_2561_field__class_Onormalizing__field__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1807 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)))) # label(fact_1048_mod__pos__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1808 (all X_a (topological_space(X_a) -> (all K hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),K)),K),sequentially))))) # label(fact_4464_LIMSEQ__const) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1809 (all X_a (order(X_a) -> (all N_1 all Ma all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,Ma)))))))) # label(fact_1497_lift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1810 (all K_4 all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit1,K_4)),hAPP(int,int,bit0,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4))) # label(fact_493_diff__bin__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1811 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> sums(X_a) = ti(fun(fun(nat,X_a),fun(X_a,bool)),sums(X_a)))) # label(tsy_c_Series_Osums_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1812 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sqrt,X))))) # label(fact_1625_real__sqrt__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1813 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2366_sin__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1814 (all X_a (semiring_0(X_a) & power(X_a) -> (all N ((N = zero_zero(nat) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),N) = one_one(X_a)) & (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)))))) # label(fact_446_power__0__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1815 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4738_LIM__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1816 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2014_less__minus__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1817 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4462_LIMSEQ__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1818 (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_965_div__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1819 (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),M)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N))))) # label(fact_424_zprime__zdvd__zmult__better) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1820 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),one_one(int))) # label(fact_65_zmult__1__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1821 (all K all F all N_1 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),N_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),one_one(nat)))),hAPP(nat,int,F,I_2)))),one_one(int))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,F,zero_zero(nat))),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),hAPP(nat,int,F,N_1))) -> (exists I_2 (hAPP(nat,int,F,I_2) = ti(int,K) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),N_1)))))))) # label(fact_2009_nat0__intermed__int__val) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1822 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B_1),A_2)),E_2)),D_1))))))) # label(fact_502_le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1823 (all X_a (real_n2089651433ebra_1(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),zero_zero(X_a)),sequentially)))))) # label(fact_4487_LIMSEQ__power__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1824 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2688_real__root__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1825 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3860_Ints__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1826 (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_124_less__int__code_I16_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1827 (all X_b all X_a (ring_1(X_a) -> (all F all A_3 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(fun(X_b,bool),int,hAPP(fun(X_b,int),fun(fun(X_b,bool),int),big_co1399186613setsum(X_b,int),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,int),fun(X_b,X_a),hAPP(fun(int,X_a),fun(fun(X_b,int),fun(X_b,X_a)),combb(int,X_a,X_b),ring_1_of_int(X_a)),F)),A_3)))) # label(fact_4170_of__int__setsum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1828 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))))) # label(fact_2804_finite__Pow__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1829 (all A_1 all B (B != A_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_625_dvd_Oneq__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1830 (all X_a (power(X_a) & mult_zero(X_a) & no_zero_divisors(X_a) & zero_neq_one(X_a) -> (all A_2 all W_1 (hAPP(int,nat,number_number_of(nat),W_1) != zero_zero(nat) & zero_zero(X_a) = ti(X_a,A_2) <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),W_1)) = zero_zero(X_a))))) # label(fact_256_power__eq__0__iff__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1831 (all Y_1 hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),tan)),Y_1)))) = hAPP(real,real,arctan,Y_1)) # label(fact_4132_arctan__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1832 (all Ma all K all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,Ma),N_1) = ti(int,K) <-> (exists S_1 exists T_4 hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_1),T_4)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,Ma),N_1))))) # label(fact_3475_xzgcd__correct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1833 (all X all Y all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z_1)),Z_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z_1)),Y))))) # label(fact_1053_div__prop2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1834 (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_4350_gcd__non__0__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1835 (all X_a all A_3 ti(fun(X_a,bool),A_3) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) # label(fact_2193_double__complement) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1836 (all X_a (real_algebra_1(X_a) -> of_real(X_a) = ti(fun(real,X_a),of_real(X_a)))) # label(tsy_c_RealVector_Oof__real_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1837 (all X_b (number(X_b) & semiring(X_b) -> (all A_1 all B all V hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),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))) = 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))))) # label(fact_95_left__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1838 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> M = N))) # label(fact_632_dvd__antisym) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1839 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1)))))) # label(fact_747_nat__mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1840 (all Ma all N_1 (zero_zero(nat) != N_1 | 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),gcd_gcd(nat),Ma),N_1))))) # label(fact_3259_gcd__pos__nat) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1841 (all B all B_5 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B_5))))))) # label(fact_1022_zdiv__mono2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1842 (all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (one_one(real) != A_1 -> one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),A_1)))) # label(fact_2642_log__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1843 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> (exists K_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),K_1)) = ti(int,B_1)))) # label(fact_421_zcong__iff__lin) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1844 (all D_2 all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (X_1 != zero_zero(real) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> D_2 = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))) -> ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> D_2 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))) -> ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))) = D_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),D_2)))))))) # label(fact_2669_DERIV__real__root__generic) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1845 (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_3720_quotient__of__inject) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1846 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all X_1 all Y_1 (ti(int,Y_1) = ti(int,X_1) <-> hAPP(int,X_a,number_number_of(X_a),Y_1) = hAPP(int,X_a,number_number_of(X_a),X_1))))) # label(fact_89_eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1847 (all X_a (ordered_ab_group_add(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B)),hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))))) # label(fact_2029_le__imp__neg__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1848 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B)))) # label(fact_942_mod__add__self2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1849 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2846_coprime__sos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1850 (all N all A_1 all B all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),P_5),N)),A_1)))))) # label(fact_201_zprime__power__zdvd__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1851 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1))))))) # label(fact_2432_zero__le__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1852 (all X_a all F all A_3 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),A_3) = hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3))) # label(fact_3943_transfer__nat__int__sum__prod2_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1853 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)))) # label(fact_1448_int__even__iff__2__dvd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1854 (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,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),L_4))) # label(fact_163_add__Bit0__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1855 (all X_a (real_normed_vector(X_a) -> (all A_1 hAPP(real,real,abs_abs(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),A_1)))) # label(fact_1859_abs__norm__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1856 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1)))),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1)))),zero_zero(real)),sequentially)) -> (exists L_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),L_3))) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L_3),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_snd(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1))),L_3),sequentially)) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,product_prod(real,real)),fun(nat,real),hAPP(fun(product_prod(real,real),real),fun(fun(nat,product_prod(real,real)),fun(nat,real)),combb(product_prod(real,real),real,nat),product_fst(real,real)),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1))),L_3),sequentially))))))))) # label(fact_4514_Bolzano__nest__unique) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1857 (all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))) # label(fact_1209_dvd__1__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1858 (all A_2 all B_1 all P_4 (hBOOL(hAPP(nat,bool,prime,P_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),B_1)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_4),A_2))))) # label(fact_3052_prime__divprod__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1859 (all X_a (comm_ring_1(X_a) -> (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N))))) # label(fact_2425_power__minus__odd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.67 1860 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Sa),Ta)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_less))))) # label(fact_3485_pair__lessI2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1861 (all Diff all F all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),H),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),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),T_4),zero_zero(real))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4))))))))) # label(fact_4281_Maclaurin__minus) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1862 (all N_1 all N_4 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),N_1)))) -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)))) # label(fact_3675_bounded__nat__set__is__finite) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1863 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)),A_1) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))) # label(fact_138_power3__eq__cube) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1864 (all V_1 all V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_2))))) # label(fact_79_less__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1865 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1)),zOdd)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd))))) # label(fact_1046_power__preserves__odd) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1866 (all X_b all X_a (comm_monoid_mult(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),A_3))))) # label(fact_3946_setprod__timesf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1867 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1)))) # label(fact_142_mult__2__right) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1868 (all N_1 all P_1 (hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,N_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(nat,bool,P_1,N_1))))) # label(fact_1654_nat__induct) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1869 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),I_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),J_2))))) # label(fact_38_zadd__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1870 (all X_a all X_b (real_algebra_1(X_b) & real_normed_vector(X_b) -> (all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),G)),hAPP(real,X_b,of_real(X_b),A_2)),A_3)))))) # label(fact_4458_of__real_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1871 (all M all N hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))))) # label(fact_3103_divmod__nat__rel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1872 (all X_a (plus(X_a) & dvd(X_a) & linorder(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_861_minf_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1873 (all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) | hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1)),Q_1)))))) # label(fact_3800_finite__Collect__conjI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1874 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 ((ti(X_a,A_1) = zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1) = zero_zero(X_a)) & (zero_zero(X_a) != ti(X_a,A_1) -> one_one(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),A_1)))))) # label(fact_1694_divide__self__if) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1875 (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]. 10.61/10.68 1876 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_2889_floor__diff__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1877 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),B))))) # label(fact_2869_coprime__divprod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1878 (all N all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N))))) # label(fact_2857_coprime__exp__imp) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1879 (all X_a (topological_space(X_a) -> (all K all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),A_2),sequentially)))))) # label(fact_4446_LIMSEQ__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1880 (all X_a all X_b (topological_space(X_b) -> (all F all L all A_3 all A_7 (hBOOL(hAPP(filter(X_a),bool,hAPP(filter(X_a),fun(filter(X_a),bool),ord_less_eq(filter(X_a)),A_3),A_7)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_7)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3))))))) # label(fact_4430_tendsto__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1881 (all N_1 all Ma (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,Ma))) <-> N_1 = Ma))) # label(fact_1236_not__less__less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1882 (all I_1 all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),K_4)) # label(fact_666_diff__diff__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1883 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,re,X)),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2998_complex__Re__le__cmod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1884 (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_2548_inverse__negative__imp__negative) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1885 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2007_abs__ln__one__plus__x__minus__x__bound__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1886 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3430_zgcd__zmult__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1887 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natfloor,X)),hAPP(real,nat,natfloor,Y))))) # label(fact_1875_natfloor__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1888 (all T_1 ord(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oord) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1889 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)))) # label(fact_301_rel__simps_I30_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1890 (all N_4 (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)) <-> (exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X_2),M_2)))))) # label(fact_3673_finite__nat__set__iff__bounded__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1891 (all X_a (ordere223160158up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_824_add__less__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1892 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),M))))) # label(fact_557_trans__less__add1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1893 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_156_rel__simps_I16_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1894 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))),N)) # label(fact_1253_mod__Suc__eq__Suc__mod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1895 (all N_1 all Q_1 all P_1 ((all X_2 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,Q_1,X_2)),hAPP(nat,nat,P_1,X_2)))) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),P_1)),Q_1)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),P_1),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),Q_1),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))))) # label(fact_4326_sum__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1896 (all Ma all X_1 hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),norRRset,Ma)) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)) # label(fact_3878_noXRRset__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1897 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2571_le__imp__inverse__le__neg) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1898 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X)))),one_one(real)))) # label(fact_3410_real__of__int__div3) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1899 (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]. 10.61/10.68 1900 (all X_b all X_a (topological_space(X_a) & power(X_b) & real_normed_algebra(X_b) -> (all N_1 all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(nat,fun(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(nat,X_b)),hAPP(fun(X_b,fun(nat,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(nat,X_b))),combb(X_b,fun(nat,X_b),X_a),power_power(X_b)),F)),N_1)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),L),N_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4556_LIM__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1901 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))) # label(fact_4682_complex__Re__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1902 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1))))))) # label(fact_798_diff__eq__diff__less) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1903 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_177_less__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1904 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))))) # label(fact_4857_transfer__int__nat__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1905 (all X_b all X_c all 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)) = combb(X_b,X_c,X_a)) # label(tsy_c_COMBB_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1906 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y_1)))))) # label(fact_4799_min__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1907 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit1,hAPP(int,int,pred,hAPP(int,int,uminus_uminus(int),K_4)))) # label(fact_2906_minus__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1908 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),min_1))))))) # label(fact_3309_ceiling__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1909 (all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> (exists N_2 L_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N_2)))) # label(fact_2733_le__Suc__ex) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1910 (all N_1 all Ma all F ((all N_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2))),hAPP(nat,nat,F,N_2))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_2)),hAPP(nat,nat,F,hAPP(nat,nat,suc,N_2)))))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,Ma)),hAPP(nat,nat,F,N_1))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,F,N_1)),hAPP(nat,nat,F,Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma))))) # label(fact_1493_dvd_Olift__Suc__mono__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1911 (all N all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),hAPP(nat,nat,suc,N)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)))))) # label(fact_1479_realpow__pos__nth2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1912 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)),zero_zero(int))))))) # label(fact_1057_zmult2__lemma__aux2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1913 (all M all N (N = M -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_528_eq__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1914 (all X_a (mult_zero(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),A_1)))) # label(fact_323_mult__zero__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1915 (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,Y) = ti(int,X)))))))) # label(fact_419_zcong__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1916 (all X_a (zero_neq_one(X_a) -> one_one(X_a) != zero_zero(X_a))) # label(fact_324_zero__neq__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1917 (all X_a all F all A_3 hAPP(int,nat,nat_1,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)) # label(fact_4246_transfer__nat__int__sum__prod2_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1918 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_1336_less__Suc__eq__le) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1919 (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) | ti(int,B) = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_1),B)))) & (ti(int,A_1) = zero_zero(int) | zero_zero(int) = ti(int,B) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B)))) # label(fact_3925_norm__frac_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1920 (all Ma all N_1 (Ma = hAPP(nat,nat,suc,zero_zero(nat)) & N_1 = hAPP(nat,nat,suc,zero_zero(nat)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1326_mult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1921 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2))))) # label(fact_3790_zero__le__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1922 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),Z_1),hAPP(real,complex,of_real(complex),hAPP(complex,real,norm_norm(complex),Z_1))) = hAPP(complex,complex,sgn_sgn(complex),Z_1)) # label(fact_2802_sgn__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1923 (all P_4 hAPP(int,fun(int,bool),sRStar,P_4) = hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),P_4)))) # label(fact_1129_SRStar__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1924 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all W_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1))),A_2)) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1)))))))) # label(fact_1748_divide__less__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1925 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),zero_zero(int))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_1)),zero_zero(real))))) # label(fact_3386_real__of__int__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1926 (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_1052_zmod__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1927 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y)) = hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))))) # label(fact_1978_ln__div) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1928 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y)) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X),Y))) # label(fact_1210_Nat__Transfer_Otransfer__int__nat__functions_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1929 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> ti(X_a,B) = ti(X_a,A_1))))))) # label(fact_1373_power__inject__base) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1930 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))))))) # label(fact_3935_Union__SetS__setprod__prop2) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1931 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),N)) # label(fact_541_plus__nat_Oadd__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1932 (all X_a (number_ring(X_a) -> (all V all W all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),W)),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),W))),Z_1)))) # label(fact_151_add__number__of__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1933 (all I all J all F ((all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),J_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,I_2)),hAPP(nat,nat,F,J_1))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,F,I)),hAPP(nat,nat,F,J)))))) # label(fact_1205_less__mono__imp__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1934 (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_3199_transfer__nat__int__factorial) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1935 (all K_4 all L_4 hAPP(int,int,bit0,K_4) != hAPP(int,int,bit1,L_4)) # label(fact_119_rel__simps_I49_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1936 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_1020_div__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1937 (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_2939_code__numeral_Oinject) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1938 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,M))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1433_div2__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1939 (all X_a (linordered_semidom(X_a) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),zero_zero(X_a))))) # label(fact_401_not__one__le__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1940 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),zero_zero(real))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)))))) # label(fact_2842_DERIV__neg__imp__decreasing) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1941 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially)))))) # label(fact_4503_summable__Leibniz_H_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1942 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1)),Z)))))) # label(fact_4798_min__less__iff__disj) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1943 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists R_2 exists A_4 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) = X & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)))))) # label(fact_2726_polar__ex1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1944 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> (exists Y_2 ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)))) # label(fact_1447_even__equiv__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1945 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,ln,X)))) # label(fact_2617_ln__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1946 (all X_a (linordered_field(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1740_mult__imp__le__div__pos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1947 (all X_a (t2_space(X_a) & comm_monoid_add(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),sequentially)))))) # label(fact_4497_summable__sumr__LIMSEQ__suminf) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1948 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))))))) # label(fact_1700_divide__le__cancel) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1949 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3194_fact__gt__zero__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1950 (all M all N hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)) # label(fact_3125_div__nat__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1951 (all X_1 all N_1 all Y_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y_1),N_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),N_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1))))) # label(fact_993_zmod__eq__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1952 (all X_a (ab_semigroup_mult(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_765_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1953 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit1,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_125_rel__simps_I17_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1954 (all B_5 all Q_5 all R_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Q_5)))))) # label(fact_264_q__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1955 (all M one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,one_one(int)),M)) # label(fact_3434_zgcd__1__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1956 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_lcm,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),X),Y)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y))) # label(fact_3658_Nitpick_Onat__lcm__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1957 (all I all 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)) = 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))) # label(fact_4225_image__Suc__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1958 (all K all Ma all N_1 (Ma = N_1 <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))) # label(fact_1250_Suc__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1959 (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_1)),N)) # label(fact_2367_sin__cos__npi) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1960 (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_246_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1961 (all X_a (real_field(X_a) -> (all A_1 all B all C all D all H_2 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)),H_2))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C)),H_2)),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D))),H_2)))) # label(fact_1801_DERIV__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1962 (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_956_zdiff__zmod__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1963 (all D_2 all X_1 (X_1 != zero_zero(real) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = D_2) -> ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X_1)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = D_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),sqrt),X_1),D_2)))))) # label(fact_2655_DERIV__real__sqrt__generic) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1964 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_3)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),H)),A_3))))) # label(fact_3954_setprod_Odistrib) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1965 (all X_a (semiring_div(X_a) -> (all N all K_4 all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N)))))))) # label(fact_949_dvd__mod) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1966 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_1018_div__nonpos__pos__le0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1967 (all Y all X (zero_zero(real) != hAPP(real,real,cos,X) -> (zero_zero(real) != hAPP(real,real,cos,Y) -> hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y)))))) # label(fact_2269_lemma__tan__add1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1968 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,Ma)),N_1))))))) # label(fact_4203_setsum__head__upt__Suc) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1969 (all N all M hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),N),M)) # label(fact_3541_plus__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1970 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_48_le__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1971 (all X_a (real_normed_vector(X_a) -> (all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,sgn_sgn(real),R_4)),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4721_sgn__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1972 (all X_a all X_b all P_5 all Q_3 (hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_5) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Q_3) -> (hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Q_3) = 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) = ti(product_prod(X_a,X_b),Q_3)))) # label(fact_3142_prod__eqI) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1973 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),A_6)),B)))) # label(fact_4712_scaleR_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1974 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) # label(fact_4385_gcd__mult__cancel__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1975 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> ti(X_a,Y_1) = ti(X_a,X_1)))))) # label(fact_1590_linorder__antisym__conv1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1976 (all P_5 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,sgn_sgn(int),hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(rat,product_prod(int,int),quotient_of,P_5)))),one_one(int)) = hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,sgn_sgn(rat),P_5))) # label(fact_3719_rat__sgn__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1977 (all Z all W_1 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),Z),W_1)) & W_1 != Z <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Z),W_1)))) # label(fact_3723_less__rat__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1978 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),zero_zero(int))))) # label(fact_1031_neg__mod__sign) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1979 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,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_2288_sin__arccos) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1980 (all R_1 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_1)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_1))))))) # label(fact_4864_vanishesD) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1981 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))))) # label(fact_1279_of__nat__0__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.68 1982 (all N all M all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),M),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),R_4)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)),R_4)))))) # label(fact_4393_divides__mult__int) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1983 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) # label(fact_955_zmod__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1984 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3834_bdd__int__set__le__finite) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1985 (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_2599_exp__real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1986 (all X_1 all P_4 (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)) <-> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1))) # label(fact_1012_StandardRes__prop3) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1987 (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_492_left__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1988 (all X_a all A_2 all P_1 ((exists X_2 ((all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> ti(X_a,X_2) = ti(X_a,Y_2))) & hBOOL(hAPP(X_a,bool,P_1,X_2)))) -> (hBOOL(hAPP(X_a,bool,P_1,A_2)) -> ti(X_a,A_2) = hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))) # label(fact_4868_some1__equality) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1989 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_4720_scaleR__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1990 (all X_a all F all A_3 hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(fun(X_a,nat),fun(X_a,int),hAPP(fun(nat,int),fun(fun(X_a,nat),fun(X_a,int)),combb(nat,int,X_a),semiring_1_of_nat(int)),F)),A_3)) # label(fact_4245_int__setsum) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1991 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),hAPP(int,int,abs_abs(int),D)))) # label(fact_1926_zdvd__self__abs1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1992 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1140_Nat__Transfer_Otransfer__nat__int__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1993 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2691_real__root__ge__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1994 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1461_even__div__2__prop1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1995 (all X_1 -(hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_1277_even__odd__conj) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1996 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4017_summable__norm__comparison__test) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1997 (all A_2 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(int,int,uminus_uminus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,X_1))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,nat,nat_1,X_1))))) # label(fact_2182_neg__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1998 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hAPP(real,real,cos,hAPP(real,real,arcsin,X)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2189_cos__arcsin) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 1999 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),X)),one_one(int)),P_5)))))) # label(fact_855_MultInv__prop2a) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2000 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))))) # label(fact_1946_ln__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2001 (all X_a (ring_1(X_a) -> ring_1_Ints(X_a) = ti(fun(X_a,bool),ring_1_Ints(X_a)))) # label(tsy_c_Int_Oring__1__class_OInts_res) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2002 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),N)) # label(fact_549_mult__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2003 (all N all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)))))) # label(fact_3437_zgcd__greatest) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2004 (all X_a all X_c all X_b all P all Q all R 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) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),P,R),Q)) # label(help_COMBC_1_1_U) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2005 (all P_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(rat,rat,uminus_uminus(rat),P_4)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),hAPP(rat,product_prod(int,int),quotient_of,P_4))) # label(fact_4028_rat__uminus__code) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2006 (all A_1 zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),log,A_1),one_one(real))) # label(fact_2638_log__one) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2007 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),N)))) # label(fact_2876_coprime__minus1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2008 (all X_1 all Y_1 (hAPP(complex,real,re,Y_1) = hAPP(complex,real,re,X_1) & hAPP(complex,real,im,Y_1) = hAPP(complex,real,im,X_1) <-> Y_1 = X_1)) # label(fact_2996_complex__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2009 (all A_2 all B_1 ((all D_3 (one_one(nat) = D_3 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_3),A_2)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_2871_coprime) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2010 (all W hAPP(int,complex,ring_1_of_int(complex),W) = hAPP(int,complex,number_number_of(complex),W)) # label(fact_3584_complex__number__of__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2011 (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,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)) = 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,number_number_of(int),V)),hAPP(int,int,number_number_of(int),W))))) # label(fact_1065_zdiv__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2012 (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),X_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,s1),Y_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),m)),one_one(int)))) -> ti(int,Y_2) = ti(int,X_2))))) # label(fact_195__096EX_B_As_O_A0_A_060_061_As_A_G_As_A_060_A4_A_K_Am_A_L_A1_A_G_A_091s1) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2013 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 ((exists K_2 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),K_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_2353_lemma__NBseq__def) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2014 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1)))) # label(fact_2521_inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2015 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y))))) # label(fact_886_mult__right_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2016 (all X_b all X_a (topological_space(X_a) & real_n1866405975lgebra(X_b) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (zero_zero(X_b) != ti(X_b,L_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4588_LIM__inverse) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2017 (all Ma all N_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) <-> N_1 = zero_zero(nat) | zero_zero(nat) = Ma)) # label(fact_551_mult__is__0) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2018 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3495_Bseq__iff) # label(axiom) # label(non_clause). [assumption]. 10.61/10.69 2019 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_4757_scaleR__right_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2020 (all X_a (ord(X_a) -> hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),max(X_a),ord_less_eq(X_a)) = ord_max(X_a))) # label(fact_4947_max__ord__max) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2021 (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_973_mod__mult__self1__is__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2022 (all K_4 hAPP(int,int,succ,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),min_1)) # label(fact_1530_diff__bin__simps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2023 (all X_3 all A_2 (hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),X_3),A_2)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),re),X_3)),hAPP(complex,real,re,A_2))))) # label(fact_4114_Re_Osums) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2024 (all X all N (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,number_number_of(real),N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natceiling,X)),hAPP(int,nat,number_number_of(nat),N))))) # label(fact_1837_natceiling__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2025 (all Ma all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> -(-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),Ma))))) # label(fact_2413_odd__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2026 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),Z)),one_one(int))) <-> zero_zero(int) = ti(int,Z))) # label(fact_1939_zabs__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2027 (all N all M all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),M)))) # label(fact_4348_coprime__exp2__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2028 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,hAPP(int,int,succ,K_4))) # label(fact_1526_succ__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2029 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),M) = ti(int,M))) # label(fact_3444_zgcd__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2030 (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_1194_divmod__int__rel__div__mod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2031 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)))))))) # label(fact_447_power__strict__increasing) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2032 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),G))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),hAPP(X_a,X_a,uminus_uminus(X_a),E_3))))))))) # label(fact_3816_DERIV__add__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2033 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),zero_zero(X_a))))))) # label(fact_2057_neg__le__0__iff__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2034 (all X_a all P_3 all X_2 (hBOOL(hAPP(X_a,bool,P_3,X_2)) -> hBOOL(hAPP(X_a,bool,P_3,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_3))))) # label(fact_4783_tfl__some) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2035 (all X_a all X_b all X_c all Q_1 all P_1 all Z (hBOOL(hAPP(X_a,bool,Q_1,hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),P_1),Z))) -> -(all X_2 all Y_2 (ti(product_prod(X_b,X_c),Z) = hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),X_2),Y_2) -> -hBOOL(hAPP(X_a,bool,Q_1,hAPP(X_c,X_a,hAPP(X_b,fun(X_c,X_a),P_1,X_2),Y_2))))))) # label(fact_4770_splitE2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2036 (all P_5 all Q_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Q_3)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int) -> hAPP(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_4408_normalize__stable) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2037 (all X_a (real_normed_vector(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),A_6)),B)))) # label(fact_4715_scaleR_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2038 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_174_semiring__norm_I110_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2039 (all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,W_1)),zero_zero(int))))) # label(fact_161_bin__less__0__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2040 (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,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y)) = 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))))))) # label(fact_1910_arctan__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2041 (all X_a (sgn_if(X_a) -> hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)) = zero_zero(X_a))) # label(fact_2203_sgn0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2042 (all K_4 hAPP(int,int,bit1,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),K_4)),K_4)) # label(fact_165_Bit1__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2043 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1711_pos__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2044 (all P_1 all N_1 ((exists M_2 (hBOOL(hAPP(nat,bool,P_1,M_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)))) <-> (exists X_2 (hBOOL(hAPP(nat,bool,P_1,X_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))))) # label(fact_4193_ex__nat__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2045 (all P_1 hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1)) = hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,int),fun(nat,bool),hAPP(fun(int,bool),fun(fun(nat,int),fun(nat,bool)),combb(int,bool,nat),P_1),semiring_1_of_nat(int))))) # label(fact_3807_Nat__Transfer_Otransfer__int__nat__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2046 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))))))) # label(fact_803_inv__less__p__minus__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2047 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)))))) # label(fact_2047_minus__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2048 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))) = hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),hAPP(int,fun(X_a,int),combk(int,X_a),C_1)),X_3))) # label(fact_4262_setsum__const) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2049 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),L)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)))) # label(fact_4265_image__add__int__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2050 (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_3596_floor__add__of__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2051 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2774_PowI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2052 (all X all A_1 hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(int,real,real_1(int),A_1))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),X)),A_1)) # label(fact_3365_floor__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2053 (all A_1 hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),one_one(int)) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),zero_zero(int))) # label(fact_3736_eq__rat_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2054 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)))))) # label(fact_4847_Divides_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2055 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1))))) # label(fact_3984_suminf__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2056 (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_2141_minus__numeral__code_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2057 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists N_3 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_3))))))))) # label(fact_3496_Bseq__iff1a) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2058 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)))))) # label(fact_1193_negDivAlg__correct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2059 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),C))))))) # label(fact_1551_ord__le__eq__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2060 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),X),Y)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),X))) # label(fact_4378_gcd__proj1__if__dvd__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2061 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all X_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),L),X_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4737_scaleR__left_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2062 (all X_1 all Y_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X_1),Y_1) = zero_zero(nat) <-> Y_1 = zero_zero(nat) & zero_zero(nat) = X_1)) # label(fact_3256_gcd__lcm__complete__lattice__nat_Oinf__eq__top__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2063 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1))),zero_zero(X_a)))))) # label(fact_2096_abs__minus__le__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2064 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)))))) # label(fact_3236_gcd__greatest__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2065 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Y_2))))) -> L = zero_zero(real))))) # label(fact_2659_DERIV__local__min) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2066 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,one_one(int)),hAPP(int,int,number_number_of(int),min_1)),M)))) # label(fact_466_one__not__neg__one__mod__m) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2067 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))))))) # label(fact_3349_powr__less__mono2__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2068 (all X_a (semiring_1(X_a) -> (all Inc all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),zero_zero(nat)),I) = ti(X_a,I)))) # label(fact_4160_of__nat__aux_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2069 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_613_incr__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2070 (all X_a (number_semiring(X_a) -> (all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),V)) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,V)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a)))))) # label(fact_1533_semiring__number__of__add__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2071 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),V))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(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))))) # label(fact_1536_nat__1__add__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2072 (all Ma all N_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1) = zero_zero(int) <-> ti(int,Ma) = zero_zero(int) & ti(int,N_1) = zero_zero(int))) # label(fact_4361_gcd__zero__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2073 (all X_a (linordered_semidom(X_a) -> (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))))))) # label(fact_1397_of__nat__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2074 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),B)))) # label(fact_4398_gcd__le2__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2075 (all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))) = hAPP(int,nat,phi,P_5))) # label(fact_1173_phi__prime) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2076 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),C_1)),F)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4736_scaleR_OLIM__right__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2077 (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_799_mult_Ocomm__neutral) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2078 (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]. 10.71/10.69 2079 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta))))))) # label(fact_4636_bset_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2080 (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V),pls)) -> zero_zero(nat) = 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)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_2898_nat__number__of__diff__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2081 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),one_one(rat)))))) # label(fact_3787_Fract__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2082 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2313_sin__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2083 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Ry))))) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2084 (all X_a (semiring_1(X_a) -> zero_zero(X_a) = hAPP(nat,X_a,semiring_1_of_nat(X_a),zero_zero(nat)))) # label(fact_1281_of__nat__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2085 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4))))) # label(fact_584_mult__le__mono1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2086 (all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))))) # label(fact_837_wset__mem__mem) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2087 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_1842_abs__le__D1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2088 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (ti(X_a,Y) != ti(X_a,X) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y))))))) # label(fact_318_order__le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2089 (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_898_SR__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2090 (all X all A_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),X)),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)))) # label(fact_3371_floor__subtract) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2091 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)))))) # label(fact_3422_reals__Archimedean__6b__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2092 (all P (fTrue = ti(bool,P) | ti(bool,P) = fFalse)) # label(help_If_3_1_T) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2093 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_1),K_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),J_2),K_4))))) # label(fact_136_zadd__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2094 (all Ma all N_1 (zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) <-> Ma = zero_zero(nat) & N_1 = zero_zero(nat))) # label(fact_543_add__is__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2095 (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_3099_divmod__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2096 (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),one_one(nat)),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),hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V))),N)))) # label(fact_1519_Suc__nat__number__of__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2097 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2321_sin__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2098 (all X_a (ab_group_add(X_a) -> (all A_1 all C all B all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C),D))))) # label(fact_722_add__diff__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.69 2099 (all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2381_fact__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2100 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hAPP(real,real,ln,X) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)) -> one_one(real) = X))) # label(fact_1938_ln__eq__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2101 (all P_1 all A_2 all B_1 all N_1 hAPP(product_prod(real,real),product_prod(real,real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(product_prod(real,real),product_prod(real,real)),product_prod_case(real,real,product_prod(real,real)),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))))),combb(fun(real,fun(product_prod(real,real),product_prod(real,real))),fun(fun(real,product_prod(real,real)),fun(real,product_prod(real,real))),real),combs(real,product_prod(real,real),product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,fun(product_prod(real,real),product_prod(real,real))))),combs(real,fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(real,fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,product_prod(real,real)),fun(real,fun(product_prod(real,real),product_prod(real,real)))),real),combs(real,product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),hAPP(fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),fun(fun(real,fun(real,bool)),fun(real,fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))))),combb(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),real),hAPP(fun(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real)))),fun(fun(real,bool),fun(real,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))))),combb(bool,fun(product_prod(real,real),fun(product_prod(real,real),product_prod(real,real))),real),if(product_prod(real,real)))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool)),hAPP(fun(fun(real,product_prod(real,real)),fun(real,bool)),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(real,bool))),combb(fun(real,product_prod(real,real)),fun(real,bool),real),hAPP(fun(product_prod(real,real),bool),fun(fun(real,product_prod(real,real)),fun(real,bool)),combb(product_prod(real,real),bool,real),P_1)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(real,real),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combc(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,fun(real,product_prod(real,real)))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,product_prod(real,real))),real),combs(real,real,product_prod(real,real))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real)))),hAPP(fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,product_prod(real,real))))),combb(fun(real,real),fun(real,fun(real,product_prod(real,real))),real),hAPP(fun(real,fun(real,product_prod(real,real))),fun(fun(real,real),fun(real,fun(real,product_prod(real,real)))),combb(real,fun(real,product_prod(real,real)),real),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),combi(real))))),hAPP(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real))),hAPP(fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,real)),fun(real,fun(real,product_prod(real,real)))),combs(real,fun(real,real),fun(real,product_prod(real,real))),hAPP(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real)))),hAPP(fun(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real)))),fun(fun(real,fun(real,product_prod(real,real))),fun(real,fun(fun(real,real),fun(real,product_prod(real,real))))),combb(fun(real,product_prod(real,real)),fun(fun(real,real),fun(real,product_prod(real,real))),real),combb(real,product_prod(real,real),real)),product_Pair(real,real))),hAPP(real,fun(real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),combc(real,real,fun(real,real)),hAPP(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,fun(real,real)),fun(real,fun(real,real))),fun(fun(real,fun(real,fun(real,real))),fun(real,fun(real,fun(real,real)))),combb(fun(real,fun(real,real)),fun(real,fun(real,real)),real),combc(real,real,real)),hAPP(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real))),hAPP(fun(fun(real,real),fun(real,fun(real,real))),fun(fun(real,fun(real,real)),fun(real,fun(real,fun(real,real)))),combb(fun(real,real),fun(real,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real))),plus_plus(real)))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1)) = hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_1))) # label(fact_4053_Bolzano__bisect_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2102 (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_3190_transfer__nat__int__factorial__closure) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2103 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = zero_zero(nat)) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)))) # label(fact_1417_div__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2104 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = M -> N = zero_zero(nat))) # label(fact_544_add__eq__self__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2105 (all A_1 all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B))))) # label(fact_3075_divmod__int__correct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2106 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_434_mult__strict__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2107 (all X_a (comm_semiring_1(X_a) -> (all M all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),B)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),B))))))) # label(fact_344_power__le__dvd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2108 (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))) -> zero_zero(X_a) = ti(X_a,A_1))))) # label(fact_234_even__power__le__0__imp__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2109 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,nat,nat_1,N_1) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3809_card__bdd__int__set__l) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2110 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2))))))) # label(fact_1715_neg__divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2111 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))) # label(fact_572_nat__add__left__cancel__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2112 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(nat,real,real_1(nat),A_1))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),A_1)))) # label(fact_2332_natceiling__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2113 (all X_a all P all X (-hBOOL(hAPP(X_a,bool,P,X)) | hBOOL(hAPP(fun(X_a,bool),bool,fEx(X_a),P)))) # label(help_fEx_1_1_U) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2114 (all X_a (division_ring(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C))))) # label(fact_1662_add__divide__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2115 (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,bit0,hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_143_power2__eq__square) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2116 (all X X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),zero_zero(nat)),X)) # label(fact_3253_gcd__0__left__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2117 (all Code_numeral_3 zero_zero(code_code_numeral) != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_3)) # label(fact_2947_code__numeral_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2118 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2))))))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2119 (all N hAPP(nat,real,real_1(nat),N) = hAPP(int,real,real_1(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_3335_real__of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2120 (all N all X (X = hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(real,nat,natfloor,X)),N) = hAPP(real,nat,natfloor,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)))) # label(fact_2334_natfloor__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2121 (all M hAPP(nat,int,semiring_1_of_nat(int),M) = hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),M))) # label(fact_1923_abs__int__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2122 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) & N_1 != Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_563_nat__less__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2123 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),zero_zero(nat))) <-> zero_zero(nat) = N_1)) # label(fact_548_le__0__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2124 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),A_3),B_2)))))) # label(fact_3659_transfer__int__nat__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2125 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2696_real__root__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2126 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y)) = hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_3006_Re_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2127 (all N N = hAPP(int,nat,nat_1,hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1228_nat__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2128 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)))))) # label(fact_4397_transfer__nat__int__gcd__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2129 (all X exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N_2)))) # label(fact_2732_reals__Archimedean2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2130 (all X_a (linord20386208strict(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_426_mult__right__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2131 (all X_a (division_ring(X_a) -> ti(fun(X_a,X_a),inverse_inverse(X_a)) = inverse_inverse(X_a))) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2132 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y))) # label(fact_4371_abs__gcd__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2133 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_2003_subset__psubset__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2134 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hAPP(X_a,X_b,F,A_2) != zero_zero(X_b) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),A_2))))))) # label(fact_4911_isCont__sgn) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2135 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)))))) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2136 (all S ((exists K_1 hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),S),hAPP(nat,fun(nat,bool),ord_lessThan(nat),K_1)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_4318_finite__nat__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2137 (all A_2 all B_1 ((all P_6 -(hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),A_2)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)))) # label(fact_3062_coprime__prime__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2138 (all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),zero_zero(real))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),one_one(nat)),N_1)) = zero_zero(real)) # label(fact_4239_lemma__STAR__cos2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2139 (all N -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))))) # label(fact_2176_not__zle__0__negative) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2140 (all X_1 hAPP(fun(product_prod(int,int),bool),product_prod(int,int),the(product_prod(int,int)),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool),hAPP(fun(rat,bool),fun(fun(product_prod(int,int),rat),fun(product_prod(int,int),bool)),combb(rat,bool,product_prod(int,int)),hAPP(rat,fun(rat,bool),fequal(rat),X_1)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),rat),hAPP(fun(product_prod(int,int),fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),rat)),combs(product_prod(int,int),int,rat),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat)),hAPP(fun(int,fun(int,rat)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,rat))),combb(int,fun(int,rat),product_prod(int,int)),fract),product_fst(int,int))),product_snd(int,int))))),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),bool)),combs(product_prod(int,int),bool,bool),hAPP(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(product_prod(int,int),bool),fun(product_prod(int,int),fun(bool,bool))),combb(bool,fun(bool,bool),product_prod(int,int)),fconj),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),bool),hAPP(fun(int,bool),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),bool)),combb(int,bool,product_prod(int,int)),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int))),product_snd(int,int)))),hAPP(int,fun(product_prod(int,int),bool),hAPP(fun(product_prod(int,int),fun(int,bool)),fun(int,fun(product_prod(int,int),bool)),combc(product_prod(int,int),int,bool),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool)),hAPP(fun(int,fun(int,bool)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,bool))),combb(int,fun(int,bool),product_prod(int,int)),fequal(int)),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),int),hAPP(fun(product_prod(int,int),fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),int)),combs(product_prod(int,int),int,int),hAPP(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(product_prod(int,int),int),fun(product_prod(int,int),fun(int,int))),combb(int,fun(int,int),product_prod(int,int)),gcd_gcd(int)),product_fst(int,int))),product_snd(int,int)))),one_one(int))))) = hAPP(rat,product_prod(int,int),quotient_of,X_1)) # label(fact_4409_quotient__of__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2141 (all X_a (dense_linorder(X_a) -> (all Z_1 all Y ((all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Z_1)))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)))))) # label(fact_2825_dense__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2142 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),zero_zero(nat)) = M) # label(fact_660_minus__nat_Odiff__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2143 (all N_1 hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),sin_coeff),N_1) = hAPP(nat,real,cos_coeff,N_1)) # label(fact_4116_sin__fdiffs2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2144 (all X_a (monoid_mult(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))),X))))) # label(fact_717_realpow__minus__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2145 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially))))) # label(fact_4502_summable__Leibniz_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2146 (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),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)))) = 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_1901_power2__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2147 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))))))) # label(fact_3299_ceiling__less__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2148 (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),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2149 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),B_2))))) # label(fact_2803_Pow__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2150 (all X_a (linordered_idom(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_104_zero__le__power2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2151 (all X_b all X_a (linordered_field(X_a) -> (all F all A_3 hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))) # label(fact_3948_abs__setprod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2152 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),pi),X))) # label(fact_2325_sin__periodic__pi2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2153 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,pls)),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_60_le__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2154 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) = hAPP(X_a,X_a,uminus_uminus(X_a),X_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_2954_compl__eq__compl__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2155 (all X_a all X_b all R_3 all S (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(product_prod(X_a,X_b),bool),bool),ord_less_eq(fun(product_prod(X_a,X_b),bool)),R_3),S)) <-> hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),R_3)),hAPP(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(product_prod(X_a,X_b),bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),hAPP(fun(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool))),fun(fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(X_a,fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)))),combb(fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(product_prod(X_a,X_b),bool),fun(X_b,bool)),X_a),combc(X_b,fun(product_prod(X_a,X_b),bool),bool)),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool)),X_a),hAPP(fun(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool)),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,fun(fun(product_prod(X_a,X_b),bool),bool))),combb(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),X_b),member(product_prod(X_a,X_b)))),product_Pair(X_a,X_b)))),S))))) # label(fact_4335_pred__subset__eq2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2156 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),X)))) # label(fact_1933_ln__less__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2157 (all Y all X ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),X)) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))) # label(fact_1458_tsub__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2158 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc))))),R_1),sequentially))) # label(fact_4492_LIMSEQ__inverse__real__of__nat__add__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2159 (all X_a all X_b all T_5 hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),T_5)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),T_5)) = ti(product_prod(X_a,X_b),T_5)) # label(fact_3129_surjective__pairing) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2160 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S)))))) # label(fact_3963_setprod__pos__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2161 (all B_2 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> (hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B_2) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3) <-> A_3 = B_2)))) # label(fact_3664_transfer__int__nat__set__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2162 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists R_2 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) & C_1 != X_2 -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_2)),zero_zero(real))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_4629_LIM__fun__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2163 (all X_1 all Y_1 (X_1 = zero_zero(real) & one_one(real) = Y_1 <-> ii = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1))) # label(fact_2766_Complex__eq__i) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2164 (all X_a (ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2031_minus__mult__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2165 (all X_b all X_a (ord(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,B_1)),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),B_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),Y_2),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,Y_2)),hAPP(X_b,X_a,F,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,C_1)),A_2)))))))) # label(fact_2834_xt6) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2166 (all X_1 (-hBOOL(hAPP(int,bool,nat_neg,X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)))) # label(fact_1503_not__neg__eq__ge__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2167 (all J all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J),zero_zero(int)),P_4)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_2),P_4),J)))))))) # label(fact_1538_MultInvPair__card__two) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2168 (all X_1 all Y_1 all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y_1),Z))))) # label(fact_3242_gcd__semilattice__nat_Ole__inf__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2169 (all X_a (dvd(X_a) & linorder(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_863_minf_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2170 (all X all Y all 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)) = 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))) # label(fact_98_zadd__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2171 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),Z)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Z)))))) # label(fact_714_real__mult__le__cancel__iff1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2172 (all N_1 hAPP(nat,fun(nat,bool),ord_atMost(nat),N_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1)) # label(fact_4948_atLeast0AtMost) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2173 (all X_1 (one_one(real) = hAPP(real,real,sqrt,X_1) <-> one_one(real) = X_1)) # label(fact_1619_real__sqrt__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2174 (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]. 10.71/10.70 2175 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))))))) # label(fact_389_mult__less__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2176 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4794_dvd_OmonoI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2177 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> (exists N_2 exists F_3 ti(fun(X_a,bool),A_3) = hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F_3),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_2)))))) # label(fact_4127_finite__conv__nat__seg__image) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2178 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_1550_xt1_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2179 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K1)),hAPP(int,int,bit0,K2))))) # label(fact_72_less__eq__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2180 (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]. 10.71/10.70 2181 (all R_4 all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(complex,complex,cnj,X)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X))) # label(fact_4692_cnj_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2182 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M)),N) = M)) # label(fact_1120_div__mult__self1__is__m) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2183 (all R_4 all X hAPP(complex,real,re,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,re,X))) # label(fact_4690_Re_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2184 (all F all K_3 all N_1 ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,P_6)),K_3)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),K_3))))) # label(fact_4288_real__setsum__nat__ivl__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2185 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (exists N_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Y_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N_2),X_1))))),X_1)))))) # label(fact_2005_best__odd__division__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2186 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_4689_scaleR_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2187 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2))))))) # label(fact_1742_neg__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2188 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_813_add__increasing2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2189 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),N_1)) <-> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N_1),Ma) = ti(int,Ma)))) # label(fact_3457_zdvd__iff__zgcd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2190 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)))))) # label(fact_1935_ln__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2191 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),min_1),hAPP(int,int,bit0,K))))) # label(fact_307_rel__simps_I25_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2192 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),Ma) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),X_2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),norRRset,Ma))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),Y_2),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_2),hAPP(int,fun(int,bool),norRRset,Ma))) -> ti(int,Y_2) = ti(int,X_2)))))))) # label(fact_3614_norR__mem__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2193 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1836_arctan__monotone) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2194 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> N = M))) # label(fact_1231_less__SucE) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2195 (all X hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),one_one(int)),zero_zero(int)) = hAPP(nat,product_prod(int,int),hAPP(nat,fun(nat,product_prod(int,int)),bezw,X),zero_zero(nat))) # label(fact_3035_bezw__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2196 (all B_5 all A_6 all A_1 all B (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_6),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) = ti(int,A_1) -> (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) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_6),B_5) = one_one(int))))) # label(fact_4351_gcd__coprime__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2197 (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),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_1729_diff__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2198 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),Q_3)))) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2199 (all X_a (linordered_semidom(X_a) -> (all N all M (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),M)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),N)))))))) # label(fact_406_less__1__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2200 (all X_3 ((all R_2 (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),R_2)) -> (exists K_1 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_1),N_2)) -> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,X_3,N_2))),R_2)))))) <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)))) # label(fact_4863_vanishes__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2201 (all Qr_2 all M all N all Qr_1 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_1)) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),Qr_2)) -> Qr_1 = Qr_2))) # label(fact_3098_divmod__nat__rel__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2202 (all K_4 all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),K_4),M))) # label(fact_314_zcong__refl) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2203 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)))))) # label(fact_4499_summable__Leibniz_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2204 (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_155_less__int__code_I15_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2205 (all X_a (ordered_ab_group_add(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)))))) # label(fact_2028_neg__le__iff__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2206 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1681_divide__neg__pos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2207 (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_1422_tsub__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.70 2208 (all Q_5 all R_5 all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (zero_zero(int) != ti(int,B) -> ti(int,Q_3) = ti(int,Q_5))))) # label(fact_1187_unique__quotient) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2209 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,exp(real),hAPP(complex,real,re,Z_1)))),hAPP(real,complex,cis,hAPP(complex,real,im,Z_1))) = hAPP(complex,complex,expi,Z_1)) # label(fact_3023_expi__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2210 (all L all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),U_1),hAPP(nat,nat,suc,L))) # label(fact_3683_card__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2211 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),one_one(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),B_1))))) # label(fact_3794_Fract__le__one__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2212 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_4047_Im_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2213 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) | Y_1 = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))) # label(fact_654_less__eq__real__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2214 (all X_a all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_2196_ComplD) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2215 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y))))) # label(fact_1141_Nat__Transfer_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2216 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W))))) # label(fact_137_double__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2217 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 hAPP(fun(product_prod(nat,nat),bool),X_a,hAPP(fun(product_prod(nat,nat),X_a),fun(fun(product_prod(nat,nat),bool),X_a),big_co1399186613setsum(product_prod(nat,nat),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(product_prod(nat,nat),X_a),product_prod_case(nat,nat,X_a),F)),hAPP(fun(product_prod(nat,nat),bool),fun(product_prod(nat,nat),bool),collect(product_prod(nat,nat)),hAPP(fun(nat,fun(nat,bool)),fun(product_prod(nat,nat),bool),product_prod_case(nat,nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),combc(nat,nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,fun(nat,bool))),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),nat),combc(nat,nat,bool)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(fun(nat,nat),fun(nat,fun(nat,bool))),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,fun(nat,bool)))),combb(fun(nat,nat),fun(nat,fun(nat,bool)),nat),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),ord_less(nat))),plus_plus(nat)))),N_1)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,fun(nat,X_a)),fun(fun(nat,nat),fun(nat,X_a)),combs(nat,nat,X_a),F)),minus_minus(nat)))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4622_setsum__triangle__reindex) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2218 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),min_1) = hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,number_number_of(int),min_1)))) # label(fact_3591_of__int__m1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2219 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),R_4) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),R_4))) # label(fact_1667_real__divide__square__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2220 (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,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))))) = one_one(real)) # label(fact_2386_sin__cos__squared__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2221 (all X_b all X_a (semiring_0(X_a) -> (all F all A_3 all R_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_3)),R_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),times_times(X_a)),F)),R_1)),A_3)))) # label(fact_4210_setsum__left__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2222 (all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3))) <-> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_3))))) # label(fact_3667_transfer__int__nat__set__relations_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2223 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all B_5 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),B_5)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),B_5))))) # label(fact_4719_scaleR_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2224 (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]. 10.71/10.71 2225 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),B)))) # label(fact_2848_coprime__lmul2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2226 (all N hAPP(real,nat,natceiling,hAPP(int,real,number_number_of(real),N)) = hAPP(int,nat,number_number_of(nat),N)) # label(fact_1889_natceiling__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2227 (all F all K all A_2 all B_1 (A_2 != B_1 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),K) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2))))) # label(fact_2667_DERIV__const__ratio__const) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2228 (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_4465_LIMSEQ__const__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2229 (all P_1 all N_1 ((exists X_2 (hBOOL(hAPP(nat,bool,P_1,X_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)),N_1))))) <-> (exists M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_1)) & hBOOL(hAPP(nat,bool,P_1,M_2)))))) # label(fact_4537_ex__nat__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2230 (all X_a all M_1 (hBOOL(hAPP(fun(list(X_a),bool),bool,finite_finite_1(list(X_a)),M_1)) -> (exists N_2 all X_2 (hBOOL(hAPP(fun(list(X_a),bool),bool,hAPP(list(X_a),fun(fun(list(X_a),bool),bool),member(list(X_a)),X_2),M_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(list(X_a),nat,size_size(list(X_a)),X_2)),N_2)))))) # label(fact_3558_finite__maxlen) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2231 (all X_a all X_b (dvd(X_b) & comm_monoid_mult(X_b) -> (all F all G all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))))) # label(fact_4427_setprod__dvd__setprod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2232 (all Z_1 hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2927_complex__mod__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2233 (all Real1_1 all Real2_1 zero_zero(nat) = hAPP(complex,nat,complex_size,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_1),Real2_1))) # label(fact_2751_complex_Osize_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2234 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)))))) # label(fact_1019_neg__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2235 (all X_a (metric_space(X_a) -> (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))))) # label(fact_3510_zero__le__dist) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2236 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> -hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3))))) # label(fact_1952_equalityE) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2237 (all X_1 all Y_1 (Y_1 = hAPP(real,real,uminus_uminus(real),X_1) <-> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1) = zero_zero(real))) # label(fact_2089_real__add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2238 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))) # label(fact_2950_times_Oidem) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2239 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2484_fact__mono__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2240 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2384_sin__gt__zero2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2241 (all X_a all F all C_1 all H ((all N_2 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),C_1),H),N_2) = hAPP(nat,X_a,F,N_2)) -> hAPP(nat,X_a,F,zero_zero(nat)) = ti(X_a,C_1))) # label(fact_4332_def__nat__rec__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2242 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_529_nat__le__linear) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2243 (all X_b all X_a (real_normed_vector(X_b) & ord(X_a) -> (all X_3 all M_1 ((all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,X_3,M_1)),hAPP(X_a,X_b,X_3,N_2)))),one_one(real))))) -> (all N_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),M_1),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,N_2))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,X_3,M_1))))))))))) # label(fact_1838_lemmaCauchy) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2244 (all X_a (division_ring(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2557_divide__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2245 (all X_a (dvd(X_a) -> dvd_dvd(X_a) = ti(fun(X_a,fun(X_a,bool)),dvd_dvd(X_a)))) # label(tsy_c_Rings_Odvd__class_Odvd_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2246 (all M all N all S_4 all S_3 all T_6 all T_5 all R_5 all R_4 all K_4 (ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,R_5),R_4) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),R_4)) -> (exists Sn exists Tn hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),K_4),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Sn),Tn)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5))))) # label(fact_3480_xzgcd__correct__aux1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2247 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3108_div__neg__pos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2248 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(real,real,cos,X)))) # label(fact_2217_cos__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2249 (all J_2 all I_1 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),I_1))) # label(fact_555_not__add__less2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2250 (all N all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,nat_1,X)),N) = hAPP(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N)))) # label(fact_1145_Nat__Transfer_Otransfer__nat__int__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2251 (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_1393_diff__Suc__diff__eq2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2252 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1812_mult__left_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2253 (all X_a (division_ring(X_a) -> (all A_2 all B_1 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),times_times(X_a),A_2),C_1) = ti(X_a,B_1) <-> ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2254 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))))) # label(fact_3331_real__of__int__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2255 (all X all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = X)) # label(fact_2676_odd__real__root__power__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2256 (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_920_zdiv__zmod__equality) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2257 (all X_a (archim1727834104eiling(X_a) -> (all V hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(int,X_a,number_number_of(X_a),V)) = hAPP(int,int,number_number_of(int),V)))) # label(fact_3283_ceiling__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2258 (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_1697_nonzero__power__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2259 (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_310_linorder__neqE__linordered__idom) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2260 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))))) # label(fact_3600_of__int__0__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2261 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_346_le__imp__power__dvd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2262 (all K_4 all L_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),hAPP(int,int,number_number_of(int),L_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),K_4)),hAPP(int,rat,number_number_of(rat),L_4))) # label(fact_3776_Fract__number__of__quotient) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2263 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),min_1))) # label(fact_2104_number__of__Min) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2264 (all X_a all X_b (zero(X_a) & metric_space(X_a) & real_n2089651433ebra_1(X_b) -> (all A_2 all K (ti(X_a,K) != zero_zero(X_a) -> -hBOOL(hAPP(filter(X_b),bool,hAPP(X_a,fun(filter(X_b),bool),hAPP(fun(X_b,X_a),fun(X_a,fun(filter(X_b),bool)),tendsto(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),K)),zero_zero(X_a)),hAPP(X_b,filter(X_b),at(X_b),A_2))))))) # label(fact_4562_LIM__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2265 (all X_a (semiring_div(X_a) -> (all A_1 all B all C ((ti(X_a,C) = zero_zero(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) & (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)))))) # label(fact_998_div__mult__mult1__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2266 (all X_a (real_normed_vector(X_a) -> (all R_4 exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_4761_scaleR__right_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2267 (all P_4 (hBOOL(hAPP(int,bool,zprime,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) = ti(int,P_4) | one_one(int) = ti(int,M_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),P_4)))) # label(fact_273_zprime__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2268 (all X_a (linord581940658strict(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),C_1))))))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2269 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,bit1,pls)),hAPP(int,int,uminus_uminus(int),W)))))) # label(fact_2185_diff__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2270 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N)))))))) # label(fact_1375_power__gt1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2271 (all X_a (comm_monoid_mult(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_801_mult__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2272 (all X_a (real_algebra_1(X_a) -> (all N hAPP(real,X_a,of_real(X_a),hAPP(nat,real,semiring_1_of_nat(real),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_2800_of__real__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2273 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2274 (all Ma all K all N_1 (Ma = N_1 | zero_zero(nat) = K <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K))) # label(fact_553_mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2275 (all A_1 all M all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),M))) # label(fact_355_zcong__zmult__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2276 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2))))) # label(fact_3793_one__le__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2277 (all I_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),M))))) # label(fact_1329_less__add__Suc1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2278 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,uminus_uminus(int),X)),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4376_gcd__neg1__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2279 (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_1042_div__add__self2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2280 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K),one_one(int)))) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_833_int__less__induct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2281 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),K)))) # label(fact_4936_finite__atMost) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2282 (all X_a all A_3 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)))) # label(fact_2776_Pow__top) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2283 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),X)),Y)),Z_1))))) # label(fact_1719_add__divide__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2284 (all X_a (comm_ring_1(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1)))))))) # label(fact_478_dvd__diff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2285 (all X_a (real_normed_vector(X_a) -> (all X ((zero_zero(X_a) != ti(X_a,X) -> hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X)) = one_one(real)) & (zero_zero(X_a) = ti(X_a,X) -> zero_zero(real) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))))) # label(fact_2234_norm__sgn) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2286 (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) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),X) = Y))) # label(fact_2674_odd__real__root__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2287 (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_26_less__eq__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2288 (all X_b all X_a (ab_group_add(X_a) -> (all F all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,X_a)),combs(X_b,X_a,X_a),hAPP(fun(X_b,X_a),fun(X_b,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_b,X_a),fun(X_b,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_b),minus_minus(X_a)),F)),G)),A_3) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4221_setsum__subtractf) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2289 (all X hAPP(complex,real,re,hAPP(complex,complex,cnj,X)) = hAPP(complex,real,re,X)) # label(fact_2995_complex__Re__cnj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2290 (all X_a (real_normed_vector(X_a) -> (all B_1 all F all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),F)),B_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),sequentially)))))) # label(fact_4445_LIMSEQ__add__const) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2291 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_5)))))) # label(fact_2828_minf_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2292 (all X all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),M))) # label(fact_958_mod__mod__is__mod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2293 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),plus_plus(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4565_LIM__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2294 (all X_a (real_normed_field(X_a) -> (all R_4 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X)),Y)))) # label(fact_4707_divide_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2295 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd))))) # label(fact_1365_IntNatAux_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2296 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1270_EvenOdd_Oeven__product) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2297 (all X_b (division_ring(X_b) & number(X_b) -> (all W hAPP(X_b,X_b,inverse_inverse(X_b),hAPP(int,X_b,number_number_of(X_b),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))))) # label(fact_2588_inverse__eq__divide__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2298 (all N_1 all Ma (hBOOL(hAPP(int,bool,nat_is_nat,Ma)) -> (hBOOL(hAPP(int,bool,nat_is_nat,N_1)) -> hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(int,nat,nat_1,Ma)),hAPP(int,nat,nat_1,N_1))) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),Ma),N_1)))) # label(fact_4839_SetInterval_Otransfer__int__nat__set__functions) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2299 (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_2178_nat__mult__distrib__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2300 (all A_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_2)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_2),one_one(nat))) <-> A_2 != one_one(nat))) # label(fact_895_gcd__lcm__complete__lattice__nat_Obot__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2301 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4551_mult__left_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2302 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> -(-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X))))) # label(fact_639_dvd_Oless__not__sym) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2303 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all L all F all G all A_2 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4766_LIM__equal) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2304 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1))))))) # label(fact_3998_summable__mult2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2305 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> (ti(X_a,B_1) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),field_char_0_Rats(X_a))))))))) # label(fact_3689_nonzero__Rats__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2306 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),hAPP(int,int,uminus_uminus(int),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4377_gcd__neg2__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2307 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))))) # label(fact_4309_setsum__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2308 (all A_1 all B ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),B) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),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_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))))) # label(fact_1067_negDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2309 (all X_a (number(X_a) -> (all W_1 all X_1 (ti(X_a,X_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> hAPP(int,X_a,number_number_of(X_a),W_1) = ti(X_a,X_1))))) # label(fact_90_number__of__reorient) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2310 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,tan,X)))))) # label(fact_2270_tan__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2311 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,bool)),ord_less(X_a)) = ord_less(X_a))) # label(tsy_c_Orderings_Oord__class_Oless_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2312 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> ti(X_a,X) != ti(X_a,Y))))) # label(fact_1569_order__less__imp__not__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2313 (all X_a (real_normed_vector(X_a) -> (all Ra all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Ra),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4696_scaleR__right_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2314 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> (K_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),K_4))))))) # label(fact_1385_prod__mn__less__k) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2315 (all X_1 all P_1 ((all A_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_4)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_4),one_one(int))))) -> hBOOL(hAPP(int,bool,P_1,A_4)))) -> hBOOL(hAPP(int,bool,P_1,X_1)))) # label(fact_832_d22set__induct__old) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2316 (all X_a (real_n1866405975lgebra(X_a) -> (all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),A_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))) # label(fact_2511_nonzero__norm__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2317 (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,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)))))) # label(fact_281_zcong__zprime__prod__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2318 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit1,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_73_rel__simps_I33_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2319 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,X_a,inverse_inverse(X_a),B_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2))))))) # label(fact_2607_inverse__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2320 (all A_1 hAPP(real,real,cos,A_1) = hAPP(complex,real,re,hAPP(real,complex,cis,A_1))) # label(fact_3026_Re__cis) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2321 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_440_power__less__imp__less__base) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2322 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))))) # label(fact_1802_divide_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2323 (all P_1 ((all X_2 exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all A_4 all B_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_4),A_4)),D_3)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),X_2)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))))))) & (all A_4 all B_4 all C_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),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_3210_lemma__BOLZANO2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2324 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_1575_xt1_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2325 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,uminus_uminus(int),W)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2040_number__of__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2326 (all M all N hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_4808_min__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2327 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N))) # label(fact_517_less__irrefl__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2328 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma)),N_1))))) # label(fact_738_nat__less__add__iff1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2329 (all N zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),zero_zero(real))) # label(fact_2670_real__root__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2330 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,re,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_3019_complex__Re__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.71 2331 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2))))))) # label(fact_4667_scaleR__right_Osums) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2332 (all X_a (divisi14063676e_zero(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),zero_zero(X_a)))) # label(fact_2526_inverse__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2333 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (zero_zero(nat) = N_1 | hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) & ti(X_a,X_1) != zero_zero(X_a) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1))))))) # label(fact_2454_zero__less__power__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2334 (all X_a (real_vector(X_a) -> (all X all Y all A_1 (zero_zero(real) != A_1 -> (hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y) -> ti(X_a,Y) = ti(X_a,X)))))) # label(fact_4701_scaleR__left__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2335 (all X_b all X_a (topological_space(X_a) & real_n2089651433ebra_1(X_b) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,real),fun(X_a,X_b),hAPP(fun(real,X_b),fun(fun(X_a,real),fun(X_a,X_b)),combb(real,X_b,X_a),of_real(X_b)),F)),A_2)))))) # label(fact_4904_isCont__of__real) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2336 (all K_4 hAPP(int,int,succ,hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit1,K_4)) # label(fact_1527_succ__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2337 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))))) # label(fact_4292_setsum__mono3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2338 (all X hAPP(int,int,abs_abs(int),X) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X)))) # label(fact_1932_int__nat__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2339 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y)) = hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),X),Y))) # label(fact_2942_cnj_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2340 (all X_a (real_normed_field(X_a) -> (all C_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),C_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),D_2),C_1))))))) # label(fact_3836_DERIV__cdivide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2341 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1)))))))))) # label(fact_3818_DERIV__mult_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2342 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1)))),hAPP(X_a,X_a,F,X_1)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4619_DERIV__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2343 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)))) # label(fact_929_mod__mult__left__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2344 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(X_a))) # label(fact_13_zero__power2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2345 (all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),log,B_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,ln,B_1)),X_1)))))) # label(fact_3904_DERIV__log) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2346 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),cnj),A_2))) # label(fact_4892_cnj_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2347 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4968_min__max_Osup__left__idem) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2348 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1))))) # label(fact_2199_sgn__sgn) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2349 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_928_mod__mult__right__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2350 (all B_1 all A_2 all Ma (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))) # label(fact_3209_Bnor__mem__zg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2351 (all R_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_4)),ii) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),R_4)) # label(fact_2813_complex__of__real__i) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2352 (all X_a all X_b (real_normed_vector(X_b) -> (all X_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),G)),X_1)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),A_2),X_1)),A_3)))))) # label(fact_4727_scaleR__left_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2353 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists D_3 ((all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1))),hAPP(real,real,F,X_1)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_2662_DERIV__pos__inc__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2354 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1029_mod__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2355 (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_80_int__one__le__iff__zero__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2356 (all X_a (ab_group_add(X_a) -> (all F all Ma all N_1 ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)) = zero_zero(X_a)) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))))))) # label(fact_4618_setsum__natinterval__difff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2357 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)))))) # label(fact_1558_linorder__linear) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2358 (all N_1 all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) & F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & (all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)))))) # label(fact_4280_Maclaurin2__objl) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2359 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,cos,X_1)))) # label(fact_4106_cos__paired) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2360 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)))))) # label(fact_1127_transfer__nat__int__relations_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2361 (all V_3 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),V_3))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,number_number_of(nat),V_3))) # label(fact_1467_one__div__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2362 (all X_a (real_normed_field(X_a) -> (all Db all F all G all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),hAPP(X_a,X_a,G,X_1)),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),Db)))))))) # label(fact_3861_DERIV__chain2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2363 (all X_a (real_normed_algebra(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_879_mult__right_Ozero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2364 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),one_one(X_a))))))) # label(fact_2575_one__less__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2365 (all X_a (linord219039673up_add(X_a) -> (all A_2 (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_2023_equal__neg__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2366 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_2962_compl__less__compl__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2367 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3039_termination__basic__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2368 (all F all Y_1 all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),F),Y_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),div_div(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)))))) # label(fact_4105_sums__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2369 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1908_real__sqrt__ge__abs1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2370 (all A_3 all B_2 all Ma (hBOOL(hAPP(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool,hAPP(product_prod(fun(int,bool),fun(int,bool)),fun(fun(product_prod(fun(int,bool),fun(int,bool)),bool),bool),member(product_prod(fun(int,bool),fun(int,bool))),hAPP(fun(int,bool),product_prod(fun(int,bool),fun(int,bool)),hAPP(fun(int,bool),fun(fun(int,bool),product_prod(fun(int,bool),fun(int,bool))),product_Pair(fun(int,bool),fun(int,bool)),A_3),B_2)),hAPP(fun(int,fun(int,bool)),fun(product_prod(fun(int,bool),fun(int,bool)),bool),bijR(int,int),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),A_3)),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),B_2)),Ma)))) # label(fact_4874_bijzcong__zcong__prod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2371 (all X_a (real_normed_vector(X_a) -> (all X_1 (ti(X_a,X_1) != zero_zero(X_a) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,norm_norm(X_a),X_1))))))) # label(fact_1787_zero__less__norm__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2372 (all X hAPP(real,real,sqrt,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(real,real,abs_abs(real),X)) # label(fact_1904_real__sqrt__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2373 (all X_1 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X_1)),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),fact_fact(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) = hAPP(real,real,exp(real),X_1)) # label(fact_3975_exp__first__two__terms) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2374 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))),C))) # label(fact_1083_div__mult1__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2375 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all X_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4574_mult__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2376 (all X_a (metric_space(X_a) -> (all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),B_1),sequentially)) -> ti(X_a,A_2) = ti(X_a,B_1)))))) # label(fact_4485_LIMSEQ__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2377 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X))))) # label(fact_1974_ln__ge__zero__imp__ge__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2378 (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]. 10.71/10.72 2379 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2076_Groups_Odiff__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2380 (all X_a (divisi14063676e_zero(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,inverse_inverse(X_a),A_2) = hAPP(X_a,X_a,inverse_inverse(X_a),B_1) <-> ti(X_a,B_1) = ti(X_a,A_2))))) # label(fact_2522_inverse__eq__iff__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2381 (all X_b all X_c all X_a all F all G ((all X_2 all Y_2 hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2) = hAPP(product_prod(X_a,X_b),X_c,G,hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2))) -> hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),F) = ti(fun(product_prod(X_a,X_b),X_c),G))) # label(fact_4329_cond__split__eta) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2382 (all A_2 all B_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1)),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),zEven))))) # label(fact_1366_even__plus__odd__prop1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2383 (all T_1 comple44059174attice(filter(T_1))) # label(arity_Limits_Ofilter___Complete__Lattice_Ocomplete__lattice) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2384 (all Ma all N_1 hAPP(fun(product_prod(nat,nat),bool),product_prod(nat,nat),the(product_prod(nat,nat)),hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,Ma),N_1)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1)) # label(fact_4144_divmod__nat__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2385 (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_329_dvd__0__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2386 (all A_1 all B ((hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = zero_zero(int) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),hAPP(int,int,uminus_uminus(int),B))) & (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)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)))) # label(fact_2170_zmod__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2387 (all N_1 (zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),N_1) <-> N_1 = zero_zero(nat))) # label(fact_1290_int__eq__0__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2388 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1594_order__less__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2389 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) != ti(fun(X_a,bool),B_2) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))) # label(fact_1999_psubset__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2390 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,ln,X)),hAPP(real,real,ln,Y))))) # label(fact_1976_ln__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2391 (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_max(X_a),X),Y) = ti(X_a,X))))) # label(fact_4979_min__max_Osup__absorb1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2392 (all N all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N)))) # label(fact_3450_zgcd__1__power__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2393 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),A_2)))))) # label(fact_4906_isCont__rabs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2394 (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_30_zle__antisym) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2395 (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]. 10.71/10.72 2396 (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_3372_ceiling__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2397 (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]. 10.71/10.72 2398 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,ln,X)),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),A_1)),X)))))) # label(fact_3421_ln__powr__bound2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2399 (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_3751_minus__rat__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2400 (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),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))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) # label(fact_3014_complex__add__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2401 (all X_1 all W_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | zero_zero(nat) = hAPP(int,nat,number_number_of(nat),W_1))) # label(fact_228_zero__less__power__nat__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2402 (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))) -> P_5 = one_one(nat) | Q_3 = one_one(nat))) # label(fact_3055_prime__product) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2403 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3))))) # label(fact_4212_abs__setsum__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2404 (all A_2 all B_1 (B_1 = zero_zero(real) & A_2 = one_one(real) <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) = one_one(complex))) # label(fact_2744_Complex__eq__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2405 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),one_one(real))))) # label(fact_2346_real__natfloor__add__one__gt) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2406 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_3)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3))))))) # label(fact_3497_BseqI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2407 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),one_one(real)))) # label(fact_2208_cos__le__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2408 (all U all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),U),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2118_realpow__square__minus__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2409 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(real,real,sin,X)))) # label(fact_2316_sin__ge__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2410 (all A_1 all B (ti(int,B) != zero_zero(int) -> (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))) & (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))))) # label(fact_2179_zdiv__zminus2__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2411 (all X_a (real_normed_algebra(X_a) -> (exists K_2 ((all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2412 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2796_of__real_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2413 (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_3110_div__pos__pos__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2414 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_2)))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))))) # label(fact_3134_Bolzano__bisect__Suc__le__snd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2415 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)),M))))) # label(fact_484_zcong__zdiff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2416 (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))))) # label(fact_3020_Re_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2417 (all B_2 all K all Diff all H all N_1 ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (N_1 = hAPP(nat,nat,suc,K) -> (all M_2 all T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(nat,fun(real,real),Diff,M_2))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(nat,bool),fun(real,real),hAPP(fun(real,fun(fun(nat,bool),real)),fun(fun(nat,bool),fun(real,real)),combc(real,fun(nat,bool),real),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),real),big_co1399186613setsum(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),M_2))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),power_power(real)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2))))),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),B_2)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),M_2)))))))),T_4),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,nat),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,real)),fun(fun(nat,nat),fun(nat,fun(real,real))),combb(nat,fun(real,real),nat),Diff),hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,suc,M_2)))),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),T_4))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),T_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,M_2))))))))))))))) # label(fact_4268_Maclaurin__lemma2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2418 (all N_1 hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,N_1)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),N_1)) # label(fact_4121_cos__fdiffs2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2419 (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,abs_abs(real),Y)))) -> zero_zero(real) = X))) # label(fact_1891_rabs__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2420 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(real,real,abs_abs(real),X))))) # label(fact_1897_abs__add__one__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2421 (all X_a (semiring_div(X_a) -> (all K_4 all M all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),M),N))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K_4),M))))))) # label(fact_950_dvd__mod__imp__dvd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2422 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1820_finite__Diff2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2423 (all L (pls = ti(int,L) <-> hAPP(int,int,bit0,L) = pls)) # label(fact_121_rel__simps_I38_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2424 (all X_b all X_a (metric_space(X_a) & real_normed_vector(X_b) -> (all L all F all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),G))),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4600_LIM__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2425 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),L)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4583_LIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2426 (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_3520_dist__complex__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2427 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),pi))) = hAPP(real,real,cos,X)) # label(fact_2239_cos__periodic) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2428 (all Q_3 all B all R_4 all C (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4))))))) # label(fact_1060_zmult2__lemma__aux3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2429 (all A_1 all B all C all D hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D))) # label(fact_2748_complex__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2430 (all X_a (field(X_a) -> (all X all Y all Z_1 (zero_zero(X_a) != ti(X_a,Z_1) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Z_1))))) # label(fact_1721_divide__add__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2431 (all X_a (real_vector(X_a) -> (all A_1 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_4688_scaleR__minus__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2432 (all X_a (preorder(X_a) -> (all X all Y (X = Y -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1556_order__eq__refl) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2433 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B))))) # label(fact_257_pos__zmult__pos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.72 2434 (all Ma all N_1 ((-(zero_zero(nat) = N_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1))) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1) = hAPP(product_prod(nat,nat),product_prod(nat,nat),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(product_prod(nat,nat),product_prod(nat,nat)),product_prod_case(nat,nat,product_prod(nat,nat)),hAPP(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat))),hAPP(fun(nat,fun(nat,product_prod(nat,nat))),fun(fun(nat,nat),fun(nat,fun(nat,product_prod(nat,nat)))),combb(nat,fun(nat,product_prod(nat,nat)),nat),product_Pair(nat,nat)),suc)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1)),N_1))) & (zero_zero(nat) = N_1 | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),Ma) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,Ma),N_1)))) # label(fact_4052_divmod__nat__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2435 (all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),X))),X) = hAPP(complex,complex,sgn_sgn(complex),X)) # label(fact_4742_complex__sgn__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2436 (all T_1 preorder(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Opreorder) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2437 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_44_number__of__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2438 (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),div_mod(X_a),B),A_1) = zero_zero(X_a))))) # label(fact_979_dvd__imp__mod__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2439 (all Z1 all Z2 all Z3 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z2),Z3)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z1),Z2)),Z3)) # label(fact_705_real__mult__assoc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2440 (all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),abs_abs(real)),A_2))) # label(fact_4913_isCont__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2441 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),A_1) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) # label(fact_4363_gcd__commute__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2442 (all X all A_1 all B hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),B)) # label(fact_3326_powr__powr) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2443 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),M)))) # label(fact_3232_dvd__gcd__D1__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2444 (all X_a (ord(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (ti(X_a,B) = ti(X_a,C) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),C))))))) # label(fact_1576_ord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2445 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2693_real__root__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2446 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)),B)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_1033_pos__mod__conj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2447 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),X))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Y)))) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4407_gcd__int__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2448 (all X_b all X_a all F all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_a,bool),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_a,bool),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,bool),fun(X_a,bool)),hAPP(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool))),hAPP(fun(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool))),fun(fun(X_b,fun(X_a,fun(bool,bool))),fun(X_b,fun(fun(X_a,bool),fun(X_a,bool)))),combb(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),X_b),combs(X_a,bool,bool)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool))),hAPP(fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,fun(bool,bool)))),combb(fun(X_a,bool),fun(X_a,fun(bool,bool)),X_b),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj)),hAPP(fun(X_a,X_b),fun(X_b,fun(X_a,bool)),hAPP(fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_a,X_b),fun(X_b,fun(X_a,bool))),combc(X_b,fun(X_a,X_b),fun(X_a,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool))),hAPP(fun(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool))),fun(fun(X_b,fun(X_b,bool)),fun(X_b,fun(fun(X_a,X_b),fun(X_a,bool)))),combb(fun(X_b,bool),fun(fun(X_a,X_b),fun(X_a,bool)),X_b),combb(X_b,bool,X_a)),fequal(X_b))),F)))),P_1))))))) # label(fact_4423_finite__image__set) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2449 (all M all N (one_one(int) = hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N)) -> hAPP(int,int,abs_abs(int),M) = one_one(int))) # label(fact_1927_abs__zmult__eq__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2450 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))) # label(fact_2369_two__realpow__gt) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2451 (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_3030_cis__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2452 (all Z all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z)))))) # label(fact_1138_nat__le__eq__zle) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2453 (all X_a (zero(X_a) -> zero_zero(X_a) = ti(X_a,zero_zero(X_a)))) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2454 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1223_Zero__neq__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2455 (all X_a all X_b (real_normed_algebra(X_b) -> (all Y_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),A_2),Y_1)),A_3)))))) # label(fact_4475_mult__left_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2456 (all X_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X_1))) = hAPP(nat,nat,suc,X_1)) # label(fact_3829_card__bdd__nat__set__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2457 (all X_a (ring_1(X_a) -> (all Z_1 all N hAPP(int,X_a,ring_1_of_int(X_a),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Z_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),N)))) # label(fact_3566_of__int__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2458 (all N all M hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),quickc495462417de_int,N),M) = hAPP(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,fun(quickcheck_code_int,product_prod(quickcheck_code_int,quickcheck_code_int)),product_Pair(quickcheck_code_int,quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),N),M))) # label(fact_3175_div__mod__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2459 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),zero_zero(real)),sequentially)))) # label(fact_4500_zeroseq__arctan__series) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2460 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_995_div__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2461 (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_2344_tan__npi) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2462 (all M all V (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,pred,V))))) # label(fact_2912_Suc__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2463 (all X_a ti(fun(X_a,fun(X_a,bool)),fequal(X_a)) = fequal(X_a)) # label(tsy_c_fequal_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2464 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4101_mult__left_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2465 (all X_1 all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1) = one_one(nat) <-> one_one(nat) = X_1 | N_1 = zero_zero(nat))) # label(fact_730_exp__eq__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2466 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y_1)),hAPP(real,real,tan,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)))))))) # label(fact_2273_tan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2467 (all X_a (linorder(X_a) -> (all A_1 all B all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4801_min__max_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2468 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1368_even__minus__odd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2469 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,uminus_uminus(int),X_1))))) # label(fact_2152_even__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2470 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_1867_abs__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2471 (all N all M all R_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),R_4)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),R_4)))))) # label(fact_2868_divides__mul) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2472 (all P_1 all I all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),K)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_2),K)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_831_int__le__induct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2473 (all X_a (semiring_div(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_1),A_2) = zero_zero(X_a))))) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2474 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y))))) # label(fact_4980_min__max_Osup__absorb2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2475 (all A_1 all B all C all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,B),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,C) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),R_4)),C))))))) # label(fact_1198_zmult1__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2476 (all X_a (linord219039673up_add(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),hAPP(X_a,X_a,uminus_uminus(X_a),Y)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4944_minus__min__eq__max) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2477 (all J_2 all K_4 all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),K_4),P_5))))))))) # label(fact_850_MultInv__zcong__prop3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2478 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),times_times(X_a)),Y_1)),A_2))))) # label(fact_4908_mult__left_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2479 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4436_LIMSEQ__inverse__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2480 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_3))))) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2481 (all X_1 all Y_1 all Z (X_1 = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y_1),Z) <-> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Z) = Y_1)) # label(fact_1178_eq__diff__eq_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2482 (all I_1 all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),K_4)))) # label(fact_562_add__lessD1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2483 (all X_b (number(X_b) & ord(X_b) -> (all U all V ((hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),V)) & (-hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V))) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),ord_max(X_b),hAPP(int,X_b,number_number_of(X_b),U)),hAPP(int,X_b,number_number_of(X_b),V)) = hAPP(int,X_b,number_number_of(X_b),U)))))) # label(fact_4989_max__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2484 (all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)))) # label(fact_1132_zero__less__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2485 (all X_a (real_normed_field(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),one_one(X_a)),X_1)))))))) # label(fact_4098_geometric__sums) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2486 (all X_a (comm_semiring_1(X_a) -> (all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),M)))) # label(fact_253_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2487 (all X all Y hAPP(complex,real,im,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)) = Y) # label(fact_2972_Im) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2488 (all X_a (linorder(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1593_leD) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2489 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,A_2,zero_zero(nat))),zero_zero(real))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat))))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2))))))))))) # label(fact_4522_summable__Leibniz_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2490 (all Y hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,tan,Y))) # label(fact_2275_tan__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2491 (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)) & (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))))))) # label(fact_2437_minus__one__even__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2492 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3195_fact__ge__one__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2493 (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),B),A_1) = 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))))) # label(fact_2519_inverse__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2494 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_1246_Suc__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2495 (all M all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),K_4)))))) # label(fact_3196_fact__mono__int__aux) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2496 (all X_a (real_normed_field(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_1656_divide_Ozero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2497 (all M one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),one_one(nat))) # label(fact_3251_gcd__1__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2498 (all X_a (monoid_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a)) = ti(X_a,A_1)))) # label(fact_775_add__0__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2499 (all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),B_2)) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_4260_setsum__diff__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2500 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),A_2)))))) # label(fact_4905_isCont__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2501 (all X one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),one_one(nat))) # label(fact_3252_gcd__lcm__complete__lattice__nat_Oinf__bot__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2502 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))) # label(fact_2036_mult_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2503 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),zero_zero(X_a))) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_1861_abs__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2504 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4021_summable__sin) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2505 (all X all Y (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y))))) # label(fact_1259_anything__times__even) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2506 (all X_a (comm_semiring_1(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2507 (all X_a (field_inverse_zero(X_a) -> (all Z_1 all X all Y (zero_zero(X_a) != ti(X_a,Y) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y))))) # label(fact_1718_add__num__frac) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2508 (all J_2 all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5)))))))) # label(fact_830_MultInvPair__distinct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2509 (all X_a (linorder(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Y))))) # label(fact_4828_min__max_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2510 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> (hAPP(X_a,X_a,G,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,F,X_1)),E_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,G,X_1)),hAPP(X_a,X_a,G,X_1))))))))))) # label(fact_3811_DERIV__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2511 (all L all K ((zero_zero(int) != ti(int,K) -> (ti(int,L) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),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)) & (zero_zero(int) != ti(int,L) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,int),fun(product_prod(int,int),product_prod(int,int)),product_apsnd(int,int,int),hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),L))),hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K))),hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),L),zero_zero(int))),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)),hAPP(product_prod(int,int),product_prod(int,int),hAPP(fun(int,fun(int,product_prod(int,int))),fun(product_prod(int,int),product_prod(int,int)),product_prod_case(int,int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int)))),combs(int,fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(int,fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))))),combb(fun(int,fun(product_prod(int,int),product_prod(int,int))),fun(fun(int,product_prod(int,int)),fun(int,product_prod(int,int))),int),combs(int,product_prod(int,int),product_prod(int,int))),hAPP(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,product_prod(int,int)),fun(int,fun(int,fun(product_prod(int,int),product_prod(int,int))))),combb(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int))),int),hAPP(fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(product_prod(int,int),fun(int,fun(product_prod(int,int),product_prod(int,int)))),combc(int,product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),hAPP(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),hAPP(fun(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)))),fun(fun(int,bool),fun(int,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))))),combb(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),int),if(product_prod(int,int))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),fequal(int)),zero_zero(int))))),hAPP(int,fun(int,product_prod(int,int)),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(int,product_prod(int,int))),combc(int,int,product_prod(int,int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),uminus_uminus(int))),zero_zero(int))))),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combc(int,fun(int,int),fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int)))),hAPP(fun(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int)))),fun(fun(int,fun(int,product_prod(int,int))),fun(int,fun(fun(int,int),fun(int,product_prod(int,int))))),combb(fun(int,product_prod(int,int)),fun(fun(int,int),fun(int,product_prod(int,int))),int),combb(int,product_prod(int,int),int)),hAPP(fun(int,int),fun(int,fun(int,product_prod(int,int))),hAPP(fun(int,fun(int,product_prod(int,int))),fun(fun(int,int),fun(int,fun(int,product_prod(int,int)))),combb(int,fun(int,product_prod(int,int)),int),product_Pair(int,int)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),minus_minus(int)),uminus_uminus(int))),one_one(int))))),hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,abs_abs(int),L))))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K),L)))))) & (ti(int,K) = zero_zero(int) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,K),L)))) # label(fact_4063_divmod__int__pdivmod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2512 (all X_a (comple44059174attice(X_a) -> (all V_1 all U_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),U_1),A_3)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),U_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),V_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)))))))) # label(fact_1765_complete__lattice__class_OSup__upper2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2513 (all X_a (boolean_algebra(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2953_double__compl) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2514 (all Z_1 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(complex,real,re,Z_1)),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,Z_1))) = hAPP(complex,complex,cnj,Z_1)) # label(fact_3012_cnj__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2515 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_1862_abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2516 (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_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),L),hAPP(X_b,filter(X_b),at(X_b),hAPP(X_a,X_b,F,A_2)))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),D_3)) & ti(X_a,A_2) != ti(X_a,X_2) -> hAPP(X_a,X_b,F,X_2) != hAPP(X_a,X_b,F,A_2))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4879_isCont__LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2517 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> Y = X))) # label(fact_633_dvd_Oantisym) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2518 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),A_3)))))) # label(fact_4472_tendsto__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2519 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),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),X_1)),zero_zero(X_a))))))) # label(fact_47_le__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2520 (all X_a (semiri456707255roduct(X_a) -> (all B_1 all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2) = ti(X_a,B_1))))) # label(fact_239_add__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2521 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),A_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_593_zdiff__power3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2522 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),K_4) = ti(int,K_4)) # label(fact_131_add__Pls) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2523 (all N all P_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,fact,N)))))) # label(fact_3532_divides__fact) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2524 (all X_a (linorder(X_a) -> (all X all Y (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_1581_linorder__cases) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2525 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4748_summable__exp__generic) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2526 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_1260_Parity_Oodd__times__odd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2527 (all K hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,K)) = hAPP(nat,fun(nat,bool),ord_atMost(nat),K)) # label(fact_4953_lessThan__Suc__atMost) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2528 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_gr676655987ssThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4234_greaterThanLessThan__subseteq__atLeastLessThan__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2529 (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_219_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2530 (all X_a (boolean_algebra(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))))))) # label(fact_2956_compl__le__compl__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2531 (all B_1 all D_1 all A_2 ((all E (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),A_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),B_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),E),D_1)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D_1),A_2)) <-> D_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_2),B_1))) # label(fact_3241_gcd__unique__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2532 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))))))) # label(fact_2602_iszero__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2533 (all N all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))))) # label(fact_4846_Nat__Transfer_Otransfer__int__nat__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2534 (all X_a (preorder(X_a) -> (all X -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),X))))) # label(fact_1560_order__less__irrefl) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2535 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,M_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4130_monoI2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2536 (all X_a (group_add(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1),Y_1) <-> hAPP(X_a,X_a,uminus_uminus(X_a),X_1) = ti(X_a,Y_1))))) # label(fact_2064_add__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2537 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> hAPP(real,X_a,of_real(X_a),zero_zero(real)) = zero_zero(X_a))) # label(fact_2782_of__real_Ozero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.73 2538 (all X all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),D))),hAPP(nat,real,real_1(nat),D))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),X)),hAPP(nat,real,real_1(nat),D)))) # label(fact_2372_real__of__nat__div__aux) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2539 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,re,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_3008_abs__Re__le__cmod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2540 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),X),Y))) # label(fact_3770_real__divide__code) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2541 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X)))),one_one(real)))) # label(fact_2359_real__of__nat__div3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2542 (all B all A_1 (zero_zero(nat) != A_1 -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2)))) # label(fact_3313_bezout__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2543 (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) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)) | one_one(int) = ti(int,A_1)))))) # label(fact_534_zcong__square__zless) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2544 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N)))) -> hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = N))) # label(fact_2877_floor__eq3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2545 (all Y all X all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),zero_zero(int)),P_5)))))) # label(fact_456_zcong__zmult__prop3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2546 (all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Ma),N_1) = zero_zero(nat) <-> zero_zero(nat) != N_1 & Ma = zero_zero(nat))) # label(fact_726_nat__power__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2547 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all A_2 all B_1 all W_1 ((hAPP(int,X_a,number_number_of(X_a),W_1) != zero_zero(X_a) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))) & (zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),W_1) -> ti(X_a,A_2) = zero_zero(X_a)) <-> ti(X_a,A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))) # label(fact_1723_eq__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2548 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_3)))) # label(fact_1825_finite__UnionD) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2549 (all X_a (comm_semiring_1(X_a) -> (all X all N (one_one(X_a) = ti(X_a,X) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))))) # label(fact_462_dvd__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2550 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_376_mult__nonneg__nonpos2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2551 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))),hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1814_diff__card__le__card__Diff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2552 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1)),F)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2))))))) # label(fact_4079_sums__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2553 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)))))) # label(fact_2015_minus__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2554 (all G all X_1 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),one_one(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),X_1)))) # label(fact_4104_sums__if_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2555 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,H,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),H),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),A_3)))))) # label(fact_4774_setsum_Ocong) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2556 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,suc,N)))) # label(fact_1208_zero__less__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2557 (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_206_zdvd__mult__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2558 t = zero_zero(int) -> zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),s),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) # label(fact_4_calculation_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2559 (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_4352_transfer__int__nat__gcd_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2560 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_1567_order__less__not__sym) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2561 (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,A_1) = ti(X_a,B)))))))) # label(fact_460_power__eq__imp__eq__base) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2562 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),zero_zero(int)))))) # label(fact_1021_div__nonneg__neg__le0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2563 (all A_1 all B all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),N)) # label(fact_3441_zgcd__power__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2564 (all X_a all Q_1 all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> ((all X_2 (hBOOL(hAPP(X_a,bool,P_1,X_2)) -> hBOOL(hAPP(X_a,bool,Q_1,X_2)))) -> hBOOL(hAPP(X_a,bool,Q_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1)))))) # label(fact_4869_someI2__ex) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2565 (all L all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),L))) -> ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),L),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,F,N_2)),E)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),L),sequentially)))))) # label(fact_4878_increasing__LIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2566 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_933_zmod__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2567 (all T_2 all T_1 (finite_finite(T_1) & finite_finite(T_2) -> finite_finite(product_prod(T_2,T_1)))) # label(arity_prod___Finite__Set_Ofinite) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2568 (all X_b all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_b,bool),nat,finite_card(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))))) # label(fact_3643_card__image__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2569 (all X_a (ab_semigroup_mult(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2570 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) <-> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1276_odd__iff__not__even) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2571 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_3121_mod__neg__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2572 (all N_1 (N_1 != zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_537_neq0__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2573 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2004_abs__ln__one__plus__x__minus__x__bound__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2574 (all A_2 all Ma hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma)))) # label(fact_3208_Bnor__fin) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2575 (all X_a (real_normed_field(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1))))))) # label(fact_4009_summable__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2576 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,re,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))) # label(fact_3021_Re_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2577 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> -hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1263_Parity_Oeven__plus__odd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2578 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_790_add__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2579 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y)))) # label(fact_1759_real__gt__half__sum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2580 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))))) # label(fact_2817_of__real_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2581 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,suc,zero_zero(nat)))))) # label(fact_3065_prime__nd__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2582 (all X_b all X_a (real_normed_field(X_a) & banach(X_b) -> (all G all F all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all H_1 all N_2 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(nat,X_b,hAPP(X_a,fun(nat,X_b),G,H_1),N_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,F,N_2)),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,fun(nat,X_b)),fun(X_a,X_b),hAPP(fun(fun(nat,X_b),X_b),fun(fun(X_a,fun(nat,X_b)),fun(X_a,X_b)),combb(fun(nat,X_b),X_b,X_a),suminf(X_b)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))))) # label(fact_4625_lemma__termdiff5) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2583 (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),inverse_divide(X_a),A_1),A_1))))) # label(fact_1695_divide__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2584 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C)) # label(fact_1090_div__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2585 (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)) -> X = hAPP(real,real,hAPP(real,fun(real,real),powr,A_1),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)))))) # label(fact_3406_powr__log__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2586 (all N all J_2 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),N)),K_4)))) # label(fact_663_less__imp__diff__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2587 (all N hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,real_1(nat),N))) = hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_2878_floor__minus__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2588 (all X_a (topological_space(X_a) -> (all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),zero_zero(complex)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4615_Re_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2589 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1)))))) # label(fact_751_nat__le__add__iff2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2590 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) -> ti(X_a,Sa) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))) # label(fact_4089_sums__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2591 (all X all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),X)),N)) # label(fact_1357_Nat__Transfer_Otransfer__int__nat__functions_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2592 (all K all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (J = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),I) <-> K = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)))) # label(fact_692_le__imp__diff__is__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2593 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),N))) # label(fact_1119_div__mult__self__is__m) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2594 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)))) # label(fact_2465_even__dvd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2595 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit0,L))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),L)))) # label(fact_128_rel__simps_I14_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2596 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,summable(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_4045_cnj_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2597 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,bit0,K_4)),hAPP(int,int,bit0,L_4))) # label(fact_480_diff__bin__simps_I7_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2598 (all X_a (linorder(X_a) -> (all Z all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),Y_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1))))))) # label(fact_4950_less__max__iff__disj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2599 (all N_1 all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) -> (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4)))))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))))))))) # label(fact_3144_not__P__Bolzano__bisect) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2600 (all X_b all X_a all Q_1 all P_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) -> ((all Y_2 (hBOOL(hAPP(X_a,bool,P_1,Y_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(X_a,fun(X_b,bool),hAPP(fun(X_b,fun(X_a,bool)),fun(X_a,fun(X_b,bool)),combc(X_b,X_a,bool),Q_1),Y_2)))))) <-> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_b,bool),fun(X_b,bool),collect(X_b),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,bool),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_b,fun(X_a,bool)),fun(X_b,bool)),combb(fun(X_a,bool),bool,X_b),fEx(X_a)),hAPP(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_b,fun(X_a,bool)),fun(X_b,fun(X_a,bool))),combb(fun(X_a,bool),fun(X_a,bool),X_b),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),P_1))),Q_1)))))))) # label(fact_4422_finite__Collect__bounded__ex) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2601 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_less)))) # label(fact_3486_pair__lessI1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2602 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),K_4)))))) # label(fact_598_mult__less__mono1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2603 (all N one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),N)) # label(fact_3266_coprime__plus__one__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2604 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),K_4))))) # label(fact_1087_div__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2605 (all X_a all X_b all X_c all X_d all X_e all Y -(all A_4 all B_4 all C_4 all D_3 all E 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_3),E)))))) # label(fact_3153_prod__cases5) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2606 (all P_5 all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),N)))))) # label(fact_454_zpower__zdvd__prop1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2607 (all X_a all R_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),A_2)) <-> (exists X_2 (ti(X_a,A_2) = ti(X_a,X_2) & (all Xa (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,Xa),X_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),Xa)))))))) # label(fact_2918_accp_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2608 (all X_a (comm_semiring_1(X_a) -> (all N all M all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),M)))))))) # label(fact_345_dvd__power__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2609 (all X_a (banach(X_a) -> (all F all G ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))),hAPP(nat,real,G,N_2))))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F))))))) # label(fact_3994_summable__comparison__test) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2610 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_592_zdiff__power2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2611 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),A_2)))) # label(fact_423_zcong__zero__equiv__div) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2612 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N_1)),one_one(real))),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),N_1),Ma)))) # label(fact_3391_int__less__real__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2613 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),C_2))))) # label(fact_1973_psubset__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2614 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4641_aset_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2615 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_27_le__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2616 (all X_a all X_b all A_3 all B_2 (hBOOL(hAPP(fun(sum_sum(X_a,X_b),bool),bool,finite_finite_1(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_3183_finite__PlusD_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2617 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_1465_even__div__2__prop2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2618 (all X_1 (hBOOL(hAPP(int,bool,twoSqu1091635170sum2sq,X_1)) <-> (exists A_4 exists B_4 ti(int,X_1) = hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))))) # label(fact_755_is__sum2sq__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2619 (all X_a (number(X_a) & field_inverse_zero(X_a) -> (all W_1 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = hAPP(int,X_a,number_number_of(X_a),W_1) <-> (ti(X_a,C_1) = zero_zero(X_a) -> hAPP(int,X_a,number_number_of(X_a),W_1) = zero_zero(X_a)) & (ti(X_a,C_1) != zero_zero(X_a) -> ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)))))) # label(fact_1724_eq__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2620 (all Z_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),Z_1)),Z_1)) # label(fact_2154_zadd__zminus__inverse2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2621 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2565_not__exp__le__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2622 (all X_a (order(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),mono(nat,X_a),dvd_dvd(nat)),F)))))) # label(fact_4792_dvd_Ostrict__mono__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2623 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) <-> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3494_Bseq__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2624 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = X)) # label(fact_3238_gcd__proj1__if__dvd__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2625 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1680_divide__pos__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2626 (all X_a (archim1727834104eiling(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),Y)),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3281_ceiling__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2627 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_580_add__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2628 (all X_b all X_a (semiring_1(X_a) -> (all Y_1 all A_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,finite_card(X_b),A_3))),Y_1) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),Y_1)),A_3)))) # label(fact_4228_setsum__constant) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2629 (all P_1 all A0 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),A0)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(fun(int,fun(int,bool)),fun(int,bool),accp(int),quickc1265749348ro_rel),I_2)) -> ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_2),zero_zero(int))) -> (ti(int,I_2) != zero_zero(int) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),I_2),one_one(int)))))) -> hBOOL(hAPP(int,bool,P_1,I_2))))) -> hBOOL(hAPP(int,bool,P_1,A0))))) # label(fact_3177_around__zero_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2630 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),N)),hAPP(int,real,real_1(int),X))))) # label(fact_3360_real__of__int__div4) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2631 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),B_2))))) # label(fact_3635_image__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2632 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta))))))) # label(fact_4632_bset_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2633 (all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_2)),one_one(real)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),X_1)),A_2)))) # label(fact_3414_floor__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2634 (all X_a (order(X_a) -> (all Y_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)) -> (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1))))))) # label(fact_1554_order__antisym__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2635 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),one_one(int)),hAPP(int,int,number_number_of(int),W)) = hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),one_one(int))),hAPP(int,int,uminus_uminus(int),hAPP(int,int,number_number_of(int),W))))))) # label(fact_3115_mod__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2636 (all V_3 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_3),pls)) -> hAPP(int,nat,number_number_of(nat),V) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(int,nat,number_number_of(nat),V_3) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_87_add__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2637 (all A_2 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),d22set,A_2)))) # label(fact_1671_d22set__fin) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2638 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,exp(real),one_one(real)))),hAPP(real,real,ln,X)) = hAPP(real,real,hAPP(real,fun(real,real),log,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X))) # label(fact_2657_log__base__10__eq2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2639 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (P_5 != Q_3 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,P_5),Q_3)))))) # label(fact_3049_distinct__prime__coprime) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2640 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))))) # label(fact_1623_real__sqrt__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2641 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)))))) # label(fact_1573_xt1_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2642 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & ti(X_a,X_1) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1585_order__less__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2643 (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_690_add__diff__assoc2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2644 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,G,X_2) = one_one(X_b))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3) = one_one(X_b)))))) # label(fact_4148_setprod_Oneutral) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2645 (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_113_mult__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2646 (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_2259_arccos__cos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2647 (all X_a (ordere216010020id_add(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_760_add__strict__increasing2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2648 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hAPP(real,real,arctan,X_1) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))))) # label(fact_3966_arctan__series) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2649 (all X_a (comm_semiring_1(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a))))) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2650 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = zero_zero(X_a) & zero_zero(X_a) = ti(X_a,X_1) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))))) # label(fact_94_sum__squares__eq__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2651 (all X_a all X_b (ordered_ab_group_add(X_b) -> (all I all F all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),Sa)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,I_2))))) -> (zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),Sa) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I),Sa)) -> zero_zero(X_b) = hAPP(X_a,X_b,F,I)))))))) # label(fact_4300_setsum__nonneg__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2652 (all X_a all P_1 all Q_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),Q_1))) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),P_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fdisj),P_1)),Q_1)))))) # label(fact_3847_finite__Collect__disjI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2653 (all X_a (field_inverse_zero(X_a) -> (all A_2 all B_1 all C_1 ((zero_zero(X_a) = ti(X_a,C_1) -> ti(X_a,A_2) = 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),times_times(X_a),A_2),C_1) = ti(X_a,B_1)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1) = ti(X_a,A_2))))) # label(fact_1685_eq__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2654 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),A_1)))) # label(fact_4399_gcd__le1__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2655 (all Q_3 all R_4 all B all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),R_4),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Q_3),C))),R_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)))))) # label(fact_1134_mod__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.74 2656 (all A_2 all B_1 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),K)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),K)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))))) # label(fact_3470_zcong__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2657 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2)) & A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_2),N) & (all Y_2 (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_2),N) = A_1 & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) -> X_2 = Y_2))))))) # label(fact_733_realpow__pos__nth__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2658 (all X_b all X_a (metric_space(X_a) & metric_space(X_b) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4653_LIM__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2659 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Y_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1462_even__div__2__l) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2660 (all Z_1 hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,Z_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) # label(fact_2991_complex__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2661 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X)),hAPP(real,nat,natceiling,Y))))) # label(fact_1888_natceiling__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2662 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_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) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> zero_zero(nat) = hAPP(X_a,nat,F,X_2)))))) # label(fact_4254_setsum__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2663 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)))) # label(fact_865_d22set__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2664 (all Y exists X_2 (Y = hAPP(real,real,tan,X_2) & (all Y_2 (Y = hAPP(real,real,tan,Y_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) -> Y_2 = X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)))) # label(fact_2283_tan__total) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2665 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2944_complex__cnj__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2666 (all X hAPP(real,real,cos,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,cos,X)) # label(fact_2198_cos__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2667 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),L_4)))))) # label(fact_586_mult__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2668 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B))) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) # label(fact_4389_Fract__coprime) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2669 (all X_a (real_normed_vector(X_a) -> (all X_1 all A_2 hBOOL(hAPP(real,bool,hAPP(fun(real,X_a),fun(real,bool),isCont(real,X_a),hAPP(X_a,fun(real,X_a),hAPP(fun(real,fun(X_a,X_a)),fun(X_a,fun(real,X_a)),combc(real,X_a,X_a),scaleR_scaleR(X_a)),X_1)),A_2))))) # label(fact_4915_scaleR__left_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2670 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),zero_zero(X_a))))) # label(fact_1657_divide__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2671 (all X_1 ((exists N_2 X_1 = hAPP(int,real,real_1(int),N_2)) <-> X_1 = hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),X_1)))) # label(fact_3325_real__of__int__floor__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2672 (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_2032_minus__mult__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2673 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3903_DERIV__sin__sin__mult2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2674 (all X_1 all 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),zero_zero(real)),X_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),X_1),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),X_1),Y_1))))) # label(fact_1699_real__0__le__divide__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2675 (all N (hAPP(int,int,number_number_of(int),min_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),N) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),N) = one_one(int))) # label(fact_606_neg__one__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2676 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Y),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) # label(fact_4370_gcd__red__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2677 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(fun(int,bool),bool),nat,finite_card(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1603_SetS__card) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2678 (all X_a (field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),field_char_0_Rats(X_a)))))))) # label(fact_3688_nonzero__Rats__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2679 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,N_1)),one_one(nat)))) # label(fact_3880_card__bdd__int__set__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2680 (all Y_1 all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),Y_1)))))))) # label(fact_2643_log__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2681 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),rcis,zero_zero(real)),A_1) = zero_zero(complex)) # label(fact_3168_rcis__zero__mod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2682 (all K_4 ti(int,K_4) = hAPP(int,int,number_number_of(int),K_4)) # label(fact_22_number__of__is__id) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2683 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,A_2)),A_3)))) # label(fact_4509_Re_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2684 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(complex,real,im,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))) # label(fact_2988_Im_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2685 (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)) & (zero_zero(int) = ti(int,L_4) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),pdivmod,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),hAPP(int,int,abs_abs(int),K_4))))) # label(fact_2720_pdivmod__posDivAlg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2686 (all V hAPP(complex,real,re,hAPP(int,complex,number_number_of(complex),V)) = hAPP(int,real,number_number_of(real),V)) # label(fact_3005_complex__Re__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2687 (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_3598_floor__diff__of__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2688 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1761_SRStar__finite) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2689 (all X_b all X_a (real_normed_vector(X_b) & real_normed_field(X_a) -> (all F all K_3 all K (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K)) -> ((all H_1 (ti(X_a,H_1) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),H_1)),K)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_a,X_b,F,H_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),K_3),hAPP(X_a,real,norm_norm(X_a),H_1))))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4626_lemma__termdiff4) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2690 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2129_arcsin__lt__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2691 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))) # label(fact_4969_min__max_Osup_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2692 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X)))) # label(fact_1977_ln__add__one__self__le__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2693 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),A_2))))) # label(fact_4898_isCont__const) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2694 (all Ma all N_1 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),Ma)))) # label(fact_1244_not__less__eq__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2695 (all X_a (real_normed_algebra(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2038_mult_Ominus__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2696 (all X all Y hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Y))) # label(fact_3245_gcd__semilattice__nat_Oinf__le2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2697 (all X_a all X_b all A_3 all B_1 all F all X_1 (hAPP(X_b,X_a,F,X_1) = ti(X_a,B_1) -> (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3)))))) # label(fact_3632_image__eqI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2698 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2886_number__of__le__floor) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2699 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),zero_zero(real))))) # label(fact_1627_real__sqrt__lt__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2700 (all N_1 zero_zero(real) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)))) # label(fact_4237_sumr__minus__one__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2701 (all X_a (zero_neq_one(X_a) -> zero_zero(X_a) != one_one(X_a))) # label(fact_325_one__neq__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2702 (all K all P_1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_1))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K)) -> (all X_2 (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),D_1)))))))))) # label(fact_611_decr__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2703 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,X)) = hAPP(real,real,sqrt,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2054_real__sqrt__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2704 (all X_1 hAPP(real,int,archim2085082626_floor(real),X_1) = hAPP(fun(int,bool),int,the(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(real,fun(int,bool),hAPP(fun(int,fun(real,bool)),fun(real,fun(int,bool)),combc(int,real,bool),hAPP(fun(int,real),fun(int,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(int,real),fun(int,fun(real,bool))),combb(real,fun(real,bool),int),ord_less_eq(real)),ring_1_of_int(real))),X_1))),hAPP(fun(int,real),fun(int,bool),hAPP(fun(real,bool),fun(fun(int,real),fun(int,bool)),combb(real,bool,int),hAPP(real,fun(real,bool),ord_less(real),X_1)),hAPP(fun(int,int),fun(int,real),hAPP(fun(int,real),fun(fun(int,int),fun(int,real)),combb(int,real,int),ring_1_of_int(real)),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),plus_plus(int)),one_one(int))))))) # label(fact_4146_floor__real__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2705 (all X hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X)) = hAPP(real,real,sin,hAPP(real,real,uminus_uminus(real),X))) # label(fact_2290_sin__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2706 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))))))) # label(fact_3506_dist__triangle) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2707 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,F,Ma)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4606_setsum__cl__ivl__Suc2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2708 (all X_a (comm_monoid_add(X_a) -> (all F all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),K))),K)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K)))))) # label(fact_4173_sumr__group) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2709 (all X X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),X)) # label(fact_3219_gcd__idem__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2710 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),Z2)),Z3) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z2),Z3))) # label(fact_28_zmult__assoc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2711 (all N_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)))) # label(fact_2468_even__even__mod__4__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2712 (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_4665_norm__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2713 (all X_a (semiring_1(X_a) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),one_one(X_a)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_12_one__power2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2714 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))) & zero_zero(X_a) != ti(X_a,C_1) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))))))) # label(fact_1678_divide__less__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2715 (all X_1 all N_1 all Y_1 ((exists Q1 exists Q2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q2))) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Y_1),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),N_1))) # label(fact_1183_nat__mod__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2716 (all I_1 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),M)))) # label(fact_4367_dvd__gcd__D1__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2717 (all X all I_1 hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,real_1(int),I_1)),pi)))) # label(fact_3399_tan__periodic__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2718 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(int,nat,nat_1,N_1) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),N_1)))))) # label(fact_3810_card__bdd__int__set__l__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2719 (all X hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),X)) = hAPP(int,int,fact_fact(int),hAPP(nat,int,semiring_1_of_nat(int),X))) # label(fact_3193_transfer__int__nat__factorial) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2720 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1247_le__SucI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2721 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all P_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),P_1)),F)),zero_zero(X_b))),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),P_1))))))) # label(fact_4186_setsum__restrict__set_H_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2722 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),hAPP(X_a,int,archim2085082626_floor(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_2864_floor__less__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2723 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),hAPP(nat,nat,suc,N))))) # label(fact_1234_less__SucI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2724 (all X_a (semiring_1(X_a) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),one_one(nat)) = one_one(X_a))) # label(fact_1288_of__nat__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2725 (all X_a (archim1804426504_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)),X)))))))) # label(fact_2724_ex__less__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2726 (all W hAPP(int,complex,number_number_of(complex),W) = hAPP(complex,complex,cnj,hAPP(int,complex,number_number_of(complex),W))) # label(fact_2932_complex__cnj__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2727 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))))) # label(fact_2108_real__add__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2728 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),M))) # label(fact_1088_div__le__dividend) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2729 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(int,X_a,ring_1_of_int(X_a),Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)))))) # label(fact_3602_of__int__0__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2730 (all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (exists X_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_2)),one_one(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2477_odd__square) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2731 (all K_4 hAPP(int,real,number_number_of(real),K_4) = hAPP(rat,real,ratreal,hAPP(int,rat,number_number_of(rat),K_4))) # label(fact_3762_number__of__real__code) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2732 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) = 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)) # label(fact_919_zdiv__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2733 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> ti(X_a,B_1) = ti(X_a,A_2))))) # label(fact_2044_neg__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2734 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K) <-> N_1 = Ma)))) # label(fact_673_eq__diff__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2735 (all X_a (comm_monoid_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat)))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),one_one(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),P_4)))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),P_4))))))) # label(fact_4604_setsum__ub__add__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2736 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),K_4)) # label(fact_678_diff__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2737 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),hAPP(int,int,uminus_uminus(int),W)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),W)) # label(fact_2161_diff__int__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2738 (all X_a (linordered_semidom(X_a) -> (all Ma all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),Ma)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)))))) # label(fact_1285_of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2739 (all X_a all A_3 all X_3 all C_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),X_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_3),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),C_2)))))) # label(fact_1651_UnionI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2740 (all A_3 all B_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less(fun(int,bool)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B_2))) <-> hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less(fun(nat,bool)),A_3),B_2)))) # label(fact_3647_transfer__nat__int__set__relations_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2741 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_2960_compl__less__swap2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2742 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),zero_zero(real))) -> (exists R_2 exists A_4 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) = X & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)))))) # label(fact_2725_polar__ex2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2743 (all A_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),N) = one_one(int) -> (exists X_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),X_2)),one_one(int)),N)))))) # label(fact_3479_zcong__lineq__ex) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2744 (all Y (Y != zero_zero(nat) -> -(all Nat_2 Y != hAPP(nat,nat,suc,Nat_2)))) # label(fact_1607_nat_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2745 (all C_1 (zero_zero(rat) = C_1 <-> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(rat,fun(nat,rat),combk(rat,nat),C_1))))) # label(fact_4843_vanishes__const) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2746 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_2163_diff__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2747 (all X_b all X_c all X_a all F all 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)) = 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)) # label(fact_3991_prod__case__beta) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2748 (all N hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),N)) # label(fact_2374_cos__npi2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2749 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (all Y_2 exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),X)))))) # label(fact_2409_reals__Archimedean3) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2750 (all X hAPP(complex,complex,cnj,hAPP(complex,complex,inverse_inverse(complex),X)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,cnj,X))) # label(fact_2929_complex__cnj__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2751 (all X hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))) # label(fact_1968_abs__power3__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2752 (all X_a (archim1727834104eiling(X_a) -> (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(X_a,int,archimedean_ceiling(X_a),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_3280_ceiling__less__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2753 (all X_a all F1 all F2 all Nat hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F2,Nat),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),Nat)) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),hAPP(nat,nat,suc,Nat))) # label(fact_4154_nat__rec__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2754 (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(int,nat,nat_1,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),V)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),V)),N)))) # label(fact_1517_power__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2755 (all X_a all X_b all X_c all F hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,X_c))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c),X_a),hAPP(fun(product_prod(X_a,X_b),X_c),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,X_c)),combb(product_prod(X_a,X_b),X_c,X_b),F)),product_Pair(X_a,X_b))) = ti(fun(product_prod(X_a,X_b),X_c),F)) # label(fact_4013_split__eta) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2756 (all Z_1 hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),Z_1),hAPP(complex,complex,cnj,Z_1)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(complex,real,im,Z_1)))),ii)) # label(fact_2970_complex__diff__cnj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2757 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),Ma)))))) # label(fact_3623_RRset2norRR__correct1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2758 (all M all N all K_4 ((zero_zero(nat) != K_4 -> 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))) & (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)))) # label(fact_1099_nat__mult__div__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2759 (all B all Q_3 all R_4 all B_5 all Q_5 all R_5 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_5),Q_5)),R_5)),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_5),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))))) # label(fact_269_zdiv__mono2__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2760 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F)))) # label(fact_4001_summable__rabs__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2761 (all Ma all N_1 ((hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> 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),N_1))))) # label(fact_2414_even__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2762 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = ti(X_a,A_1))))) # label(fact_1860_abs__of__nonneg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2763 (all X_a (boolean_algebra(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),hAPP(X_a,X_a,uminus_uminus(X_a),X))))))) # label(fact_2957_compl__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2764 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y))) # label(fact_1617_real__sqrt__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2765 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),hAPP(nat,nat,suc,N_2)))))))) # label(fact_3133_Bolzano__bisect__fst__le__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2766 (all N_1 all X_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1)))))) # label(fact_4286_Maclaurin__all__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2767 (all X_a (number_ring(X_a) -> (all K_4 hAPP(int,X_a,number_number_of(X_a),K_4) = hAPP(int,X_a,ring_1_of_int(X_a),K_4)))) # label(fact_3581_number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.75 2768 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C_1)))))))) # label(fact_2833_order__le__less__subst2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2769 (all X_a (division_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))) # label(fact_2560_inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2770 (all A_1 all N all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),N))) -> (N != zero_zero(nat) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B))))) # label(fact_870_pow__divides__pow__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2771 (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_2859_floor__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2772 (all X_a (metric_space(X_a) -> (all E_2 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E_2)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E_2))))))))))) # label(fact_3523_metric__CauchyD) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2773 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),K_4))))) # label(fact_527_le__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2774 (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]. 10.71/10.76 2775 (all X_a (semiring_div(X_a) -> (all B all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_914_mod__div__equality2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2776 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(nat,fun(real,real),root,M),X))))) # label(fact_2673_real__root__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2777 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y))) # label(fact_4373_gcd__abs__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2778 (all K_4 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),K_4)),X))))) # label(fact_1013_int__div__less__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2779 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)))))) # label(fact_338_dvd__mult__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2780 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))))))) # label(fact_4002_summable__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2781 (all X_a (linorder(X_a) -> (all X all Y ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4942_min__max_Osup__inf__absorb) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2782 (all X_a (division_ring(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)))))) # label(fact_2077_nonzero__minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2783 (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_1395_mod__mult__self4) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2784 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),N)))) # label(fact_1101_mod__less__divisor) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2785 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) | Y_1 = X_1)) # label(fact_621_dvd_Ole__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2786 (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_3405_ln__powr) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2787 (all X_1 all A_2 (A_2 = X_1 <-> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),hAPP(real,real,uminus_uminus(real),A_2)))) # label(fact_2088_real__add__minus__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2788 (all X_a (linordered_semidom(X_a) -> (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N))))))) # label(fact_1283_less__imp__of__nat__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2789 (all R_4 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_4),hAPP(real,real,cos,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,sin,A_1))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2385_sin__cos__squared__add2__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2790 (all N all M hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),N),M) = hAPP(int,quickcheck_code_int,quickcheck_of_int,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N)),hAPP(quickcheck_code_int,int,quickcheck_int_of,M)))) # label(fact_3550_div__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2791 (all M all N hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),xzgcd,M),N) = hAPP(int,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))) # label(fact_3084_xzgcd__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2792 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K)),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),min_1)))) # label(fact_306_rel__simps_I11_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2793 (all X_a (banach(X_a) & real_normed_field(X_a) -> hAPP(X_a,X_a,exp(X_a),zero_zero(X_a)) = one_one(X_a))) # label(fact_2583_exp__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2794 (all B all Bq all Br all A_1 all C all Aq all Ar (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,A_1),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Aq),Ar))) -> (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Bq),Br))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Aq),Bq)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ar),Br)),C)))))))) # label(fact_3097_divmod__nat__rel__add1__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2795 (all A_2 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),A_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),A_2))))) # label(fact_4432_LIMSEQ__le__const2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2796 (all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),M)))) # label(fact_3192_fact__ge__zero__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2797 (all X_a all X_c all X_b (real_normed_vector(X_c) & topological_space(X_b) -> (all F all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,X_2)),X_1)))) -> hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),A_3)),X_1))))))) # label(fact_4926_isCont__setsum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2798 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z),one_one(int)))))) # label(fact_85_zle__add1__eq__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2799 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Z_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),T_5),X_2)))))) # label(fact_2830_minf_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2800 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))) # label(fact_178_semiring__one__add__one__is__two) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2801 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))))))) # label(fact_1870_abs__triangle__ineq2__sym) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2802 (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_2448_even__nat__mod__two__eq__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2803 (all N (N != zero_zero(nat) -> (exists M_2 hAPP(nat,nat,suc,M_2) = N))) # label(fact_1653_not0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2804 (all X_a (number_ring(X_a) -> (all V all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),V),W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_475_number__of__diff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2805 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)))))))) # label(fact_4011_summable__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2806 (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(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),sRStar,P_4))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) # label(fact_1520_SRStar__card) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2807 (all X hAPP(real,real,sin,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)))) # label(fact_2376_sin__periodic) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2808 (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),minus_minus(nat),M),N) = zero_zero(nat))) # label(fact_683_diff__is__0__eq_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2809 (all B_1 all C_1 all A_2 all D_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),D_1) = one_one(int) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B_1),C_1) = one_one(int) -> (hAPP(int,int,abs_abs(int),B_1) = hAPP(int,int,abs_abs(int),A_2) & hAPP(int,int,abs_abs(int),D_1) = hAPP(int,int,abs_abs(int),C_1) <-> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),A_2)),hAPP(int,int,abs_abs(int),C_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),B_1)),hAPP(int,int,abs_abs(int),D_1)))))) # label(fact_4400_coprime__crossproduct__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2810 (all X_a (metric_space(X_a) -> (all X2_1 all Y all X1_1 all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X1_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),X2_1)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3502_dist__triangle__half__r) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2811 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)),Z_1)) # label(fact_3227_gcd__semilattice__nat_Oinf__assoc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2812 (all X all Y all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),X)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,M),Y))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)),M)))) # label(fact_901_StandardRes__prop4) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2813 (all A_1 all B all C all D hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D))) # label(fact_3754_divide__rat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2814 (all A_2 all B_1 hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_2),B_1) = hAPP(fun(int,fun(int,bool)),fun(product_prod(int,int),bool),product_prod_case(int,int,bool),hAPP(fun(int,bool),fun(int,fun(int,bool)),hAPP(fun(int,fun(fun(int,bool),fun(int,bool))),fun(fun(int,bool),fun(int,fun(int,bool))),combc(int,fun(int,bool),fun(int,bool)),hAPP(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool))),hAPP(fun(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool))),fun(fun(int,fun(int,fun(bool,bool))),fun(int,fun(fun(int,bool),fun(int,bool)))),combb(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),int),combs(int,bool,bool)),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool))),hAPP(fun(fun(int,bool),fun(int,fun(bool,bool))),fun(fun(int,fun(int,bool)),fun(int,fun(int,fun(bool,bool)))),combb(fun(int,bool),fun(int,fun(bool,bool)),int),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj)),hAPP(fun(int,fun(int,int)),fun(int,fun(int,bool)),hAPP(fun(fun(int,int),fun(int,bool)),fun(fun(int,fun(int,int)),fun(int,fun(int,bool))),combb(fun(int,int),fun(int,bool),int),hAPP(fun(int,bool),fun(fun(int,int),fun(int,bool)),combb(int,bool,int),hAPP(int,fun(int,bool),fequal(int),A_2))),hAPP(fun(int,int),fun(int,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(int,int),fun(int,fun(int,int))),combb(int,fun(int,int),int),plus_plus(int)),hAPP(int,fun(int,int),times_times(int),B_1)))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),B_1))))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(bool,bool),fun(fun(int,bool),fun(int,bool)),combb(bool,bool,int),hAPP(bool,fun(bool,bool),fimplies,hAPP(bool,bool,fNot,hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),B_1))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int)),zero_zero(int)))))))) # label(fact_4031_divmod__int__rel__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2815 (all X_1 all K (ti(int,X_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K)),one_one(int)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)))) # label(fact_903_zOddI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2816 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1))))) # label(fact_2427_even__difference__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2817 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,arctan,hAPP(real,real,tan,X)) = X))) # label(fact_2279_arctan__tan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2818 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2819 (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(nat,fun(real,complex)),fun(fun(nat,real),fun(nat,complex)),combs(nat,real,complex),hAPP(fun(nat,real),fun(nat,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(nat,real),fun(nat,fun(real,complex))),combb(real,fun(real,complex),nat),complex_1),X_3)),Y_3)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1)),sequentially))))) # label(fact_4513_LIMSEQ__Complex) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2820 (all N all M zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M))) # label(fact_682_diff__add__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2821 (all X_b all X_a all P_1 all Y_1 all X_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_1),X_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1))),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X_1),Y_1)))))) # label(fact_3123_exI__realizer) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2822 (all K_4 -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),zero_zero(int)))) # label(fact_1293_int__less__0__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2823 (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_2586_mult__exp__exp) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2824 (all X_a number_of_frac(X_a) = ti(fun(int,X_a),number_of_frac(X_a))) # label(tsy_c_Nitpick_Onumber__of__frac_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2825 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3699_Rats__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2826 (all X_a (real_normed_vector(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)) & (all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))))) # label(fact_4755_scaleR_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2827 (all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,int,number_number_of(int),V) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1513_int__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2828 (all X_a (linord20386208strict(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_429_mult__less__imp__less__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2829 (all A_2 all C_1 all D_1 all B_1 (ti(int,B_1) != 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_2),B_1)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C_1),D_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C_1),B_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)))))))) # label(fact_3779_less__rat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2830 (all X_a (metric_space(X_a) -> dist_dist(X_a) = ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)))) # label(tsy_c_RealVector_Odist__class_Odist_1_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2831 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_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_4940_min__max_Osup__inf__distrib1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2832 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),one_one(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_1),hAPP(int,int,bit1,pls))))))) # label(fact_59_le__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2833 (all X_a measure(X_a) = ti(fun(fun(X_a,nat),fun(product_prod(X_a,X_a),bool)),measure(X_a))) # label(tsy_c_Wellfounded_Omeasure_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2834 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,ln,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1))))) # label(fact_1975_ln__ge__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2835 (all X_a (number_ring(X_a) & linord1117847801e_zero(X_a) -> (all R_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),R_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1756_half__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2836 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),one_one(X_b))),S) = hAPP(X_a,X_b,B_1,A_2)) & (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),fequal(X_a),A_2))),B_1)),one_one(X_b))),S)))))) # label(fact_3955_setprod__delta_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2837 (all W all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),one_one(int))),Z_1)))) # label(fact_83_zless__imp__add1__zle) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2838 (all M all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_4)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)))) # label(fact_578_add__leD1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2839 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) = 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)) # label(fact_912_zdiv__zadd1__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2840 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),M))) # label(fact_3214_gcd__dvd1__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2841 (all A_2 all Ma all X_1 (ti(int,X_1) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,fun(int,int)),fun(int,fun(int,int)),combc(int,int,int),times_times(int)),X_1)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))))) # label(fact_3932_Bnor__prod__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2842 (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),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)) = 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_2515_inverse__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2843 (all X_a (field(X_a) -> (all N_1 all X_1 (ti(X_a,X_1) != one_one(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),X_1),N_1)),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),one_one(X_a))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))))) # label(fact_4179_geometric__sum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2844 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_3400_real__of__int__floor__ge__diff__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2845 (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))))) -> one_one(int) = ti(int,X) | zero_zero(int) = ti(int,X)))) # label(fact_185_int__pos__lt__two__imp__zero__or__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2846 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> hAPP(real,nat,natceiling,X) = zero_zero(nat))) # label(fact_1899_natceiling__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2847 (all X_a (real_normed_vector(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_1797_norm__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2848 (all R_4 exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2))) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2))) & one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) & hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),Y_2)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_2)) = R_4 -> Y_2 = X_2)) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) = one_one(int) & hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),X_2)),hAPP(product_prod(int,int),int,product_snd(int,int),X_2)) = R_4)) # label(fact_4410_quotient__of__unique) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2849 (all X all Y (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),X)) | ti(int,X) = ti(int,Y) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),Y)))) # label(fact_93_zless__linear) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2850 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all F all L (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),L)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4091_sums__summable) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2851 (all X_a (linordered_idom(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(X_a)))))) # label(fact_10_power2__less__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2852 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> (exists K_1 N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),K_1))))) # label(fact_1491_less__imp__Suc__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2853 (all X_1 (X_1 = hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),X_1)) <-> (exists N_2 X_1 = hAPP(int,real,real_1(int),N_2)))) # label(fact_3341_real__of__int__ceiling__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2854 (all X_a (real_normed_vector(X_a) -> ti(fun(fun(nat,X_a),bool),bseq(X_a)) = bseq(X_a))) # label(tsy_c_SEQ_OBseq_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2855 (all X_1 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_4),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)))) # label(fact_422_zcong__eq__zdvd__prop) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2856 (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_473_zprime__factor__exists) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2857 (all 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)))))) = hAPP(complex,real,norm_norm(complex),Z_1)) # label(fact_3018_cmod__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2858 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N_1)),one_one(real))),hAPP(nat,real,real_1(nat),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)))) # label(fact_2341_nat__less__real__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2859 (all N hAPP(nat,nat,suc,zero_zero(nat)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) # label(fact_1354_power__Suc__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2860 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1))))) # label(fact_2700_real__root__gt__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2861 (all X_a (real_n2089651433ebra_1(X_a) & banach(X_a) -> (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))))) # label(fact_4025_complete__algebra__summable__geometric) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2862 (all N hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,real_1(int),N)) = ti(int,N)) # label(fact_3340_ceiling__real__of__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2863 (all X_a all F all X_1 all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(X_a,int,F,I_2)),X_1) = one_one(int))) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3)),X_1) = one_one(int))) # label(fact_4414_setprod__coprime__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2864 (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_2746_complex__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2865 (all R_4 all S_3 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,number_number_of(real),R_4)),hAPP(int,real,number_number_of(real),S_3)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(int,rat,number_number_of(rat),R_4)),hAPP(int,rat,number_number_of(rat),S_3)))) # label(fact_3734_Ratreal__number__of__quotient2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2866 (all X_a ti(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),nat_case(X_a)) = nat_case(X_a)) # label(tsy_c_Nat_Onat_Onat__case_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2867 (all X_a (order(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))))))) # label(fact_4524_atLeastatMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2868 (all N_1 hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) # label(fact_4317_atLeast0LessThan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2869 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> (B != A_1 -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B))))) # label(fact_629_dvd_Ole__neq__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2870 (all X_a all X_b (order(X_b) & order(X_a) -> (all F all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,B_1)),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_2),Y_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,F,Y_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,A_2)),C_1)))))))) # label(fact_2832_order__less__le__subst2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2871 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),hAPP(X_a,X_a,uminus_uminus(X_a),X))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,uminus_uminus(X_a),Y))))))) # label(fact_2958_compl__le__swap1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2872 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),zero_zero(int))) -> zero_zero(int) = hAPP(int,int,fact_fact(int),M))) # label(fact_3188_fact__neg__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2873 (all Y all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (-hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1261_Parity_Oodd__plus__odd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2874 (all N all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)))))) # label(fact_4368_gcd__greatest__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2875 (all X_a (dist_norm(X_a) -> (all X all Y hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)))) # label(fact_3503_dist__norm) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2876 (all X_b all X_a (topological_space(X_a) & topological_space(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),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)))))) # label(fact_4880_isCont__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2877 (all X_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_4),X_1)))),hAPP(int,fun(int,bool),sRStar,P_4)))))))) # label(fact_1073_SRStar__mult__prop2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2878 (all X_a (group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1) = zero_zero(X_a)))) # label(fact_2067_left__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2879 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3))))) # label(fact_3849_Im_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2880 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all 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)) = 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_1666_power__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2881 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)) = ti(X_a,X)))) # label(fact_4941_min__max_Oinf__sup__absorb) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2882 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)))))) # label(fact_4454_tendsto__norm__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2883 (all X_a all X_b all A_1 all B hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_1),B)) = ti(X_a,A_1)) # label(fact_3140_fst__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2884 (all A_2 all B_1 (A_2 = B_1 <-> hAPP(rat,product_prod(int,int),quotient_of,B_1) = hAPP(rat,product_prod(int,int),quotient_of,A_2))) # label(fact_3721_quotient__of__inject__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2885 (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_3016_complex__mult__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2886 (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_2110_abs__real__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2887 (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_3448_zgcd__zmult__distrib2__abs) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2888 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_146_number__of__Pls) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2889 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),A_1)))))) # label(fact_3320_ln__powr__bound) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2890 (all Z_1 zero_zero(real) = hAPP(complex,real,im,hAPP(int,complex,ring_1_of_int(complex),Z_1))) # label(fact_3563_complex__Im__of__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2891 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zOdd))))) # label(fact_1369_odd__minus__even) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2892 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),C))))) # label(fact_948_mod__mod__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2893 (all X_a (linordered_idom(X_a) -> (all K_4 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_4),hAPP(X_a,X_a,sgn_sgn(X_a),K_4)) = hAPP(X_a,X_a,abs_abs(X_a),K_4)))) # label(fact_2214_abs__sgn) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2894 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_4845_Nat__Transfer_Otransfer__int__nat__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2895 (all A_2 all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),A_2)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),B_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1))))) # label(fact_3352_powr__less__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2896 (all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),N)) -> 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)) = I_1)) # label(fact_672_diff__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2897 (all B all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> ti(int,A_1) = ti(int,B))))))) # label(fact_453_zcong__zless__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2898 (all X_a (field(X_a) -> (all X_1 all W_1 all Z all Y_1 (ti(X_a,Y_1) != 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),inverse_divide(X_a),X_1),Y_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),W_1),Z) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),Z) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),W_1),Y_1))))))) # label(fact_1691_frac__eq__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2899 (all X_a all A_2 all F all V_1 all N_1 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),N_1)),hAPP(nat,X_a,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1)))) # label(fact_4108_nat__case__add__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2900 (all X_a (number_ring(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_140_mult__2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2901 (all X_a all X_b (ordere779506340up_add(X_b) & comm_monoid_add(X_b) -> (all F all G all K_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),K_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,I_2)),hAPP(X_a,X_b,G,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),K_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),K_3))))))) # label(fact_4343_setsum__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2902 (all X all A_1 zero_zero(real) != hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) # label(fact_3322_powr__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2903 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),F),A_3) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),hAPP(fun(int,nat),fun(int,X_a),hAPP(fun(nat,X_a),fun(fun(int,nat),fun(int,X_a)),combb(nat,X_a,int),F),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3))))) # label(fact_3944_transfer__nat__int__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.76 2904 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),zero_zero(real))) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_2),one_one(int))))))))) # label(fact_3423_reals__Archimedean__6c__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2905 (all X_b all X_a (real_normed_field(X_b) & topological_space(X_a) -> (all Y_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),L),Y_1)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4563_divide_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2906 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N_1))))) # label(fact_2335_real__of__nat__gt__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2907 (all X_a (real_normed_vector(X_a) -> (all X_3 all K_3 ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_3))) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3500_BseqI_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2908 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,abs_abs(int),K_4)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N))) # label(fact_4380_gcd__mult__distrib__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2909 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2131_arcsin__lbound) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2910 (all X_a (real_normed_vector(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),zero_zero(X_a))))) # label(fact_4703_scaleR_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2911 (all A_3 all X_1 (hBOOL(hAPP(int,bool,nat_is_nat,X_1)) -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),hAPP(int,nat,nat_1,X_1)),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)))))) # label(fact_4859_transfer__int__nat__set__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2912 (all X_3 ((all J_1 exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,X_3,M_2)),hAPP(nat,real,X_3,N_2)))),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,J_1))))))))) <-> hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)))) # label(fact_3314_Cauchy__iff2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2913 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all G all M_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),L_2),M_1)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4548_LIM__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2914 (all X_a (group_add(X_a) -> (all A_1 zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_1)))) # label(fact_795_diff__self) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2915 (all N zero_zero(real) = 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))) # label(fact_2333_sin__2npi) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2916 (all X_a (ordere142940540dd_abs(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,abs_abs(X_a),zero_zero(X_a)))) # label(fact_1851_abs__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2917 (all X_a (real_normed_vector(X_a) -> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),zero_zero(X_a)))) # label(fact_2201_sgn__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2918 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_4),B_4))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_4),zero_zero(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_1179_negDivAlg_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2919 (all I all K all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),J)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J))))) # label(fact_694_le__diff__conv2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2920 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),zero_zero(X_a))))) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2921 (all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_2),B_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,B_1),A_2)))) # label(fact_2855_coprime__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2922 (all X_a all X_b all X_c (topological_space(X_c) & topological_space(X_a) & topological_space(X_b) -> (all F all A_2 all G all L (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),hAPP(X_a,X_b,G,L)),hAPP(X_a,filter(X_a),at(X_a),L))) -> (hBOOL(hAPP(filter(X_c),bool,hAPP(X_a,fun(filter(X_c),bool),hAPP(fun(X_c,X_a),fun(X_a,fun(filter(X_c),bool)),tendsto(X_c,X_a),F),L),hAPP(X_c,filter(X_c),at(X_c),A_2))) -> hBOOL(hAPP(filter(X_c),bool,hAPP(X_b,fun(filter(X_c),bool),hAPP(fun(X_c,X_b),fun(X_b,fun(filter(X_c),bool)),tendsto(X_c,X_b),hAPP(fun(X_c,X_a),fun(X_c,X_b),hAPP(fun(X_a,X_b),fun(fun(X_c,X_a),fun(X_c,X_b)),combb(X_a,X_b,X_c),G),F)),hAPP(X_a,X_b,G,L)),hAPP(X_c,filter(X_c),at(X_c),A_2)))))))) # label(fact_4558_LIM__compose) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2923 (all X hAPP(complex,real,im,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2980_Im_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2924 (all I_1 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))) # label(fact_533_power__dvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2925 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),Y_1)),zEven))))) # label(fact_1271_EvenOdd_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2926 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X all Y hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y))))) # label(fact_2589_exp__diff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2927 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),exp(X_a)),X_1),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_2632_DERIV__exp) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2928 (all K all L ((exists N_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_2) = L) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),L)))) # label(fact_1799_le__Suc__ex__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2929 (all A_2 all B_1 all C_1 all X_1 (hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C_1),hAPP(int,nat,nat_1,X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),B_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(int,nat,nat_1,X_1))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1) = one_one(int) -> (exists K_1 ti(int,A_2) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),K_1),hAPP(int,nat,nat_1,X_1)))))))) # label(fact_3474_int__relprime__odd__power__divisors) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2930 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))) # label(fact_2074_diff__minus__eq__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2931 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2932 (all X_a (division_ring(X_a) -> inverse_divide(X_a) = ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)))) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2933 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (A_1 != one_one(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,A_1),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_1),X)))))) # label(fact_2650_log__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2934 (all X_a all X_b prod(X_a,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))) # label(tsy_c_Nitpick_Oprod_res) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2935 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2147_zdiv__zminus2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2936 (all N_1 all X_1 exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,sin,X_1))) # label(fact_4241_Maclaurin__sin__expansion2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2937 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),hAPP(nat,nat,suc,N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) | hAPP(nat,nat,suc,N_1) = Ma)) # label(fact_1245_le__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2938 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3109_div__pos__pos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2939 (all X_a (real_algebra_1(X_a) & real_normed_vector(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_2794_of__real_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2940 (all N_1 all X_1 ((hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1))),X_1))) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hAPP(real,real,uminus_uminus(real),hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1))),hAPP(real,real,uminus_uminus(real),X_1))))) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> zero_zero(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1))))) # label(fact_4136_root__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2941 (all Ma all X_2 all Xa (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_2),Xa),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcongm,Ma),X_2),Xa)))) # label(fact_4872_zcongm__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2942 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))))) # label(fact_2459_even__num__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2943 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya)))) # label(fact_1664_divide_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2944 (all X_a (real_vector(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),Y)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_4718_scaleR__right_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2945 (all 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))) = hAPP(code_code_numeral,nat,size_size(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2))) # label(fact_2969_code__numeral_Osize_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2946 (all P_4 hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,P_4),hAPP(int,fun(int,bool),sRStar,P_4)))) # label(fact_2917_ResSet__SRStar__prop) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2947 (all X_a (real_div_algebra(X_a) -> (all X all A_1 (A_1 != zero_zero(real) -> (ti(X_a,X) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))))) # label(fact_4743_nonzero__inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2948 (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)))) # label(fact_24_zle__linear) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2949 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4592_LIM__rabs__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2950 (all P all Q (hBOOL(Q) | -hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fconj,P),Q)))) # label(help_fconj_3_1_U) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2951 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N)) -> hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))),hAPP(int,int,fact_fact(int),N)))) # label(fact_3201_fact__plus__one__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2952 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4008_divide_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2953 (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_2085_dvd__neg__div) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2954 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),K))))) # label(fact_3802_finite__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2955 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)))) # label(fact_3112_div__neg__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2956 (all Y_1 hAPP(real,real,arcsin,Y_1) = hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),sin)),Y_1))))) # label(fact_4133_arcsin__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2957 (all X_a (comm_monoid_mult(X_a) & comm_monoid_add(X_a) -> (all F all G all A_3 all B_2 (A_3 = B_2 -> (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B_2)) -> ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hAPP(int,X_a,F,X_2) = hAPP(int,X_a,G,X_2))) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),G),B_2) = hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co1399186613setsum(int,X_a),F),A_3))))))) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2958 (all X_a (real_n1866405975lgebra(X_a) -> (all A_2 (ti(X_a,A_2) != zero_zero(X_a) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),inverse_inverse(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4547_LIM__inverse__fun) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2959 (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_4722_scaleR_Oprod__diff__prod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2960 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3693_Rats__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2961 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),one_one(int))),zEven)))) # label(fact_1400_odd__minus__one__even) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2962 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arcsin),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))))) # label(fact_2656_DERIV__arcsin) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2963 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),K)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),min_1),hAPP(int,int,bit1,K))))) # label(fact_295_rel__simps_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2964 (all P_1 all K all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I)) -> (hBOOL(hAPP(int,bool,P_1,K)) -> ((all I_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),I_2)) -> (hBOOL(hAPP(int,bool,P_1,I_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),I_2),one_one(int))))))) -> hBOOL(hAPP(int,bool,P_1,I)))))) # label(fact_834_int__ge__induct) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2965 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),zero_zero(X_a))))))) # label(fact_3603_of__int__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2966 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),P_5)))) # label(fact_3051_prime__g__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2967 (all X all Y ((zero_zero(nat) = Y -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) & (zero_zero(nat) != Y -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)))) # label(fact_3275_gcd__nat_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2968 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)),I_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),I_1)),K_4))) # label(fact_689_diff__add__assoc2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2969 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),zero_zero(X_a)))))) # label(fact_1863_abs__not__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2970 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (((exists X_2 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3))) -> one_one(nat) = zero_zero(nat)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)))) # label(fact_1830_card_Oneutral) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2971 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3876_bdd__int__set__l__l__finite) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2972 (all X_1 (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1274_not__odd__impl__even) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2973 (all X_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),X_1))))) # label(fact_3827_bdd__nat__set__le__finite) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2974 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,int,uminus_uminus(int),B_1))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),zero_zero(int))) -> (-(ti(int,A_2) = zero_zero(int) | ti(int,B_1) = zero_zero(int)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_2),B_1))),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B_1),hAPP(int,int,hAPP(int,fun(int,int),int_gcd,A_2),B_1)))) & (zero_zero(int) = ti(int,B_1) | zero_zero(int) = ti(int,A_2) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_2),B_1))))) # label(fact_3919_norm__frac_Opsimps) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2975 (all X_a (linordered_idom(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),A_1)),hAPP(X_a,X_a,sgn_sgn(X_a),B)) = hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2205_sgn__times) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2976 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,Y)),hAPP(real,real,tan,X))))))) # label(fact_2272_tan__monotone) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2977 (all Z all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3706_SupInf_OSup__upper) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2978 (all X_1 all Y_1 all F ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real)))) -> hAPP(real,real,F,X_1) = hAPP(real,real,F,Y_1))) # label(fact_2731_DERIV__isconst__all) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2979 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_2106_real__0__le__add__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2980 (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]. 10.71/10.77 2981 (all N all A_1 all B (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)),B))) # label(fact_3449_zgcd__1__power__left__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2982 (all X_a (number_ring(X_a) -> -hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_2621_not__iszero__Numeral1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2983 (all X_a (power(X_a) -> power_power(X_a) = hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),hAPP(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),power_1(X_a),one_one(X_a)),times_times(X_a)))) # label(fact_2838_power__power__power) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2984 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3611_le__ceiling__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2985 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),Y_1)),sequentially)))))) # label(fact_4478_mult__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2986 (all M all K_4 all N (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K_4),N) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_4391_coprime__dvd__mult__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2987 (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) -> Ys != Xs)) # label(fact_3557_neq__if__length__neq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2988 (all X all Y all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),Z_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Z_1))) # label(fact_3225_gcd__semilattice__nat_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2989 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),Z_1)) # label(fact_66_zmult__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2990 (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_4022_summable__cos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2991 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),one_one(nat)) = ti(X_a,A_1)))) # label(fact_351_power__one__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2992 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_1568_order__less__imp__not__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2993 (all X_a (field_inverse_zero(X_a) -> (all X_1 (ti(X_a,X_1) = one_one(X_a) <-> one_one(X_a) = hAPP(X_a,X_a,inverse_inverse(X_a),X_1))))) # label(fact_2517_inverse__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2994 (all X_a (division_ring(X_a) -> (all A_1 all B all C (ti(X_a,C) != zero_zero(X_a) -> (ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C) -> ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))) # label(fact_1693_eq__divide__imp) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2995 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_386_mult__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2996 (all N_1 all Ma hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N_1)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),ord_max(nat),N_1))),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N_1)),Ma)) # label(fact_4954_max__Suc1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2997 (all Z_4 all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4)))) # label(fact_1139_nat__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2998 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))))) # label(fact_4939_min__max_Oinf__sup__distrib1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 2999 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real)))))) # label(fact_2701_real__root__lt__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3000 (all X_a all X_b (real_normed_field(X_b) -> (all F all X_1 all F_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(X_a,fun(X_b,X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_a,fun(X_b,X_b)),combc(X_b,X_a,X_b),F),N_2)),X_1),hAPP(X_a,X_b,hAPP(X_b,fun(X_a,X_b),F_2,X_1),N_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),hAPP(fun(X_b,X_b),fun(X_b,fun(X_b,bool)),deriv(X_b),hAPP(fun(X_a,bool),fun(X_b,X_b),hAPP(fun(X_b,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(X_b,X_b)),combc(X_b,fun(X_a,bool),X_b),hAPP(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(X_b,fun(X_a,X_b)),fun(X_b,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),X_b),big_co1399186613setsum(X_a,X_b)),F)),S)),X_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),F_2,X_1)),S)))))))) # label(fact_4304_DERIV__setsum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3001 (all X_a (real_n2089651433ebra_1(X_a) -> (all Z_1 hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),Z_1)) = hAPP(X_a,real,norm_norm(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3575_norm__of__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3002 (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) -> (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_6),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) = B -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_6),B_5) = one_one(nat))))) # label(fact_3286_gcd__coprime__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3003 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,L)),U_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_gr676655987ssThan(nat),L),U_1)) # label(fact_4222_atLeastSucLessThan__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3004 (all W_1 all Ma (Ma = hAPP(int,nat,nat_1,W_1) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> Ma = zero_zero(nat)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> hAPP(nat,int,semiring_1_of_nat(int),Ma) = ti(int,W_1)))) # label(fact_1407_nat__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3005 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),hAPP(X_a,X_a,F,X_1)),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),G),F)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),E_3),D_2)))))))) # label(fact_3862_DERIV__chain_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3006 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B)) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3028_cis__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3007 (all X_a (order(X_a) -> (all N_1 all N_7 all F ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_2)),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2))))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),N_7)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,N_1)),hAPP(nat,X_a,F,N_7)))))))) # label(fact_1495_lift__Suc__mono__le) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3008 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4593_LIM__rabs__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3009 (all N -hBOOL(hAPP(int,bool,nat_neg,hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_1501_not__neg__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3010 (all X_a (comm_semiring_1(X_a) -> (all B all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))) # label(fact_335_dvd__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3011 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_556_nat__add__left__cancel__less) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3012 (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,number_number_of(int),K)),hAPP(int,int,number_number_of(int),L))))) # label(fact_64_less__number__of__int__code) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3013 (all X_a (linordered_idom(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),Y)),X))))) # label(fact_1879_abs__mult__pos) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3014 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1)),zero_zero(X_a)))))))) # label(fact_392_mult__pos__neg2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3015 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1702_divide__nonneg__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3016 (all X_a all D_2 all B_2 all A_3 all C_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),C_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),D_2),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),C_2),D_2)))))) # label(fact_1996_Diff__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3017 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),Z_1) = ti(int,Z_1)) # label(fact_135_zadd__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3018 (all X_a (number_ring(X_a) -> (all V hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V)),one_one(X_a))))) # label(fact_2184_diff__special_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3019 (all X_a (real_vector(X_a) -> (all A_2 all X_1 (zero_zero(X_a) = ti(X_a,X_1) | A_2 = zero_zero(real) <-> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1) = zero_zero(X_a))))) # label(fact_4708_scaleR__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3020 (all X_a all A_3 hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),one_one(nat))),A_3) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)) # label(fact_4255_card__eq__setsum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3021 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),L_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),L_4))))) # label(fact_671_diff__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3022 (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]. 10.71/10.77 3023 (all L all U_1 hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int))),U_1) = hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1)) # label(fact_4261_atLeastPlusOneLessThan__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3024 (all X_a all F all G all Ma all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co1399186613setsum(X_a,int),G),S)),Ma)))) # label(fact_4333_setsum__same__function__zcong) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3025 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,monoseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3924_monoseq__realpow) # label(axiom) # label(non_clause). [assumption]. 10.71/10.77 3026 (all X_3 ((all R_2 exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_2),hAPP(nat,real,X_3,N_2))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),X_3)),zero_zero(real)),sequentially)))) # label(fact_4660_LIMSEQ__inverse__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3027 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)))))) # label(fact_1824_psubset__card__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3028 (all X_a (linord1117847801e_zero(X_a) -> (all B_1 all C_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1736_divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3029 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all G all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),B_2))))))))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3030 (all N zero_zero(real) = hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),N)))) # label(fact_2296_sin__npi2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3031 (all X_1 all N_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),N_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),hAPP(int,nat,number_number_of(nat),N_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,number_number_of(real),N_1))))))) # label(fact_1913_natceiling__le__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3032 (all J all K all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K)),I)))) # label(fact_698_le__diff__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3033 (all Ma all N_1 (N_1 = one_one(nat) & Ma = one_one(nat) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1) = one_one(nat))) # label(fact_588_nat__1__eq__mult__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3034 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N))) # label(fact_530_le__refl) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3035 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))))) # label(fact_334_dvd__mult2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3036 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)) = hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),X)))) # label(fact_2683_real__root__mult__exp) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3037 (all R_4 all Q_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),Q_3)))))) # label(fact_189_self__quotient__aux1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3038 (all X_a (linord581940658strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_387_mult__neg__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3039 (all L_4 hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),hAPP(int,int,bit0,L_4))) # label(fact_511_diff__bin__simps_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3040 (all B hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),B) = zero_zero(int)) # label(fact_953_zmod__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3041 (all X_a (semiring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B_5)),C)))))) # label(fact_934_mod__mult__cong) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3042 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),A_6)),B)))) # label(fact_885_mult_Odiff__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3043 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real)))))) # label(fact_1966_ln__le__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3044 (all X_a (order(X_a) -> (all A_1 all B (ti(X_a,B) != ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_1591_order__neq__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3045 (all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y)))) # label(fact_2126_arctan__lbound) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3046 (all L_4 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit1,L_4)) = hAPP(int,int,bit1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),min_1),L_4))) # label(fact_510_diff__bin__simps_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3047 (all B_1 all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),A_2)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))))) # label(fact_843_wset__mem) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3048 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),B) = zero_zero(X_a)))) # label(fact_974_mod__mult__self2__is__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3049 (all X_a all X_b all 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) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),P_4)) # label(fact_4004_fst__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3050 (all X_a (ordere779506340up_add(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D)))))))) # label(fact_781_add__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3051 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) # label(fact_531_nat__mult__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3052 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),pls)))) # label(fact_154_rel__simps_I12_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3053 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),N)) # label(fact_587_nat__mult__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3054 (all N_1 all Ma (zero_zero(int) != ti(int,Ma) -> (one_one(int) = hAPP(int,int,abs_abs(int),N_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1)),Ma))))) # label(fact_1969_zdvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3055 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),negDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int)))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_1))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),B_1)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_2),B_1))))) # label(fact_1174_negDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3056 (all Ma (one_one(int) = hAPP(int,int,abs_abs(int),Ma) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,zero_zero(int)),Ma))) # label(fact_3464_zgcd__0__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3057 (all X_a (dense_linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))) <-> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2))))))) # label(fact_4528_atLeastLessThan__subseteq__atLeastAtMost__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3058 (all X_a (linordered_field(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1683_divide__strict__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3059 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),of_real(X_a)),X_3)),hAPP(real,X_a,of_real(X_a),A_2))))))) # label(fact_4084_of__real_Osums) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3060 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)))) # label(fact_1416_div__geq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3061 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X)),hAPP(real,real,exp(real),X))))) # label(fact_2618_exp__ge__add__one__self__aux) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3062 (all X_a (real_algebra_1(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(real,X_a,of_real(X_a),X)) = hAPP(real,X_a,of_real(X_a),hAPP(real,real,uminus_uminus(real),X))))) # label(fact_2795_of__real__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3063 (all K_4 hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,number_number_of(rat),K_4)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3730_quotient__of__number_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3064 (all A_2 all B_1 all W_1 (hAPP(int,complex,number_number_of(complex),W_1) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) <-> A_2 = hAPP(int,real,number_number_of(real),W_1) & B_1 = zero_zero(real))) # label(fact_2742_Complex__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3065 (all M all N all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M)))))) # label(fact_3472_zrelprime__zdvd__zmult__aux) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3066 (all X_a (linord1117847801e_zero(X_a) & number_ring(X_a) -> (all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),R_4)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),R_4),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_1757_half__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3067 (all X_b all X_a (real_vector(X_a) -> (all G all A_3 all X_1 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),hAPP(fun(X_b,fun(X_a,X_a)),fun(X_a,fun(X_b,X_a)),combc(X_b,X_a,X_a),hAPP(fun(X_b,real),fun(X_b,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(X_b,real),fun(X_b,fun(X_a,X_a))),combb(real,fun(X_a,X_a),X_b),scaleR_scaleR(X_a)),G)),X_1)),A_3) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_3)),X_1)))) # label(fact_4731_scaleR__left_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3068 (all K all L hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),hAPP(int,bool,hAPP(int,fun(int,bool),fequal(int),L),zero_zero(int))),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),L),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,abs_abs(int),K)),hAPP(int,int,abs_abs(int),L))))) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),K),L)) # label(fact_4401_gcd__code__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3069 (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_4963_max__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3070 (all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,V)) = hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,suc,hAPP(int,nat,number_number_of(nat),V)) = one_one(nat)))) # label(fact_1537_Suc__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3071 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),one_one(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))))))) # label(fact_3302_ceiling__le__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3072 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),Z)))))) # label(fact_3609_floor__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3073 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sin,X)),one_one(real)))) # label(fact_2300_sin__le__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3074 (all N all K_4 all M (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),M) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)),M)))) # label(fact_3431_zgcd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3075 (all U_1 all Ma all N_1 all I all J (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I),J)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma) <-> Ma = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),I)),U_1)),N_1)))) # label(fact_749_nat__eq__add__iff2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3076 (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_1728_divide__diff__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3077 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2244_cos__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3078 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_2),Ma)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B_1),Ma)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_960_zcong__zmod) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3079 (all X_b all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,real),fun(X_b,X_a),hAPP(fun(real,X_a),fun(fun(X_b,real),fun(X_b,X_a)),combb(real,X_a,X_b),of_real(X_a)),G)),A_3) = hAPP(real,X_a,of_real(X_a),hAPP(fun(X_b,bool),real,hAPP(fun(X_b,real),fun(fun(X_b,bool),real),big_co1399186613setsum(X_b,real),G),A_3))))) # label(fact_4189_of__real_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3080 (all X all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B) = one_one(nat) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B)) -> X = one_one(nat))))) # label(fact_3264_coprime__common__divisor__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3081 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4591_LIM__norm) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3082 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2884_one__le__floor) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3083 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N))))) # label(fact_1444_le__div__geq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3084 (all P_1 all Ma all N_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),Ma),N_1))) <-> (exists Q_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),hAPP(nat,nat,suc,Q_4)))) & hBOOL(hAPP(nat,bool,P_1,Q_4)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Q_4)),Ma)))) | zero_zero(nat) = N_1 & hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))) # label(fact_1443_split__div_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3085 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)) # label(fact_1428_add__2__eq__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3086 (all Z_1 ti(int,Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),zero_zero(int))) # label(fact_134_zadd__0__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3087 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))),B)))) # label(fact_977_mod__mult__self1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3088 (all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> X = Y | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)))) # label(fact_628_dvd_Ole__imp__less__or__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3089 (all X_a all X_b (ordere216010020id_add(X_b) -> (all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> ((all B_4 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_4),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),B_2),A_3))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,B_4))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),B_2))))))))) # label(fact_4293_setsum__mono2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3090 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(real,nat,natfloor,A_1)),hAPP(real,nat,natfloor,B))),hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_1905_le__mult__natfloor) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3091 (all X_a (linord581940658strict(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1)))))))) # label(fact_435_mult__le__cancel__left__neg) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3092 (all I all J all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I),K)),J)))) # label(fact_686_less__diff__conv) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3093 (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_1286_of__nat__add) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3094 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),min_1) = hAPP(int,int,pred,K_4)) # label(fact_2907_add__Min__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3095 (all K_4 all L_4 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),K_4)),L_4) != zero_zero(int) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))) # label(fact_2158_zmod__zminus1__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3096 (all X_a (real_normed_vector(X_a) & real_algebra_1(X_a) -> (exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))))) # label(fact_2822_of__real_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3097 (all X_1 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))) = hAPP(real,real,sin,X_1)) # label(fact_3970_sin__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3098 (all X_a (linorder(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),A_2),B_1) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),C_1),D_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),D_1)) -> ti(X_a,C_1) = ti(X_a,A_2))))))) # label(fact_4196_atLeastLessThan__inj_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3099 (all X_a (comm_monoid_add(X_a) & comm_monoid_mult(X_a) -> (all F all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> hAPP(fun(int,bool),X_a,hAPP(fun(int,X_a),fun(fun(int,bool),X_a),big_co302546470etprod(int,X_a),F),A_3) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co302546470etprod(nat,X_a),hAPP(fun(nat,int),fun(nat,X_a),hAPP(fun(int,X_a),fun(fun(nat,int),fun(nat,X_a)),combb(int,X_a,nat),F),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A_3)))))) # label(fact_3945_transfer__int__nat__sum__prod_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3100 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),N))) # label(fact_3213_gcd__dvd2__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3101 (all X_a (semiring_1(X_a) -> (all M hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,M)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),M))))) # label(fact_1218_of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3102 (all N all D (zero_zero(int) != ti(int,D) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),N)) -> hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N),D)) = 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))))) # label(fact_3395_real__of__int__div) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3103 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,X))))) # label(fact_1629_real__sqrt__ge__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3104 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1916_abs__ln__one__plus__x__minus__x__bound) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3105 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),A_2))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),B_1))) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),A_2))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),B_1)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),A_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_1))))))) # label(fact_4621_Cauchy__product) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3106 (all X_a (ab_sem1668676832m_mult(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_2952_mult__left__idem) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3107 (all X hAPP(int,int,abs_abs(int),X) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),X)) # label(fact_4372_gcd__idem__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3108 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),Z)))))) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3109 (all X_a (semiring_char_0(X_a) -> (all N zero_zero(X_a) != hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2486_of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3110 (all X all Y hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,abs_abs(int),X)),Y)) # label(fact_4375_gcd__abs1__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3111 (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_3216_coprime__exp2__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3112 (all X_a (number_ring(X_a) -> (all K_4 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),K_4)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,succ,K_4))))) # label(fact_1531_number__of__succ) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3113 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3909_DERIV__sin__realpow2a) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3114 (all M all V hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),hAPP(int,nat,number_number_of(nat),V)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),hAPP(int,nat,number_number_of(nat),V))) # label(fact_1436_Suc__div__eq__add3__div__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3115 (all X_a (linordered_semidom(X_a) -> (all N all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),N))))))))) # label(fact_276_power__strict__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3116 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a))))))))) # label(fact_1730_less__half__sum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3117 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))))))) # label(fact_3298_ceiling__le__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3118 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),A_2)) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),A_2))))))) # label(fact_3921_monoseq__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3119 (all Ma all K all N_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K),N_1) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1)))))) # label(fact_3289_coprime__dvd__mult__iff__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3120 (all X_b all X_a (topological_space(X_b) & topological_space(X_a) -> (all K all X_1 hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),K),hAPP(X_a,filter(X_a),at(X_a),X_1)))))) # label(fact_4561_LIM__const) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3121 (all X_1 all Y_1 (X_1 = Y_1 <-> hAPP(real,real,exp(real),Y_1) = hAPP(real,real,exp(real),X_1))) # label(fact_2524_exp__inj__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3122 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3123 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),X)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),X)))) # label(fact_3392_lemma__floor2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3124 (all X_a (ordered_semiring(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_367_mult__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3125 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2541_inverse__positive__iff__positive) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3126 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(real,nat,natceiling,X_1)),one_one(nat))))) # label(fact_1903_natceiling__le__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3127 (all X_a (comm_monoid_add(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),A_1)))) # label(fact_777_add__0) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3128 (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),one_one(X_a)) = zero_zero(X_a)))) # label(fact_975_mod__by__1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3129 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1331_Suc__le__lessD) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3130 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y)) -> (exists X_2 (Y = hAPP(real,real,exp(real),X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Y),one_one(real)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))))) # label(fact_2628_lemma__exp__total) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3131 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),legendre,A_1),P_5)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5))))) # label(fact_1166_Euler__Criterion) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3132 (all X_a (linord219039673up_add(X_a) -> (all A_2 (ti(X_a,A_2) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2))))) # label(fact_776_double__zero__sym) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3133 (all M all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),M),one_one(int))),K_4))))))) # label(fact_3200_fact__less__mono__int__aux) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3134 (all U_1 all Ma all N_1 all J all I (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J),I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I),U_1)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J),U_1)),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I),J)),U_1)),Ma)),N_1))))) # label(fact_754_nat__le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3135 (all X_a (no_zero_divisors(X_a) -> (all B all A_1 (zero_zero(X_a) != ti(X_a,A_1) -> (zero_zero(X_a) != ti(X_a,B) -> 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_320_no__zero__divisors) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3136 (all X_a all X_b (real_normed_field(X_b) -> (all G all B_1 all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),B_1),A_3)) -> (ti(X_b,B_1) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),F)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_2),B_1)),A_3)))))))) # label(fact_4452_tendsto__divide) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3137 (all Y (Y != zero_zero(real) -> zero_zero(real) = hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))))) # label(fact_2756_cos__arg__i__mult__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3138 (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]. 10.71/10.78 3139 (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)))) -> hAPP(real,int,archim2085082626_floor(real),X) = ti(int,N)))) # label(fact_3412_floor__eq2) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3140 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastLessThan(real),Y_1),X_1)) = X_1)) # label(fact_4244_Sup__atLeastLessThan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3141 (all X_a (number_ring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),min_1)) = hAPP(X_a,X_a,uminus_uminus(X_a),Z_1)))) # label(fact_2102_mult__minus1__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3142 (all M (hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | 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))) # label(fact_1169_mod__exhaust__less__4) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3143 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),C_1),D_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))))))) # label(fact_797_diff__eq__diff__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3144 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_1),X_1)) -> X_1 = hAPP(fun(real,bool),real,complete_Sup_Sup(real),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),Y_1),X_1)))) # label(fact_3704_Sup__greaterThanLessThan) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3145 (all X_a (ordered_ab_group_add(X_a) -> (all X_1 all Y_1 hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1)),hAPP(X_a,X_a,uminus_uminus(X_a),X_1)) = hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,X_a),fun(fun(X_a,bool),fun(X_a,bool)),image(X_a,X_a),uminus_uminus(X_a)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),X_1),Y_1))))) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3146 (all X_a (linord581940658strict(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) != ti(X_a,X_1) | zero_zero(X_a) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y_1),Y_1)))))))) # label(fact_108_sum__squares__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3147 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,real_1(int),N_1))))) # label(fact_3385_real__of__int__ge__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3148 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),A_2))))))) # label(fact_4909_isCont__mult) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3149 (all X_a all X_b (ord(X_b) -> (all F all G ((all X_2 hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2)))) -> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)))))) # label(fact_1655_le__funI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3150 (all N all M ((zero_zero(nat) = M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N) = N) & (M != zero_zero(nat) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)))) # label(fact_1415_add__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3151 (all Y_1 hAPP(fun(real,bool),real,the(real),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)))),hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,fun(bool,bool)),fun(fun(real,bool),fun(real,bool)),combs(real,bool,bool),hAPP(fun(real,bool),fun(real,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(real,bool),fun(real,fun(bool,bool))),combb(bool,fun(bool,bool),real),fconj),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real)),pi))),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),cos)),Y_1)))) = hAPP(real,real,arccos,Y_1)) # label(fact_4137_arccos__def) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3152 (all N_1 hAPP(nat,nat,fact_fact(nat),N_1) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),combi(nat)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),one_one(nat)),N_1))) # label(fact_4541_fact__altdef__nat) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3153 (all X_a (number_ring(X_a) -> (all X_1 (one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),X_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit1,pls)))))))))) # label(fact_2503_eq__special_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.78 3154 (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_2033_minus__mult__minus) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3155 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2681_real__root__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3156 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C)))) # label(fact_936_zmod__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3157 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2)))))) # label(fact_1816_card__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3158 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit0,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K1),K2)))) # label(fact_127_less__int__code_I13_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3159 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,M)),N)))) # label(fact_1333_Suc__leI) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3160 (all X_a (comm_semiring_1(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),zero_zero(X_a)))))) # label(fact_282_dvd__0__right) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3161 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),N) = hAPP(nat,nat,suc,N)) # label(fact_1344_Suc__eq__plus1__left) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3162 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_2) <-> hBOOL(P_1))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_1)) <-> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(P_2))))) # label(fact_546_imp__le__cong) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3163 (all N all D all A_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),N)) = one_one(int))) # label(fact_4359_coprime__exp__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3164 (all X_a (linordered_field(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)))))) # label(fact_2559_nonzero__abs__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3165 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),hAPP(real,real,exp(real),Y))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)))) # label(fact_2513_exp__less__cancel) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3166 (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),times_times(X_a),A_1),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = one_one(X_a))))) # label(fact_2579_right__inverse) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3167 (all X_a (ordered_semiring(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_368_mult__mono_H) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3168 (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_522_nat__add__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3169 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Y),X)) -> hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,abs_abs(int),X)),hAPP(int,int,abs_abs(int),Y)))) # label(fact_1936_abs__div) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3170 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),zero_zero(rat))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),zero_zero(int)))))) # label(fact_3782_Fract__less__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3171 (all N_1 all V_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_3894_less__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3172 (all X_b all X_a (real_vector(X_a) -> (all A_2 all G all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2)),G)),A_3) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),G),A_3))))) # label(fact_4730_scaleR__right_Osetsum) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3173 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),Ta))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Ta))))))))) # label(fact_488_inf__period_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3174 (all X_a (real_normed_field(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),zero_zero(X_a)),sequentially)))))) # label(fact_4435_summable__LIMSEQ__zero) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3175 (all R_4 all P_5 all Q_3 (hAPP(product_prod(int,int),product_prod(int,int),normalize,R_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),P_5),Q_3) = one_one(int))) # label(fact_4404_normalize__coprime) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3176 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)),Y))) # label(fact_4347_gcd__dvd2__int) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3177 (all X_a all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> zero_zero(nat) = hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) # label(fact_1823_card__infinite) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3178 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | N_1 = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))))) # label(fact_198_zero__less__power__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3179 (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]. 10.71/10.79 3180 (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]. 10.71/10.79 3181 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),one_one(real))),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))))) # label(fact_2349_real__natfloor__gt__diff__one) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3182 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),W))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,one_one(int)),hAPP(int,int,number_number_of(int),W))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(int,int,number_number_of(int),W))) -> hAPP(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))))))) # label(fact_1078_posDivAlg__eqn__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3183 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,ln,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,ln,X)))) # label(fact_2355_ln__realpow) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3184 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))))) # label(fact_783_add__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3185 (all Z_1 hAPP(complex,real,re,hAPP(complex,complex,sgn_sgn(complex),Z_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1))) # label(fact_3009_Re__sgn) # label(axiom) # label(non_clause). [assumption]. 10.71/10.79 3186 (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_220_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3187 (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]. 10.80/10.79 3188 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(X_a) <-> one_one(X_a) = ti(X_a,A_2) | ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2116_power2__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3189 (all K1 all K2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K1)),hAPP(int,int,bit1,K2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K1),K2)))) # label(fact_52_less__eq__int__code_I14_J) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3190 (all X_a (metric_space(X_a) -> (all X2_1 all X1_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X2_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),E_1),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X1_1),X2_1)),E_1))))))) # label(fact_3521_dist__triangle__half__l) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3191 (all N all M hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N))) # label(fact_923_zmult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3192 (all X_a all A_3 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),combc(fun(X_a,bool),fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool))),A_3))) # label(fact_2778_Pow__def) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3193 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1273_even__minus__even) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3194 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4747_scaleR_OLIM__left__zero) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3195 (all V_3 all K_4 all V ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V),V_3))),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_3)),K_4)))) # label(fact_1512_nat__number__of__add__left) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3196 (all M all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N) = M -> N = one_one(nat) | M = zero_zero(nat))) # label(fact_600_mult__eq__self__implies__10) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3197 (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))))) # label(fact_2438_minus__one__even__power) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3198 (all B_1 all A_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),B_1)))) # label(fact_866_d22set__g__1) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3199 (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),hAPP(real,real,uminus_uminus(real),A_1)),B)))) # label(fact_4685_scaleR_Ominus__left) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3200 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = hAPP(product_prod(int,int),int,product_fst(int,int),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))))))) # label(fact_3111_div__pos__neg) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3201 (all A_2 all B_1 (-(exists P_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_6),A_2)) & hBOOL(hAPP(int,bool,zprime,P_6)))) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),B_1))) # label(fact_3467_zgcd1__iff__no__common__primedivisor) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3202 (all X_a (number_ring(X_a) & field_inverse_zero(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),pls)) = zero_zero(X_a)))) # label(fact_1732_divide__Numeral0) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3203 (all X_a (abs_if(X_a) -> ti(fun(X_a,X_a),abs_abs(X_a)) = abs_abs(X_a))) # label(tsy_c_Groups_Oabs__class_Oabs_0_res) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3204 (all X_a (group_add(X_a) -> (all A_2 (hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = zero_zero(X_a) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3205 (all X_a (preorder(X_a) -> (all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> hBOOL(P_1)))))) # label(fact_1571_order__less__imp__triv) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3206 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4981_min__max_Ole__supI2) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3207 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = zero_zero(real) <-> zero_zero(real) = X_1))) # label(fact_2679_real__root__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3208 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,zero_zero(nat)),D_1)) <-> D_1 = one_one(nat))) # label(fact_2867_coprime__0_H) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3209 (all M zero_zero(real) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),pi),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2287_cos__pi__eq__zero) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3210 (all X_a (monoid_mult(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_1456_power__odd__eq) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3211 (all C all A_1 all B (B = A_1 -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C))))) # label(fact_630_dvd_Oord__eq__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3212 (all X_c all X_b all 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)) = product_apsnd(X_c,X_b,X_a)) # label(tsy_c_Product__Type_Oapsnd_res) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3213 (all X_a (one(X_a) -> one_one(X_a) = ti(X_a,one_one(X_a)))) # label(tsy_c_Groups_Oone__class_Oone_res) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3214 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),A_2)))))) # label(fact_2056_minus__le__self__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3215 (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]. 10.80/10.79 3216 (all X_2 ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_2),hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),X_2))) = hAPP(nat,real,sin_coeff,X_2)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),X_2)) -> hAPP(nat,real,sin_coeff,X_2) = zero_zero(real)))) # label(fact_2478_sin__coeff__def) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3217 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1))),hAPP(real,real,cos,X_1)))))) # label(fact_3883_DERIV__cos__cos__mult) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3218 (all N ti(int,N) = hAPP(quickcheck_code_int,int,quickcheck_int_of,hAPP(int,quickcheck_code_int,quickcheck_of_int,N))) # label(fact_3537_int__of__of__int) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3219 (all Code_numeral_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(code_code_numeral,nat,code_c271388182l_size,Code_numeral_2)),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(code_code_numeral,nat,code_c271388182l_size,hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_2))) # label(fact_2926_code__numeral_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3220 (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]. 10.80/10.79 3221 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),zero_zero(int))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1)),zero_zero(int)))))) # label(fact_983_pos__imp__zdiv__neg__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3222 (all N hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,real_1(nat),N))),pi)) = one_one(real)) # label(fact_2393_cos__2npi) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3223 (all X_a (archim1727834104eiling(X_a) -> (all X hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),hAPP(X_a,int,archimedean_ceiling(X_a),X))))))) # label(fact_3586_le__of__int__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3224 (all A_1 zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),A_1)) # label(fact_952_zmod__self) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3225 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) -> ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2)))) # label(fact_1919_equalityI) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3226 (all X_a all C_2 all A_3 ((all X_4 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_4),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),X_4),C_2)))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)),C_2)))) # label(fact_2730_Union__least) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3227 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X_1),Y_1) = ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)))))) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3228 (all X_1 (X_1 = hAPP(real,real,exp(real),hAPP(real,real,ln,X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_2600_exp__ln__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3229 (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_2584_nonzero__inverse__eq__divide) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3230 (all Z_1 ti(int,Z_1) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,uminus_uminus(int),Z_1))) # label(fact_2143_zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3231 (all X_a (linordered_field(X_a) -> (all X all Y ((all E (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),E)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),E))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1540_field__le__epsilon) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3232 (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_3455_zgcd__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3233 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1))))) # label(fact_4918_isCont__root__neg) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3234 (all X_a all P_1 ((exists X1 hBOOL(hAPP(X_a,bool,P_1,X1))) -> hBOOL(hAPP(X_a,bool,P_1,hAPP(fun(X_a,bool),X_a,hilbert_Eps(X_a),P_1))))) # label(fact_4785_someI__ex) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3235 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z))))) # label(fact_1126_nat__mono__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3236 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4642_bset_I7_J) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3237 (all N exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),P_6)))) # label(fact_3105_euclid) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3238 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(real,X_a,of_real(X_a),hAPP(real,real,exp(real),X)) = hAPP(X_a,X_a,exp(X_a),hAPP(real,X_a,of_real(X_a),X))))) # label(fact_2799_exp__of__real) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3239 (all X_a (linord1117847801e_zero(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),Y) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))) # label(fact_1884_abs__div__pos) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3240 (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))) & 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,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_2278_arctan) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3241 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3855_Bseq__minus__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3242 (all F all F_2 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),hAPP(real,real,F_2,X_2))))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Z_2),B_1)) & hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,F,B_1)),hAPP(real,real,F,A_2)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),hAPP(real,real,F_2,Z_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),Z_2))))))) # label(fact_2721_MVT2) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3243 (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]. 10.80/10.79 3244 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),negDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_927_negDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3245 (all X_a (division_ring(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_2078_nonzero__minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3246 (all F all J all N_1 all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (exists B_6 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),J)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B_6),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1))))) = hAPP(real,real,F,H)))) # label(fact_4272_Maclaurin__lemma) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3247 (all X_a (linordered_semidom(X_a) -> (all X_1 all Y_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),X_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B_1),Y_1)))))))) # label(fact_449_power__strict__increasing__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3248 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))))) # label(fact_3377_ge__one__powr__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3249 (all X_a (power(X_a) & semiring_0(X_a) -> (all N zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),zero_zero(X_a)),hAPP(nat,nat,suc,N))))) # label(fact_1300_power__0__Suc) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3250 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,tan,X)),zero_zero(real)))))) # label(fact_2277_tan__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3251 (all X_1 all Y_1 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),Y_1)),hAPP(product_prod(int,int),int,product_snd(int,int),X_1)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,product_fst(int,int),X_1)),hAPP(product_prod(int,int),int,product_snd(int,int),Y_1)) & zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),Y_1) & zero_zero(int) != hAPP(product_prod(int,int),int,product_snd(int,int),X_1) <-> hBOOL(hAPP(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool,hAPP(product_prod(product_prod(int,int),product_prod(int,int)),fun(fun(product_prod(product_prod(int,int),product_prod(int,int)),bool),bool),member(product_prod(product_prod(int,int),product_prod(int,int))),hAPP(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int)),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(product_prod(int,int),product_prod(int,int))),product_Pair(product_prod(int,int),product_prod(int,int)),X_1),Y_1)),ratrel)))) # label(fact_3732_ratrel__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3252 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)))))) # label(fact_1195_posDivAlg__correct) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3253 (all X_a all F all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),F_1)) -> one_one(nat) = hAPP(X_a,nat,F,X_2))) <-> one_one(nat) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),F_1)))) # label(fact_3938_setprod__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3254 (all X_a (archim1727834104eiling(X_a) -> ti(fun(X_a,int),archim2085082626_floor(X_a)) = archim2085082626_floor(X_a))) # label(tsy_c_Archimedean__Field_Ofloor__ceiling__class_Ofloor_res) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3255 (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_3616_floor__exists) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3256 (all Z_1 all Z_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Z_1),Z_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,Z_1)),hAPP(int,nat,nat_1,Z_4))))) # label(fact_1144_nat__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3257 (all X_a (linordered_idom(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,sgn_sgn(X_a),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2211_sgn__greater) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3258 (all X_a (banach(X_a) -> (all F all C_1 all N_4 ((all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_4),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_2)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C_1),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,F,N_2))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C_1)) | hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)))))) # label(fact_4055_ratio__test__lemma2) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3259 (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),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),M),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M))))) # label(fact_254_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3260 (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_2890_floor__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3261 (all X_a all A_3 hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)) = hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool),collect(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),fEx(fun(X_a,bool))),hAPP(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combs(fun(X_a,bool),bool,bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),fun(bool,bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool)),fun(X_a,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(fun(X_a,bool),bool),fun(fun(X_a,bool),fun(bool,bool))),combb(bool,fun(bool,bool),fun(X_a,bool)),fconj)),hAPP(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),fun(fun(X_a,bool),bool))),combc(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),hAPP(fun(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool))),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)))),combb(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),fun(X_a,bool)),fun(fun(X_a,bool),bool)),fun(X_a,bool)),combb(fun(X_a,bool),bool,fun(X_a,bool))),fequal(fun(X_a,bool)))),uminus_uminus(fun(X_a,bool)))))),hAPP(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool),hAPP(fun(fun(fun(X_a,bool),bool),bool),fun(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),bool)),combb(fun(fun(X_a,bool),bool),bool,fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),A_3)),pow(X_a)))))) # label(fact_4428_Pow__Compl) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3262 (all N_4 ((exists M_2 all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),N_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_2),M_2)))) <-> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),N_4)))) # label(fact_3674_finite__nat__set__iff__bounded) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3263 (all X_1 all N_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y_1),hAPP(nat,nat,suc,N_1)))))) # label(fact_1360_exp__mono__lt) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3264 (all P_1 all N_1 ((all X_2 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),X_2),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))) -> hBOOL(hAPP(nat,bool,P_1,X_2)))) <-> (all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(nat,bool,P_1,M_2)))))) # label(fact_4194_all__nat__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3265 (all X_a (monoid_mult(X_a) -> (all Z_1 all W hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_3871_power__number__of__even) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3266 (all P_1 all I (hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,I))) <-> (all N_2 (ti(int,I) = hAPP(nat,int,semiring_1_of_nat(int),N_2) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) & (hBOOL(hAPP(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_1405_split__nat) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3267 (all X_a all X_b all X_c all X_d all X_e all X_1 all P_1 ((all A_4 all B_4 all C_4 all D_3 all E hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,hAPP(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),hAPP(X_a,fun(product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))))),product_Pair(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),A_4),hAPP(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e))),hAPP(X_b,fun(product_prod(X_c,product_prod(X_d,X_e)),product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),product_Pair(X_b,product_prod(X_c,product_prod(X_d,X_e))),B_4),hAPP(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e)),hAPP(X_c,fun(product_prod(X_d,X_e),product_prod(X_c,product_prod(X_d,X_e))),product_Pair(X_c,product_prod(X_d,X_e)),C_4),hAPP(X_e,product_prod(X_d,X_e),hAPP(X_d,fun(X_e,product_prod(X_d,X_e)),product_Pair(X_d,X_e),D_3),E))))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,product_prod(X_c,product_prod(X_d,X_e)))),bool,P_1,X_1)))) # label(fact_3152_prod__induct5) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3268 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),im),G)),hAPP(complex,real,im,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4597_Im_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3269 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) = ti(X_a,B)))) # label(fact_2049_add__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3270 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(rat,real,ratreal,X_1)),hAPP(rat,real,ratreal,Y_1))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),X_1),Y_1)))) # label(fact_3766_real__less__eq__code) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3271 (all A_2 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,X_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,uminus_uminus(int),A_2)),hAPP(int,nat,nat_1,X_1))))) # label(fact_2181_neg__even__power) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3272 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X_1),N_1)),zEven))))) # label(fact_1398_power__preserves__even) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3273 (all Diff all F all N_1 all 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),H),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),zero_zero(real))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),zero_zero(real))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),T_4),zero_zero(real))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) = hAPP(real,real,F,H) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H),T_4)))))) # label(fact_4283_Maclaurin__minus__objl) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3274 (all N_1 all V_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1))))) # label(fact_3895_le__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3275 (all X_a all C_2 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),C_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),C_2))))) # label(fact_1953_subset__trans) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3276 (all X_a (power(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_1_res) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3277 (all X_a (ring_n68954251visors(X_a) -> (all A_2 all B_1 (zero_zero(X_a) = ti(X_a,B_1) | zero_zero(X_a) = ti(X_a,A_2) <-> zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))))) # label(fact_321_mult__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3278 (all A_1 all B (zero_zero(nat) != B -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),B)))) # label(fact_3261_gcd__le2__nat) # label(axiom) # label(non_clause). [assumption]. 10.80/10.79 3279 (all A_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),A_2)),one_one(real))),X_1)))) # label(fact_3413_less__floor__eq) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3280 (all X_a (real_normed_algebra(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))) # label(fact_2035_mult__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3281 (all X_1 all Y_1 (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),Y_1)),hAPP(int,int,number_number_of(int),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,number_number_of(int),X_1)),hAPP(int,int,number_number_of(int),Y_1))))) # label(fact_1038_zdvd__iff__zmod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3282 (all V_1 all V_2 ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> ti(int,V_1) = ti(int,V_2)) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_2))) -> zero_zero(int) = hAPP(int,int,number_number_of(int),V_1))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_2)),zero_zero(int)))) <-> hAPP(int,nat,number_number_of(nat),V_1) = hAPP(int,nat,number_number_of(nat),V_2))) # label(fact_1511_eq__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3283 (all W all Z_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),W))),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z_1))) = hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)))) # label(fact_1942_nat__abs__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3284 (all M all N hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)))) # label(fact_3100_divmod__nat__rel__divmod__nat) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3285 (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)) -> one_one(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),X)) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(X_a,X_a,sgn_sgn(X_a),X))))))) # label(fact_2232_sgn__if) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3286 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> X = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1640_real__sqrt__pow2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3287 (all X_a (ring_1(X_a) -> (all Z hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),ring_1_Ints(X_a)))))) # label(fact_3804_Ints__of__int) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3288 (all X_1 all Y_1 all P_1 ((-hBOOL(P_1) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1)) = hAPP(int,nat,nat_1,Y_1)) & (hBOOL(P_1) -> hAPP(int,nat,nat_1,X_1) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),hAPP(bool,fun(int,fun(int,int)),if(int),P_1),X_1),Y_1))))) # label(fact_1081_nat__if__cong) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3289 (all X_a (real_n2089651433ebra_1(X_a) -> (all R_4 hAPP(real,real,abs_abs(real),R_4) = hAPP(X_a,real,norm_norm(X_a),hAPP(real,X_a,of_real(X_a),R_4))))) # label(fact_2797_norm__of__real) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3290 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X_1)))))) # label(fact_3310_zero__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3291 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),N_1) = zero_zero(nat))) # label(fact_684_diff__is__0__eq) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3292 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_3212_number__of__le__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3293 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),B_2) = ti(fun(X_a,bool),A_3) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_1959_set__eq__subset) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3294 (all X all Y (Y = X -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)))) # label(fact_626_dvd_Oeq__refl) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3295 (all X_a (semiring_1(X_a) -> (all Inc all N_1 all I hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),hAPP(nat,nat,suc,N_1)),I) = hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),Inc),N_1),hAPP(X_a,X_a,Inc,I))))) # label(fact_4161_of__nat__aux_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3296 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1)),Ma)) <-> N_1 = one_one(nat)))) # label(fact_505_dvd__mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3297 (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),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(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_887_mult_Odiff__right) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3298 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arctan),X_1))) # label(fact_4888_isCont__arctan) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3299 (all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3)))))) # label(fact_3705_Sup__upper__EX) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3300 (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)) -> ti(X_a,A_1) = hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_1865_abs__of__pos) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3301 (all X_a (semiring_div(X_a) -> (all A_1 all C all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))))) # label(fact_932_mod__mult__mult2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3302 (all X_a (linorder(X_a) -> (all B all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4982_min__max_Ole__supI1) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3303 (all J_2 all A_1 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),K_4)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),A_1),P_5))))))) # label(fact_852_aux______2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3304 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (zero_zero(X_a) != ti(X_a,A_2) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,abs_abs(X_a),A_2))))))) # label(fact_1864_zero__less__abs__iff) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3305 (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),A_1)))) # label(fact_924_mod__self) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3306 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,real_1(nat),Ma))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_2306_real__of__nat__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3307 (all X_b all X_c all X_a (comm_monoid_add(X_a) -> (all F all B_2 all A_3 hAPP(fun(X_c,bool),X_a,hAPP(fun(X_c,X_a),fun(fun(X_c,bool),X_a),big_co1399186613setsum(X_c,X_a),hAPP(fun(X_b,bool),fun(X_c,X_a),hAPP(fun(X_c,fun(fun(X_b,bool),X_a)),fun(fun(X_b,bool),fun(X_c,X_a)),combc(X_c,fun(X_b,bool),X_a),hAPP(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a)),hAPP(fun(fun(X_b,X_a),fun(fun(X_b,bool),X_a)),fun(fun(X_c,fun(X_b,X_a)),fun(X_c,fun(fun(X_b,bool),X_a))),combb(fun(X_b,X_a),fun(fun(X_b,bool),X_a),X_c),big_co1399186613setsum(X_b,X_a)),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_c,fun(X_b,X_a)),combc(X_b,X_c,X_a),F))),A_3)),B_2) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_c,bool),fun(X_b,X_a),hAPP(fun(X_b,fun(fun(X_c,bool),X_a)),fun(fun(X_c,bool),fun(X_b,X_a)),combc(X_b,fun(X_c,bool),X_a),hAPP(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a)),hAPP(fun(fun(X_c,X_a),fun(fun(X_c,bool),X_a)),fun(fun(X_b,fun(X_c,X_a)),fun(X_b,fun(fun(X_c,bool),X_a))),combb(fun(X_c,X_a),fun(fun(X_c,bool),X_a),X_b),big_co1399186613setsum(X_c,X_a)),F)),B_2)),A_3)))) # label(fact_4214_setsum__commute) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3308 (all N zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),zero_zero(nat)),N)) # label(fact_4807_min__0L) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3309 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),N),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),M)) | M = N | M = zero_zero(nat))) # label(fact_610_divides__cases) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3310 (all Z_1 all X all Y all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Z_1)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y),Z_1)),M)))) # label(fact_363_zcong__zpower) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3311 (all X_b all X_a (ordere142940540dd_abs(X_a) -> (all F all A_3 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),F),A_3))),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,X_a),fun(X_b,X_a),hAPP(fun(X_a,X_a),fun(fun(X_b,X_a),fun(X_b,X_a)),combb(X_a,X_a,X_b),abs_abs(X_a)),F)),A_3)))))) # label(fact_4165_setsum__abs) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3312 (all D_1 all A_2 all B_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),B_1) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),A_2) = one_one(nat) <-> one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1)))) # label(fact_3267_coprime__mul__eq__nat) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3313 (all N_1 all Ma (hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),N_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(quickcheck_code_int,int,quickcheck_int_of,N_1)),hAPP(quickcheck_code_int,int,quickcheck_int_of,Ma))))) # label(fact_3159_less__eq__code__int__def) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3314 (all X_a all X_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1956_in__mono) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3315 (all X_a (linorder(X_a) -> (all Y_1 all X_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1)))))) # label(fact_1564_linorder__antisym__conv3) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3316 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit1,pls))))))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1200_inv__inv__aux) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3317 (all Ma all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))))) # label(fact_3206_Bnor__mem__zle__swap) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3318 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all K all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))))) # label(fact_4543_setsum__shift__bounds__cl__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3319 (all A_2 all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),A_2)),hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),B_1)))))) # label(fact_3378_powr__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3320 (all M ((zero_zero(nat) != M -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat)))) = hAPP(nat,nat,fact_fact(nat),M)) & (M = zero_zero(nat) -> one_one(nat) = hAPP(nat,nat,fact_fact(nat),M)))) # label(fact_2500_fact__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3321 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))))))) # label(fact_1882_abs__triangle__ineq4) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3322 (all K_4 hAPP(int,int,pred,hAPP(int,int,bit1,K_4)) = hAPP(int,int,bit0,K_4)) # label(fact_2900_pred__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3323 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))))) # label(fact_1760_neg__one__special) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3324 (all X_a (linordered_idom(X_a) -> (all X all W (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W))) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),hAPP(int,nat,number_number_of(nat),W)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),W)))))) # label(fact_2444_power__even__abs__number__of) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3325 (all Z all Y_1 all X_1 all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),X_3)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3))))))) # label(fact_3714_SupInf_OSup__upper2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3326 (all X_a (ordere453448008miring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_377_mult__nonneg__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3327 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),K_4),zero_zero(int))) = zero_zero(rat)) # label(fact_3708_Frct__code__post_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3328 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_461_one__less__power) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3329 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1229_Suc__less__SucD) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3330 (all X_a (field_char_0(X_a) -> ti(fun(X_a,bool),field_char_0_Rats(X_a)) = field_char_0_Rats(X_a))) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3331 (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_1171_zmod__eq__0D) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3332 (all N all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),X))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),X))))) # label(fact_2328_real__of__nat__div4) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3333 (all X all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)),X) = hAPP(real,real,hAPP(nat,fun(real,real),root,M),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)))))) # label(fact_2707_real__root__pos__mult__exp) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3334 (all N all A_1 hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)) = hAPP(complex,real,im,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N))) # label(fact_3024_sin__n__Im__cis__pow__n) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3335 (all X_a (real_normed_field(X_a) -> (all N all Z_1 all K_5 all H_2 (ti(X_a,H_2) != zero_zero(X_a) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),Z_1)),K_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H_2))),K_5)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),H_2)),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),N))),H_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),N)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),K_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(X_a,real,norm_norm(X_a),H_2)))))))))) # label(fact_1773_lemma__termdiff3) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3336 (all Z_1 all X all Y all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),one_one(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1))),one_one(int)),P_5)))) # label(fact_455_zcong__zpower__zmult) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3337 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),A_2)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)))))) # label(fact_4473_tendsto__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3338 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,ln,X)),zero_zero(real)))))) # label(fact_1950_ln__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3339 (all X hAPP(complex,real,im,hAPP(complex,complex,cnj,X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))) # label(fact_2973_complex__Im__cnj) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3340 (all A_2 all B_1 (hAPP(int,int,abs_abs(int),A_2) = hAPP(int,int,abs_abs(int),B_1) <-> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1980_power2__eq__iff__abs__eq) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3341 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all B_1 all W_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1))),A_2)) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))))))))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3342 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3301_one__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3343 (all X all A_1 hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),hAPP(real,real,ln,X))) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)) # label(fact_3382_powr__def) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3344 (all X_a (linorder(X_a) & dvd(X_a) & plus(X_a) -> (all D_1 all Sa exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Sa)))))))) # label(fact_868_pinf_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3345 (all A_1 all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,A_1)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,zero_zero(nat))),C))),C))) # label(fact_1419_div__Suc) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3346 (all A_2 all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,finite_finite_1(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))))) # label(fact_1798_SetS__finite) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3347 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hAPP(real,real,F,Y_2) = hAPP(real,real,F,X_1))) -> L = zero_zero(real))))) # label(fact_2661_DERIV__local__const) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3348 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3375_powr__mono2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3349 (all X_1 all N_1 exists T_4 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(real,fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(real,fun(nat,fun(real,real))),combc(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),zero_zero(real))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),div_div(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),T_4),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,real_1(nat),N_1))),pi)))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,sin,X_1)) # label(fact_4267_Maclaurin__sin__expansion) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3350 (all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(int,real,real_1(int),A_2))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X_1)),A_2)))) # label(fact_3367_ceiling__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3351 (all X_a all X_b all Sa all Ta (ti(product_prod(X_a,X_b),Sa) = ti(product_prod(X_a,X_b),Ta) <-> hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Sa) = hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Ta) & hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Ta) = hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Sa))) # label(fact_3143_prod__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3352 (all Z_1 hBOOL(hAPP(int,bool,nat_is_nat,hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_4854_Nat__Transfer_Otransfer__int__nat__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3353 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arctan,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,arctan,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2125_arctan__bounded) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3354 (all X_a (dvd(X_a) -> (all A_1 all B all K_4 (ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),K_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),A_1)))))) # label(fact_337_dvdI) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3355 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3356 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N_1)) -> hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1))))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N_1),one_one(int)))) # label(fact_3881_int__card__bdd__int__set__l__l) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3357 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,suc,X_2))),hAPP(nat,X_a,C_1,hAPP(nat,nat,suc,X_2)))))) # label(fact_4118_diffs__def) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3358 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1089_mod__less) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3359 (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_1781_norm__one) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3360 (all X_a (metric_space(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_1))))))))) # label(fact_4521_metric__LIMSEQ__D) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3361 (all X_a all X_b (real_normed_algebra(X_b) -> (all X_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),A_2)),A_3)))))) # label(fact_4476_mult__right_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3362 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),one_one(real)))) # label(fact_1840_cos__x__y__le__one) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3363 (all X_a all X_b (minus(X_b) -> (all A_3 all B_2 all X_2 hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,A_3,X_2)),hAPP(X_a,X_b,B_2,X_2)) = hAPP(X_a,X_b,hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),minus_minus(fun(X_a,X_b)),A_3),B_2),X_2)))) # label(fact_2963_fun__diff__def) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3364 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),cos)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,cos,X_2))),hAPP(real,real,sin,X_2)))))) # label(fact_3917_DERIV__sin__circle__all) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3365 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zOdd)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zOdd)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven))))) # label(fact_1370_odd__minus__odd) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3366 (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]. 10.81/10.80 3367 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),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)))))) = X)) # label(fact_2460_odd__nat__div__two__times__two__plus__one) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3368 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)) <-> ti(X_a,X_1) = ti(X_a,Y_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)))))) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3369 (all G all F all X_1 all D_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hAPP(real,real,G,hAPP(real,real,F,Z_2)) = Z_2)) -> ((all Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),Z_2)))) -> (exists Z_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),Z_2),X_1))),D_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,Z_2))))))))) # label(fact_4933_lemma__isCont__inj) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3370 (all X_a all X_b (comm_semiring_1(X_b) -> (all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = zero_zero(X_b)))))) # label(fact_3950_setprod__zero) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3371 (all X_a (ord(X_a) -> ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),max(X_a)) = max(X_a))) # label(tsy_c_Orderings_Oord_Omax_res) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3372 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & hAPP(real,real,cos,hAPP(real,real,arccos,Y)) = Y))) # label(fact_2280_arccos) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3373 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),X) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3))))) # label(fact_1309_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3374 (all X_a (real_normed_field(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),Ya))))) # label(fact_1661_divide_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3375 (all X_a (linordered_semidom(X_a) -> (all N all R_4 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),R_4)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),R_4),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),R_4),hAPP(nat,nat,suc,N))),R_4))))))) # label(fact_1403_realpow__Suc__le__self) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3376 (all I_1 all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),N)))) # label(fact_4366_dvd__gcd__D2__int) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3377 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A_1)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A_1))),one_one(int)))) # label(fact_900_neg__zmod__mult__2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3378 (all X_a all A_3 all F all N_1 (hAPP(fun(nat,bool),fun(X_a,bool),hAPP(fun(nat,X_a),fun(fun(nat,bool),fun(X_a,bool)),image(nat,X_a),F),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) = ti(fun(X_a,bool),A_3) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_3868_nat__seg__image__imp__finite) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3379 (all X_a (metric_space(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_4488_LIMSEQ__imp__Cauchy) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3380 (all K_4 all I_1 all J_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),J_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),J_2),K_4)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),I_1),K_4))))) # label(fact_652_real__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3381 (all X_1 all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),B_1)) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,X_1))))))) # label(fact_4928_DERIV__isconst2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3382 (all A_1 all B hAPP(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,sgn_sgn(int),A_1)),hAPP(int,int,sgn_sgn(int),B))) = hAPP(rat,rat,sgn_sgn(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3781_sgn__rat) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3383 (all N all M ((M != zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),one_one(nat))),N)))) & (M = zero_zero(nat) -> hAPP(nat,nat,fact_fact(nat),N) = hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))))) # label(fact_2481_fact__add__num__eq__if2__nat) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3384 (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_2518_power__inverse) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3385 (all A_2 all A_3 all Ma ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> hAPP(fun(int,bool),int,hilbert_Eps(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2)),Ma))),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(fun(int,bool),bool)),fun(fun(int,bool),fun(int,bool)),combc(int,fun(int,bool),bool),member(int)),hAPP(int,fun(int,bool),norRRset,Ma)))) = hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)) & (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) & hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3))) -> hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2) = zero_zero(int)))) # label(fact_4153_RRset2norRR__def) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3386 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3387 (all X_a (linordered_idom(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a)))))) # label(fact_7_not__sum__power2__lt__zero) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3388 (all B all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),log,B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),hAPP(real,real,hAPP(real,fun(real,real),log,B),X)))) # label(fact_2647_log__nat__power) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3389 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,A_2)),hAPP(real,real,F,B_1)))))) # label(fact_3529_DERIV__nonneg__imp__nonincreasing) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3390 (all X_a (field_inverse_zero(X_a) -> (all X all Z_1 all Y (ti(X_a,Y) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))) # label(fact_1720_add__frac__num) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3391 (all X_1 hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),cos_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))) = hAPP(real,real,cos,X_1)) # label(fact_3972_cos__def) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3392 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),I_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),K_4)),J_2)))))) # label(fact_1402_zmult__zless__mono2__lemma) # label(axiom) # label(non_clause). [assumption]. 10.81/10.80 3393 (all R_4 all X hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),hAPP(complex,real,im,X)) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X))) # label(fact_4691_Im_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3394 (all A_9 all B_8 all Y all R_6 (hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_8),Y)),R_6) = 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),R_6),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_8),R_6))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_6),B_8)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_6))) -> (ti(int,B_8) != zero_zero(int) -> ti(int,Y) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_9),B_8))))) # label(fact_1054_divmod__int__rel__div__eq) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3395 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3))))))) # label(fact_4100_mult__right_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3396 (all X_a (uminus(X_a) -> ti(fun(X_a,X_a),uminus_uminus(X_a)) = uminus_uminus(X_a))) # label(tsy_c_Groups_Ouminus__class_Ouminus_res) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3397 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))),R_4))) # label(fact_3344_real__of__int__floor__le) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3398 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)))))) # label(fact_2082_abs__le__D2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3399 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,B_1),A_2),Ma)))) # label(fact_313_zcong__sym) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3400 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))) # label(fact_2051_minus__add__distrib) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3401 (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(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N))))))) # label(fact_1751_power__diff) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3402 (all X_a (ring_1(X_a) -> (all N_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1)),ring_1_Ints(X_a))))))) # label(fact_3851_Ints__power) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3403 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),N)) = one_one(X_a)))) # label(fact_1896_abs__power__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3404 (all X_a (linord1117847801e_zero(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B),C)))))))) # label(fact_1673_divide__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3405 (all X_a (boolean_algebra(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),Y)),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))))) # label(fact_2959_compl__le__swap2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3406 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,exp(real),hAPP(real,real,ln,X)) = X)) # label(fact_2601_exp__ln) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3407 (all X_a (linorder(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),A_1)))) # label(fact_4817_min__max_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3408 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all R_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)) & (all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_1))))))))))) # label(fact_4645_LIM__D) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3409 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),zero_zero(X_a)))))))) # label(fact_1706_divide__nonpos__pos) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3410 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X))))) # label(fact_4694_scaleR__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3411 (all K_4 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N))))) # label(fact_497_dvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3412 (all X_a (real_normed_vector(X_a) -> (all X_3 ((exists K_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_1)) & (exists X_2 all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(X_a,X_a,uminus_uminus(X_a),X_2)))),K_1))))) <-> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)))))) # label(fact_3491_Bseq__iff2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3413 (all X_1 all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) -> (X_1 != zero_zero(real) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),root,N_1)),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))))))) # label(fact_2716_DERIV__odd__real__root) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3414 (all X_1 all Y_1 all Z (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))) # label(fact_713_real__mult__le__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3415 (all B_2 all P_2 all P_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P_2,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,P_1,X_2)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)))))) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P_2,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_2)))) <-> hBOOL(hAPP(int,bool,P_2,X_2)))) -> ((exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & (exists Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),B_2)) & hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xa),X_2))))))) | (exists X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) & hBOOL(hAPP(int,bool,P_2,X_2)))) <-> (exists X1 hBOOL(hAPP(int,bool,P_1,X1))))))))) # label(fact_4873_cpmi) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3416 (all Ma all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) & hAPP(int,nat,nat_1,Z) = Ma <-> ti(int,Z) = hAPP(nat,int,semiring_1_of_nat(int),Ma))) # label(fact_1377_int__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3417 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2570_le__imp__inverse__le) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3418 (all X_a (real_normed_field(X_a) & banach(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_2535_exp__minus) # label(axiom) # label(non_clause). [assumption]. 10.81/10.81 3419 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> -(hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1918_DiffE) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3420 (all X_a (number_ring(X_a) -> hAPP(int,X_a,number_number_of(X_a),pls) = zero_zero(X_a))) # label(fact_147_semiring__norm_I112_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3421 (all X_a (ordered_ab_group_add(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),B_1)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2016_neg__less__iff__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3422 (all X_a (preorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)))))) # label(fact_1580_order__less__asym) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3423 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)))))) # label(fact_2080_abs__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3424 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2936_cnj_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3425 (all X_a all C_1 all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3))))) # label(fact_2191_ComplI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3426 (all X1_2 all X2_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),standardRes,Ma),X2_2) = hAPP(int,int,hAPP(int,fun(int,int),standardRes,Ma),X1_2) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X1_2),X2_2),Ma))))) # label(fact_1051_StandardRes__prop2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3427 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 all C_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1735_le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3428 (all N_1 all Ma (hAPP(int,quickcheck_code_int,quickcheck_of_int,N_1) = hAPP(int,quickcheck_code_int,quickcheck_of_int,Ma) <-> ti(int,Ma) = ti(int,N_1))) # label(fact_3534_Quickcheck__Narrowing_Oof__int__inject) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3429 (all Z_4 all Z_1 all W_3 all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_3),W)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_4),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_3),Z_4)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)))))) # label(fact_56_zadd__zless__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3430 (all X_a (linordered_idom(X_a) -> (all A_2 (hAPP(X_a,X_a,sgn_sgn(X_a),A_2) = one_one(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2222_sgn__1__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3431 (all R_4 all A_1 all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1)),N) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_4),N)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3158_DeMoivre2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3432 (all X_a (order(X_a) -> (all X_1 all Y_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_1),X_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_1),Y_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_1)),hAPP(nat,X_a,F,Y_1)))))))) # label(fact_4790_dvd_Ostrict__monoD) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3433 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (zero_zero(real) = X -> zero_zero(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N)) & (zero_zero(real) != X -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N)))))) # label(fact_3420_powr__realpow2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3434 (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_3832_Nat__Transfer_Otransfer__nat__int__set__functions_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3435 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))))) # label(fact_716_divides__mul__r) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3436 (all X_a all X_b all B_2 all F all A_3 ((exists AA (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),AA),A_3)) & ti(fun(X_a,bool),B_2) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),AA))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))))) # label(fact_3634_subset__image__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3437 (all X_a (ordere223160158up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_789_add__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3438 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))) <-> zero_zero(nat) = N_1)) # label(fact_1321_less__Suc0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3439 (all X_1 ((exists Y_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Y_2)),one_one(int)) = ti(int,X_1)) <-> -hBOOL(hAPP(int,bool,even_odd_even(int),X_1)))) # label(fact_1469_odd__equiv__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3440 (all X_a (real_normed_vector(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> zero_zero(real) = hAPP(X_a,real,norm_norm(X_a),X_1))))) # label(fact_1777_norm__eq__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3441 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_2 hAPP(X_a,X_a,exp(X_a),X_2) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_2)))))) # label(fact_4750_lemma__exp__ext) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3442 (all X all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N)))))) # label(fact_3056_prime__divexp__n) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3443 (all X_a (linordered_field(X_a) -> (all X all Z_1 all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),Y))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)),Z_1))))))) # label(fact_1712_mult__imp__div__pos__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3444 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),pls) = ti(int,K_4)) # label(fact_130_add__Pls__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3445 (all X_a (number_semiring(X_a) -> zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),pls))) # label(fact_145_semiring__numeral__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3446 (all X_a (real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),combi(X_a)),X_1),one_one(X_a)))))) # label(fact_3839_DERIV__ident) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3447 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,real_1(nat),N))) # label(fact_3278_ceiling__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3448 (all A_1 hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),hAPP(int,int,number_number_of(int),min_1)) = hAPP(int,int,uminus_uminus(int),A_1)) # label(fact_2172_zdiv__minus1__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3449 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),Y))))) # label(fact_1096_nat__mod__distrib) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3450 (all X_a (field_char_0(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),field_char_0_Rats(X_a))))) # label(fact_3691_Rats__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3451 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),M) = zero_zero(nat)) # label(fact_659_diff__self__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3452 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,tan,X_2))))))) # label(fact_2285_lemma__tan__total) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3453 (all N all I_1 ((I_1 != zero_zero(code_code_numeral) -> hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,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))) & (zero_zero(code_code_numeral) = I_1 -> N = hAPP(nat,nat,hAPP(code_code_numeral,fun(nat,nat),code_nat_of_aux,I_1),N)))) # label(fact_1487_nat__of__aux__code) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3454 (all X_a (real_normed_field(X_a) -> (all Y exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1810_divide_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3455 (all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(int,bool,P_1,X_2)))) <-> (all X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))))) # label(fact_1297_transfer__int__nat__quantifiers_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3456 (all X_a (semiring_1(X_a) -> ti(fun(fun(X_a,X_a),fun(nat,fun(X_a,X_a))),semiri532925092at_aux(X_a)) = semiri532925092at_aux(X_a))) # label(tsy_c_Nat_Osemiring__1__class_Oof__nat__aux_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3457 (all X_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),hAPP(real,nat,natfloor,X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X_1)))) # label(fact_1902_le__natfloor__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3458 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y)) = hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),X),Y))) # label(fact_3767_real__plus__code) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3459 (all A_1 all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),powr,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)),A_1)))) # label(fact_3376_powr__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3460 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))) # label(fact_917_div__mod__equality) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3461 (all X_a (comm_monoid_add(X_a) -> (all K all F (zero_zero(X_a) = hAPP(nat,X_a,F,zero_zero(nat)) -> hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,zero_zero(nat))),K)))))) # label(fact_4198_setsum__shift__lb__Suc0__0__upt) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3462 (all N_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),N_1)))))) # label(fact_3813_bdd__int__set__l__finite) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3463 (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_1340_mult__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3464 (all B all M all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M))))))) # label(fact_417_zcong__not) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3465 (all X -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),X)))) # label(fact_619_dvd_Oless__irrefl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3466 (all X_a (number_ring(X_a) -> (all Y_1 (zero_zero(X_a) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),pls),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_2624_eq__special_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.81 3467 (all X_b all X_a (real_normed_vector(X_a) & topological_space(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),hAPP(fun(X_a,X_a),fun(X_a,X_b),hAPP(fun(X_a,X_b),fun(fun(X_a,X_a),fun(X_a,X_b)),combb(X_a,X_b,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2))),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),hAPP(X_a,X_b,F,A_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4578_LIM__isCont__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3468 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y))))) # label(fact_1611_real__sqrt__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3469 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) = ti(int,X_1))) # label(fact_1100_StandardRes__SRStar__prop3) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3470 (all X_a (topological_space(X_a) -> (all A_2 hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),combi(X_a)),A_2),hAPP(X_a,filter(X_a),at(X_a),A_2)))))) # label(fact_4560_LIM__ident) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3471 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),one_one(X_a)))))))) # label(fact_3610_ceiling__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3472 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))) # label(fact_2715_real__root__inverse__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3473 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),J_2)))))) # label(fact_599_mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3474 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_1314_Nat__Transfer_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3475 (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]. 10.83/10.82 3476 (all X all Y hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,re,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,im,Y)))) # label(fact_3011_complex__Re__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3477 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) | Ma = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))))) # label(fact_1238_less__Suc__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3478 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1)),zero_zero(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_1),hAPP(real,real,uminus_uminus(real),X_1))))) # label(fact_2107_real__add__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3479 (all N hAPP(nat,nat,suc,N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))) # label(fact_1343_Suc__eq__plus1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3480 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),Ma),N_1))))) # label(fact_3243_gcd__greatest__iff__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3481 (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_67_plus__numeral__code_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3482 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3) = zero_zero(X_b))))) # label(fact_4208_setsum__infinite) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3483 (all X_a (sgn_div_norm(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),hAPP(X_a,real,norm_norm(X_a),X))),X)))) # label(fact_4725_sgn__div__norm) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3484 (all Q all P (hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fdisj,P),Q)) | -hBOOL(P))) # label(help_fdisj_1_1_U) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3485 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1))),hAPP(nat,X_a,F,hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,N_1)),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4603_setsum__cl__ivl__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3486 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1)) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),hilbert_Eps(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b)))) # label(fact_4782_Eps__split) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3487 (all X_a (metric_space(X_a) & comm_monoid_add(X_a) -> (all F hAPP(fun(nat,X_a),X_a,lim(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F)))) # label(fact_4328_suminf__eq__lim) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3488 (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_1128_posDivAlg__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3489 (all I_1 all U all J_2 all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),U)),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),K_4))) # label(fact_745_left__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3490 (all X_a (idom(X_a) -> (all A_2 all B_1 (ti(X_a,A_2) = hAPP(X_a,X_a,uminus_uminus(X_a),B_1) | ti(X_a,B_1) = ti(X_a,A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),B_1))))) # label(fact_2034_square__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3491 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),D))))) # label(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3492 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),X))))))) # label(fact_1998_ln__one__plus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3493 (all X_a (archim1727834104eiling(X_a) -> (all Z_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)),one_one(X_a))),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))) -> hAPP(X_a,int,archimedean_ceiling(X_a),X) = ti(int,Z_1)))))) # label(fact_3606_ceiling__unique) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3494 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),one_one(int)),P_5))))))) # label(fact_1079_Euler__part3) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3495 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),D_2),E_3)))))))) # label(fact_3822_DERIV__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3496 (all Ma all K all F ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,F,M_2)),hAPP(nat,nat,F,N_2))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,F,Ma)),K)),hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),K)))))) # label(fact_857_mono__nat__linear__lb) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3497 (all M all N all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N) = Q_3)) # label(fact_3101_div__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3498 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),one_one(int)),P_5)))))) # label(fact_854_MultInv__prop2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3499 (all Ma all V_1 (Ma = hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),V_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V_1))) <-> hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(int,int,number_number_of(int),V_1))) # label(fact_1408_int__eq__iff__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3500 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),N)))))) # label(fact_3187_fact__less__mono__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3501 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all X_1 all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1)),G)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),X_1),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4550_mult__right_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3502 (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]. 10.83/10.82 3503 (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_1242_add__Suc__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3504 (all X_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) -> hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))))) # label(fact_3615_card__nor__eq__noX) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3505 (all Y all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,Y),A_1))))))) # label(fact_3348_powr__less__mono2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3506 (all N_1 all X_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) & (all M_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),X_2),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),X_2)))) -> (exists T_4 (hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))))))) # label(fact_4285_Maclaurin__all__le__objl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3507 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B))))) # label(fact_913_semiring__div__class_Omod__div__equality_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3508 (all X_a (real_normed_vector(X_a) -> (all R_4 all X all Xa_1 hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),R_4),X)),Xa_1)))) # label(fact_4698_scaleR__left_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3509 (all X_a accp(X_a) = ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,bool)),accp(X_a))) # label(tsy_c_Wellfounded_Oaccp_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3510 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2489_fact__gt__zero__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3511 (all X all N hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,real_1(int),X)),N) = hAPP(int,real,real_1(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),N))) # label(fact_3333_power__real__of__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3512 (all X_a all F all A_3 hAPP(int,real,real_1(int),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),A_3)) = hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co302546470etprod(X_a,real),hAPP(fun(X_a,int),fun(X_a,real),hAPP(fun(int,real),fun(fun(X_a,int),fun(X_a,real)),combb(int,real,X_a),real_1(int)),F)),A_3)) # label(fact_3940_real__of__int__setprod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3513 (all X all Y hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,uminus_uminus(real),Y))) = hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Y),hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2093_abs__minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3514 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)))) # label(fact_737_norR__mem__unique__aux) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3515 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)))))))) # label(fact_411_power__increasing) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3516 (all X_a (linordered_idom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))),zero_zero(X_a))))))) # label(fact_1471_odd__power__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3517 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_5),A_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5))))))) # label(fact_1075_zfact__prop) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3518 (all P all Q (-hBOOL(hAPP(bool,bool,hAPP(bool,fun(bool,bool),fimplies,P),Q)) | hBOOL(Q) | -hBOOL(P))) # label(help_fimplies_3_1_U) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3519 (all R_4 all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),A_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_4683_complex__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3520 (all X_a (group_add(X_a) -> (all A_1 all B (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,B) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2069_minus__unique) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3521 (all X_a (linordered_idom(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,sgn_sgn(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2231_sgn__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3522 (all K all L (ti(int,K) = ti(int,L) <-> hAPP(int,int,bit0,L) = hAPP(int,int,bit0,K))) # label(fact_92_rel__simps_I48_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3523 (all B_1 all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> (-hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))),P_4))) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))) -> ti(int,B_1) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_4),A_2) | ti(int,A_2) = ti(int,B_1))))) # label(fact_841_wset__mem__imp__or) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3524 (all Z_3 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_3)) -> (hAPP(int,nat,nat_1,Z) = hAPP(int,nat,nat_1,Z_3) <-> ti(int,Z) = ti(int,Z_3))))) # label(fact_1108_eq__nat__nat__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3525 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_370_mult__right__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3526 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),ln),X_1)))) # label(fact_4883_isCont__ln) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3527 (all P_5 hAPP(product_prod(int,int),product_prod(int,int),normalize,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),zero_zero(int))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),one_one(int))) # label(fact_3727_normalize__denom__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3528 (all X_a (real_normed_vector(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),Y_3))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),B_1))),sequentially))))))) # label(fact_4438_LIMSEQ__add__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3529 (all X_a (ring_1(X_a) -> (all N_1 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),ring_1_Ints(X_a)))))) # label(fact_3805_Ints__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3530 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),B)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)))))))) # label(fact_2546_less__imp__inverse__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3531 (all N_1 all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),G)),N_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,G,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),one_one(nat))))),Ma))))) # label(fact_3879_DERIV__fun__pow) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3532 (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]. 10.83/10.82 3533 (all R_4 all A_1 hAPP(real,real,abs_abs(real),R_4) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1))) # label(fact_3166_complex__mod__rcis) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3534 (all U_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_lessThan(nat),U_1)) = U_1) # label(fact_4315_card__lessThan) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3535 (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]. 10.83/10.82 3536 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2614_inv__real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3537 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_4406_transfer__nat__int__gcd_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3538 (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_1413_Suc__pred_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3539 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma)),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))))) # label(fact_3629_Bnor__in__RsetR) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3540 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),B) = ti(X_a,A_1)))) # label(fact_808_add__diff__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3541 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (one_one(nat) != B -> (exists X_2 exists Y_2 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),X_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),Y_2)),one_one(nat)))))) # label(fact_2897_coprime__bezout__strong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3542 (all X_a all X_b all S all R_3 ((all X_2 all Xa (hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),S)) <-> hBOOL(hAPP(fun(product_prod(X_a,X_b),bool),bool,hAPP(product_prod(X_a,X_b),fun(fun(product_prod(X_a,X_b),bool),bool),member(product_prod(X_a,X_b)),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Xa)),R_3)))) <-> ti(fun(product_prod(X_a,X_b),bool),S) = ti(fun(product_prod(X_a,X_b),bool),R_3))) # label(fact_4338_pred__equals__eq2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3543 (all X_a (number_ring(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W))))) # label(fact_170_number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3544 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,sqrt,Y_1))))) # label(fact_1631_real__sqrt__ge__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3545 (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,I_2) = hAPP(nat,nat,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_2),K_1))))) # label(fact_3552_weak__decr__stable) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3546 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),one_one(X_a))))) # label(fact_402_zero__less__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3547 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)),Ya)))) # label(fact_883_mult__left_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3548 (all N all M all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),M)),R_4)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N))))) # label(fact_3408_lemma__floor) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3549 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))))))) # label(fact_2573_inverse__le__imp__le__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3550 (all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))),zero_zero(int)))) # label(fact_2166_negative__zle__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3551 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2271_arccos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3552 (all F all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),A_3)) -> (all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),A_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,F,X_2)),hAPP(int,int,F,Xa)),Ma)) -> ti(int,X_2) = ti(int,Xa)))))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),F),A_3))))))) # label(fact_3644_ResSet__image) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3553 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1)))))) # label(fact_2677_real__root__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3554 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Y),Z_1))))) # label(fact_3042_termination__basic__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3555 (all X all Y all R_4 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),R_4)),Y) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y)),hAPP(real,complex,of_real(complex),R_4))) # label(fact_2810_Complex__add__complex__of__real) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3556 (all X_a (comm_semiring_1(X_a) -> (all Lx all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ry)))) # label(fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3557 (all D all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),A_1))) # label(fact_4383_coprime__lmult__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3558 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),hAPP(real,nat,natfloor,X))),X)))) # label(fact_2330_real__natfloor__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3559 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),C_1)),zero_zero(real)),sequentially)))) # label(fact_4491_LIMSEQ__rabs__realpow__zero2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3560 (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]. 10.83/10.82 3561 (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),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_1118_nat__mult__div__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3562 (all X_a (number_ring(X_a) -> (all W hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(int,X_a,number_number_of(X_a),W))),hAPP(int,X_a,number_number_of(X_a),W)) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,W))))) # label(fact_171_number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3563 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> (all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))) = hAPP(fun(int,bool),nat,finite_card(int),X_2)))))))) # label(fact_1539_SetS__elems__card) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3564 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1714_neg__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3565 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),B_2))))) # label(fact_1749_Union__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3566 (all X_a all A_3 all B_2 (ti(fun(X_a,bool),A_3) = ti(fun(X_a,bool),B_2) | hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2000_subset__iff__psubset__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3567 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all R_1 all G all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4735_scaleR__right_OLIM__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3568 (all X_a (metric_space(X_a) -> (all X all Y (ti(X_a,X) != ti(X_a,Y) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y))))))) # label(fact_3512_dist__pos__lt) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3569 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),exp(X_a)),X_1))))) # label(fact_4891_isCont__exp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3570 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),K_4)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),K_4)) # label(fact_581_add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3571 (all X_a (order(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_1547_xt1_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3572 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))))))) # label(fact_4531_summable) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3573 (all X_a all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),F),A_3) = one_one(nat) <-> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & (all Xa (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Xa),A_3)) -> (ti(X_a,Xa) != ti(X_a,X_2) -> zero_zero(nat) = hAPP(X_a,nat,F,Xa)))) & hAPP(X_a,nat,F,X_2) = one_one(nat)))))) # label(fact_4257_setsum__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3574 (all X all Y all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),Y)),P_5))))) # label(fact_842_MultInv__prop1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3575 (all X_a (semiring_div(X_a) -> (all C_1 all B_1 all A_2 (ti(X_a,A_2) != zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)) -> (ti(X_a,B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B_1),A_2) = ti(X_a,C_1))))))) # label(fact_1044_dvd__div__eq__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3576 (all X_1 all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X_1)),N_1))) <-> zero_zero(nat) = N_1 | ti(int,X_1) != zero_zero(int))) # label(fact_1967_zero__less__zpower__abs__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3577 (all X hAPP(int,nat,nat_1,hAPP(real,int,archim2085082626_floor(real),X)) = hAPP(real,nat,natfloor,X)) # label(fact_2860_natfloor__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3578 (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),minus_minus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1))),hAPP(X_a,X_a,inverse_inverse(X_a),B))))))) # label(fact_2582_division__ring__inverse__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3579 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B))))))) # label(fact_1795_norm__diff__ineq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3580 (all X_a (real_normed_field(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),C_1))))))) # label(fact_4086_sums__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3581 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all H all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hAPP(X_a,X_b,H,X_2) = hAPP(X_a,X_b,G,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),H),A_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3)))))) # label(fact_4769_setprod_Ocong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3582 (all X_a (metric_space(X_a) -> (all X zero_zero(real) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),X)))) # label(fact_3516_dist__self) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3583 (all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)),Z_1) != zero_zero(int)) # label(fact_166_odd__nonzero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3584 (all X_1 (zero_zero(real) = hAPP(real,real,sqrt,X_1) <-> X_1 = zero_zero(real))) # label(fact_1613_real__sqrt__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3585 (all N (zero_zero(nat) != N -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N) = hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1460_Suc__Suc__mult__two__diff__two) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3586 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),B),hAPP(nat,nat,suc,N)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_1374_power__le__imp__le__base) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3587 (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_3775_rat__number__collapse_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3588 (all Z1 all Z2 all 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)) = 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)) # label(fact_706_real__add__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3589 (all V_1 all V_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2))) <-> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),V_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),V_1),pls))))) # label(fact_212_le__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3590 (all X_a (real_vector(X_a) -> (all X all Xa_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,uminus_uminus(real),X)),Xa_1)))) # label(fact_4687_scaleR__left_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3591 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_445_power__gt1__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3592 (all X_a (ordere142940540dd_abs(X_a) -> (all A_2 (hAPP(X_a,X_a,abs_abs(X_a),A_2) = zero_zero(X_a) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_1850_abs__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3593 (all X_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),F))))) # label(fact_4306_pos__summable) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3594 (all N all M hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),code_d418564891umeral,N),M) = hAPP(code_code_numeral,product_prod(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,fun(code_code_numeral,product_prod(code_code_numeral,code_code_numeral)),product_Pair(code_code_numeral,code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),N),M)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),N),M))) # label(fact_3081_div__mod__code__numeral__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.82 3595 (all X_a (semiring_1(X_a) -> (all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,nat_1,X))))))) # label(fact_1204_of__nat__double) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3596 (all X_a all X all Y (ti(X_a,X) = ti(X_a,Y) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)))) # label(help_fequal_1_1_T) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3597 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A_1),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),A_1)) -> hAPP(int,int,abs_abs(int),A_1) = hAPP(int,int,abs_abs(int),B)))) # label(fact_1924_zdvd__antisym__abs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3598 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (exists M_2 hAPP(nat,nat,suc,M_2) = N))) # label(fact_1494_gr0__implies__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3599 (all X_a all X_b all B_2 all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2))))) # label(fact_3654_finite__surjI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3600 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B)),X) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B),X))))) # label(fact_4672_real__vector_Oscale__scale) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3601 (all V_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),V_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),V_1)))) # label(fact_49_less__0__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3602 (all X_1 (zero_zero(real) = hAPP(int,real,real_1(int),X_1) <-> ti(int,X_1) = zero_zero(int))) # label(fact_3330_real__of__int__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3603 (all N all D (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),D),N)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),D)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,real_1(nat),N)),hAPP(nat,real,real_1(nat),D))))) # label(fact_2354_real__of__nat__div) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3604 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> N = M))) # label(fact_526_le__antisym) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3605 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> (exists Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),Y_2)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,A_2)),hAPP(real,real,F,B_1)))))) # label(fact_2839_DERIV__pos__imp__increasing) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3606 (all Ma all N_1 (Ma = zero_zero(nat) & hAPP(nat,nat,suc,zero_zero(nat)) = N_1 | zero_zero(nat) = N_1 & hAPP(nat,nat,suc,zero_zero(nat)) = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_1324_add__is__1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3607 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1)),sequentially)))))) # label(fact_4740_scaleR__left_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3608 (all X_a (metric_space(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_1),Y_1))) <-> ti(X_a,Y_1) != ti(X_a,X_1))))) # label(fact_3513_zero__less__dist__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3609 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),R_4),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))))) # label(fact_3345_real__of__int__ceiling__ge) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3610 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3))))))) # label(fact_3983_suminf__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3611 (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]. 10.83/10.83 3612 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2132_arcsin__ubound) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3613 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),sin),X_1))) # label(fact_4890_isCont__sin) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3614 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,exp(real),X)))) # label(fact_2566_exp__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3615 (all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)) != zero_zero(real)) # label(fact_2420_real__of__nat__fact__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3616 (all K_4 all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),A_1)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),B)),M)))) # label(fact_359_zcong__scalar2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3617 (all V_3 all V ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),V),V_3))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V),pls)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3))))) # label(fact_231_mult__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3618 (all X_a (real_vector(X_a) -> (all A_2 all X_1 all B_1 (A_2 = B_1 | zero_zero(X_a) = ti(X_a,X_1) <-> hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),B_1),X_1) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_2),X_1))))) # label(fact_4704_scaleR__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3619 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(int,int,uminus_uminus(int),hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))) = hAPP(X_a,int,archimedean_ceiling(X_a),X)))) # label(fact_3295_ceiling__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3620 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),Y)),one_one(real))) -> hAPP(real,real,sin,hAPP(real,real,arccos,Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2401_sin__arccos__abs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3621 (all X_a (inverse(X_a) & real_normed_vector(X_a) -> inverse_divide(X_a) = ti(fun(X_a,fun(X_a,X_a)),inverse_divide(X_a)))) # label(tsy_c_Fields_Oinverse__class_Odivide_0_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3622 (all N all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),Y),hAPP(nat,nat,suc,N)))))) # label(fact_1361_divides__rexp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3623 (all P_1 ((exists X_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),X_2)))) <-> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,P_1,X_2)))))) # label(fact_1296_transfer__int__nat__quantifiers_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3624 (all X_a (idom(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) = ti(X_a,X_1) | hAPP(X_a,X_a,uminus_uminus(X_a),Y_1) = ti(X_a,X_1) <-> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_2100_realpow__two__disj) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3625 (all A_1 all 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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)) # label(fact_3222_gcd__semilattice__nat_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3626 (all X_a all X_b all X_1 all Y_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_b,bool),fun(X_a,fun(X_b,bool)),hAPP(fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_b,bool),fun(X_a,fun(X_b,bool))),combc(X_a,fun(X_b,bool),fun(X_b,bool)),hAPP(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool))),hAPP(fun(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool))),fun(fun(X_a,fun(bool,bool)),fun(X_a,fun(fun(X_b,bool),fun(X_b,bool)))),combb(fun(bool,bool),fun(fun(X_b,bool),fun(X_b,bool)),X_a),combb(bool,bool,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(X_a,fun(X_a,bool),fequal(X_a),X_1)))),hAPP(X_b,fun(X_b,bool),fequal(X_b),Y_1)))) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_1),Y_1)) # label(fact_4142_The__split__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3627 (all X hAPP(nat,real,real_1(nat),X) = hAPP(real,real,abs_abs(real),hAPP(nat,real,real_1(nat),X))) # label(fact_2291_abs__real__of__nat__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3628 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1225_Suc__not__Zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3629 (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_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),M_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ti(X_b,M_1) = ti(X_b,L_2)))))) # label(fact_4546_LIM__unique) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3630 (all X_a (number_ring(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(int,X_a,number_number_of(X_a),min_1))) # label(fact_2103_arith__simps_I31_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3631 (all X_c all X_b all X_a all Q_1 all F all P_1 all P_4 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),P_4)),hAPP(product_prod(X_b,X_a),X_b,product_fst(X_b,X_a),P_4))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,Y_2),X_2)) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(X_a,X_c,hAPP(X_b,fun(X_a,X_c),F,X_2),Y_2))))) -> hBOOL(hAPP(X_c,bool,Q_1,hAPP(product_prod(X_b,X_a),X_c,hAPP(fun(X_b,fun(X_a,X_c)),fun(product_prod(X_b,X_a),X_c),product_prod_case(X_b,X_a,X_c),F),P_4)))))) # label(fact_4126_exE__realizer) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3632 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) -> (one_one(nat) = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),Ma)),Ma))))) # label(fact_506_dvd__mult__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3633 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all G all X_1 all Ma (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Ma)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),exp(X_a)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,G,X_1))),Ma))))))) # label(fact_3864_DERIV__fun__exp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3634 (all D_1 all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),B_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),A_2)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_2),B_1))))) # label(fact_2851_coprime__mul__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3635 (all Q_3 ((hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_3),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_3) = hAPP(rat,rat,uminus_uminus(rat),Q_3)) & (-hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),Q_3),zero_zero(rat))) -> hAPP(rat,rat,abs_abs(rat),Q_3) = Q_3))) # label(fact_3715_abs__rat__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3636 (all X_a (number_semiring(X_a) -> (all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z_1),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Z_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_141_semiring__mult__2__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3637 (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),minus_minus(nat),hAPP(int,nat,nat_1,Z)),hAPP(int,nat,nat_1,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)))))) # label(fact_3835_diff__nat__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3638 (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_2792_of__real__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3639 (all M all N hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N))) # label(fact_2307_real__of__nat__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3640 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)))))))) # label(fact_4012_summable__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3641 (all X_b all X_a (order(X_a) & order(X_b) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_2831_xt7) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3642 (all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1157_Int2_Oaux__2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3643 (all Ma hAPP(int,nat,phi,Ma) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),norRRset,Ma))) # label(fact_3613_phi__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3644 (all X_b all X_a (uminus(X_a) -> (all A_3 all X_1 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_b,X_a,A_3,X_1)) = hAPP(X_b,X_a,hAPP(fun(X_b,X_a),fun(X_b,X_a),uminus_uminus(fun(X_b,X_a)),A_3),X_1)))) # label(fact_2928_uminus__apply) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3645 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_3622_RRset2norRR__correct2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3646 (all X all Y hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,cos,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,sin,Y)))) # label(fact_2323_sin__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3647 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)))) # label(fact_4815_min__max_Oinf__commute) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3648 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arctan,X)),hAPP(real,real,arctan,Y))))) # label(fact_1834_arctan__monotone_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3649 (all X_b all X_a (topological_space(X_a) & real_normed_algebra(X_b) -> (all C_1 all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),C_1)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4575_LIM__mult__left__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3650 (all A_1 all B hAPP(product_prod(int,int),int,product_snd(int,int),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) # label(fact_3116_mod__int__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3651 (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]. 10.83/10.83 3652 (all X_b all X_a (comm_monoid_add(X_a) -> (all A_3 hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(X_a,fun(X_b,X_a),combk(X_a,X_b),zero_zero(X_a))),A_3) = zero_zero(X_a)))) # label(fact_4217_setsum__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3653 (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))) & 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_1030_neg__mod__conj) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3654 (all X_a (ordere236663937imp_le(X_a) -> (all A_2 all C_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)))))) # label(fact_792_add__less__cancel__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3655 (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_4816_min__max_Oinf_Ocommute) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3656 (all A_1 all C hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),A_1) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,zero_zero(int)),C)) # label(fact_3741_eq__rat_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3657 (all X all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),P_5)))))) # label(fact_3070_prime__coprime__lt) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3658 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),minus_minus(X_b)),F)),G)),A_2))))))) # label(fact_4895_isCont__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3659 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M)))) # label(fact_582_le__square) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3660 (all X_a all B_2 all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),B_2))))) # label(fact_1955_set__rev__mp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3661 (all X_a (linord893533164strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_384_comm__mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3662 (all X_a (ordere236663937imp_le(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Y),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),Z_1)))) # label(fact_4805_min__add__distrib__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3663 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X),Y)))))) # label(fact_259_Nat__Transfer_Otransfer__nat__int__function__closures_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3664 (all X_a (real_normed_algebra(X_a) -> (all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),zero_zero(X_a)),Y) = zero_zero(X_a)))) # label(fact_877_mult__left_Ozero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3665 (all X_c all X_a all X_b all C_1 all P_4 all Q_2 (ti(product_prod(X_a,X_b),P_4) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),P_4) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),C_1),Q_2))) # label(fact_3995_split__weak__cong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3666 (all X_b (number(X_b) & ring(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),B),C)) = hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),B)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(int,X_b,number_number_of(X_b),V)),C))))) # label(fact_491_right__diff__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3667 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,ln,X))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X))))) # label(fact_1951_ln__gt__zero__imp__gt__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3668 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B)))))) # label(fact_1856_abs__add__abs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3669 (all X_a (ab_group_add(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),A_1) = zero_zero(X_a)))) # label(fact_2068_ab__left__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3670 (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_3017_complex__add__cnj) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3671 (all X_a (linordered_semidom(X_a) -> (all M all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))))) # label(fact_448_power__less__imp__less__exp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3672 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),X) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2013_norm__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3673 (all X_a (real_normed_algebra(X_a) -> (all A_1 all A_6 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_6),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),A_6)),B)))) # label(fact_882_mult_Oadd__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3674 (all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K),N_1)))) # label(fact_476_dvd__reduce) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3675 (all X_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),X_1),sequentially)) -> (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,M_2)),hAPP(nat,real,A_2,N_2))))) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,N_2)),X_1))) | (all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,N_2)),hAPP(nat,real,A_2,M_2))))) & (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),hAPP(nat,real,A_2,N_2))))))) # label(fact_4434_monoseq__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3676 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(int,real,real_1(int),A_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1)))) # label(fact_3368_ceiling__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3677 (all K all L (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),L)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),hAPP(int,int,bit1,L))))) # label(fact_53_rel__simps_I32_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3678 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N)))) # label(fact_2410_lemma__STAR__cos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3679 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),A_3)))))) # label(fact_4453_tendsto__norm__zero__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3680 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),Ma),N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4544_setsum__shift__bounds__cl__Suc__ivl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3681 (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_162_add__Bit1__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3682 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1707_divide__nonpos__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3683 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_385_mult__strict__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3684 (all N all K_4 all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),K_4))))) # label(fact_674_Nat_Odiff__diff__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3685 (all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1))))) # label(fact_2694_real__root__gt__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3686 (all X_b all X_a (comm_monoid_mult(X_a) -> (all H all G all S all R_3 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,one_one(X_a)),one_one(X_a))) -> ((all X1 all Y1 all X2 all Y2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,X1),X2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,Y1),Y2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X1),Y1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X2),Y2))))) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),S)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),S)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(X_b,X_a,H,X_2)),hAPP(X_b,X_a,G,X_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_3,hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),H),S)),hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),G),S)))))))))) # label(fact_4779_setprod_Orelated) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3687 (all X_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X_1),Ma) = one_one(int) -> hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),noXRRset,Ma),X_1)),Ma))))) # label(fact_3618_noX__is__RRset) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3688 (all X_a (order(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (ti(X_a,C) = ti(X_a,B) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),A_1))))))) # label(fact_1577_xt1_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3689 (all X all M all Y hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),M)),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),M)) # label(fact_963_zpower__zmod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3690 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(real,real,sin,X_1)))) # label(fact_4096_sin__converges) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3691 (all X_a (linorder(X_a) -> (all Y all Z_1 all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Y),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Z_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1)),X)))) # label(fact_4937_min__max_Oinf__sup__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3692 (all X_a (banach(X_a) & real_n2089651433ebra_1(X_a) -> (all X_1 hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))))))) # label(fact_4749_summable__norm__exp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3693 (all M all N all K_4 all L_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),L_4) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N))))) # label(fact_561_less__add__eq__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3694 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3)))))) # label(fact_1515_div__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3695 (all X_a (number_ring(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),pls)) = ti(X_a,A_1)))) # label(fact_149_add__numeral__0__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3696 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,B_1))))) # label(fact_4929_DERIV__isconst__end) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3697 (all D_1 all Ta (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),Ta)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,uminus_uminus(int),D_1)),Ta)))) # label(fact_2145_uminus__dvd__conv_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3698 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_595_nat__0__less__mult__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3699 (all F all Y_1 all X_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Y_1),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),A_2),B_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> hAPP(real,real,F,Y_1) = hAPP(real,real,F,X_1)))))) # label(fact_3687_DERIV__isconst3) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3700 (all X_a all F1 all F2 ti(X_a,F1) = hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),F1),F2),zero_zero(nat))) # label(fact_4155_nat__rec__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3701 (all Q_3 all R_4 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),hAPP(int,int,uminus_uminus(int),R_4)) = hAPP(product_prod(int,int),product_prod(int,int),negateSnd,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) # label(fact_3072_negateSnd__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3702 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_459_power__strict__decreasing) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3703 (all X_a all A_3 hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),A_3),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3))))) # label(fact_2806_subset__Pow__Union) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3704 (all X all Z_1 all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D))),Z_1)))) # label(fact_1986_decr__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3705 (all X_a (ordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C)))))))) # label(fact_373_mult__right__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3706 (all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> hAPP(int,fun(int,bool),norRRset,Ma) = hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma)),A_3)))) # label(fact_3630_RRset2norRR__eq__norR) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3707 (all N_1 all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,N_1)),Ma)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)))) # label(fact_1337_less__eq__Suc__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3708 (all X_a (sgn_div_norm(X_a) -> sgn_sgn(X_a) = ti(fun(X_a,X_a),sgn_sgn(X_a)))) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3709 (all X_a (linord219039673up_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,uminus_uminus(X_a),A_2))))))) # label(fact_2058_le__minus__self__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3710 (all X_a (ring_11004092258visors(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_14_zero__eq__power2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3711 (all X_a all X_b (linordered_semidom(X_b) -> (all G all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),zero_zero(X_b)),hAPP(X_a,X_b,F,X_2))) & hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),hAPP(X_a,X_b,G,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))))) # label(fact_4150_setprod__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3712 (all A_9 all B_8 all Q_6 all Y (ti(int,A_9) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_8),Q_6)),Y) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y),B_8)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_8)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_8),Y)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Y),zero_zero(int)))) -> (zero_zero(int) != ti(int,B_8) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_9),B_8) = ti(int,Y))))) # label(fact_1056_divmod__int__rel__mod__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3713 (all X_a (banach(X_a) -> (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),F)))))))) # label(fact_4023_summable__norm) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3714 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),hAPP(X_a,X_a,uminus_uminus(X_a),B))))) # label(fact_2020_minus__divide__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3715 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,W_1)))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))))) # label(fact_1504_neg__number__of__Bit1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3716 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)))) # label(fact_2001_psubset__imp__subset) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3717 (all X all Y 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))))) = zero_zero(real)) # label(fact_2399_sin__cos__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3718 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx all Ry hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Ry)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Rx),Ry))))) # label(fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3719 (all X_a (ab_group_add(X_a) -> (all F all P_4 all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),P_4)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),P_4))),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),N_1),P_4))))))) # label(fact_4200_setsum__diff__nat__ivl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3720 (all X_a (real_normed_algebra(X_a) -> (all X all Y all Ya hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),Ya) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Ya)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Ya))))) # label(fact_884_mult__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3721 (all M hAPP(int,int,abs_abs(int),M) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),zero_zero(int))) # label(fact_3452_zgcd__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3722 (all A_2 all B_1 all K all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K),Ma) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),A_2)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),B_1)),Ma)))))) # label(fact_3471_zcong__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3723 (all F (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),F),zero_zero(real)),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),abs_abs(real)),F)),zero_zero(real)),sequentially)))) # label(fact_4482_LIMSEQ__rabs__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3724 (all X_a (ring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))),B)))) # label(fact_2012_mod__minus__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3725 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K_4)) -> (exists N_2 (ti(int,K_4) = hAPP(nat,int,semiring_1_of_nat(int),N_2) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_2)))))) # label(fact_1480_zero__less__imp__eq__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3726 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(nat,fun(real,real),root,N_1)),X_1))))) # label(fact_4919_isCont__root__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3727 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3821_Ints__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3728 (all X_a (linord20386208strict(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_391_zero__less__mult__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3729 (all Nat_1 hAPP(nat,nat,nat_size,hAPP(nat,nat,suc,Nat_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,nat_size,Nat_1)),hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2920_nat_Osize_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3730 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_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),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))))))) # label(fact_2456_power__less__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3731 (all K_4 all I_1 all J_2 (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),J_2))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),I_1),K_4))))) # label(fact_3463_zrelprime__dvd__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3732 (all X_a (power(X_a) -> (all A_1 all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,N))))) # label(fact_1308_power__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3733 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2388_sin__squared__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3734 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> zero_zero(real) = hAPP(real,real,cos,hAPP(complex,real,arg,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,zero_zero(real)),Y))))) # label(fact_2752_cos__arg__i__mult__zero__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.83 3735 (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_240_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3736 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),uminus_uminus(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),D_2))))))) # label(fact_3856_DERIV__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3737 (all X_a (linordered_semidom(X_a) -> (all K all F all K_3 all N_1 ((all P_6 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),P_6),N_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,F,P_6)),K_3)))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),K_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),K_3)))))))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3738 (all X_a all X_b all X_c ti(fun(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c)),product_prod_case(X_a,X_b,X_c)) = product_prod_case(X_a,X_b,X_c)) # label(tsy_c_Product__Type_Oprod_Oprod__case_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3739 (all X_a (comple44059174attice(X_a) -> (all X_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_1),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3))))))) # label(fact_1763_complete__lattice__class_OSup__upper) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3740 (all X_a (semiring_div(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B))))) # label(fact_994_div__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3741 (all A_2 all P_4 hAPP(fun(int,bool),fun(fun(int,bool),bool),hAPP(fun(int,fun(int,bool)),fun(fun(int,bool),fun(fun(int,bool),bool)),image(int,fun(int,bool)),hAPP(int,fun(int,fun(int,bool)),hAPP(int,fun(int,fun(int,fun(int,bool))),multInvPair,A_2),P_4)),hAPP(int,fun(int,bool),sRStar,P_4)) = hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)) # label(fact_3653_SetS__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3742 (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]. 10.83/10.84 3743 (all V_1 (zero_zero(nat) = hAPP(int,nat,number_number_of(nat),V_1) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_2911_neg__number__of__pred__iff__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3744 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),ln),X_1),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X_1))))) # label(fact_2645_DERIV__ln__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3745 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),one_one(int))) # label(fact_2905_pred__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3746 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)))) # label(fact_1964_DiffD1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3747 (all X_1 (hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sqrt,X_1)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)))) # label(fact_1641_real__sqrt__pow2__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3748 (all X_a (linordered_idom(X_a) -> (all A_1 all N hAPP(X_a,X_a,abs_abs(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N)))) # label(fact_1844_power__abs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3749 (all X_a all X_b all X_c all X_2 all Xa hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),X_2,hAPP(product_prod(X_a,X_b),X_a,product_fst(X_a,X_b),Xa)),hAPP(product_prod(X_a,X_b),X_b,product_snd(X_a,X_b),Xa)) = hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),X_2),Xa)) # label(fact_4014_split__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3750 (all Ma all W_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,W_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),Ma)))))) # label(fact_1423_nat__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3751 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),N))) # label(fact_3404_powr__realpow) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3752 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),B))))))) # label(fact_2081_abs__leI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3753 (all X_a all X_b (comm_monoid_add(X_b) -> (all B_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),zero_zero(X_b))),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(X_a,X_b,B_1,A_2) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),zero_zero(X_b))),S)))))) # label(fact_4215_setsum__delta) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3754 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(fun(X_a,bool),bool),fun(fun(fun(X_a,bool),bool),bool),ord_less_eq(fun(fun(X_a,bool),bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),A_3)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),B_2))))) # label(fact_4870_Powp__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3755 (all X (hAPP(real,real,cos,X) != zero_zero(real) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,cos,X))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2627_tan__sec) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3756 (all X_a (number_ring(X_a) -> (all V ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(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))) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(int,nat,number_number_of(nat),V)) = zero_zero(X_a)))))) # label(fact_1446_of__nat__number__of__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3757 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)))))) # label(fact_3988_mult__right_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3758 (all X_a all X_b (real_n1866405975lgebra(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> (zero_zero(X_b) != ti(X_b,A_2) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),inverse_inverse(X_b)),F)),hAPP(X_b,X_b,inverse_inverse(X_b),A_2)),A_3))))))) # label(fact_4481_tendsto__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3759 (all V_1 all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))) # label(fact_4797_min__Suc__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3760 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),K)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K))) <-> (all I_2 all J_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),J_1)) & ti(int,N_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),I_2)),J_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),J_1),K)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1))))))) # label(fact_1008_split__pos__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3761 (all X_b all X_a (order(X_b) & order(X_a) -> (all C_1 all F all B_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),C_1),hAPP(X_a,X_b,F,B_1))) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_2),X_2)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),hAPP(X_a,X_b,F,Y_2)),hAPP(X_a,X_b,F,X_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),C_1),hAPP(X_a,X_b,F,A_2))))))))) # label(fact_2827_xt5) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3762 (exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,cnj,X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)))) # label(fact_2966_cnj_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3763 (all X_a (order(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y_1),X_1)))))) # label(fact_1557_order__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3764 (all X_a (linordered_field(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(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)) = 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_1871_nonzero__abs__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3765 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M))))) # label(fact_874_dvd__pos__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3766 (all X_a (real_vector(X_a) -> (all X all Y all Xa_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X),Xa_1)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),Y),Xa_1)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y)),Xa_1)))) # label(fact_4716_scaleR__left_Odiff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3767 (all X_b all X_a all R_3 all K all T_3 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),T_3)) -> K = hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),S))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))))) -> hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),T_3)))),R_3)))),S) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),hAPP(fun(X_b,bool),nat,finite_card(X_b),T_3)))))) # label(fact_4298_setsum__multicount) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3768 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W),Z_1)) # label(fact_99_zadd__commute) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3769 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1303_int__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3770 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),C))),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)))) # label(fact_978_mod__mult__self2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3771 (all X_a (linorder(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)))))) # label(fact_1584_linorder__le__less__linear) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3772 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),A_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_1))))) # label(fact_2099_abs__of__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3773 (all X_a (linordered_idom(X_a) -> (all B all D all A_1 all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),C)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),B)),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),D)))))))) # label(fact_1866_abs__mult__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3774 (all M all N (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = M)) # label(fact_685_add__diff__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3775 (all D all C all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (ti(int,B) = ti(int,C) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),D),M)))))) # label(fact_315_zcong__eq__trans) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3776 (all X_a (comm_semiring_1(X_a) -> (all X all Y all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),Q_3)))) # label(fact_247_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3777 (all Sa (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Sa)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),powr),real_1(nat))),hAPP(real,real,uminus_uminus(real),Sa))),zero_zero(real)),sequentially)))) # label(fact_4493_LIMSEQ__neg__powr) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3778 (all N zero_zero(nat) = hAPP(int,nat,nat_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N)))) # label(fact_2167_nat__zminus__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3779 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a))),X_1)))))) # label(fact_2893_number__of__less__floor) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3780 (all B all Q_5 all R_5 all Q_3 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),Q_5))))))) # label(fact_268_unique__quotient__lemma__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3781 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_5),X)),P_5)))) # label(fact_1010_StandardRes__ubound) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3782 (all N_1 all Ma (zero_zero(nat) = Ma & N_1 = zero_zero(nat) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)))))) # label(fact_2165_int__zle__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3783 (all I_1 all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),I_1))))) # label(fact_1328_less__add__Suc2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3784 (all X_1 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,X_1) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)))) # label(fact_1450_zEvenI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3785 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 all C_1 all K_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),K_3)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),X_1)),hAPP(X_a,real,norm_norm(X_a),K_3))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,X_a),hAPP(fun(fun(nat,X_a),X_a),fun(fun(X_a,fun(nat,X_a)),fun(X_a,X_a)),combb(fun(nat,X_a),X_a,X_a),suminf(X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),C_1))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(X_a,fun(nat,X_a))),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combs(X_a,X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(X_a,fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),X_a),combc(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a))),hAPP(fun(nat,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(nat,X_a),fun(X_a,fun(nat,X_a))),combc(X_a,fun(nat,X_a),fun(nat,X_a)),hAPP(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a))),hAPP(fun(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a))),fun(fun(X_a,fun(nat,fun(X_a,X_a))),fun(X_a,fun(fun(nat,X_a),fun(nat,X_a)))),combb(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),X_a),combs(nat,X_a,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a))),hAPP(fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),fun(fun(X_a,fun(nat,X_a)),fun(X_a,fun(nat,fun(X_a,X_a)))),combb(fun(nat,X_a),fun(nat,fun(X_a,X_a)),X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a))),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_1))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))))),combi(X_a))))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),semiring_1_of_nat(X_a))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(X_a)),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a))))))))) # label(fact_4532_termdiffs__aux) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3786 (all X_a all X_b all F all G ((all X_2 hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)) -> ti(fun(X_a,X_b),G) = ti(fun(X_a,X_b),F))) # label(fact_75_ext) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3787 (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_647_dvd_Oless__asym_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3788 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),cnj),hAPP(complex,complex,cnj,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4570_cnj_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3789 (all X_a (linord219039673up_add(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),A_2) <-> ti(X_a,A_2) = zero_zero(X_a))))) # label(fact_115_double__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3790 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,sqrt,X)),hAPP(real,real,sqrt,Y)) = hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y))) # label(fact_1668_real__sqrt__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3791 (all N N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),zero_zero(nat))) # label(fact_4960_max__0R) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3792 (all X_c all X_b all X_a all P_4 all F all G all Q_2 ((all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),Q_2) -> hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),G,X_2),Y_2) = hAPP(X_b,X_c,hAPP(X_a,fun(X_b,X_c),F,X_2),Y_2))) -> (ti(product_prod(X_a,X_b),Q_2) = ti(product_prod(X_a,X_b),P_4) -> hAPP(product_prod(X_a,X_b),X_c,hAPP(fun(X_a,fun(X_b,X_c)),fun(product_prod(X_a,X_b),X_c),product_prod_case(X_a,X_b,X_c),G),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)))) # label(fact_4771_split__cong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3793 (all R1 all A_1 all R2 all 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)) = 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))) # label(fact_3172_rcis__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3794 (all Q_5 all R_5 all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_5),R_5))) -> (ti(int,B) != zero_zero(int) -> ti(int,R_4) = ti(int,R_5))))) # label(fact_1186_unique__remainder) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3795 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),N))))))) # label(fact_2502_Ln_Oaux1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3796 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1))))) # label(fact_1237_Suc__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3797 (all N all F_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),F_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),M),N)))))) # label(fact_961_zdvd__zmod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3798 (all X_a all X_b (real_normed_vector(X_b) -> (all R_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1)),G)),hAPP(X_b,X_b,hAPP(real,fun(X_b,X_b),scaleR_scaleR(X_b),R_1),A_2)),A_3)))))) # label(fact_4728_scaleR__right_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3799 (all U_1 hAPP(nat,nat,suc,U_1) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),ord_atMost(nat),U_1))) # label(fact_4973_card__atMost) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3800 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,fact_fact(nat),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N),hAPP(nat,nat,fact_fact(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))))) # label(fact_2501_fact__reduce__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3801 (all A_3 hAPP(fun(int,bool),nat,finite_card(int),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),A_3)) = hAPP(fun(nat,bool),nat,finite_card(nat),A_3)) # label(fact_3651_Nat__Transfer_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3802 (all A_1 all C all D all B (zero_zero(int) != ti(int,B) -> (zero_zero(int) != ti(int,D) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,C),D))))) # label(fact_3785_add__rat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3803 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),M)) -> M != N)) # label(fact_518_less__not__refl2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3804 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,fact_fact(nat),N)))) # label(fact_2496_fact__ge__Suc__0__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3805 (all X_b all X_a all B_2 all A_3 ((-(hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)) = zero_zero(nat)) & (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2)) = hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2))))) # label(fact_3180_card__Plus__conv__if) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3806 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_594_add__gr__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3807 (all N_1 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> (exists M_2 hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M_2)) = N_1))) # label(fact_2469_odd__Suc__mult__two__ex) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3808 (all X_a (linordered_idom(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),B_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_2)),B_1)))))) # label(fact_2083_abs__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3809 (all X_a (comm_semiring_1(X_a) -> (all X all N hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3810 (all W hAPP(int,rat,hAPP(int,fun(int,rat),fract,W),one_one(int)) = hAPP(int,rat,number_number_of(rat),W)) # label(fact_3747_rat__number__of__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3811 (all X_b all X_a (real_normed_algebra(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),times_times(X_b)),F)),G)),A_2))))))) # label(fact_4910_mult_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3812 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_547_less__eq__nat_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3813 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_150_less__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3814 (all Z_1 all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Z_1),W) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) # label(fact_23_zmult__commute) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3815 (all C_1 all D_1 all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_2),D_1)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_1),D_1)),Ma))))) # label(fact_356_zcong__zmult__prop1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3816 (all P_1 all X_1 all Y_1 (hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),X_1),Y_1)))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) -> hBOOL(hAPP(int,bool,P_1,zero_zero(int)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Y_1),X_1)) -> hBOOL(hAPP(int,bool,P_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))))) # label(fact_1425_zdiff__int__split) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3817 (all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),U)))) # label(fact_1766_lemma__real__divide__sqrt__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3818 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),K_4)),one_one(int)))) # label(fact_3707_Frct__code__post_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3819 (all X_a (ring_1(X_a) -> (all C_1 all X_2 hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),C_1),X_2)) = hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),diffs(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),C_1)),X_2)))) # label(fact_4113_diffs__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3820 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))))))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3821 (all X hAPP(real,real,arctan,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))))))))))) # label(fact_1831_arctan__half) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3822 (all X_a (number_ring(X_a) & ring_char_0(X_a) -> (all W_1 (hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,W_1)))) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),W_1))))))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3823 (all P_1 ((all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(int,nat,nat_1,X_2))))) <-> (all X1 hBOOL(hAPP(nat,bool,P_1,X1))))) # label(fact_1106_all__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3824 (all X_b all X_a (real_normed_vector(X_b) & real_normed_vector(X_a) -> (all F all L_2 all A_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists S_1 ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),S_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L_2))),R_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1)))))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4644_LIM__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3825 (all X_a (ordered_ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1)),D_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1))))))) # label(fact_501_le__add__iff1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3826 (all X_a (number_ring(X_a) -> (all X (hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X))))) # label(fact_2457_Parity_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3827 (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_330_power__mult__distrib) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3828 (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]. 10.83/10.84 3829 (all X_a all X_b all F all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_3))) # label(fact_1177_transfer__morphism__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3830 (all X hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_2389_cos__squared__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3831 (all X_a (linordered_semidom(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),one_one(X_a)))))) # label(fact_439_zero__less__two) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3832 (all X_a (semiring_1(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),zero_zero(X_a))))) # label(fact_2554_iszero__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3833 (all X_1 hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,X_1)) = hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),sin_coeff)),hAPP(real,fun(nat,real),power_power(real),X_1))))) # label(fact_3974_lemma__sin__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3834 (all M all N hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N)) # label(fact_3094_divmod__nat__div__mod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3835 (all X_a (linorder(X_a) -> ord_max(X_a) = hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a)),min(X_a),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),ord_less_eq(X_a))))) # label(fact_4991_dual__min) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3836 (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)) -> one_one(int) = hAPP(int,int,abs_abs(int),X))))) # label(fact_4402_coprime__common__divisor__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3837 (all X_a (real_normed_algebra(X_a) -> (all X_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1)),X_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),A_2)),sequentially)))))) # label(fact_4479_mult__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3838 (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_892_gcd__lcm__complete__lattice__nat_Otop__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3839 (all X_a (comple44059174attice(X_a) -> (all A_3 all B_1 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),B_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(fun(X_a,bool),X_a,complete_Sup_Sup(X_a),A_3)),B_1)))))) # label(fact_1762_Sup__le__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3840 (all X_a all A_2 all F all V_1 hAPP(nat,X_a,hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(X_a,fun(fun(nat,X_a),fun(nat,X_a)),nat_case(X_a),A_2),F),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),A_2),hAPP(nat,X_a,F,hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))))) # label(fact_4125_nat__case__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3841 (all X_a all X_b (t2_space(X_b) -> (all L_1 all F all L all A_3 (-hBOOL(hAPP(filter(X_a),bool,trivial_limit(X_a),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),A_3)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_1),A_3)) -> ti(X_b,L) = ti(X_b,L_1))))))) # label(fact_4767_tendsto__unique) # label(axiom) # label(non_clause). [assumption]. 10.83/10.84 3842 (all X_a (ord(X_a) -> min(X_a) = ti(fun(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,X_a))),min(X_a)))) # label(tsy_c_Orderings_Oord_Omin_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3843 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3594_less__ceiling__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3844 (all X_a (metric_space(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,N_2)),L_2)),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4662_metric__LIMSEQ__I) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3845 (all I (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I),zero_zero(int))) <-> hAPP(int,nat,nat_1,I) = zero_zero(nat))) # label(fact_1124_nat__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3846 (all P_2 all P_1 all X_1 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(P_1) <-> hBOOL(P_2))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) & hBOOL(P_1) <-> hBOOL(P_2) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))))) # label(fact_545_conj__le__cong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3847 (all U all M all N all J_2 all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),J_2),I_1)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),I_1),U)),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),J_2),U)),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),J_2)),U)),M)),N))) # label(fact_753_nat__diff__add__eq1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3848 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),im),hAPP(complex,real,im,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4569_Im_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3849 (all W hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W),W))) # label(fact_21_zle__refl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3850 (all Z_1 exists A_4 exists R_2 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(complex,complex,expi,A_4)) = Z_1) # label(fact_2914_complex__expi__Ex) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3851 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),W_1),Z)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),one_one(int))),Z)))) # label(fact_84_add1__zle__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3852 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),X)),one_one(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))),N))))) # label(fact_2370_LIMSEQ__inverse__realpow__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3853 (all X_a all G all B_1 all F all A_2 all Net (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),A_2),Net)) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),G),B_1),Net)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,real),fun(X_a,complex),hAPP(fun(X_a,fun(real,complex)),fun(fun(X_a,real),fun(X_a,complex)),combs(X_a,real,complex),hAPP(fun(X_a,real),fun(X_a,fun(real,complex)),hAPP(fun(real,fun(real,complex)),fun(fun(X_a,real),fun(X_a,fun(real,complex))),combb(real,fun(real,complex),X_a),complex_1),F)),G)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1)),Net))))) # label(fact_4505_tendsto__Complex) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3854 (all X_a all X_b (comm_monoid_add(X_b) & ordere779506340up_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(X_a,X_b,F,X_2)),zero_zero(X_b))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3)),zero_zero(X_b))))))) # label(fact_4308_setsum__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3855 (all P_4 all N_1 (hBOOL(hAPP(nat,bool,prime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_4),N_1))) <-> N_1 = one_one(nat) & hBOOL(hAPP(nat,bool,prime,P_4)))) # label(fact_3059_prime__exp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3856 (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_1449_nat__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3857 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),zero_zero(X_a))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),pls)))))) # label(fact_176_less__special_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3858 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),N)))) # label(fact_2289_real__of__nat__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3859 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),Y_1)))) # label(fact_1633_real__sqrt__gt__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3860 (all X_a all X_b (real_normed_field(X_b) -> (all Y_1 all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),inverse_divide(X_b)),G)),Y_1)),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),inverse_divide(X_b),A_2),Y_1)),A_3)))))) # label(fact_4456_divide_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3861 (all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),N_1)) -> hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),N_1)) = hAPP(int,int,fact_fact(int),N_1))) # label(fact_4614_fact__altdef__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3862 (all Z_1 exists R_2 exists A_4 hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),R_2)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_4)),hAPP(real,real,sin,A_4))) = Z_1) # label(fact_2823_complex__split__polar) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3863 (all Y all X (hAPP(real,real,exp(real),Y) = X -> hAPP(real,real,ln,X) = Y)) # label(fact_2507_ln__unique) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3864 (all X_a (real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),Y)))) # label(fact_2017_divide_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3865 (all X_1 all N_1 all Diff all F (F = hAPP(nat,fun(real,real),Diff,zero_zero(nat)) -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),T_4)),hAPP(real,real,abs_abs(real),X_1))) & hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),X_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),N_1))) = hAPP(real,real,F,X_1)))))) # label(fact_4278_Maclaurin__bi__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3866 (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> (hBOOL(hAPP(fun(nat,rat),bool,vanishes,Y_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),X_3)),Y_3)))))) # label(fact_4841_vanishes__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3867 (all Y all X exists R_2 exists A_4 (X = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,cos,A_4)) & Y = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_2),hAPP(real,real,sin,A_4)))) # label(fact_3492_polar__Ex) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3868 (all A_1 all B hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_568_zspecial__product) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3869 (all X_1 hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_4103_Ln_Oaux2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3870 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_810_inv__not__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3871 (all X_a (dvd(X_a) -> ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)) = times_times(X_a))) # label(tsy_c_Groups_Otimes__class_Otimes_2_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3872 (all Z_1 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),Z_1)))) # label(fact_1295_Nat__Transfer_Otransfer__nat__int__function__closures_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3873 (all X_a (metric_space(X_a) -> (all X_3 ((all E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) -> (exists M_3 all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),M_2)) -> (all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))),E)))))))) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)))))) # label(fact_3525_metric__CauchyI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3874 (all A_1 all N all B hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),N)) = 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)) # label(fact_3217_gcd__exp__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3875 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N))) # label(fact_1084_div__mod__equality_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3876 (all D all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D),A_1)))) # label(fact_2849_coprime__rmul2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3877 (all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,N)))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,N)))))) # label(fact_471_number__of1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3878 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,X_1)),hAPP(int,nat,nat_1,Y_1))))))) # label(fact_1136_transfer__nat__int__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3879 (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_1349_Divides_Otransfer__int__nat__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3880 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = zero_zero(X_a) & ti(X_a,Y_1) = zero_zero(X_a) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(X_a))))))) # label(fact_106_sum__power2__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3881 (all X_1 (hAPP(real,real,hAPP(real,fun(real,real),powr,X_1),one_one(real)) = X_1 <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)))) # label(fact_3379_powr__one__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3882 (all Ma all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),Z)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),hAPP(int,nat,nat_1,hAPP(int,int,abs_abs(int),Z)))))) # label(fact_1971_int__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3883 (all X_a (real_normed_vector(X_a) -> (all X_3 all L_2 ((all R_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_2)))))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)))))) # label(fact_4659_LIMSEQ__I) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3884 (all X all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)))) # label(fact_3347_powr__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3885 (all X one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),one_one(nat)),X)) # label(fact_3250_gcd__lcm__complete__lattice__nat_Oinf__bot__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3886 (all X_a (field_inverse_zero(X_a) & field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),field_char_0_Rats(X_a))))))) # label(fact_3701_Rats__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3887 (all X all Y hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,X),Y)))) # label(fact_3446_zgcd__geq__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3888 (all X_a (linordered_field(X_a) -> (all Z_1 all W all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),W)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),W),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),Y),W)))))))))) # label(fact_1703_frac__less2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3889 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N)) # label(fact_1411_Suc3__eq__add__3) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3890 (all X_b (semiring(X_b) & number(X_b) -> (all V all B all C hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),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)) = 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))))) # label(fact_96_right__distrib__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3891 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,Y)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,Y)),hAPP(real,real,sin,X))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y))) # label(fact_2338_cos__diff2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3892 (all X_a (ring_1(X_a) -> (all F all N_1 all R_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),R_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),R_1)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))))) # label(fact_4172_sumr__diff__mult__const2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3893 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_966_div__by__1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3894 (all X_a (ordered_ring(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_369_mult__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3895 (all B_1 all P_4 all A_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),one_one(int))),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4)))))) # label(fact_838_wset__subset) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3896 (all X_b all X_a all F all B_2 all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),hAPP(X_a,X_b,F,X_2)),B_2)))) -> hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3)),B_2)))) # label(fact_3655_image__subsetI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3897 (all Z_1 -(all M_2 all N_2 ti(int,Z_1) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,semiring_1_of_nat(int),M_2)),hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_1521_int__diff__cases) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3898 (all S ((all X_2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)))) <-> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,S)))) # label(fact_3662_nat__set__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3899 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ma),hAPP(int,int,number_number_of(int),N_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),Ma)),hAPP(int,real,number_number_of(real),N_1))))) # label(fact_3389_number__of__le__real__of__int__iff2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3900 (all A_1 all B hAPP(complex,complex,expi,hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A_1),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,expi,A_1)),hAPP(complex,complex,expi,B))) # label(fact_2820_expi__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3901 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),F)),C_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)))))) # label(fact_3989_suminf__mult2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3902 (all X_a (comm_monoid_add(X_a) -> (all F all Ma all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),hAPP(nat,nat,suc,Ma)),hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))))) # label(fact_4187_setsum__shift__bounds__Suc__ivl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3903 (all M all 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))) & (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))))) # label(fact_2482_fact__add__num__eq__if__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3904 (all X_a all A_3 all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),powp(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3)),X_2)) <-> hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),X_2),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3))))) # label(fact_4871_Powp__Pow__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3905 (all M all N (ti(int,N) != zero_zero(int) -> 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_3789_Fract__add__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3906 (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_4374_gcd__abs2__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3907 (all X_a (ring_1(X_a) -> (all N one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) # label(fact_2121_power__minus1__even) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3908 (all X (zero_zero(real) != X -> hAPP(real,real,arctan,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),X)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sgn_sgn(real),X)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(real,real,arctan,X)))) # label(fact_2187_arctan__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3909 (all X_a (number_ring(X_a) & field_inverse_zero(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)),X) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),one_one(X_a)),X))))) # label(fact_2114_minus1__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3910 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B all C (zero_zero(X_a) != ti(X_a,C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B))))) # label(fact_1690_mult__divide__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3911 (all V_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))) <-> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))))) # label(fact_3893_less__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3912 (all X_1 all Ma (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),Ma) = hAPP(nat,nat,suc,zero_zero(nat)) <-> X_1 = hAPP(nat,nat,suc,zero_zero(nat)) | zero_zero(nat) = Ma)) # label(fact_1353_nat__power__eq__Suc__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3913 (all N_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_1)),ring_1_Ints(real)))) # label(fact_3852_Ints__real__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3914 (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_3220_gcd__commute__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3915 (all N (N != zero_zero(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),N) = one_one(nat))) # label(fact_3287_coprime__minus__one__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3916 (all X hAPP(complex,complex,uminus_uminus(complex),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X)))) # label(fact_3015_complex__minus__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3917 (all N hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,N)),one_one(code_code_numeral)) = N) # label(fact_2955_Suc__code__numeral__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3918 (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_2684_real__root__power) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3919 (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),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_648_dvd_Oless__trans) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3920 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C))))) # label(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3921 (all K_4 hAPP(product_prod(int,int),rat,frct,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),K_4)) = zero_zero(rat)) # label(fact_3709_Frct__code__post_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3922 (all F all G ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,G,N_2)))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),G)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),F)),hAPP(fun(nat,real),real,suminf(real),G))))))) # label(fact_4129_summable__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3923 (all B all A_1 (ti(int,A_1) != zero_zero(int) | zero_zero(int) != ti(int,B) -> (exists C_4 exists D_3 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,C_4),D_3) = one_one(int) & ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_1),B)),D_3) & ti(int,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))))) # label(fact_3484_make__zrelprime) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3924 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2))),F)),zero_zero(X_b))),A_3))))) # label(fact_4185_setsum__restrict__set_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3925 (all A_1 all B (ti(int,B) != zero_zero(int) -> (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)) & (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),A_1)),B)))) # label(fact_2180_zdiv__zminus1__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3926 (all X_a (linordered_semidom(X_a) -> (all B all C all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)))))))) # label(fact_399_pos__add__strict) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3927 (all X_a (linordered_idom(X_a) -> (all X all Y all N (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),N)))))))) # label(fact_2421_power__mono__odd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3928 (all X all A_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),X)),A_1) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(int,real,real_1(int),A_1)))) # label(fact_3374_ceiling__subtract) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3929 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,N_1),N_1)) <-> one_one(nat) = N_1)) # label(fact_2852_coprime__refl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3930 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),one_one(nat)),A_1))) # label(fact_894_gcd__lcm__complete__lattice__nat_Obot__least) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3931 (all A_2 all B_1 ((all D_3 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),B_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_3),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_3)) <-> one_one(int) = ti(int,D_3))) <-> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),B_1))) # label(fact_4405_coprime__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3932 (all X_a (semiring_1(X_a) -> (all Z (zero_zero(X_a) = ti(X_a,Z) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),Z)))))) # label(fact_2555_iszero__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3933 (all X (hAPP(real,real,sin,X) = zero_zero(real) -> one_one(real) = hAPP(real,real,abs_abs(real),hAPP(real,real,cos,X)))) # label(fact_2337_sin__zero__abs__cos__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3934 (all X_b all X_a all X all Y all A_1 (ti(X_a,A_1) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(X_a,product_prod(X_b,X_a),hAPP(X_b,fun(X_a,product_prod(X_b,X_a)),product_Pair(X_b,X_a),X),Y)) -> ti(X_a,A_1) = ti(X_a,Y))) # label(fact_3139_snd__eqD) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3935 (all A_1 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),M)) -> (exists X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),M)) & (all Y_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Y_2),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),Y_2),M)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_2)) -> ti(int,X_2) = ti(int,Y_2))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),X_2),M)))))) # label(fact_616_zcong__zless__unique) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3936 (all V_1 all K all A_2 all B_1 (A_2 != B_1 -> ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),V_1),X_2),K))) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,V_1,A_2)),hAPP(real,real,V_1,B_1))),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,V_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_2),B_1)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2658_DERIV__const__average) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3937 (all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,nat_1,X_1)))))) # label(fact_2462_pos__int__even__equiv__nat__even) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3938 (all X_a (cancel146912293up_add(X_a) -> (all A_1 all B all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B) -> ti(X_a,B) = ti(X_a,C))))) # label(fact_767_add__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3939 (all X_a all X_b (comm_monoid_add(X_b) -> (all F all A_3 ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> zero_zero(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))) # label(fact_4775_setsum__0_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3940 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all X_3 all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),X_3),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (all S_2 ((all N_2 ti(X_a,A_2) != hAPP(nat,X_a,S_2,N_2)) & hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),S_2),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(nat,X_a),fun(nat,X_b),hAPP(fun(X_a,X_b),fun(fun(nat,X_a),fun(nat,X_b)),combb(X_a,X_b,nat),X_3),S_2)),L_2),sequentially)))))))) # label(fact_4655_LIMSEQ__SEQ__conv1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3941 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (exists N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))),X))))) # label(fact_2629_reals__Archimedean) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3942 (all M all N all R_5 all S_4 all S_3 all T_6 all T_5 all R_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_4),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),R_5),R_4)),S_3),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),S_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),S_3))),T_5),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),T_6),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),R_5),R_4)),T_5)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),R_4),zero_zero(int))) -> hAPP(product_prod(int,int),product_prod(int,product_prod(int,int)),hAPP(int,fun(product_prod(int,int),product_prod(int,product_prod(int,int))),product_Pair(int,product_prod(int,int)),R_5),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),S_4),T_6)) = hAPP(int,product_prod(int,product_prod(int,int)),hAPP(int,fun(int,product_prod(int,product_prod(int,int))),hAPP(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))),hAPP(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int)))))))),hAPP(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,fun(int,product_prod(int,product_prod(int,int))))))))),xzgcda,M),N),R_5),R_4),S_4),S_3),T_6),T_5)))) # label(fact_3083_xzgcda_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3943 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N),M) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),M)),M)) # label(fact_4957_nat__minus__add__max) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3944 (all X_a (field_char_0(X_a) -> (all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),field_char_0_Rats(X_a))))))) # label(fact_3698_Rats__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3945 (all D_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,D_1),zero_zero(nat))) <-> one_one(nat) = D_1)) # label(fact_2866_coprime__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3946 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y),Y)))))) # label(fact_1635_real__sqrt__mult__self__sum__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3947 (all N hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),pi)) = zero_zero(real)) # label(fact_2297_sin__npi) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3948 (all X_a (comm_semiring_1(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),one_one(X_a)),A_1)))) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3949 (all X (-hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),one_one(int)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1472_odd__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3950 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),X_1),Y_1))))) # label(fact_4535_SetInterval_Otransfer__nat__int__set__function__closures) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3951 (all X_a all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)) = hAPP(fun(fun(X_a,bool),bool),nat,finite_card(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),pow(X_a),A_3)))) # label(fact_2773_card__Pow) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3952 (all W_1 (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),W_1))) <-> hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,W_1)))))) # label(fact_1506_neg__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3953 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_536_not__less0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3954 (all M one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),one_one(int))) # label(fact_4360_gcd__1__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3955 (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & zero_zero(real) = hAPP(real,real,cos,X_2) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) & hAPP(real,real,cos,Y_2) = zero_zero(real) -> X_2 = Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_2)))) # label(fact_2249_cos__is__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3956 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)))))))) # label(fact_1741_neg__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3957 (all M all N all Z_1 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))),Z_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),N)),Z_1))) # label(fact_1313_zadd__int__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3958 (all X_a (semiring(X_a) -> times_times(X_a) = ti(fun(X_a,fun(X_a,X_a)),times_times(X_a)))) # label(tsy_c_Groups_Otimes__class_Otimes_3_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3959 (all X_a (group_add(X_a) -> (all A_2 (zero_zero(X_a) = ti(X_a,A_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),A_2) = zero_zero(X_a))))) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3960 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ta),one_one(int))),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa) != ti(int,X_2))))) -> (ti(int,X_2) = ti(int,Ta) -> ti(int,Ta) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2))))))) # label(fact_4638_aset_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3961 (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_3107_div__int__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3962 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),M)) -> hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N)))) # label(fact_2327_real__of__nat__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3963 (all A_1 all B hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B))) # label(fact_2150_zmod__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3964 (all N_1 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,real_1(nat),N_1)),field_char_0_Rats(real)))) # label(fact_3682_Rats__real__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3965 (all X_a (topological_space(X_a) -> (all G all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,complex),fun(X_a,real),hAPP(fun(complex,real),fun(fun(X_a,complex),fun(X_a,real)),combb(complex,real,X_a),re),G)),hAPP(complex,real,re,L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4596_Re_OLIM) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3966 (all K_4 hAPP(int,int,uminus_uminus(int),hAPP(int,int,bit0,K_4)) = hAPP(int,int,bit0,hAPP(int,int,uminus_uminus(int),K_4))) # label(fact_2138_minus__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.85 3967 (all Y_3 all Y_1 all X_3 all X_1 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),X_3),X_1),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),Y_3),Y_1),sequentially)) -> ((exists N_3 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_3),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,X_3,N_2)),hAPP(nat,real,Y_3,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)))))) # label(fact_4431_LIMSEQ__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3968 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arccos,Y)),pi))))) # label(fact_2264_arccos__ubound) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3969 (all X_a (real_normed_algebra(X_a) -> (all C_1 all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),C_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1))))))) # label(fact_4080_sums__mult2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3970 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)) = hAPP(int,fun(int,bool),sRStar,P_4))))) # label(fact_1604_MultInvPair__prop2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3971 (all X_a (linord20386208strict(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),A_1))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B))))))) # label(fact_390_zero__less__mult__pos2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3972 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1) = hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1) <-> ti(X_a,X_1) = ti(X_a,Y_1))))) # label(fact_4316_lessThan__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3973 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)))))) # label(fact_4463_LIMSEQ__imp__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3974 (all B_1 all A_2 all F all G all X_1 all D_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),hAPP(real,real,G,X_1)),D_2)) -> (D_2 != zero_zero(real) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),B_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),Y_2)) -> hAPP(real,real,F,hAPP(real,real,G,Y_2)) = Y_2)) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),G),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),hAPP(real,real,inverse_inverse(real),D_2)))))))))) # label(fact_4925_DERIV__inverse__function) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3975 (all X all Y hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y))) # label(fact_609_real__sum__squared__expand) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3976 (all A_1 all N hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1))) # label(fact_3033_DeMoivre) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3977 (all B all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),B)) -> (exists D_3 ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),Y_2))),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_1),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),B)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_1914_lemma__interval) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3978 (all X_a (real_n1866405975lgebra(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (zero_zero(X_a) != ti(X_a,A_2) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),inverse_inverse(X_a)),X_3)),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),sequentially))))))) # label(fact_4483_LIMSEQ__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3979 (all X all Y all M hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y)),M) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Y),M))),M)) # label(fact_957_zdiff__zmod__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3980 (all X_a (linordered_idom(X_a) -> (all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),zero_zero(int))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),zero_zero(X_a))))))) # label(fact_3601_of__int__less__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3981 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3))))))) # label(fact_4670_scaleR__right_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3982 (all X_a (ordere779506340up_add(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))))))) # label(fact_782_add__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3983 (all X all Y all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Z_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Y),Z_1))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Z_1)),Y))))) # label(fact_1027_div__prop1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3984 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1599_order__less__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3985 (all Y all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y) = Y)) # label(fact_3237_gcd__proj2__if__dvd__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3986 (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]. 10.83/10.86 3987 (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]. 10.83/10.86 3988 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_761_add__neg__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3989 (all P_1 all A_2 all B_1 hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1) = hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),zero_zero(nat))) # label(fact_3132_Bolzano__bisect_Osimps_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3990 (all Y all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))))) # label(fact_2706_real__root__mult__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3991 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),X_1),Y_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)) & hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),Y_1)))) # label(fact_2415_even__sum__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3992 (all A_1 all B (zero_zero(int) != hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) -> (exists A_5 exists B_3 (hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B_3),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)) = ti(int,B) & hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_5),B_3) = one_one(int) & 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_4777_gcd__coprime__exists__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3993 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> -(all K_1 hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),K_1) != ti(int,X_1)))) # label(fact_1477_zEvenE) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3994 (all X_a (real_normed_vector(X_a) -> (all B zero_zero(X_a) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),zero_zero(real)),B)))) # label(fact_4710_scaleR_Ozero__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3995 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,fact,N)))) # label(fact_3544_fact__lt) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3996 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),A_2))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_2)),hAPP(X_a,X_a,inverse_inverse(X_a),B_1))))))) # label(fact_2606_inverse__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3997 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),uminus_uminus(X_b)),F)),hAPP(X_b,X_b,uminus_uminus(X_b),L_2)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4554_LIM__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3998 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(real,real,sqrt,hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U))))) # label(fact_1839_real__sqrt__sum__squares__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 3999 (all J_2 all K_4 all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),J_2)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),K_4)),M)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),K_4) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),J_2)))) # label(fact_465_neg__one__power__eq__mod__m) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4000 (all R_4 all Q_3 all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_3),one_one(int))))))) # label(fact_190_self__quotient__aux2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4001 (all A_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A_1)) -> (exists R_2 (A_1 = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),R_2),N) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_734_realpow__pos__nth) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4002 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) & zero_zero(X_a) != ti(X_a,X_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | hAPP(int,nat,number_number_of(nat),W_1) = zero_zero(nat) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1)))))))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4003 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1)),sequentially)))))) # label(fact_4449_divide_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4004 (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),im),X_3)),hAPP(complex,real,im,A_2)),sequentially)))) # label(fact_4512_Im_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4005 (all X_a all R1_1 all R2_1 (hBOOL(hAPP(fun(X_a,fun(X_a,bool)),bool,hAPP(fun(X_a,fun(X_a,bool)),fun(fun(X_a,fun(X_a,bool)),bool),ord_less_eq(fun(X_a,fun(X_a,bool))),R1_1),R2_1)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R2_1)),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R1_1))))) # label(fact_2913_accp__subset) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4006 (all Ma all W_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> zero_zero(nat) = Ma) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),W_1)) -> hAPP(nat,int,semiring_1_of_nat(int),Ma) = ti(int,W_1)) <-> hAPP(int,nat,nat_1,W_1) = Ma)) # label(fact_1406_nat__eq__iff2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4007 (all W_1 all Z (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),W_1),Z)) <-> (exists N_2 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),W_1),hAPP(nat,int,semiring_1_of_nat(int),N_2)) = ti(int,Z)))) # label(fact_1306_zle__iff__zadd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4008 (all X all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),X)),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),X),hAPP(real,nat,natfloor,A_1))))) # label(fact_2331_le__natfloor) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4009 (all X_a (group_add(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),B)))) # label(fact_809_diff__add__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4010 (all X_1 hAPP(real,real,ln,X_1) = hAPP(fun(real,bool),real,the(real),hAPP(real,fun(real,bool),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),hAPP(fun(real,fun(real,bool)),fun(fun(real,real),fun(real,fun(real,bool))),combb(real,fun(real,bool),real),fequal(real)),exp(real))),X_1))) # label(fact_4134_ln__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4011 (all Ma all N_1 ((exists J_1 (Ma = hAPP(nat,nat,suc,J_1) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),N_1)))) | Ma = zero_zero(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),hAPP(nat,nat,suc,N_1))))) # label(fact_1320_less__Suc__eq__0__disj) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4012 (all X hAPP(real,real,uminus_uminus(real),hAPP(int,real,real_1(int),X)) = hAPP(int,real,real_1(int),hAPP(int,int,uminus_uminus(int),X))) # label(fact_3342_real__of__int__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4013 (all X_a (linordered_idom(X_a) -> (all A_1 all N (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)))))) # label(fact_1470_odd__0__le__power__imp__0__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4014 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(nat,int,semiring_1_of_nat(int),X_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2429_even__nat__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4015 (all X_a (power(X_a) -> (all M all N ((N != zero_zero(nat) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),M),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat)))) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N)) & (zero_zero(nat) = N -> one_one(X_a) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),M),N)))))) # label(fact_735_realpow__num__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4016 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)))))))) # label(fact_2712_real__root__increasing) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4017 (all X_a all X_b (real_normed_vector(X_b) -> (all F all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),hAPP(X_b,real,norm_norm(X_b),A_2)),A_3)))))) # label(fact_4459_tendsto__norm) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4018 (all M all N all K_4 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N)))) # label(fact_3453_zgcd__zdvd__zgcd__zmult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4019 (all X all N hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),X)),N)))) # label(fact_1941_zero__le__zpower__abs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4020 (all X hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),hAPP(complex,real,im,X))),hAPP(complex,real,norm_norm(complex),X)))) # label(fact_2983_abs__Im__le__cmod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4021 (all X_a (real_normed_field(X_a) -> (all N_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),hAPP(nat,nat,suc,N_1))),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),one_one(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),N_1))))))))) # label(fact_3887_DERIV__power__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4022 (all X all Y all Z_1 hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),Y)),Z_1) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Y),Z_1))) # label(fact_203_zpower__zpower) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4023 (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_3870_zpower__number__of__even) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4024 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3240_gcd__semilattice__nat_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4025 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),ord_lessThan(nat),N_1))),hAPP(nat,X_a,F,N_1))))) # label(fact_4321_setsum__lessThan__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4026 (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_1068_zprime__zOdd__eq__grt__2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4027 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),one_one(X_a)))))))) # label(fact_3311_ceiling__less__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4028 (all Y_1 all X_1 all A_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),X_1)),hAPP(real,real,hAPP(real,fun(real,real),log,A_2),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1))))))) # label(fact_2646_log__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4029 (all Ma all N_1 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)),N_1)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)) = Ma & (zero_zero(nat) = N_1 -> zero_zero(nat) = hAPP(product_prod(nat,nat),nat,product_fst(nat,nat),Qr)) & (N_1 != zero_zero(nat) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),zero_zero(nat)))) & (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(product_prod(nat,nat),nat,product_snd(nat,nat),Qr)),N_1)))) <-> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,Ma),N_1),Qr)))) # label(fact_3127_divmod__nat__rel__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4030 (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),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)))) # label(fact_3228_gcd__semilattice__nat_Oless__infI2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4031 (all X0 all F all R_3 ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X_2)))))) -> (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X0),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),hAPP(real,real,uminus_uminus(real),R_3)),R_3))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),suc)))),X0),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),F)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),hAPP(real,fun(nat,real),power_power(real),X0))))))))) # label(fact_4036_DERIV__power__series_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4032 (all X_a (metric_space(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))))))) # label(fact_3505_dist__triangle2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4033 (all A_1 all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,A_1) -> ti(int,Q_3) = one_one(int)))) # label(fact_1190_self__quotient) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4034 (all M all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3076_prime__dvd__square) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4035 (all X_a (comm_semiring_1(X_a) -> (all A_1 all M hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),M)),M) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),one_one(X_a))),M)))) # label(fact_255_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4036 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)),M))) # label(fact_1091_mod__less__eq__dividend) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4037 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X))),X),P_5)))))) # label(fact_846_MultInv__prop4) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4038 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)) | K = zero_zero(nat))) # label(fact_748_nat__mult__dvd__cancel__disj) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4039 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),L)),one_one(int))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),L),U_1))) # label(fact_4605_card__atLeastAtMost__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4040 (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_2149_zmod__zminus2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4041 (all Sa all Ta all A_2 all B_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_2),B_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Sa),Ta)) -> hBOOL(hAPP(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool,hAPP(product_prod(product_prod(nat,nat),product_prod(nat,nat)),fun(fun(product_prod(product_prod(nat,nat),product_prod(nat,nat)),bool),bool),member(product_prod(product_prod(nat,nat),product_prod(nat,nat))),hAPP(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat)),hAPP(product_prod(nat,nat),fun(product_prod(nat,nat),product_prod(product_prod(nat,nat),product_prod(nat,nat))),product_Pair(product_prod(nat,nat),product_prod(nat,nat)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),A_2),Sa)),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),B_1),Ta))),pair_leq))))) # label(fact_3488_pair__leqI2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4042 (all X_c all X_a all X_b all C_1 all P_4 all Z (hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4),Z)) -> -(all X_2 all Y_2 (hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),X_2),Y_2) = ti(product_prod(X_a,X_b),P_4) -> -hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,X_2),Y_2),Z)))))) # label(fact_4058_splitE_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4043 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2736_ex__less__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4044 (all 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)) = 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))) # label(fact_2368_sin__double) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4045 (all X_a (comm_ring(X_a) & monoid_mult(X_a) -> (all Z all H all Ma hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z))),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Ma)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H))),hAPP(nat,fun(nat,nat),minus_minus(nat),Ma)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),Ma))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),Ma))))) # label(fact_4226_lemma__termdiff1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4046 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)))) # label(fact_4970_min__max_Osup__commute) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4047 (all B all Q_5 all R_5 all Q_3 all R_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_5)),R_5)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3)),R_4))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_5),B)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Q_5),Q_3))))))) # label(fact_266_unique__quotient__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4048 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),hAPP(real,real,exp(real),Y_1))))) # label(fact_2512_exp__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4049 (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_727_divides__rev) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4050 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archimedean_ceiling(X_a),zero_zero(X_a)) = zero_zero(int))) # label(fact_3279_ceiling__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4051 (all W hAPP(int,complex,number_number_of(complex),W) != ii) # label(fact_2762_complex__i__not__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4052 (all A_1 all B hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(complex,complex,inverse_inverse(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B))) # label(fact_2750_complex__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4053 (all X (hAPP(real,real,cos,X) != 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)) != zero_zero(real) -> hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(real,real,tan,X))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,tan,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2250_tan__double) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4054 (all X_a (order(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1)) -> (ti(X_a,B) != ti(X_a,A_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1))))))) # label(fact_1598_xt1_I11_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4055 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) = ti(X_a,Y_1) <-> hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1) = hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1))))) # label(fact_4962_atMost__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4056 (all X_a (linordered_idom(X_a) -> (all X_1 all W_1 (zero_zero(nat) != hAPP(int,nat,number_number_of(nat),W_1) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1))) | zero_zero(X_a) = ti(X_a,X_1) & hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),W_1)))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),W_1))),zero_zero(X_a))))))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4057 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,abs_abs(real),X)),one_one(real))),X))) # label(fact_1893_abs__add__one__not__less__self) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4058 (all X (hAPP(real,real,cos,X) = one_one(real) -> hAPP(real,real,sin,X) = zero_zero(real))) # label(fact_2318_cos__one__sin__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4059 (all X_a (semiring_div(X_a) -> (all A_1 all B ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_1074_mod__div__decomp) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4060 (all R_1 hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),plus_plus(real),R_1)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),suc)))),R_1),sequentially))) # label(fact_4437_LIMSEQ__inverse__real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4061 (all N_1 all V_1 (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))) = N_1) <-> hAPP(int,nat,number_number_of(nat),V_1) = hAPP(nat,nat,suc,N_1))) # label(fact_3884_Suc__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4062 (all M all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),J_2))))) # label(fact_574_trans__le__add2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4063 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4610_LIM__norm__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4064 (all X_a all X_c all X_b all Z all C_1 all A_2 all B_1 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(X_c,fun(X_a,bool),hAPP(X_b,fun(X_c,fun(X_a,bool)),C_1,A_2),B_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),Z),hAPP(product_prod(X_b,X_c),fun(X_a,bool),hAPP(fun(X_b,fun(X_c,fun(X_a,bool))),fun(product_prod(X_b,X_c),fun(X_a,bool)),product_prod_case(X_b,X_c,fun(X_a,bool)),C_1),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),A_2),B_1)))))) # label(fact_4038_mem__splitI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4065 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,im,hAPP(complex,complex,inverse_inverse(complex),X))) # label(fact_2992_complex__Im__inverse) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4066 (all 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,bit1,hAPP(int,int,bit1,pls)))) = 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)))))) # label(fact_187_cube__square) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4067 (all Ma all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,Ma),X_1)) <-> (exists Y_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),Y_2),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),Ma))))) # label(fact_608_QuadRes__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4068 (all N all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),N),M)) -> ti(int,M) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),M),N)))) # label(fact_992_zdvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4069 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_427_mult__less__imp__less__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4070 (all D_1 all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_1)) -> ((all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),Y_2))),D_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,F,Y_2)),hAPP(real,real,F,X_1))))) -> L = zero_zero(real))))) # label(fact_2660_DERIV__local__max) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4071 (all N hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))) # label(fact_2324_real__of__nat__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4072 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> -(all M_2 hAPP(nat,int,semiring_1_of_nat(int),M_2) != ti(int,Z_1)))) # label(fact_1488_nonneg__eq__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4073 (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_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> (hBOOL(hAPP(X_b,bool,hAPP(fun(X_b,X_c),fun(X_b,bool),isCont(X_b,X_c),G),hAPP(X_a,X_b,F,A_2))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_c),fun(X_a,bool),isCont(X_a,X_c),hAPP(fun(X_a,X_b),fun(X_a,X_c),hAPP(fun(X_b,X_c),fun(fun(X_a,X_b),fun(X_a,X_c)),combb(X_b,X_c,X_a),G),F)),A_2))))))) # label(fact_4900_isCont__o2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4074 (all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_2470_lemma__even__div2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4075 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all X hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,uminus_uminus(X_a),X))))) # label(fact_2037_mult__right_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.86 4076 (all A_1 A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),A_1)) # label(fact_3218_gcd__semilattice__nat_Oinf_Oidem) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4077 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),N)),one_one(real)))) -> hAPP(real,nat,natfloor,X) = N))) # label(fact_2363_natfloor__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4078 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)),X))))) # label(fact_3624_ex__of__int__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4079 (all A_1 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,cis,A_1)),hAPP(real,complex,cis,B)) = hAPP(real,complex,cis,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),B))) # label(fact_3031_cis__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4080 (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_3973_powser__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4081 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y))))) # label(fact_649_dvd_Oless__asym) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4082 (all X_a all N hAPP(int,X_a,number_of_frac(X_a),N) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),N),one_one(int)))) # label(fact_3685_Nitpick_Onumber__of__frac__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4083 (all P_5 all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),A_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),B)) & hBOOL(hAPP(nat,bool,prime,P_5))))) # label(fact_3060_coprime__prime) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4084 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))),hAPP(real,real,uminus_uminus(real),X)))))) # label(fact_2119_ln__one__minus__pos__upper__bound) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4085 (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_1437_Suc__div__eq__add3__div) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4086 (all M M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),M)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1147_add__self__div__2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4087 (all I_1 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,I_1))),N)))) # label(fact_1388_diff__Suc__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4088 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_4),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)) # label(fact_665_Nat_Odiff__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4089 (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),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_2787_of__real_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4090 (all D hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),D)),D))) # label(fact_1925_zdvd__self__abs2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4091 (all K_4 all I_1 all J_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),J_2)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_2),K_4)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),I_1),K_4))))) # label(fact_29_zle__trans) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4092 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_812_add__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4093 (all X_b all X_a (topological_space(X_b) & real_normed_vector(X_a) -> (all L all F all G all A_2 all R_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_3)) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),R_3)) -> hAPP(X_a,X_b,F,X_2) = hAPP(X_a,X_b,G,X_2)))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4646_LIM__equal2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4094 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1))))) # label(fact_604_mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4095 (all X_a (metric_space(X_a) -> (all X_3 all L_2 all A_2 (hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),X_3),L_2),hAPP(real,filter(real),at(real),A_2))) <-> (all S_2 ((all N_2 hAPP(nat,real,S_2,N_2) != A_2) & hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),S_2),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,real),fun(nat,X_a),hAPP(fun(real,X_a),fun(fun(nat,real),fun(nat,X_a)),combb(real,X_a,nat),X_3),S_2)),L_2),sequentially)))))))) # label(fact_4634_LIMSEQ__SEQ__conv) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4096 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)))))) # label(fact_4849_Nat__Transfer_Otransfer__int__nat__function__closures_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4097 (all X_a all B_2 all C_1 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1921_DiffI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4098 (all A_1 (ti(int,A_1) != zero_zero(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),A_1))) # label(fact_984_zdiv__self) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4099 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_2224_cos__monotone__0__pi) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4100 (all K all N_1 all F_3 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_1),K)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))) # label(fact_4181_sumr__offset2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4101 (all Y all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> (hBOOL(hAPP(int,bool,nat_is_nat,Y)) -> hBOOL(hAPP(int,bool,nat_is_nat,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_4848_Divides_Otransfer__int__nat__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4102 (all A_1 all 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)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_2148_zdiv__zminus__zminus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4103 (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_1109_mod__geq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4104 (all Ma all N_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),Ma),hAPP(nat,nat,suc,N_1)) = hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),hAPP(nat,nat,suc,N_1)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_max(nat)),N_1))),Ma)) # label(fact_4955_max__Suc2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4105 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,exp(X_a),X)),hAPP(X_a,X_a,exp(X_a),Y)) = hAPP(X_a,X_a,exp(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y))))) # label(fact_2585_exp__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4106 (all X_a (no_zero_divisors(X_a) -> (all A_1 all B (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B) -> zero_zero(X_a) = ti(X_a,B) | ti(X_a,A_1) = zero_zero(X_a))))) # label(fact_319_divisors__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4107 (all X_a (linordered_ring(X_a) -> (all A_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1)))))) # label(fact_381_zero__le__square) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4108 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),M))) # label(fact_669_Nat_Odiff__le__self) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4109 (all X_a all X_b (real_n2089651433ebra_1(X_a) & metric_space(X_b) -> (all K all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(X_b,fun(X_a,X_b),combk(X_b,X_a),K)),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ti(X_b,K) = ti(X_b,L_2))))) # label(fact_4557_LIM__const__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4110 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M)) -> zero_zero(int) = ti(int,X))))) # label(fact_451_Int2_Ozcong__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4111 (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)) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) != one_one(int))))) # label(fact_4412_Rat__cases) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4112 (all M all K_4 all N hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),N) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),M),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),M)),N))) # label(fact_4353_gcd__add__mult__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4113 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,P_4))))) # label(fact_1116_SRStar__SR__prop) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4114 (all X_a (semiring_div(X_a) -> (all A_1 all B (zero_zero(X_a) != ti(X_a,B) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1)),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),A_1),B)),one_one(X_a)))))) # label(fact_1041_div__add__self1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4115 (all X_a (number(X_a) & linord1117847801e_zero(X_a) -> (all A_2 all B_1 all W_1 ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1)))))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(int,X_a,number_number_of(X_a),W_1))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),hAPP(int,X_a,number_number_of(X_a),W_1))),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),hAPP(int,X_a,number_number_of(X_a),W_1)))))))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4116 (all X_a all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),A_3))) # label(fact_1960_subset__refl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4117 (all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> -(all N_2 ti(int,K_4) != hAPP(nat,int,semiring_1_of_nat(int),N_2)))) # label(fact_1489_nonneg__int__cases) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4118 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N),zero_zero(nat)) = zero_zero(nat)) # label(fact_4806_min__0R) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4119 (all X_1 all Y_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_1),Y_1)),zEven)) <-> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))))) # label(fact_1272_even__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4120 (all A_3 all K (hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),A_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_3))))) -> A_3 = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),K),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),hAPP(fun(nat,bool),nat,finite_card(nat),A_3))))) # label(fact_4232_subset__card__intvl__is__intvl) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4121 (all X_a (comm_semiring_1(X_a) -> (all X all P_5 all Q_3 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),P_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),P_5),Q_3))))) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4122 (all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1))))) # label(fact_1399_zero__less__int__conv) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4123 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1))))))) # label(fact_4000_mult__left_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4124 (all A_1 all R_4 all B all M all C all D all N hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),N))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),N)))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),B))),M)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),R_4),D))),N))) # label(fact_499_xzgcda__linear__aux1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4125 (all X_a (ordere236663937imp_le(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),B))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)))))) # label(fact_779_add__le__imp__le__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4126 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)))))) # label(fact_2556_nonzero__inverse__minus__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4127 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (one_one(real) = X_1 <-> one_one(real) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)))) # label(fact_2686_real__root__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4128 (all A_2 hBOOL(hAPP(complex,bool,hAPP(fun(complex,real),fun(complex,bool),isCont(complex,real),re),A_2))) # label(fact_4894_Re_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4129 (all X_a (linordered_field(X_a) -> (all B_1 all A_2 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1738_pos__divide__le__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4130 (all X_a (preorder(X_a) -> (all Z_1 all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),Z_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Z_1))))))) # label(fact_1601_order__le__less__trans) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4131 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B)),C)) # label(fact_4365_gcd__assoc__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4132 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hAPP(real,real,arcsin,hAPP(real,real,sin,X)) = X))) # label(fact_2398_arcsin__sin) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4133 (all X_a (metric_space(X_a) -> (all X all Y all A_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),X)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),A_1),Y))))))) # label(fact_3504_dist__triangle3) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4134 (all X_a (real_normed_vector(X_a) -> (all K all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),X_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K)))))))) # label(fact_3825_Bseq__ignore__initial__segment) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4135 (all Ma (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = one_one(nat) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1153_mod2__gr__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4136 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),zero_zero(int)),P_4)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),quadRes,P_4),A_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(fun(fun(int,bool),bool),fun(int,bool),complete_Sup_Sup(fun(int,bool)),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_2),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_4))))))) # label(fact_3927_Union__SetS__setprod__prop1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4137 (all X_a (semiring_1(X_a) -> (all N_1 hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(nat,fun(X_a,X_a)),semiri532925092at_aux(X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),plus_plus(X_a)),one_one(X_a))),N_1),zero_zero(X_a)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)))) # label(fact_4158_semiring__1__class_Oof__nat__code) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4138 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1)),hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1))))) # label(fact_2680_real__root__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4139 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))))) # label(fact_1632_real__sqrt__lt__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4140 (all X_a (real_normed_vector(X_a) & inverse(X_a) -> (all F all A_2 all D_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),F)),hAPP(X_a,X_a,F,A_2)))),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),minus_minus(X_a)),A_2))),D_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(X_a,fun(filter(X_a),bool),hAPP(fun(X_a,X_a),fun(X_a,fun(filter(X_a),bool)),tendsto(X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),inverse_divide(X_a)),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),minus_minus(X_a)),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),F),hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2)))),hAPP(X_a,X_a,F,A_2)))),combi(X_a))),D_2),hAPP(X_a,filter(X_a),at(X_a),zero_zero(X_a)))))))) # label(fact_4607_DERIV__LIM__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4141 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 ((all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,X_1)),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X_1),H_1))))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3))))))) # label(fact_2663_DERIV__neg__dec__left) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4142 (all Ta all A_3 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Ta),one_one(int))),A_3)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),X_2),Ta)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4630_aset_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4143 (all J_2 all A_1 all P_5 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),J_2),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),K_4)),P_5)))) # label(fact_835_aux______1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4144 (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_3007_complex__Re__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4145 (all K_4 hAPP(int,rat,ring_1_of_int(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),one_one(int))) # label(fact_3744_of__int__rat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4146 (all M all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),N))))) # label(fact_3054_prime__dvd__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4147 (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_3336_real__of__int__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4148 (all R1 all A_1 all R2 all B hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R1),A_1)),hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R2),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R1),R2)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3171_rcis__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4149 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2447_odd__nat__mod__two__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4150 (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]. 10.83/10.87 4151 (all X_a (semiring_div(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B)),B) = zero_zero(X_a)))) # label(fact_909_mod__div__trivial) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4152 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),M)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N)))))) # label(fact_1383_n__less__m__mult__n) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4153 (all L all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),L),U_1)))) # label(fact_4243_finite__atLeastLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4154 (all X_a (real_normed_algebra(X_a) -> (all Y exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_2),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4155 (all A_1 all B ((-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int)))) -> hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_1),B)) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_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)),posDivAlg,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)))) # label(fact_1077_posDivAlg_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4156 (all M all N all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,M),N),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = R_4)) # label(fact_3102_mod__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4157 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),sin)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3910_DERIV__sin__realpow2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4158 (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]. 10.83/10.87 4159 (all Z_1 all X all D (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,abs_abs(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Z_1))),one_one(int))),D)))))) # label(fact_1987_incr__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4160 (all X -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X)),zero_zero(real)))) # label(fact_2568_not__exp__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4161 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)) = hAPP(X_a,X_a,abs_abs(X_a),A_1)))) # label(fact_1852_abs__idempotent) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4162 (all X_a (real_normed_vector(X_a) -> (all A_1 all B hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B))),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B))))))) # label(fact_1796_norm__triangle__ineq2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4163 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),Y)),X)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2))),Y)))))))) # label(fact_2407_reals__Archimedean4) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4164 (all X_a (linordered_idom(X_a) -> (all Ma all K (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),Ma),K)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,abs_abs(X_a),Ma)),K)))))) # label(fact_1846_abs__dvd__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4165 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,re,X)),hAPP(complex,real,im,Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,im,X)),hAPP(complex,real,re,Y))) = hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y))) # label(fact_3010_complex__Im__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4166 (all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),M))))) # label(fact_583_le__cube) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4167 (all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),uminus_uminus(real)))),sin))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),uminus_uminus(real)))),cos))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2),zero_zero(real)))) # label(fact_3918_lemma__DERIV__sin__cos__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4168 (all X_a (linordered_idom(X_a) -> (all A_2 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_2),N_1))) <-> hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2434_zero__le__power__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4169 (all X all N hAPP(real,real,tan,X) = hAPP(real,real,tan,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),N)),pi)))) # label(fact_2257_tan__periodic__n) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4170 (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]. 10.83/10.87 4171 (all X_a (real_normed_algebra(X_a) -> (exists K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) & (all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(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_1805_mult_Opos__bounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4172 (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_77_Collect__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4173 (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_4356_coprime__plus__one__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4174 (all Ma all K all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),N_1),K))))) # label(fact_605_mult__le__cancel2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4175 (all R_4 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),R_4)) -> (exists N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_2)),R_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),R_4),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N_2)))))))) # label(fact_2408_reals__Archimedean6a) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4176 (all X_a all F all G all Ma all S ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(X_a,int,F,X_2)),hAPP(X_a,int,G,X_2)),Ma)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),F),S)),hAPP(fun(X_a,bool),int,hAPP(fun(X_a,int),fun(fun(X_a,bool),int),big_co302546470etprod(X_a,int),G),S)),Ma)))) # label(fact_4419_setprod__same__function__zcong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4177 (all X all Y hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X),Y)) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,semiring_1_of_nat(int),X)),hAPP(nat,int,semiring_1_of_nat(int),Y))) # label(fact_1359_Divides_Otransfer__int__nat__functions_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4178 (all X_a (real_algebra_1(X_a) -> (all X_1 (X_1 = zero_zero(real) <-> hAPP(real,X_a,of_real(X_a),X_1) = zero_zero(X_a))))) # label(fact_2781_of__real__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4179 (all X_a (linord581940658strict(X_a) -> (all C all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_382_mult__strict__left__mono__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4180 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),one_one(X_a)),ring_1_Ints(X_a))))) # label(fact_3837_Ints__1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4181 (all X all Y hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),X)),hAPP(int,real,real_1(int),Y)) = hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X),Y))) # label(fact_3332_real__of__int__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4182 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),pi)) & hAPP(real,real,sin,hAPP(real,real,arcsin,Y)) = Y & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y)))))) # label(fact_2402_arcsin__pi) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4183 (all X_1 all Y_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),X_1)),hAPP(int,real,real_1(int),Y_1))))) # label(fact_3321_real__of__int__less__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4184 (all X_a all C_1 all X_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),X_3)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,semiring_1_of_nat(int),C_1)),hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,finite_card(X_a),X_3))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(nat,fun(X_a,nat),combk(nat,X_a),C_1)),X_3)))) # label(fact_4263_setsum__const2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4185 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),N))) # label(fact_470_le0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4186 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1))))) # label(fact_3661_Nat__Transfer_Otransfer__nat__int__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4187 (all Ma all N_1 (N_1 != Ma <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_515_nat__neq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4188 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3223_gcd__semilattice__nat_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4189 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,cos,X) -> (exists N_2 (-hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = X))))) # label(fact_2476_cos__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4190 (all X_a power_1(X_a) = ti(fun(X_a,fun(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)))),power_1(X_a))) # label(tsy_c_Power_Opower_Opower_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4191 (all M all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X),M)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),M))))) # label(fact_418_zcong__not__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4192 (all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)))) # label(fact_3078_prime__ge__2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4193 (all X_a (real_normed_algebra(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),sequentially))))))) # label(fact_4477_LIMSEQ__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4194 (all X_1 (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1))) <-> X_1 = zero_zero(real))) # label(fact_474_not__real__square__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4195 (all Ta all B_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta)))))))) # label(fact_4648_bset_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4196 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),arccos),X_1))))) # label(fact_4921_isCont__arccos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4197 (all N (hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(nat) -> hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_2474_lemma__even__mod__4__div__2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4198 (all X hAPP(complex,real,re,hAPP(complex,complex,uminus_uminus(complex),X)) = hAPP(real,real,uminus_uminus(real),hAPP(complex,real,re,X))) # label(fact_3004_Re_Ominus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4199 (all X_a all A_3 hAPP(fun(X_a,bool),real,hAPP(fun(X_a,real),fun(fun(X_a,bool),real),big_co1399186613setsum(X_a,real),hAPP(real,fun(X_a,real),combk(real,X_a),one_one(real))),A_3) = hAPP(nat,real,real_1(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3))) # label(fact_4229_real__of__card) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4200 (all I_1 all J_2 -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),J_2)),I_1))) # label(fact_554_not__add__less1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4201 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),B)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B)))) # label(fact_1032_mod__pos__pos__trivial) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4202 (all X_a (comm_ring_1(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_1424_realpow__two__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4203 (all X_a (cancel_semigroup_add(X_a) -> (all B all A_1 all C (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),A_1) -> ti(X_a,C) = ti(X_a,B))))) # label(fact_766_add__right__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4204 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),A_1)),one_one(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),P_5)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),one_one(int)),P_5)))))) # label(fact_535_zcong__square) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4205 (all A_1 (zero_zero(int) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),zero_zero(int)) & ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),zero_zero(int)))) # label(fact_908_DIVISION__BY__ZERO) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4206 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),sequentially)))))) # label(fact_4469_LIMSEQ__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4207 (all P_1 all N_1 all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),zero_zero(int))) -> ((all I_2 all J_1 (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,N_1) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),J_1),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),J_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,I_2),J_1)))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),N_1),K)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),N_1),K)))))) # label(fact_1007_split__neg__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.87 4208 (all Z all X_3 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),Z),X_3)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),X_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),Z)))) -> hAPP(fun(real,bool),real,complete_Sup_Sup(real),X_3) = Z))) # label(fact_3713_Sup__eq__maximum) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4209 (all X_b all X_a (topological_space(X_a) & real_normed_vector(X_b) -> (all G all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),F),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),G),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,real),fun(X_a,fun(X_b,X_b)),hAPP(fun(real,fun(X_b,X_b)),fun(fun(X_a,real),fun(X_a,fun(X_b,X_b))),combb(real,fun(X_b,X_b),X_a),scaleR_scaleR(X_b)),F)),G)),A_2))))))) # label(fact_4916_isCont__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4210 (all X_a all F all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co302546470etprod(X_a,nat),F),S))) <-> (all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(X_a,nat,F,X_2)))))))) # label(fact_3939_setprod__pos__nat__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4211 (all X all A_1 hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,uminus_uminus(real),A_1)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))) # label(fact_3381_powr__minus__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4212 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_lessThan(X_a),Y_1))))))) # label(fact_4319_lessThan__subset__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4213 (all X_1 (hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(nat,nat,suc,X_1))) <-> -hBOOL(hAPP(nat,bool,even_odd_even(nat),X_1)))) # label(fact_2417_even__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4214 (all X_a (field_char_0(X_a) -> (all Z hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),field_char_0_Rats(X_a)))))) # label(fact_3702_Rats__of__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4215 (all X_a (number(X_a) & linorder(X_a) -> (all V_1 all W_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),hAPP(int,X_a,number_number_of(X_a),W_1))) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_50_le__number__of__eq__not__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4216 (all X_b all X_a all H all F_1 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),F_1)) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),H),F_1))))) # label(fact_3633_finite__imageI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4217 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)))))))) # label(fact_4088_sums__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4218 (all X_a (ring_1(X_a) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),zero_zero(X_a)),ring_1_Ints(X_a))))) # label(fact_3838_Ints__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4219 (all X_a (semiri456707255roduct(X_a) -> (all C all D all A_1 all B all R_4 (ti(X_a,R_4) != zero_zero(X_a) -> (ti(X_a,D) != ti(X_a,C) & ti(X_a,B) = ti(X_a,A_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_4),D)) != hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),R_4),C))))))) # label(fact_252_add__scale__eq__noteq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4220 (all N_1 all P_1 (-hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))) -> (hBOOL(hAPP(nat,bool,P_1,N_1)) -> (exists K_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K_1),one_one(nat)))) & (all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_2),K_1)) -> -hBOOL(hAPP(nat,bool,P_1,I_2)))) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_1),N_1))))))) # label(fact_612_ex__least__nat__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4221 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))))) # label(fact_596_mult__less__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4222 (all R_4 all A_1 hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(real,real,cos,A_1)) = hAPP(complex,real,re,hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),A_1))) # label(fact_3169_Re__rcis) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4223 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,exp(real),X_1))))) # label(fact_2597_one__less__exp__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4224 (all X_3 (hBOOL(hAPP(fun(nat,rat),bool,vanishes,X_3)) -> hBOOL(hAPP(fun(nat,rat),bool,vanishes,hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(rat,rat),fun(fun(nat,rat),fun(nat,rat)),combb(rat,rat,nat),uminus_uminus(rat)),X_3))))) # label(fact_4844_vanishes__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4225 (all X_a (linord1117847801e_zero(X_a) & number(X_a) -> (all W_1 all B_1 all C_1 ((hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1)),B_1))) & (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),zero_zero(X_a)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),C_1))))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),W_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))))))) # label(fact_1753_le__divide__eq__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4226 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1))))) # label(fact_88_le__imp__0__less) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4227 (all A_2 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),hAPP(real,int,archim2085082626_floor(real),X_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_2)),X_1)))) # label(fact_3364_le__floor__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4228 (all X_b all X_a all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),hAPP(fun(X_a,bool),fun(X_b,bool),hAPP(fun(X_a,X_b),fun(fun(X_a,bool),fun(X_b,bool)),image(X_a,X_b),F),A_3))) -> (exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & -hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,bool)),hAPP(fun(X_b,fun(X_b,bool)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,bool))),combb(X_b,fun(X_b,bool),X_a),fequal(X_b)),F)),hAPP(X_a,X_b,F,X_2))))))))))) # label(fact_4331_pigeonhole__infinite) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4229 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_2),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4))))) # label(fact_1232_less__trans__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4230 (all X_a (ring_char_0(X_a) -> (all W_1 all Z (ti(int,W_1) = ti(int,Z) <-> hAPP(int,X_a,ring_1_of_int(X_a),W_1) = hAPP(int,X_a,ring_1_of_int(X_a),Z))))) # label(fact_3574_of__int__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4231 (all K_4 all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) # label(fact_1092_mod__mult__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4232 (all X_a all X_b nat_tr1645093318rphism(X_a,X_b) = ti(fun(fun(X_a,X_b),fun(fun(X_a,bool),bool)),nat_tr1645093318rphism(X_a,X_b))) # label(tsy_c_Nat__Transfer_Otransfer__morphism_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4233 (all P_1 all A_2 all B_1 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_1))) <-> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) & (all D_3 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_1),D_3) = A_2 -> hBOOL(hAPP(nat,bool,P_1,D_3)))))) # label(fact_700_nat__diff__split) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4234 (all X_a (linorder(X_a) -> (all Ma all I all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),I),N_1)) -> hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),Ma)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),I),N_1)) = hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastLessThan(X_a),N_1),Ma))))) # label(fact_4205_ivl__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4235 (all X_a (number(X_a) -> ti(fun(int,X_a),number_number_of(X_a)) = number_number_of(X_a))) # label(tsy_c_Int_Onumber__class_Onumber__of_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4236 (all M all N all K_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),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))) # label(fact_523_nat__add__assoc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4237 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),zero_zero(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sin,X)),zero_zero(real)))))) # label(fact_2394_sin__less__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4238 (all X_a (linordered_idom(X_a) -> (all X all Y hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_107_sum__power2__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4239 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),Ma)),hAPP(nat,int,semiring_1_of_nat(int),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)))) # label(fact_1298_zless__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4240 (all X_a all X_b (comm_monoid_add(X_b) -> (all G all F all S all T_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),T_3)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),S),T_3)) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),T_3),S))) -> zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) -> ((all X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),S)) -> hAPP(X_a,X_b,G,X_2) = hAPP(X_a,X_b,F,X_2))) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),T_3) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),G),S)))))))) # label(fact_4417_setsum__mono__zero__cong__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4241 (all X all A_1 all 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)) = hAPP(real,real,hAPP(real,fun(real,real),powr,X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A_1),B))) # label(fact_3356_powr__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4242 (all N_1 all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,nat,suc,N_1)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4935_max__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4243 (all X_a (real_algebra_1(X_a) -> (all X all Y hAPP(real,X_a,of_real(X_a),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(real,X_a,of_real(X_a),X)),hAPP(real,X_a,of_real(X_a),Y))))) # label(fact_2784_of__real__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4244 (all X_a (cancel_semigroup_add(X_a) -> (all A_2 all B_1 all C_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),C_1) <-> ti(X_a,C_1) = ti(X_a,B_1))))) # label(fact_770_add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4245 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all A_2 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),B_1),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_2836_order__le__less__subst1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4246 (all C all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (ti(int,B) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),Q_3),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Q_3),C))),R_4)))))))) # label(fact_1185_zmult2__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4247 (all X_3 (hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),X_3)) -> hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),cnj),X_3))))) # label(fact_3848_cnj_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4248 (all X_a (number_ring(X_a) -> (all X_1 all Y_1 (hAPP(int,X_a,number_number_of(X_a),X_1) = hAPP(int,X_a,number_number_of(X_a),Y_1) <-> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_1),hAPP(int,int,uminus_uminus(int),Y_1))))))))) # label(fact_2622_eq__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4249 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) & ti(X_a,X_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),F) <-> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X_1)))))) # label(fact_4093_sums__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4250 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)))))))) # label(fact_758_add__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4251 (all X_a (order(X_a) -> (all A_2 all B_1 all C_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),D_1)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C_1),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),D_1)) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),D_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),A_2))) | -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),B_1))) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),A_2),B_1)),hAPP(X_a,fun(X_a,bool),hAPP(X_a,fun(X_a,fun(X_a,bool)),ord_atLeastAtMost(X_a),C_1),D_1))))))) # label(fact_4527_atLeastatMost__psubset__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4252 (all X_a (field_inverse_zero(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,uminus_uminus(X_a),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))) # label(fact_2018_minus__divide__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4253 (all V_1 all N_1 ((-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(nat,nat,suc,N_1))))) # label(fact_3896_le__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4254 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),Y_3),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),plus_plus(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)))))))) # label(fact_4087_sums__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4255 (all A_1 hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,cos,A_1)),hAPP(real,real,sin,A_1)) = hAPP(real,complex,cis,A_1)) # label(fact_3032_cis__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4256 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2497_dvd__fact__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4257 (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_3002_Re_Oadd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4258 (all X_a (linorder(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),A_1) = ti(X_a,A_1)))) # label(fact_4972_min__max_Osup_Oidem) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4259 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3692_Rats__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4260 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),C)),D) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D))))) # label(fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4261 (all X_a (real_algebra_1(X_a) & real_normed_vector(X_a) -> (all A_2 hBOOL(hAPP(filter(real),bool,hAPP(X_a,fun(filter(real),bool),hAPP(fun(real,X_a),fun(X_a,fun(filter(real),bool)),tendsto(real,X_a),of_real(X_a)),hAPP(real,X_a,of_real(X_a),A_2)),hAPP(real,filter(real),at(real),A_2)))))) # label(fact_4555_of__real_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4262 (all X_a (order(X_a) -> (all C all A_1 all B (ti(X_a,B) = ti(X_a,A_1) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),A_1))))))) # label(fact_1552_xt1_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4263 (all P_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_4)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),P_4),zOdd)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1050_Euler_Oaux__2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4264 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & (all Y_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),Y_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y_2),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & Y = hAPP(real,real,sin,Y_2) -> Y_2 = X_2)) & hAPP(real,real,sin,X_2) = Y))))) # label(fact_2405_sin__total) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4265 (all A_2 all P_4 all X_2 (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),X_2),hAPP(int,fun(fun(int,bool),bool),hAPP(int,fun(int,fun(fun(int,bool),bool)),setS,A_2),P_4))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_2)))) # label(fact_1670_SetS__elems__finite) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4266 (all Z1 all Z2 all Z3 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z2),Z3)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Z1),Z2)),Z3)) # label(fact_97_zadd__assoc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4267 (all X_a (linordered_semidom(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y))))))) # label(fact_103_power2__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4268 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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_2753_cos__arg__i__mult__zero__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4269 (all X all Y hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_1649_real__sqrt__sum__squares__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4270 (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_996_div__mult__self1__is__id) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4271 (all A_1 all 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))))) & 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))))) # label(fact_3792_rat__floor__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4272 (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]. 10.83/10.88 4273 (all X_b all X_a all R_3 all K all Ta all Sa (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),Sa)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),Ta)) -> ((all X_2 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(X_b,fun(fun(X_b,bool),bool),member(X_b),X_2),Ta)) -> hAPP(fun(X_a,bool),nat,finite_card(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),Sa))),hAPP(X_b,fun(X_a,bool),hAPP(fun(X_a,fun(X_b,bool)),fun(X_b,fun(X_a,bool)),combc(X_a,X_b,bool),R_3),X_2)))) = hAPP(X_b,nat,K,X_2))) -> hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),K),Ta) = hAPP(fun(X_a,bool),nat,hAPP(fun(X_a,nat),fun(fun(X_a,bool),nat),big_co1399186613setsum(X_a,nat),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,nat),hAPP(fun(fun(X_b,bool),nat),fun(fun(X_a,fun(X_b,bool)),fun(X_a,nat)),combb(fun(X_b,bool),nat,X_a),finite_card(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),collect(X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,bool),fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),fun(X_a,fun(X_b,bool))),combb(fun(X_b,bool),fun(X_b,bool),X_a),hAPP(fun(X_b,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,bool)),combs(X_b,bool,bool),hAPP(fun(X_b,bool),fun(X_b,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_b,bool),fun(X_b,fun(bool,bool))),combb(bool,fun(bool,bool),X_b),fconj),hAPP(fun(X_b,bool),fun(X_b,bool),hAPP(fun(X_b,fun(fun(X_b,bool),bool)),fun(fun(X_b,bool),fun(X_b,bool)),combc(X_b,fun(X_b,bool),bool),member(X_b)),Ta)))),R_3)))),Sa))))) # label(fact_4303_setsum__multicount__gen) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4274 (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(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),B))) & (-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_1070_negDivAlg__eqn) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4275 (all X_a (archim1727834104eiling(X_a) -> (all X_1 all V_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archimedean_ceiling(X_a),X_1)),hAPP(int,int,number_number_of(int),V_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),V_1))))))) # label(fact_3304_ceiling__le__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4276 (all X_a (field(X_a) & number_ring(X_a) -> (all X ti(X_a,X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_1734_divide__Numeral1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4277 (all X_a (finite_finite(X_a) -> (all A_3 hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3))))) # label(fact_1818_finite__code) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4278 (all Nat_3 zero_zero(nat) != hAPP(nat,nat,suc,Nat_3)) # label(fact_1226_nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4279 (all X_a (real_normed_field(X_a) -> (all Y_1 all A_2 hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_a),fun(X_a,bool),isCont(X_a,X_a),hAPP(X_a,fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(X_a,fun(X_a,X_a)),combc(X_a,X_a,X_a),inverse_divide(X_a)),Y_1)),A_2))))) # label(fact_4897_divide_OisCont) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4280 (all X all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),N) = X))) # label(fact_2711_real__root__pow__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4281 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1473_even__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4282 (all X all 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))) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y))) # label(fact_3211_bezw__aux) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4283 (all X_a (archim1727834104eiling(X_a) -> (all X all Z_1 hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),Z_1) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_1)))))) # label(fact_3599_ceiling__diff__of__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4284 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1701_divide__nonneg__pos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4285 (all X_a (ring_11004092258visors(X_a) -> (all X_1 (one_one(X_a) = ti(X_a,X_1) | ti(X_a,X_1) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X_1),X_1) = one_one(X_a))))) # label(fact_2072_square__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4286 (all X_a all X_b (comm_semiring_1(X_b) -> (all D_1 all F all A_3 ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),A_3)) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(X_a,X_b,F,I_2))))) -> hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),dvd_dvd(X_b),D_1),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),F),A_3))))))) # label(fact_4773_dvd__setsum) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4287 (all X_a (number_ring(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)),Y)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Y)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_591_power2__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4288 (all X_1 all Y_1 (zero_zero(real) = X_1 & zero_zero(real) = Y_1 <-> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X_1),X_1)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Y_1),Y_1)))) # label(fact_707_real__two__squares__add__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4289 (all X_a (real_normed_algebra(X_a) & banach(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),A_2))) -> (hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),B_1))) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(nat,fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combs(nat,fun(nat,bool),X_a),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a)),hAPP(fun(fun(nat,X_a),fun(fun(nat,bool),X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(fun(nat,bool),X_a))),combb(fun(nat,X_a),fun(fun(nat,bool),X_a),nat),big_co1399186613setsum(nat,X_a)),hAPP(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,X_a),fun(nat,X_a)),fun(fun(nat,fun(nat,X_a)),fun(nat,fun(nat,X_a))),combb(fun(nat,X_a),fun(nat,X_a),nat),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),A_2))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a)),hAPP(fun(fun(nat,nat),fun(nat,X_a)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,X_a))),combb(fun(nat,nat),fun(nat,X_a),nat),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),B_1)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),A_2)),hAPP(fun(nat,X_a),X_a,suminf(X_a),B_1))))))))) # label(fact_4623_Cauchy__product__sums) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4290 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),Ma),N_1) <-> ti(int,N_1) = one_one(int) & one_one(int) = ti(int,Ma)))) # label(fact_114_pos__zmult__eq__1__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4291 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,sin,X)))))) # label(fact_2314_sin__gt__zero__pi) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4292 (all N all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),P_5),N)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),P_5)))) # label(fact_3466_zprime__imp__zrelprime) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4293 (all X_a all X_b (comm_semiring_1(X_b) & no_zero_divisors(X_b) -> (all F all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> ((exists X_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),X_2),A_3)) & zero_zero(X_b) = hAPP(X_a,X_b,F,X_2))) <-> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = zero_zero(X_b)))))) # label(fact_3949_setprod__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4294 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C)))) # label(fact_944_mod__diff__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4295 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (ti(X_b,L) != zero_zero(X_b) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_b,X_b),fun(fun(X_a,X_b),fun(X_a,X_b)),combb(X_b,X_b,X_a),sgn_sgn(X_b)),F)),hAPP(X_b,X_b,sgn_sgn(X_b),L)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4590_LIM__sgn) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4296 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y)) -> (exists X_2 Y = hAPP(real,real,exp(real),X_2)))) # label(fact_2718_exp__total) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4297 (all W hAPP(int,int,ring_1_of_int(int),W) = hAPP(int,int,number_number_of(int),W)) # label(fact_3583_int__number__of__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4298 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> (all K_3 all F all L_2 all X_1 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),X_1))) -> (ti(X_b,L_2) = ti(X_b,K_3) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),K_3),hAPP(X_a,filter(X_a),at(X_a),X_1)))))))) # label(fact_4545_LIM__cong__limit) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4299 (all A_2 all B_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),posDivAlg_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_2),B_1))) -> (-(hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int)))) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),B_1) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B_1)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B_1),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,A_2),B_1) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),A_2)))) # label(fact_1180_posDivAlg_Opsimps) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4300 (all X_a (linordered_idom(X_a) -> (all A_2 (zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),A_2) <-> zero_zero(X_a) = ti(X_a,A_2))))) # label(fact_2202_sgn__0__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4301 (all X_a (field_char_0(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),field_char_0_Rats(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),field_char_0_Rats(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),field_char_0_Rats(X_a)))))))) # label(fact_3696_Rats__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4302 (all X_2 hAPP(real,real,uminus_uminus(real),hAPP(nat,real,sin_coeff,X_2)) = hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),cos_coeff),X_2)) # label(fact_4122_cos__fdiffs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4303 (all N all M hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)))) # label(fact_570_le__add1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4304 (all A_1 all B hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,uminus_uminus(int),A_1)),B) = hAPP(rat,rat,uminus_uminus(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3755_minus__rat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4305 (all X_a (real_algebra_1(X_a) -> zero_zero(X_a) = hAPP(real,X_a,of_real(X_a),zero_zero(real)))) # label(fact_2783_of__real__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4306 (all B all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),zero_zero(int))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A_1)) -> hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B) = zero_zero(int)))) # label(fact_1016_div__neg__neg__trivial) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4307 (all X all D (ti(int,D) != zero_zero(int) -> 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)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),D))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(int,real,real_1(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X),D))),hAPP(int,real,real_1(int),D))))) # label(fact_3411_real__of__int__div__aux) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4308 (all F all L all C_1 (hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),F),L),hAPP(real,filter(real),at(real),C_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),L)) -> (exists R_2 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C_1),X_2))),R_2)) & C_1 != X_2 -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,F,X_2))))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_2))))))) # label(fact_4628_LIM__fun__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4309 (all X_a (linordered_field(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),A_1))))))) # label(fact_2572_inverse__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4310 (all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hAPP(int,int,number_number_of(int),min_1) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,number_number_of(int),min_1)),B))) # label(fact_1047_div__eq__minus1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4311 (all K_4 all L_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),K_4),L_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),L_4)))))) # label(fact_560_add__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4312 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(nat,real,real_1(nat),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(real,nat,natfloor,X)),N))))) # label(fact_2356_less__natfloor) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4313 (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),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_2649_log__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4314 (all X_a (ordere142940540dd_abs(X_a) -> abs_abs(X_a) = ti(fun(X_a,X_a),abs_abs(X_a)))) # label(tsy_c_Groups_Oabs__class_Oabs_1_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4315 (all M all N all K_4 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)))) # label(fact_3215_gcd__dvd__prod__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4316 (all X_a (real_normed_field(X_a) -> (all A_1 all B (ti(X_a,B) != zero_zero(X_a) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(X_a,real,norm_norm(X_a),A_1)),hAPP(X_a,real,norm_norm(X_a),B)) = hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_1),B)))))) # label(fact_1790_nonzero__norm__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4317 (all X_a (linordered_idom(X_a) -> (all X_1 all Y_1 (ti(X_a,X_1) != zero_zero(X_a) | zero_zero(X_a) != ti(X_a,Y_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4318 (all M all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),M))))) # label(fact_3044_prime__dvd__power__two) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4319 (all X_a (ring_div(X_a) -> (all B all B_5 all A_1 all C all A_6 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_6),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B_5),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_6),B_5)),C)))))) # label(fact_943_mod__diff__cong) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4320 (all K all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),Ma)))) # label(fact_4369_gcd__greatest__iff__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.88 4321 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> zero_zero(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,fact_fact(nat),N)),hAPP(nat,nat,fact_fact(nat),M)))) # label(fact_2499_fact__mod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4322 (all X_a (archim1727834104eiling(X_a) -> (all V_1 all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),V_1)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),V_1)),hAPP(X_a,int,archimedean_ceiling(X_a),X_1))))))) # label(fact_3303_number__of__less__ceiling) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4323 (all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),pi)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))))))) # label(fact_2216_cos__monotone__0__pi_H) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4324 (all X_a (real_vector(X_a) -> scaleR_scaleR(X_a) = ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4325 (all X_a (order(X_a) -> (all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),Y)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> ti(X_a,X) = ti(X_a,Y)))))) # label(fact_1549_order__antisym) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4326 (all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),cos),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sin,hAPP(real,real,G,X_1)))),Ma))))) # label(fact_3854_DERIV__fun__cos) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4327 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X))),one_one(real)))))) # label(fact_2243_cos__double__less__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4328 (all K all Ma all N_1 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),N_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),K),Ma) <-> Ma = N_1)) # label(fact_524_nat__add__left__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4329 (all X_a all X_b (ord(X_b) -> (all F all G (-hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),G),F)) & hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less_eq(fun(X_a,X_b)),F),G)) <-> hBOOL(hAPP(fun(X_a,X_b),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,X_b),bool),ord_less(fun(X_a,X_b)),F),G)))))) # label(fact_1609_less__fun__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4330 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,K)),min_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K),min_1)))) # label(fact_294_rel__simps_I13_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4331 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_826_less__iff__diff__less__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4332 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X_1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(X_a,X_a,exp(X_a),X_1)))))) # label(fact_4752_exp__converges) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4333 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))))) # label(fact_2494_of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4334 (all A_1 all J_2 all K_4 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),K_4))),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5)))))))) # label(fact_851_MultInv__zcong__prop2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4335 (all X_a (semiring_div(X_a) -> (all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> ti(X_a,B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),A_1)))))) # label(fact_1004_dvd__mult__div__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4336 (all Z all W_1 (ti(int,W_1) != ti(int,Z) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),W_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z),W_1)))) # label(fact_37_zless__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4337 (all X all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))) -> -(hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),B))))) # label(fact_3230_gcd__semilattice__nat_Ole__infE) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4338 (all X hAPP(real,real,arctan,hAPP(real,real,uminus_uminus(real),X)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,arctan,X))) # label(fact_2055_arctan__minus) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4339 (all M (hBOOL(hAPP(int,bool,zprime,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),M)),one_one(int)))) -> hAPP(int,int,hAPP(int,fun(int,int),legendre,hAPP(int,int,number_number_of(int),min_1)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),M)),one_one(int))) = one_one(int))) # label(fact_469_Legendre__1mod4) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4340 (all N_1 (N_1 = zero_zero(nat) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),N_1)),zero_zero(real))))) # label(fact_2315_real__of__nat__le__zero__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4341 (all X_a all X all Y (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),fequal(X_a),X),Y)) | ti(X_a,X) != ti(X_a,Y))) # label(help_fequal_2_1_T) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4342 (all X_a (one(X_a) -> (all X_1 (ti(X_a,X_1) = one_one(X_a) <-> one_one(X_a) = ti(X_a,X_1))))) # label(fact_772_one__reorient) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4343 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sRStar,P_4))) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X_1),zero_zero(int)),P_4)))) # label(fact_1130_StandardRes__SRStar__prop1a) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4344 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1))))),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),hAPP(fun(nat,nat),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,nat),fun(nat,real))),fun(fun(nat,nat),fun(real,fun(nat,real))),combc(real,fun(nat,nat),fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real))),hAPP(fun(fun(nat,real),fun(fun(nat,nat),fun(nat,real))),fun(fun(real,fun(nat,real)),fun(real,fun(fun(nat,nat),fun(nat,real)))),combb(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),real),combb(nat,real,nat)),power_power(real))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))),X_1),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))) # label(fact_3967_DERIV__arctan__series) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4345 (all A_1 all B all Q_3 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_4) = 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_eq(int),R_4),zero_zero(int))) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),R_4))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),R_4),B)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),R_4))) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4)))))) # label(fact_1197_divmod__int__relI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4346 (all X_a all X_b all F all A_2 all B_1 (hBOOL(hAPP(product_prod(X_a,X_b),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),F),hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1))) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),F,A_2),B_1)))) # label(fact_4043_splitD) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4347 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,semiring_1_of_nat(int),M)),N)) # label(fact_1355_int__power) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4348 (all X all Y hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),X),Y)) # label(fact_3660_gcd__eq__nitpick__gcd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4349 (all X all Y hAPP(rat,real,ratreal,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),X),Y)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,ratreal,X)),hAPP(rat,real,ratreal,Y))) # label(fact_3771_real__times__code) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4350 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),N_1)),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),N_1)),Ma)))) # label(fact_3390_number__of__le__real__of__int__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4351 (all X_a (real_normed_vector(X_a) -> (all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)))))) # label(fact_4470_LIMSEQ__minus__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4352 (all X hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,re,X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),hAPP(complex,real,im,X))),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,re,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,im,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) = hAPP(complex,complex,inverse_inverse(complex),X)) # label(fact_2990_complex__inverse__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4353 (all N all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),N))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_2133_negative__zle) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4354 (all V_1 all V_2 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(int,nat,number_number_of(nat),V_1)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),V_2),pls)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,number_number_of(nat),V_1)),hAPP(int,nat,number_number_of(nat),V_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2))))),zero_zero(nat)),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),V_1),hAPP(int,int,uminus_uminus(int),V_2)))))))) # label(fact_3911_diff__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4355 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(real,real,arcsin,Y))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,arcsin,Y)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))) # label(fact_2130_arcsin__bounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4356 (all W hAPP(int,int,hAPP(int,fun(int,int),times_times(int),pls),W) = pls) # label(fact_62_mult__Pls) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4357 (all A_2 all P_4 (hBOOL(hAPP(int,bool,zprime,P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_4),one_one(int)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),wset,A_2),P_4))),one_one(int)),P_4)))))) # label(fact_3934_wset__zcong__prod__1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4358 (all R_4 all X hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,re,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X)))) # label(fact_4744_complex__scaleR__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4359 (all M all K_4 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4) != M -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),K_4))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),K_4))))) # label(fact_1386_one__less__k) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4360 (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_2577_division__ring__inverse__add) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4361 (all X_a (real_normed_vector(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,bseq(X_a),X_3)) -> -(all K_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),K_2)) -> -(all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(nat,X_a,X_3,N_2))),K_2))))))))) # label(fact_3501_BseqE) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4362 (all X_a (number_ring(X_a) & linordered_idom(X_a) -> (all X ((-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(int,X_a,number_number_of(X_a),X)),zero_zero(X_a))) -> hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),X)) = 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_2113_abs__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4363 (all X_a (topological_space(X_a) -> (all F all L (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L),sequentially)) <-> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),L),sequentially)))))) # label(fact_4461_LIMSEQ__Suc__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4364 (all X_a (real_normed_field(X_a) -> (all Y_3 all B_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),Y_3),B_1),sequentially)) -> (zero_zero(X_a) != ti(X_a,B_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),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_3)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),sequentially)))))))) # label(fact_4451_LIMSEQ__divide) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4365 (all N_1 all V_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,suc,N_1)),hAPP(int,nat,number_number_of(nat),V_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),hAPP(bool,fun(nat,fun(nat,nat)),if(nat),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),zero_zero(nat)),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),N_1),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1))))))) # label(fact_4796_min__number__of__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4366 (all A_1 all B all P_5 all Q_3 hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),P_5)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),Q_3))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),P_5)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_1),B))),hAPP(product_prod(int,int),int,twoSqu1094008024sum2sq,hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3)))) # label(fact_743_mult__sum2sq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4367 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),J_2))) # label(fact_3429_zgcd__zdvd2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4368 (all Ta all A_3 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),A_3)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Xb),Xa))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),D_2)),Ta)))))))) # label(fact_4650_aset_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4369 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Ly),Rx))))) # label(fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4370 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1))))) # label(fact_634_dvd_Oorder__trans) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4371 (all X hAPP(int,real,real_1(int),hAPP(int,int,abs_abs(int),X)) = hAPP(real,real,abs_abs(real),hAPP(int,real,real_1(int),X))) # label(fact_3343_real__of__int__abs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4372 (all X all Y all Z_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Z_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),Z_1),Y)))))) # label(fact_712_real__mult__less__mono2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4373 (all X_a (order(X_a) -> (all X_3 ((all M_2 all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,M_2)),hAPP(nat,X_a,X_3,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4131_monoI1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4374 (all P_5 hAPP(product_prod(int,int),rat,frct,P_5) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(product_prod(int,int),int,product_fst(int,int),P_5)),hAPP(product_prod(int,int),int,product_snd(int,int),P_5))) # label(fact_3778_Frct__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4375 (all Ma all N_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),Ma),N_1))) <-> zero_zero(int) != ti(int,N_1) | zero_zero(int) != ti(int,Ma))) # label(fact_4381_gcd__pos__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4376 (all V_3 all V ((hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = zero_zero(nat)) & (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> (-hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,number_number_of(int),V)),hAPP(int,int,number_number_of(int),V_3)))) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V_3))) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(int,nat,number_number_of(nat),V)),hAPP(int,nat,number_number_of(nat),V_3)) = hAPP(int,nat,number_number_of(nat),V))))) # label(fact_1518_mod__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4377 (all A_2 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),Ma)) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),bnorRset,A_2),Ma))),Ma))) # label(fact_3931_Bnor__prod__zgcd) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4378 (all X_a (dist_norm(X_a) -> ti(fun(X_a,fun(X_a,real)),dist_dist(X_a)) = dist_dist(X_a))) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4379 (all X_a (real_normed_field(X_a) & banach(X_a) -> (all X hAPP(X_a,X_a,exp(X_a),X) != zero_zero(X_a)))) # label(fact_2537_exp__not__eq__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4380 (all X_a all X_b all F all A_3 hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),bool),nat_tr1645093318rphism(X_a,X_b),F),A_3))) # label(fact_1176_transfer__morphismI) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4381 (all X_a (number_semiring(X_a) -> (all N hAPP(int,X_a,number_number_of(X_a),hAPP(nat,int,semiring_1_of_nat(int),N)) = hAPP(nat,X_a,semiring_1_of_nat(X_a),N)))) # label(fact_1212_number__of__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4382 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),Ta),one_one(int))),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),X_2)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Ta),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2))))))))) # label(fact_4633_bset_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4383 (all Z all P_1 ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(nat,int,semiring_1_of_nat(int),N_2)))) -> ((all N_2 hBOOL(hAPP(int,bool,P_1,hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N_2)))))) -> hBOOL(hAPP(int,bool,P_1,Z))))) # label(fact_3527_int__of__nat__induct) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4384 (all X_a (linord626643107strict(X_a) -> (all V all U all Y all X all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),U)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),V)) -> (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),U),V) = one_one(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),U),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),V),Y))),A_1)))))))))) # label(fact_277_convex__bound__lt) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4385 (all R_4 hAPP(real,real,abs_abs(real),R_4) = hAPP(real,real,norm_norm(real),R_4)) # label(fact_1857_real__norm__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4386 (all A_1 all B all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,B) -> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B) = ti(int,R_4)))) # label(fact_1192_divmod__int__rel__mod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4387 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,Ma)),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(fun(nat,bool),fun(nat,bool),hAPP(bool,fun(fun(nat,bool),fun(nat,bool)),nat_case(bool),fFalse),hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma)),N_1)))) # label(fact_4120_less__eq__nat_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4388 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,real,norm_norm(X_a),X) = hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),zero_zero(X_a))))) # label(fact_3524_norm__conv__dist) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4389 (all I all M_1 (-hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3873_card__less__Suc2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4390 (all X all N_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),N_5)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N_5),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X))))))) # label(fact_2699_real__root__decreasing) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4391 (all X_a (comm_semiring_1(X_a) -> (all A_1 all B all C (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),B),C)))))) # label(fact_339_dvd__mult__right) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4392 (all X_a (linordered_ring(X_a) -> (all X all Y -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Y),Y))),zero_zero(X_a)))))) # label(fact_109_not__sum__squares__lt__zero) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4393 (all X_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_3)) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),X_3))))) # label(fact_2915_ResSet__finite) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4394 (all X_a (topological_space(X_a) & comm_monoid_add(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) <-> (exists X1 hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),X1))))))) # label(fact_4090_summable__def) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4395 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)))))) # label(fact_3985_divide_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4396 (all A_1 all B all C hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))) # label(fact_1082_mod__mult2__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4397 (all M all N ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = M) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),N)))) # label(fact_1110_mod__if) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4398 (all X_1 all P_4 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),hAPP(int,fun(int,bool),sr,P_4))) -> hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_4),X_1) = ti(int,X_1))) # label(fact_910_StandardRes__SR__prop) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4399 (all K_4 hAPP(nat,rat,semiring_1_of_nat(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(nat,int,semiring_1_of_nat(int),K_4)),one_one(int))) # label(fact_3743_Fract__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4400 (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 X = 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)))))) # label(fact_1172_nat__mod__eq__lemma) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4401 (all X all Y hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X),Y))) # label(fact_2735_complex__norm) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4402 (all X_a (real_algebra_1(X_a) -> (all X_1 all Y_1 (hAPP(real,X_a,of_real(X_a),X_1) = hAPP(real,X_a,of_real(X_a),Y_1) <-> X_1 = Y_1)))) # label(fact_2777_of__real__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4403 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N)) # label(fact_3248_gcd__add1__nat) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4404 (all N_1 all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),M_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,F,M_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4275_series__pos__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4405 (all M all N hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,semiring_1_of_nat(int),M)),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_1312_zadd__int) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4406 (all M zero_zero(nat) != hAPP(nat,nat,suc,M)) # label(fact_1227_Zero__not__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4407 (all N hAPP(nat,nat,size_size(nat),N) = N) # label(fact_2923_nat__size) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4408 (all X_a all X_b (comm_monoid_mult(X_b) -> (all G all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> one_one(X_b) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),G),A_3))))) # label(fact_3952_setprod_Oinfinite) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4409 (all K_4 all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,bit0,K_4)),L_4)) # label(fact_63_mult__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4410 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Z_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),Y),Z_1))))))) # label(fact_4945_min__max_Odistrib__inf__le) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4411 (all X (hBOOL(hAPP(int,bool,nat_is_nat,X)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,fact_fact(int),X))))) # label(fact_4858_transfer__int__nat__factorial__closure) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4412 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int))),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5)))))) # label(fact_1164_Euler__part2) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4413 (all Real1 all Real2 all Real1_2 all Real2_2 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1_2),Real2_2) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,Real1),Real2) <-> Real2_2 = Real2 & Real1 = Real1_2)) # label(fact_2739_complex_Oinject) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4414 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N)))))))) # label(fact_444_power__less__power__Suc) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4415 (all Y (zero_zero(code_code_numeral) != Y -> -(all Code_numeral_1 Y != hAPP(code_code_numeral,code_code_numeral,code_S1047413653umeral,Code_numeral_1)))) # label(fact_2971_code__numeral_Oexhaust) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4416 (all R_4 hAPP(real,complex,of_real(complex),R_4) = hAPP(real,complex,hAPP(real,fun(real,complex),rcis,R_4),zero_zero(real))) # label(fact_3165_rcis__zero__arg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4417 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archim2085082626_floor(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(X_a,int,archim2085082626_floor(X_a),X)),one_one(int))))) # label(fact_2887_floor__add__one) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4418 (all X_a (linordered_semidom(X_a) -> (all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))) # label(fact_407_zero__less__power) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4419 (all X_a (linorder(X_a) -> (all Y all X (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)))))) # label(fact_1589_not__leE) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4420 (all X_a (comm_ring_1(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),Y_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),X_1),Y_1)))))) # label(fact_2046_dvd__minus__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4421 (all X_a (real_normed_algebra(X_a) -> (exists K_2 all A_4 all B_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_4),B_4))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),A_4)),hAPP(X_a,real,norm_norm(X_a),B_4))),K_2)))))) # label(fact_1811_mult_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4422 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1))))))) # label(fact_4102_divide_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4423 (all N_1 hAPP(nat,fun(nat,bool),ord_atMost(nat),N_1) = hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),N_1)))) # label(fact_4934_SetInterval_Otransfer__nat__int__set__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4424 (all X hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(real,real,abs_abs(real),X)) = hAPP(real,real,sgn_sgn(real),X)) # label(fact_2213_real__sgn__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4425 (all X_a (ordere216010020id_add(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),zero_zero(X_a)))))))) # label(fact_819_add__neg__neg) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4426 (all X_a (monoid_mult(X_a) -> (all Y all P_5 all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),P_5),N)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),P_5))),Y) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,N)),P_5)))))) # label(fact_1412_lemma__realpow__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4427 (all P_1 all N_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B_1),A_2)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_1))))) # label(fact_3128_Bolzano__bisect__diff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4428 (all Y all U all X1_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X1_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X1_1),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),U))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X)),Y)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),X1_1)),U))))))) # label(fact_2590_real__mult__inverse__cancel) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4429 (all X_a all X_b (order(X_b) & order(X_a) -> (all C_1 all A_2 all F all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,B_1))) -> (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),B_1),C_1)) -> ((all X_2 all Y_2 (hBOOL(hAPP(X_b,bool,hAPP(X_b,fun(X_b,bool),ord_less_eq(X_b),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_b,X_a,F,X_2)),hAPP(X_b,X_a,F,Y_2))))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_b,X_a,F,C_1))))))))) # label(fact_2837_order__less__le__subst1) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4430 (all L_4 pls != hAPP(int,int,bit1,L_4)) # label(fact_117_rel__simps_I39_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4431 (all X_a (real_normed_field(X_a) -> (all N_1 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(nat,fun(X_a,X_a),hAPP(fun(X_a,fun(nat,X_a)),fun(nat,fun(X_a,X_a)),combc(X_a,nat,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(nat,X_a)),hAPP(fun(X_a,fun(nat,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(nat,X_a))),combb(X_a,fun(nat,X_a),X_a),power_power(X_a)),F)),N_1)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_2),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))))) # label(fact_3889_DERIV__power) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4432 (all X_a (ring_1(X_a) -> (all W all Z_1 hAPP(int,X_a,ring_1_of_int(X_a),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),W),Z_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(int,X_a,ring_1_of_int(X_a),W)),hAPP(int,X_a,ring_1_of_int(X_a),Z_1))))) # label(fact_3588_of__int__mult) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4433 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B))))) # label(fact_4814_min__max_Oinf_Oleft__idem) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4434 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),N))) # label(fact_1441_mod__Suc__eq__mod__add3) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4435 (all X_a (comm_monoid_add(X_a) & t2_space(X_a) -> (all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),hAPP(fun(nat,X_a),X_a,suminf(X_a),F))))))) # label(fact_4092_summable__sums) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4436 (all X_a (ord(X_a) -> ti(fun(X_a,fun(X_a,X_a)),ord_min(X_a)) = ord_min(X_a))) # label(tsy_c_Orderings_Oord__class_Omin_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4437 (all X_b all X_c all X_a (topological_space(X_a) & real_normed_vector(X_b) & real_normed_vector(X_c) -> (all G all Ma all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,norm_norm(X_c),hAPP(X_c,X_c,hAPP(X_c,fun(X_c,X_c),minus_minus(X_c),hAPP(X_a,X_c,G,X_2)),Ma))),hAPP(X_b,real,norm_norm(X_b),hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),minus_minus(X_b),hAPP(X_a,X_b,F,X_2)),L)))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),Ma),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4654_LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4438 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A_2))))) # label(fact_1025_pos__imp__zdiv__nonneg__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.89 4439 (all X_a all A_3 all B_2 hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2) = hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,bool)),combs(X_a,bool,bool),hAPP(fun(X_a,bool),fun(X_a,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(X_a,bool),fun(X_a,fun(bool,bool))),combb(bool,fun(bool,bool),X_a),fconj),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),B_2))))) # label(fact_1961_set__diff__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4440 (all X_a (real_normed_vector(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> zero_zero(X_a) = hAPP(X_a,X_a,sgn_sgn(X_a),X_1))))) # label(fact_2200_sgn__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4441 (all P_1 all Ma all N_1 ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Ma),N_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> ((N_1 = Ma -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),P_1,N_1),Ma)))))) # label(fact_520_nat__less__cases) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4442 (all X_a (topological_space(X_a) -> (all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),hAPP(real,real,abs_abs(real),L)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4553_LIM__rabs) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4443 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),zero_zero(nat)),N) = zero_zero(nat)) # label(fact_661_diff__0__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4444 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1579_xt1_I10_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4445 (all X_a (comm_semiring_1(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),D)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))) # label(fact_336_mult__dvd__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4446 (all X all A_1 all B (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_1),B)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1)),hAPP(real,real,hAPP(real,fun(real,real),powr,X),B)))))) # label(fact_3353_powr__less__mono) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4447 (all X_b all X_a all A_2 all B_1 all A_8 all B_7 (ti(X_a,A_2) = ti(X_a,A_8) & ti(X_b,B_1) = ti(X_b,B_7) <-> hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_2),B_1) = 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))) # label(fact_3136_Pair__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4448 (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),inverse_divide(real),hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),Y))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,Y))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,tan,X)),hAPP(real,real,tan,Y))))) # label(fact_2371_add__tan__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4449 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),Ma)) & hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),hAPP(int,int,hAPP(int,fun(int,int),hAPP(fun(int,bool),fun(int,fun(int,int)),rRset2norRR,A_3),Ma),A_2)),hAPP(int,fun(int,bool),norRRset,Ma))))))) # label(fact_3621_RRset2norRR__correct) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4450 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),zero_zero(real))))) # label(fact_2596_exp__less__one__iff) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4451 (all X_a (linordered_idom(X_a) -> (all L_4 all K_4 (hAPP(X_a,X_a,abs_abs(X_a),L_4) = hAPP(X_a,X_a,abs_abs(X_a),K_4) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),L_4),K_4)))))) # label(fact_1847_dvd__if__abs__eq) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4452 (all P_1 hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),P_1))))) # label(fact_3831_Nat__Transfer_Otransfer__int__nat__set__function__closures_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4453 (all X_a (dense_linorder(X_a) -> ord_gr676655987ssThan(X_a) = ti(fun(X_a,fun(X_a,fun(X_a,bool))),ord_gr676655987ssThan(X_a)))) # label(tsy_c_SetInterval_Oord__class_OgreaterThanLessThan_0_res) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4454 (all P_1 all A_2 all B_1 (-((exists D_3 (-hBOOL(hAPP(nat,bool,P_1,D_3)) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B_1),D_3) = A_2)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A_2),B_1)) & -hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))) <-> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A_2),B_1))))) # label(fact_701_nat__diff__split__asm) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4455 (all P_1 all N_1 all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),N_1),K))) <-> (K = zero_zero(nat) -> hBOOL(hAPP(nat,bool,P_1,N_1))) & (zero_zero(nat) != K -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,J_1)))))))) # label(fact_1133_split__mod) # label(axiom) # label(non_clause). [assumption]. 10.83/10.90 4456 (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_4751_exp__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4457 (all X_a ti(fun(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a))),nat_rec(X_a)) = nat_rec(X_a)) # label(tsy_c_Nat_Onat_Onat__rec_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4458 (all A_2 all B_1 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),A_3)) -> ti(int,A_2) = ti(int,B_1))))))) # label(fact_3620_RRset__zcong__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4459 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),R_4),one_one(real))),hAPP(int,real,real_1(int),hAPP(real,int,archim2085082626_floor(real),R_4))))) # label(fact_3401_real__of__int__floor__gt__diff__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4460 (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) = hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)))))) # label(fact_2439_minus__one__odd__power) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4461 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),standardRes,P_5),X))))) # label(fact_1049_StandardRes__lbound) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4462 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),X_1)),zero_zero(real)),sequentially))))) # label(fact_4429_LIMSEQ__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4463 (all X_a (linorder(X_a) -> (all A_1 all X all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),B)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B))))))) # label(fact_4952_min__max_Oless__supI2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4464 (all A_1 all B hAPP(complex,complex,cnj,hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)) = hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),hAPP(real,real,uminus_uminus(real),B))) # label(fact_2948_complex__cnj) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4465 (all Ma all N_1 hAPP(nat,nat,hAPP(fun(nat,nat),fun(nat,nat),hAPP(nat,fun(fun(nat,nat),fun(nat,nat)),nat_case(nat),zero_zero(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),suc),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),ord_min(nat)),N_1))),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),Ma),hAPP(nat,nat,suc,N_1))) # label(fact_4832_min__Suc2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4466 (all Ma all D_1 (hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),Ma),D_1) = zero_zero(int) <-> (exists Q_4 ti(int,Ma) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),Q_4)))) # label(fact_991_zmod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4467 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)),zero_zero(X_a))))))) # label(fact_2545_negative__imp__inverse__negative) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4468 (all X_a (comm_semiring_1(X_a) -> (all Lx all Ly all Rx hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Rx)),Ly) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Lx),Ly)),Rx)))) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4469 (all X_a (comm_monoid_add(X_a) -> (all F all N_1 all Ma ((hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> zero_zero(X_a) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),hAPP(nat,nat,suc,N_1)))) & (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N_1),Ma)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),N_1))),hAPP(nat,X_a,F,N_1)) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),Ma),hAPP(nat,nat,suc,N_1)))))))) # label(fact_4204_setsum__op__ivl__Suc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4470 (all B all A_1 all X (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),A_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),X)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B))))) # label(fact_3229_gcd__semilattice__nat_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4471 (all X_a (order(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),X_1)),hAPP(X_a,fun(X_a,bool),ord_atMost(X_a),Y_1))))))) # label(fact_4990_atMost__subset__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4472 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,M)),hAPP(nat,nat,suc,N))) # label(fact_1251_diff__Suc__Suc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4473 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),nat_tsub,X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1199_Nat__Transfer_Otransfer__nat__int__functions_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4474 (all A_1 all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,real_1(nat),A_1)),X)) -> hAPP(real,nat,natceiling,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),X),hAPP(nat,real,real_1(nat),A_1))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(real,nat,natceiling,X)),A_1))) # label(fact_2350_natceiling__subtract) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4475 (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),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)) = 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))))) # label(fact_1660_times__divide__times__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4476 (all N all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_4),N)) = ti(int,K_4))) # label(fact_3454_zgcd__zmult__eq__self) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4477 (all N_1 all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),power_power(real)),N_1)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3891_DERIV__pow) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4478 (all U_1 hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)))) # label(fact_4253_finite__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4479 (all F (hBOOL(hAPP(fun(nat,real),bool,summable(real),F)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,F,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(fun(nat,real),real,suminf(real),F)))))) # label(fact_4071_suminf__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4480 (all X_a (monoid_mult(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),one_one(X_a)) = ti(X_a,A_1)))) # label(fact_800_mult__1__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4481 (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_1221_int__Suc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4482 (all Y hAPP(real,real,tan,hAPP(real,real,arctan,Y)) = Y) # label(fact_2254_tan__arctan) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4483 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),Y_1)) -> (ti(X_a,Y_1) = ti(X_a,X_1) <-> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1))))))) # label(fact_1595_linorder__antisym__conv2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4484 (all Z (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(int,nat,nat_1,Z))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),Z)))) # label(fact_1431_one__less__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4485 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),P_1) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),hAPP(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool)),hAPP(fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),fun(fun(X_a,fun(X_b,product_prod(X_a,X_b))),fun(X_a,fun(X_b,bool))),combb(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool),X_a),hAPP(fun(product_prod(X_a,X_b),bool),fun(fun(X_b,product_prod(X_a,X_b)),fun(X_b,bool)),combb(product_prod(X_a,X_b),bool,X_b),P_1)),product_Pair(X_a,X_b))))) # label(fact_4143_split__paired__The) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4486 (all X_3 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),Ma)) -> hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,int),fun(fun(int,bool),fun(int,bool)),image(int,int),hAPP(int,fun(int,int),standardRes,Ma)),X_3)),hAPP(fun(int,bool),fun(int,bool),collect(int),hAPP(fun(int,bool),fun(int,bool),hAPP(fun(int,fun(bool,bool)),fun(fun(int,bool),fun(int,bool)),combs(int,bool,bool),hAPP(fun(int,bool),fun(int,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(int,bool),fun(int,fun(bool,bool))),combb(bool,fun(bool,bool),int),fconj),hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)))),hAPP(int,fun(int,bool),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less(int)),Ma))))))) # label(fact_3897_SR__pos) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4487 (all Ta all B_2 all D_1 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),D_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa) != ti(int,X_2))))) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X_2),Ta))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2)),Ta)))))))) # label(fact_4649_bset_I9_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4488 (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,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),powr,X),A_1))) # label(fact_3359_powr__minus) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4489 (all C all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),A_1)) -> (B = C -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),C),A_1))))) # label(fact_645_dvd_Oord__less__eq__trans) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4490 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),Y)))) # label(fact_2687_real__root__divide) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4491 (all Y all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),X)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),Y)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(real,nat,natfloor,X)),Y) = hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X),hAPP(nat,real,real_1(nat),Y)))))) # label(fact_2382_natfloor__div__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4492 (all X_a (banach(X_a) & real_normed_field(X_a) -> (all Z all F all X_1 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),Z)),hAPP(X_a,real,norm_norm(X_a),X_1))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,X_a),fun(nat,real),hAPP(fun(X_a,real),fun(fun(nat,X_a),fun(nat,real)),combb(X_a,real,nat),norm_norm(X_a)),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),F)),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)))))))))) # label(fact_3996_powser__insidea) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4493 (all Q_3 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),Q_3),hAPP(rat,rat,inverse_inverse(rat),R_4)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),Q_3),R_4)) # label(fact_3717_divide__rat__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4494 (all N -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),zero_zero(nat)))) # label(fact_538_less__nat__zero__code) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4495 (all X_a (division_ring(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),one_one(X_a)) = one_one(X_a))) # label(fact_2516_inverse__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4496 (all X_a (dvd(X_a) & comm_ring(X_a) -> (all Ta all D_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),D_2)) -> (all X_2 all K_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X_2),Ta))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),D_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),K_1),D_2))),Ta))))))))) # label(fact_487_inf__period_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4497 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all G all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),G),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),hAPP(fun(X_a,X_b),fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,X_b)),combs(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_b,fun(X_b,X_b)),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combb(X_b,fun(X_b,X_b),X_a),plus_plus(X_b)),F)),G)),zero_zero(X_b)),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4579_LIM__add__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4498 (all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),one_one(nat))),N))) # label(fact_2873_coprime__plus1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4499 (all X all Y (X != Y -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X),Y)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),Y),X))))) # label(fact_516_linorder__neqE__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4500 (all P_1 all I hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),P_1)),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I)))))) # label(fact_3869_finite__M__bounded__by__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4501 (all K (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),K),pls)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,bit0,K)),pls)))) # label(fact_54_rel__simps_I27_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4502 (all C_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),C_1)),one_one(real))) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),C_1))),zero_zero(real)),sequentially)))) # label(fact_4490_LIMSEQ__rabs__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4503 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),P_5)) -> ti(int,A_1) = hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))))) # label(fact_763_inv__inv) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4504 (all X_a (linord1117847801e_zero(X_a) -> (all B_1 all C_1 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1)),A_2)) <-> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C_1),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1)))) & (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)))))))) # label(fact_1709_divide__less__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4505 (all N_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat)),N_1))) = hAPP(nat,nat,suc,N_1)) # label(fact_3828_card__Collect__le__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4506 (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_4357_coprime__minus__one__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4507 (all X_b all X_a all X_c all F all X_1 hAPP(X_c,X_a,F,hAPP(product_prod(X_b,X_c),X_c,product_snd(X_b,X_c),X_1)) = hAPP(product_prod(X_b,X_a),X_a,product_snd(X_b,X_a),hAPP(product_prod(X_b,X_c),product_prod(X_b,X_a),hAPP(fun(X_c,X_a),fun(product_prod(X_b,X_c),product_prod(X_b,X_a)),product_apsnd(X_c,X_a,X_b),F),X_1))) # label(fact_4067_snd__apsnd) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4508 (all Z_1 hAPP(real,real,sqrt,hAPP(complex,real,re,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1)))) = hAPP(complex,real,norm_norm(complex),Z_1)) # label(fact_3013_complex__mod__sqrt__Re__mult__cnj) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4509 (all K all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,K)),N_1))))) # label(fact_1342_Suc__mult__le__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4510 (all X_b all X_a (metric_space(X_b) & metric_space(X_a) -> (all R_1 all F all L_2 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L_2),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists S_1 ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X_2),A_2)),S_1)) & ti(X_a,X_2) != ti(X_a,A_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L_2)),R_1)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),S_1))))))))) # label(fact_4651_metric__LIM__D) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4511 (all X_a (archim1727834104eiling(X_a) -> (all X hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a))) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),one_one(int))))) # label(fact_3307_ceiling__diff__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4512 (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_5_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4513 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> zero_zero(nat) != N)) # label(fact_539_gr__implies__not0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4514 (all X_a (order(X_a) -> (all F ((all X_2 all Y_2 (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y_2),X_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X_2),Y_2)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,F,X_2)),hAPP(nat,X_a,F,Y_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,X_a),bool),strict_mono(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combs(nat,fun(nat,bool),fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool))),hAPP(fun(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool))),fun(fun(nat,fun(nat,fun(bool,bool))),fun(nat,fun(fun(nat,bool),fun(nat,bool)))),combb(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),nat),combs(nat,bool,bool)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool))),hAPP(fun(fun(nat,bool),fun(nat,fun(bool,bool))),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,fun(bool,bool)))),combb(fun(nat,bool),fun(nat,fun(bool,bool)),nat),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj)),dvd_dvd(nat)))),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),hAPP(fun(fun(nat,bool),fun(nat,bool)),fun(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool))),combb(fun(nat,bool),fun(nat,bool),nat),hAPP(fun(bool,bool),fun(fun(nat,bool),fun(nat,bool)),combb(bool,bool,nat),fNot)),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat))))),F)))))) # label(fact_4791_dvd_Ostrict__monoI) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4515 (all R_4 all X hAPP(complex,real,im,hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),R_4),X)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),R_4),hAPP(complex,real,im,X))) # label(fact_4681_complex__Im__scaleR) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4516 (all X_a finite_psubset(X_a) = ti(fun(product_prod(fun(X_a,bool),fun(X_a,bool)),bool),finite_psubset(X_a))) # label(tsy_c_Wellfounded_Ofinite__psubset_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4517 (all B all A_1 (zero_zero(nat) != A_1 -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),A_1)))) # label(fact_3260_gcd__le1__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4518 (all K_4 hAPP(int,rat,number_number_of(rat),K_4) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,hAPP(int,int,number_number_of(int),K_4)),one_one(int))) # label(fact_3774_rat__number__expand_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4519 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),sin)),sin)),X_1),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X_1)),hAPP(real,real,sin,X_1)))))) # label(fact_3819_DERIV__sin__sin__mult) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4520 (all R_4 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,real_1(int),hAPP(real,int,archimedean_ceiling(real),R_4))),one_one(real))),R_4))) # label(fact_3403_real__of__int__ceiling__diff__one__le) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4521 (all X_a (archim1727834104eiling(X_a) -> hAPP(X_a,int,archim2085082626_floor(X_a),one_one(X_a)) = one_one(int))) # label(fact_2870_floor__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4522 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),B_1),zero_zero(X_a))) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),B_1)))))) # label(fact_1676_zero__less__divide__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4523 (all X_b all X_c all X_a (metric_space(X_c) & metric_space(X_b) & topological_space(X_a) -> (all G all Ma all F all L all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),L),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> ((all X_2 (ti(X_a,A_2) != ti(X_a,X_2) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_c,real,hAPP(X_c,fun(X_c,real),dist_dist(X_c),hAPP(X_a,X_c,G,X_2)),Ma)),hAPP(X_b,real,hAPP(X_b,fun(X_b,real),dist_dist(X_b),hAPP(X_a,X_b,F,X_2)),L))))) -> hBOOL(hAPP(filter(X_a),bool,hAPP(X_c,fun(filter(X_a),bool),hAPP(fun(X_a,X_c),fun(X_c,fun(filter(X_a),bool)),tendsto(X_a,X_c),G),Ma),hAPP(X_a,filter(X_a),at(X_a),A_2)))))))) # label(fact_4656_metric__LIM__imp__LIM) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4524 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)) = hAPP(real,real,hAPP(nat,fun(real,real),root,N),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),X),Y)))) # label(fact_2682_real__root__mult) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4525 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_432_mult__less__le__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4526 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_575_add__le__mono1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4527 (all M all N hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),N)),hAPP(nat,nat,suc,M)))) # label(fact_1339_diff__less__Suc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4528 (all X_a (linorder(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),A_1),B) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),B),A_1)))) # label(fact_4971_min__max_Osup_Ocommute) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4529 (all X_a (monoid_mult(X_a) & comm_ring(X_a) -> (all X_1 all N_1 all Y_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),hAPP(nat,nat,suc,N_1))),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1),hAPP(nat,nat,suc,N_1))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_1),Y_1)),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))))))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4530 (all M all N M = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N)),N)) # label(fact_668_diff__add__inverse2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4531 (all M all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (zero_zero(nat) != N -> (N = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),P_5),M) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))))) # label(fact_3066_prime__factor__lt) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4532 (all Ma all Ta all K (ti(int,K) != zero_zero(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ma)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ta))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),Ta))))) # label(fact_601_zdvd__mono) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4533 (all X_1 all A_3 (hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A_3)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),A_3)) -> hBOOL(hAPP(int,bool,nat_is_nat,X_1))))) # label(fact_4850_Nat__Transfer_Otransfer__int__nat__set__function__closures_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4534 (all K_3 all K all F ((all N_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),K),hAPP(nat,real,F,N_2))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),K_3)))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),F)))) # label(fact_4312_BseqI2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4535 (all X_a (ring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_945_mod__diff__left__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4536 (all X_a all X_b all P_1 hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool),hAPP(fun(product_prod(X_a,X_b),fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_b),fun(product_prod(X_a,X_b),bool)),combs(product_prod(X_a,X_b),X_b,bool),hAPP(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool)),hAPP(fun(X_a,fun(X_b,bool)),fun(fun(product_prod(X_a,X_b),X_a),fun(product_prod(X_a,X_b),fun(X_b,bool))),combb(X_a,fun(X_b,bool),product_prod(X_a,X_b)),P_1),product_fst(X_a,X_b))),product_snd(X_a,X_b))) = hAPP(fun(product_prod(X_a,X_b),bool),product_prod(X_a,X_b),the(product_prod(X_a,X_b)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(X_a,X_b),bool),product_prod_case(X_a,X_b,bool),P_1))) # label(fact_4145_The__split) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4537 (all X_b all X_a all F all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),A_3))) -> (exists C_3 (hBOOL(hAPP(fun(X_b,bool),bool,hAPP(fun(X_b,bool),fun(fun(X_b,bool),bool),ord_less_eq(fun(X_b,bool)),C_3),A_3)) & ti(fun(X_a,bool),B_2) = hAPP(fun(X_b,bool),fun(X_a,bool),hAPP(fun(X_b,X_a),fun(fun(X_b,bool),fun(X_a,bool)),image(X_b,X_a),F),C_3) & hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),C_3))))))) # label(fact_3645_finite__subset__image) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4538 (all X_a (ab_sem1668676832m_mult(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X) = ti(X_a,X)))) # label(fact_2951_mult__idem) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4539 (all X hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),X),zero_zero(int)) = hAPP(int,int,abs_abs(int),X)) # label(fact_4388_gcd__0__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4540 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),X_1)),Y_1)))) # label(fact_2109_real__0__less__add__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4541 (all X_a (division_ring(X_a) -> (all A_1 (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = zero_zero(X_a) -> zero_zero(X_a) = ti(X_a,A_1))))) # label(fact_2530_inverse__zero__imp__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4542 (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_482_zdiff__zmult__distrib2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4543 (all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),B)) -> B = zero_zero(nat) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A_1),B)))) # label(fact_723_divides__ge) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4544 (all F all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),B_1)) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) -> hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_2)))) -> ((all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A_2),X_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_2),zero_zero(real))))) -> (all X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_2),B_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),X_2)) -> hAPP(real,real,F,A_2) = hAPP(real,real,F,X_2))))))) # label(fact_4930_DERIV__isconst1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4545 (all X_a (idom(X_a) -> (all C_1 all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),A_2)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C_1),B_1))) <-> zero_zero(X_a) = ti(X_a,C_1) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_2),B_1)))))) # label(fact_409_dvd__mult__cancel__left) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4546 (all X_a (ring_1(X_a) -> (all B_1 all A_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),ring_1_Ints(X_a))) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),B_1),ring_1_Ints(X_a))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1)),ring_1_Ints(X_a)))))))) # label(fact_3824_Ints__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4547 (all M all N hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),M)),hAPP(nat,real,real_1(nat),N)) = hAPP(nat,real,real_1(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),N))) # label(fact_2308_real__of__nat__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4548 (all Ma all N_1 (Ma = N_1 <-> hAPP(nat,int,semiring_1_of_nat(int),Ma) = hAPP(nat,int,semiring_1_of_nat(int),N_1))) # label(fact_1486_int__int__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4549 (all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> ti(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))))))) # label(fact_1454_two__times__even__div__two) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4550 (all X_a (order(X_a) -> (all X_3 ((all N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,X_3,N_2)),hAPP(nat,X_a,X_3,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(fun(nat,X_a),bool,monoseq(X_a),X_3)))))) # label(fact_4141_mono__SucI1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4551 (all X_a (number_ring(X_a) & real_algebra_1(X_a) -> (all W hAPP(int,X_a,number_number_of(X_a),W) = hAPP(real,X_a,of_real(X_a),hAPP(int,real,number_number_of(real),W))))) # label(fact_2785_of__real__number__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4552 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),C)),B)),C)))) # label(fact_939_mod__add__left__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4553 (all N_1 ((exists M_2 hAPP(nat,nat,suc,M_2) = N_1) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)))) # label(fact_1322_gr0__conv__Suc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4554 (all X_a (ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X)),one_one(X_a)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),X),one_one(X_a))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),one_one(X_a)))))) # label(fact_731_real__squared__diff__one__factored) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4555 (all L_4 hAPP(int,int,bit0,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),L_4)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),pls),hAPP(int,int,bit0,L_4))) # label(fact_495_diff__bin__simps_I3_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4556 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4800_min__max_Oless__infI1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4557 (all X_a (number(X_a) & semiring_div(X_a) -> (all X_1 all Y_1 (zero_zero(X_a) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(int,X_a,number_number_of(X_a),Y_1)),hAPP(int,X_a,number_number_of(X_a),X_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),hAPP(int,X_a,number_number_of(X_a),X_1)),hAPP(int,X_a,number_number_of(X_a),Y_1))))))) # label(fact_1009_dvd__eq__mod__eq__0__number__of) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4558 (all Z_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),Z_5),zero_zero(int))) <-> hBOOL(hAPP(int,bool,nat_neg,Z_5)))) # label(fact_1502_neg__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4559 (all Z_1 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> zero_zero(int) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> ti(int,Z_1) = hAPP(nat,int,semiring_1_of_nat(int),hAPP(int,nat,nat_1,Z_1))))) # label(fact_1376_int__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4560 (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) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,Y_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),X_1),Y_1))) & (Y_1 = zero_zero(nat) -> X_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X_1),Y_1)))) # label(fact_3670_nat__gcd_Opsimps) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4561 (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]. 10.93/10.90 4562 (all A_1 all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),hAPP(real,int,archim2085082626_floor(real),X))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,real_1(int),A_1)),X)))) # label(fact_3363_real__le__floor) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4563 (all X all Y all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(nat,fun(real,real),root,N),X)),hAPP(real,real,hAPP(nat,fun(real,real),root,N),Y)))))) # label(fact_2678_real__root__le__mono) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4564 (all Y_1 all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y_1)) -> ((hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y_1),zEven)) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven))) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,Y_1)))))) # label(fact_1468_neg__one__power__parity) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4565 (all X (-hBOOL(hAPP(nat,bool,even_odd_even(nat),X)) -> 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)))) = 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))))))) # label(fact_2445_odd__nat__plus__one__div__two) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4566 (all X_a (monoid_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_1_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4567 (all X_a (semiring_div(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),zero_zero(X_a))))) # label(fact_925_mod__by__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.90 4568 (all N_1 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,A_2,N_2)))) -> ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A_2,hAPP(nat,nat,suc,N_2))),hAPP(nat,real,A_2,N_2)))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1)),one_one(nat)))))))))) # label(fact_4504_summable__Leibniz_H_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4569 (all X_a (zero(X_a) -> (all Diff all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(X_a,fun(nat,real),hAPP(fun(nat,fun(X_a,real)),fun(X_a,fun(nat,real)),combc(nat,X_a,real),Diff),zero_zero(X_a)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,N_1),zero_zero(X_a))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),N_1))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))) = hAPP(X_a,real,hAPP(nat,fun(X_a,real),Diff,zero_zero(nat)),zero_zero(X_a)))))) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4570 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_a,bool),nat,finite_card(X_a),B_2))) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less(fun(X_a,bool)),A_3),B_2)))))) # label(fact_1827_card__psubset) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4571 (all X_1 all Y_1 all Xa_2 (hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,X_1),Y_1) = hAPP(real,complex,of_real(complex),Xa_2) <-> X_1 = Xa_2 & Y_1 = zero_zero(real))) # label(fact_2790_complex__eq__cancel__iff2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4572 (all Z_1 hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,im,Z_1)),hAPP(complex,real,norm_norm(complex),Z_1)) = hAPP(complex,real,im,hAPP(complex,complex,sgn_sgn(complex),Z_1))) # label(fact_2985_Im__sgn) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4573 (all X_a (real_normed_vector(X_a) -> (all K all Sa all F (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),F)) -> (hAPP(fun(nat,X_a),X_a,suminf(X_a),F) = ti(X_a,Sa) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Sa),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K)))))))) # label(fact_4168_suminf__minus__initial__segment) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4574 (all I all M_1 (hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),zero_zero(nat)),M_1)) -> hAPP(nat,nat,suc,hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),hAPP(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool)),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,nat),fun(nat,fun(fun(nat,bool),bool))),combb(nat,fun(fun(nat,bool),bool),nat),member(nat)),suc)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),I))))) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(bool,bool)),fun(fun(nat,bool),fun(nat,bool)),combs(nat,bool,bool),hAPP(fun(nat,bool),fun(nat,fun(bool,bool)),hAPP(fun(bool,fun(bool,bool)),fun(fun(nat,bool),fun(nat,fun(bool,bool))),combb(bool,fun(bool,bool),nat),fconj),hAPP(fun(nat,bool),fun(nat,bool),hAPP(fun(nat,fun(fun(nat,bool),bool)),fun(fun(nat,bool),fun(nat,bool)),combc(nat,fun(nat,bool),bool),member(nat)),M_1))),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),hAPP(nat,nat,suc,I))))))) # label(fact_3875_card__less__Suc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4575 (all X_a (semiring_1(X_a) -> (all M all N hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),M),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),M)),N)))) # label(fact_1292_of__nat__power) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4576 (all X_a (linorder(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),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_max(X_a),Y),Z_1))))) # label(fact_4966_min__max_Osup__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4577 (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_566_le__neq__implies__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4578 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),pi)),X)) -> hAPP(real,real,arccos,hAPP(real,real,cos,X)) = hAPP(real,real,uminus_uminus(real),X)))) # label(fact_2265_arccos__cos2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4579 (all X_a all X_b all A_3 all B_2 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)))) # label(fact_4877_fin__bijRr) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4580 (all Ta all B_2 all D_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_2)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Ta),B_2)) -> (all X_2 ((all Xa (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xa),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastAtMost(int),one_one(int)),D_2))) -> (all Xb (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Xb),B_2)) -> ti(int,X_2) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),Xb),Xa))))) -> (ti(int,Ta) != ti(int,X_2) -> hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),D_2) != ti(int,Ta))))))) # label(fact_4640_bset_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4581 (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_3587_of__int__of__nat__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4582 (all C all D all A_1 all B all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),M)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C),D),M)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A_1),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D)),M))))) # label(fact_361_zcong__zadd) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4583 (all X all K_4 all N all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (zero_zero(nat) != N -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),K_4) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X),N) -> (exists I_2 X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),P_5),I_2)))))) # label(fact_3087_prime__power__exp) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4584 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),arccos),X_1),hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))))))) # label(fact_2631_DERIV__arccos) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4585 (all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Ma),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)))) # label(fact_500_zcong__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4586 (all Z_1 (hBOOL(hAPP(int,bool,nat_neg,Z_1)) -> zero_zero(nat) = hAPP(int,nat,nat_1,Z_1))) # label(fact_1507_neg__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4587 (all X_a (comm_semiring_1(X_a) -> (all X all Q_3 hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),hAPP(nat,nat,suc,Q_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),Q_3))))) # label(fact_1311_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4588 (all X_1 (hBOOL(hAPP(int,bool,even_odd_even(int),X_1)) <-> hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = zero_zero(int))) # label(fact_1453_even__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4589 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,exp(real),X_1)),one_one(real))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),zero_zero(real))))) # label(fact_2594_exp__le__one__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4590 (all X_a all A_2 all F all V_1 all N_1 hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),V_1)),N_1)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),hAPP(bool,fun(X_a,fun(X_a,X_a)),if(X_a),hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),N_1)),hAPP(X_a,X_a,hAPP(nat,fun(X_a,X_a),F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1)),hAPP(nat,X_a,hAPP(fun(nat,fun(X_a,X_a)),fun(nat,X_a),hAPP(X_a,fun(fun(nat,fun(X_a,X_a)),fun(nat,X_a)),nat_rec(X_a),A_2),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,nat_1,hAPP(int,int,number_number_of(int),hAPP(int,int,pred,V_1)))),N_1))))) # label(fact_4152_nat__rec__add__eq__if) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4591 (all P_5 all A_1 hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),P_5)) # label(fact_1159_WilsonRuss_Oinv__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4592 (all X_a (divisi14063676e_zero(X_a) & real_div_algebra(X_a) -> (all A_1 all X hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)) = hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),hAPP(real,real,inverse_inverse(real),A_1)),hAPP(X_a,X_a,inverse_inverse(X_a),X))))) # label(fact_4684_inverse__scaleR__distrib) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4593 (all X_a (real_normed_vector(X_a) -> (all K all F all Sa (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Sa),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))))))))) # label(fact_4167_sums__split__initial__segment) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4594 (all X_a all C_1 all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),A_3),B_2)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2))))) # label(fact_1920_subsetD) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4595 (all N all D all A_1 (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A_1),N)) = one_one(nat))) # label(fact_3277_coprime__exp__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4596 (all I_1 all J_2 hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,I_1),J_2)),I_1))) # label(fact_3428_zgcd__zdvd1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4597 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,cos,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,sin,X)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = one_one(real)) # label(fact_2387_sin__cos__squared__add2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4598 (all X_a (number_ring(X_a) -> one_one(X_a) = hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))) # label(fact_173_numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4599 (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_3841_finite__divisors__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4600 (all A_1 all B hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)) # label(fact_3749_floor__Fract) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4601 (all X_b all X_a (real_normed_vector(X_b) & topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,X_b),fun(X_a,bool),isCont(X_a,X_b),F),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,real),fun(X_a,bool),isCont(X_a,real),hAPP(fun(X_a,X_b),fun(X_a,real),hAPP(fun(X_b,real),fun(fun(X_a,X_b),fun(X_a,real)),combb(X_b,real,X_a),norm_norm(X_b)),F)),A_2)))))) # label(fact_4901_isCont__norm) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4602 (all X_a (ring_1(X_a) -> (all N hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N)))))) # label(fact_2123_power__minus1__odd) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4603 (all X_a (sgn_div_norm(X_a) -> scaleR_scaleR(X_a) = ti(fun(real,fun(X_a,X_a)),scaleR_scaleR(X_a)))) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4604 (all L all U_1 hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),U_1),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),L),one_one(int)))) = hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_gr676655987ssThan(int),L),U_1))) # label(fact_3676_card__greaterThanLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4605 (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),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_646_dvd_Oless__le__trans) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4606 (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_508_Euler_Oaux1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4607 (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_643_dvd_Oless__imp__not__eq2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4608 (all X_a (real_normed_vector(X_a) -> (all X exists K_2 ((all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),X_2),X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),X_2)),K_2)))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),K_2)))))) # label(fact_4756_scaleR__left_Ononneg__bounded) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4609 (all M all I_1 all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),M),I_1)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),I_1)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),M),N)),I_1)) # label(fact_4804_min__diff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4610 (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]. 10.93/10.91 4611 (all X_a (number_semiring(X_a) -> hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)) = one_one(X_a))) # label(fact_172_semiring__numeral__1__eq__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4612 (all X hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(real,nat,natceiling,X)))) # label(fact_1887_zero__le__natceiling) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4613 (all X hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,X)),hAPP(real,real,cos,X))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,sin,X)),hAPP(real,real,sin,X))) = one_one(real)) # label(fact_2336_sin__cos__squared__add3) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4614 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,real_1(nat),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,real_1(nat),Ma)),one_one(real)))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N_1),Ma)))) # label(fact_2342_nat__le__real__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4615 (all X_b all X_a all Q_1 all P_1 all X_1 all Y_1 (hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),P_1,X_1),Y_1)) -> (hBOOL(hAPP(fun(X_a,fun(X_b,bool)),bool,hAPP(fun(X_a,fun(X_b,bool)),fun(fun(X_a,fun(X_b,bool)),bool),ord_less_eq(fun(X_a,fun(X_b,bool))),P_1),Q_1)) -> hBOOL(hAPP(X_b,bool,hAPP(X_a,fun(X_b,bool),Q_1,X_1),Y_1))))) # label(fact_4341_rev__predicate2D) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4616 (all X_a (power(X_a) & comm_monoid_add(X_a) -> (all X_1 all Y_1 all N_1 hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1))) = hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Y_1)),hAPP(nat,fun(nat,nat),minus_minus(nat),N_1)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,N_1)))))) # label(fact_4175_lemma__realpow__rev__sumr) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4617 (all A_1 all B hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A_1),B)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(nat,int,semiring_1_of_nat(int),A_1)),hAPP(nat,int,semiring_1_of_nat(int),B))) # label(fact_1348_zdiv__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4618 (all X_a all F1 all Real1 all 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)) = hAPP(real,X_a,hAPP(real,fun(real,X_a),F1,Real1),Real2)) # label(fact_2758_complex_Orecs) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4619 (all Ma all D_1 ((exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),D_1),Q_4) = Ma) <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),Ma),D_1) = zero_zero(nat))) # label(fact_1104_mod__eq__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4620 (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_1516_power__nat__number__of__number__of) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4621 (all N hAPP(nat,int,semiring_1_of_nat(int),N) = hAPP(int,int,ring_1_of_int(int),hAPP(nat,int,semiring_1_of_nat(int),N))) # label(fact_3577_of__int__int__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4622 (all X_a all X_b (comm_monoid_mult(X_b) -> (all B_1 all C_1 all A_2 all S (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),S)) -> (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(fun(X_a,bool),nat,finite_card(X_a),S)) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),C_1)),S)) & (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),A_2),S)) -> hAPP(X_b,X_b,hAPP(X_b,fun(X_b,X_b),times_times(X_b),hAPP(X_a,X_b,B_1,A_2)),hAPP(nat,X_b,hAPP(X_b,fun(nat,X_b),power_power(X_b),C_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),S)),one_one(nat)))) = hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),hAPP(X_b,fun(X_a,X_b),hAPP(fun(X_a,fun(X_b,X_b)),fun(X_b,fun(X_a,X_b)),combc(X_a,X_b,X_b),hAPP(fun(X_a,X_b),fun(X_a,fun(X_b,X_b)),hAPP(fun(X_a,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,X_b),fun(X_a,fun(X_b,X_b))),combs(X_a,X_b,fun(X_b,X_b)),hAPP(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b))),hAPP(fun(bool,fun(X_b,fun(X_b,X_b))),fun(fun(X_a,bool),fun(X_a,fun(X_b,fun(X_b,X_b)))),combb(bool,fun(X_b,fun(X_b,X_b)),X_a),if(X_b)),hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,fun(X_a,bool)),combc(X_a,X_a,bool),fequal(X_a)),A_2))),B_1)),C_1)),S)))))) # label(fact_3936_setprod__gen__delta) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4623 (all L_4 all K_4 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),K_4)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),posDivAlg,K_4),L_4) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),K_4),L_4))))) # label(fact_1155_posDivAlg__div__mod) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4624 (all X_a (linorder(X_a) -> (all X_1 all Y_1 (ti(X_a,Y_1) != ti(X_a,X_1) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),X_1)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Y_1)))))) # label(fact_1561_linorder__neq__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4625 (all P_5 all Q_3 hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),P_5),Q_3)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),P_5),Q_3)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),divmod_int,P_5),Q_3)) # label(fact_3080_divmod__int__mod__div) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4626 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(int,nat,nat_1,X)),hAPP(int,nat,nat_1,Y))))) # label(fact_1095_Divides_Otransfer__nat__int__functions_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4627 (all Nat all Nat_5 (hAPP(nat,nat,suc,Nat_5) = hAPP(nat,nat,suc,Nat) <-> Nat = Nat_5)) # label(fact_1215_nat_Oinject) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4628 (all X_a all A_3 all B_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),B_2),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)),hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),B_2))))) # label(fact_2135_Compl__subset__Compl__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4629 (all B all A_1 (zero_zero(int) != ti(int,B) | ti(int,A_1) != zero_zero(int) -> one_one(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))))) # label(fact_4390_div__gcd__coprime__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4630 (all W (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),W)),zero_zero(int))) -> hAPP(product_prod(int,int),int,product_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))))) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),one_one(int)),hAPP(int,int,number_number_of(int),W)))) # label(fact_3106_div__pos__neg__1__number__of) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4631 (all K_4 hAPP(int,int,pred,K_4) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),min_1),K_4)) # label(fact_2908_add__Min) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4632 (all B_1 all Q_2 all R_1 hAPP(product_prod(int,int),product_prod(int,int),hAPP(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int)),hAPP(bool,fun(product_prod(int,int),fun(product_prod(int,int),product_prod(int,int))),if(product_prod(int,int)),hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),B_1))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Q_2)),one_one(int))),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),R_1),B_1))),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),Q_2)),R_1)) = hAPP(product_prod(int,int),product_prod(int,int),hAPP(int,fun(product_prod(int,int),product_prod(int,int)),adjust,B_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_2),R_1))) # label(fact_3798_adjust__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4633 (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_2365_cos__expansion__lemma) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4634 (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 (hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_1) = J_2 & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_1)))))) # label(fact_860_less__imp__add__positive) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4635 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,M)),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)))) # label(fact_1230_Suc__lessD) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4636 (all X_a (ring(X_a) -> (all X all Y all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),B))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),A_1)),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B))))) # label(fact_729_mult__diff__mult) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4637 (all Z_1 all X all Y (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Y)) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Y),Z_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),X),Z_1)) & -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Z_1),X))))) # label(fact_637_dvd_Ole__less__trans) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4638 (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_2901_pred__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4639 (all X_c all X_b all X_a (topological_space(X_b) & topological_space(X_c) & real_normed_vector(X_a) -> (all G all C_1 all F all B_1 all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(X_b,fun(filter(X_a),bool),hAPP(fun(X_a,X_b),fun(X_b,fun(filter(X_a),bool)),tendsto(X_a,X_b),F),B_1),hAPP(X_a,filter(X_a),at(X_a),A_2))) -> (hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),G),C_1),hAPP(X_b,filter(X_b),at(X_b),B_1))) -> ((exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all X_2 (ti(X_a,X_2) != ti(X_a,A_2) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X_2),A_2))),D_3)) -> hAPP(X_a,X_b,F,X_2) != ti(X_b,B_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_1),hAPP(X_a,filter(X_a),at(X_a),A_2))))))))) # label(fact_4608_LIM__compose2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4640 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),K_4),N)))) # label(fact_3231_dvd__gcd__D2__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4641 (all X_a (number_ring(X_a) -> (all A_1 ti(X_a,A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit1,pls)))))) # label(fact_111_mult__numeral__1__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4642 (all X all Y (Y != zero_zero(nat) -> 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_3276_gcd__non__0__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4643 (all F all X_1 all L (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),F),X_1),L)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),L),zero_zero(real))) -> (exists D_3 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D_3)) & (all H_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),H_1),D_3)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,F,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X_1),H_1))),hAPP(real,real,F,X_1))))))))))) # label(fact_2664_DERIV__neg__dec__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4644 (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]. 10.93/10.91 4645 (all X_a (number_ring(X_a) -> hBOOL(hAPP(X_a,bool,iszero(X_a),hAPP(int,X_a,number_number_of(X_a),pls))))) # label(fact_2603_iszero__Numeral0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4646 (all T all A ti(T,ti(T,A)) = ti(T,A)) # label(help_ti_idem) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4647 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(X_a,int,archim2085082626_floor(X_a),X_1)),one_one(int))))))) # label(fact_2847_floor__le__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4648 (all Z_1 all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),Z_1),N)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),N))))) # label(fact_210_zdvd__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4649 (all X_a (linordered_idom(X_a) -> (all X all N (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N))))) # label(fact_2426_power__even__abs) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4650 (all N ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> hAPP(int,int,zfact,N) = one_one(int)) & (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N),zero_zero(int))) -> hAPP(int,int,zfact,N) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),N),hAPP(int,int,zfact,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),N),one_one(int))))))) # label(fact_827_zfact_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4651 (all X_a (archim1804426504_field(X_a) -> (all X exists Z_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),hAPP(int,X_a,ring_1_of_int(X_a),Z_2)))))) # label(fact_3625_ex__less__of__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4652 (all Ma (zero_zero(nat) != Ma -> hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),dvd_dvd(nat)),Ma)))))) # label(fact_3842_finite__divisors__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4653 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N)) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),N))) # label(fact_3439_zgcd__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4654 (all X_a (division_ring(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),A_1) = hAPP(X_a,X_a,inverse_inverse(X_a),B) -> (ti(X_a,A_1) != zero_zero(X_a) -> (ti(X_a,B) != zero_zero(X_a) -> ti(X_a,A_1) = ti(X_a,B))))))) # label(fact_2531_nonzero__inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4655 (all X_a (ordered_ring(X_a) -> (all B all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),zero_zero(X_a))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B),zero_zero(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)))))))) # label(fact_374_mult__nonpos__nonpos) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4656 (all N all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),N)),one_one(real)))) -> hAPP(real,int,archimedean_ceiling(real),X) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N),one_one(int))))) # label(fact_3419_ceiling__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4657 (all K_4 all A_1 all J_2 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,J_2),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),J_2)),K_4)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2)),A_1)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),J_2))),P_5))))))) # label(fact_853_aux______4) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4658 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),one_one(nat)))) # label(fact_2853_coprime__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4659 (all X_a (ordered_ab_group_add(X_a) -> (all A_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_2)),zero_zero(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_2)))))) # label(fact_2062_neg__less__0__iff__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4660 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),M),N))) # label(fact_1341_mult__Suc__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4661 (all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,fact_fact(nat),M)),hAPP(nat,nat,fact_fact(nat),N)))))) # label(fact_2490_fact__less__mono__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4662 (all B_1 all A_2 all D_1 (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_2),B_1) = ti(int,D_1) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),D_1)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D_1),B_1)) & (all E (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),A_2)) & hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),B_1)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E),D_1)))))) # label(fact_4395_gcd__unique__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4663 (all A_3 all Ma (hBOOL(hAPP(fun(fun(int,bool),bool),bool,hAPP(fun(int,bool),fun(fun(fun(int,bool),bool),bool),member(fun(int,bool)),A_3),hAPP(int,fun(fun(int,bool),bool),rsetR,Ma))) -> hBOOL(hAPP(fun(int,bool),bool,finite_finite_1(int),A_3)))) # label(fact_3628_RsetR__fin) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4664 (all A_1 all P_5 (hBOOL(hAPP(int,bool,zprime,P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),P_5),one_one(int)))) -> one_one(int) != hAPP(int,int,hAPP(int,fun(int,int),inv,P_5),A_1))))) # label(fact_806_inv__not__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4665 (all X_a (linordered_idom(X_a) -> (all X_1 all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),zero_zero(X_a))) & -hBOOL(hAPP(nat,bool,even_odd_even(nat),N_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X_1),N_1)),zero_zero(X_a))))))) # label(fact_2436_power__less__zero__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4666 (all X_1 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),cos)),cos)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,min_1))),hAPP(real,real,cos,X_1))),hAPP(real,real,sin,X_1))))) # label(fact_3892_DERIV__cos__cos__mult2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4667 (all K hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),K))))) # label(fact_3801_finite__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4668 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,N))))) # label(fact_2317_real__of__nat__Suc__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4669 (all X_a all A_1 all B hAPP(int,X_a,hAPP(int,fun(int,X_a),frac(X_a),A_1),B) = hAPP(product_prod(int,int),X_a,abs_Frac(X_a),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),norm_frac,A_1),B))) # label(fact_4420_Nitpick_Ofrac__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4670 (all X_b all X_a all X_c (real_normed_vector(X_c) -> (all F all A_2 all A_3 all S ((all I_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),I_2),S)) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(X_a,fun(X_b,X_c),F,I_2)),hAPP(X_a,X_c,A_2,I_2)),A_3)))) -> hBOOL(hAPP(filter(X_b),bool,hAPP(X_c,fun(filter(X_b),bool),hAPP(fun(X_b,X_c),fun(X_c,fun(filter(X_b),bool)),tendsto(X_b,X_c),hAPP(fun(X_a,bool),fun(X_b,X_c),hAPP(fun(X_b,fun(fun(X_a,bool),X_c)),fun(fun(X_a,bool),fun(X_b,X_c)),combc(X_b,fun(X_a,bool),X_c),hAPP(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c)),hAPP(fun(fun(X_a,X_c),fun(fun(X_a,bool),X_c)),fun(fun(X_b,fun(X_a,X_c)),fun(X_b,fun(fun(X_a,bool),X_c))),combb(fun(X_a,X_c),fun(fun(X_a,bool),X_c),X_b),big_co1399186613setsum(X_a,X_c)),hAPP(fun(X_a,fun(X_b,X_c)),fun(X_b,fun(X_a,X_c)),combc(X_a,X_b,X_c),F))),S)),hAPP(fun(X_a,bool),X_c,hAPP(fun(X_a,X_c),fun(fun(X_a,bool),X_c),big_co1399186613setsum(X_a,X_c),A_2),S)),A_3)))))) # label(fact_4763_tendsto__setsum) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4671 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2431_real__of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4672 (all K_4 all I_1 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_2)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),J_2),K_4))))) # label(fact_559_add__less__mono1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4673 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),combk(X_a,nat),zero_zero(X_a))),zero_zero(X_a))))) # label(fact_4078_sums__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4674 (all B all D all A_1 all C (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A_1),C)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),A_1),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),C),D)))))) # label(fact_3233_gcd__semilattice__nat_Oinf__mono) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4675 (all X_a (real_normed_field(X_a) -> (all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),uminus_uminus(X_a)),X_3)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)))))) # label(fact_3986_suminf__minus) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4676 (all X_a (semiring_div(X_a) -> (all Ma all K all N_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),N_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),Ma)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),K),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),Ma),N_1)))))))) # label(fact_947_dvd__mod__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4677 (all X_b all X_a (semiring_1(X_a) -> (all F all A_3 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co1399186613setsum(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co1399186613setsum(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_3)))) # label(fact_4171_of__nat__setsum) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4678 (all Q_3 all R_4 hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),Q_3),R_4) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),Q_3),hAPP(rat,rat,uminus_uminus(rat),R_4))) # label(fact_3722_diff__rat__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4679 (all X_a (real_normed_field(X_a) -> (all Y_1 all X_3 all A_2 (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),X_3),A_2)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),inverse_divide(X_a)),X_3)),Y_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),Y_1))))))) # label(fact_4085_divide_Osums) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4680 (all X_b all X_a (topological_space(X_a) & topological_space(X_b) -> 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]. 10.93/10.91 4681 (all X_a (semiring_div(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),zero_zero(X_a)),A_1) = zero_zero(X_a)))) # label(fact_926_mod__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4682 (all A_2 hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),re),hAPP(complex,real,re,A_2)),hAPP(complex,filter(complex),at(complex),A_2)))) # label(fact_4568_Re_Ocont) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4683 (all A_2 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),X_1)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),A_2)),hAPP(real,fun(nat,real),power_power(real),X_1))),zero_zero(real)),sequentially)))) # label(fact_4486_LIMSEQ__divide__realpow__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4684 (all I_1 all K_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,suc,I_1)),K_4)) -> -(all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_1),J_1)) -> hAPP(nat,nat,suc,J_1) != K_4)))) # label(fact_1543_Suc__lessE) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4685 (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_eq(int),hAPP(int,int,bit1,K)),pls)))) # label(fact_70_rel__simps_I29_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4686 (all X_a (real_normed_algebra(X_a) -> (all X exists K_2 all X_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),X_2))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(X_a,real,norm_norm(X_a),X_2)),K_2)))))) # label(fact_1813_mult__right_Obounded) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4687 (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,Q_1,A_4)) & hBOOL(hAPP(X_a,bool,P_1,A_4)))))))) # label(fact_4866_EulerFermat_Oaux) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4688 (all B (ti(int,B) != zero_zero(int) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,zero_zero(int)),B),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),zero_zero(int)),zero_zero(int)))))) # label(fact_1189_divmod__int__rel__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4689 (all X_a (real_normed_vector(X_a) -> (all X all Y all C (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,norm_norm(X_a),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(X_a,real,norm_norm(X_a),Y)))) -> zero_zero(X_a) = ti(X_a,X)))))) # label(fact_1785_norm__ratiotest__lemma) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4690 (all Y_1 all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X_1),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),Y_1) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),X_1),Y_1)),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1464_even__prod__div__2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4691 (all X_1 all Y_1 (zero_zero(real) = X_1 & zero_zero(real) = Y_1 <-> zero_zero(real) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_615_realpow__two__sum__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4692 (all E_1 all B all D all A_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),D),A_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),E_1),B)) -> (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_1),B) = one_one(int) -> one_one(int) = hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),E_1))))) # label(fact_4358_coprime__divisors__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.91 4693 (all N_1 all Diff all F all H (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),H)) -> (hAPP(nat,fun(real,real),Diff,zero_zero(nat)) = F -> ((all M_2 all T_4 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M_2),N_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),T_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),Diff,M_2)),T_4),hAPP(real,real,hAPP(nat,fun(real,real),Diff,hAPP(nat,nat,suc,M_2)),T_4))))) -> (exists T_4 (hAPP(real,real,F,H) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),Diff),zero_zero(real)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),H))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(nat,fun(real,real),Diff,N_1),T_4)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N_1)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),H),N_1))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),T_4),H)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),T_4)))))))) # label(fact_4282_Maclaurin2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4694 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_1),A_2))))) # label(fact_3788_one__less__Fract__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4695 (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_3580_of__int__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4696 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),M),zero_zero(nat)) = M) # label(fact_542_Nat_Oadd__0__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4697 (all K all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),N_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),N_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K),Ma)))))) # label(fact_207_zdvd__reduce) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4698 (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)))) -> ti(int,Z_1) = hAPP(X_a,int,archim2085082626_floor(X_a),X)))))) # label(fact_3605_floor__unique) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4699 (all X_a (linorder(X_a) -> (all X all Y hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),X),Y))))) # label(fact_4813_min__max_Oinf__left__idem) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4700 (all X_a (linorder(X_a) -> (all X all Y (ti(X_a,Y) != ti(X_a,X) -> (-hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y),X))))))) # label(fact_1565_linorder__neqE) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4701 (all X_a (linordered_semidom(X_a) -> (all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(nat,nat,fact_fact(nat),N))))))) # label(fact_2495_of__nat__fact__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4702 (all K_4 ti(int,K_4) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),K_4),pls)) # label(fact_479_diff__bin__simps_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4703 (all X_c all X_b all X_a all C_1 all X_1 all P_4 ((all A_4 all B_4 (ti(product_prod(X_a,X_b),P_4) = hAPP(X_b,product_prod(X_a,X_b),hAPP(X_a,fun(X_b,product_prod(X_a,X_b)),product_Pair(X_a,X_b),A_4),B_4) -> hBOOL(hAPP(X_c,bool,hAPP(X_b,fun(X_c,bool),hAPP(X_a,fun(X_b,fun(X_c,bool)),C_1,A_4),B_4),X_1)))) -> hBOOL(hAPP(X_c,bool,hAPP(product_prod(X_a,X_b),fun(X_c,bool),hAPP(fun(X_a,fun(X_b,fun(X_c,bool))),fun(product_prod(X_a,X_b),fun(X_c,bool)),product_prod_case(X_a,X_b,fun(X_c,bool)),C_1),P_4),X_1)))) # label(fact_4060_splitI2_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4704 (all X_a (linordered_idom(X_a) -> (all A_1 all N hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),N)))))) # label(fact_1880_zero__le__power__abs) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4705 (all X hAPP(int,real,number_number_of(real),X) = hAPP(int,real,ring_1_of_int(real),X)) # label(fact_3582_number__of__real__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4706 (all X_a (linord1117847801e_zero(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X_1)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_1),one_one(X_a))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),X_1))))))) # label(fact_2608_one__le__inverse__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4707 (all X_a (zero(X_a) -> (all X_1 (ti(X_a,X_1) = zero_zero(X_a) <-> ti(X_a,X_1) = zero_zero(X_a))))) # label(fact_764_zero__reorient) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4708 (all X_a (semiring_div(X_a) -> (all A_1 all B all C hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),C) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),B),C))),C)))) # label(fact_940_mod__add__right__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4709 (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_1356_zpower__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4710 (all K_4 all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N)),M)),N)) # label(fact_1111_mod__mult__self3) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4711 (all X all M hAPP(real,real,sin,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,suc,M))),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),M)),pi)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_2351_sin__expansion__lemma) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4712 (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_max(X_a),X),X)))) # label(fact_4956_Max_Oidem) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4713 (all X_a (archim1804426504_field(X_a) -> (all X exists N_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_2)))))) # label(fact_2737_ex__le__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4714 (all K_4 all L_4 ((-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4) = hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),hAPP(int,int,uminus_uminus(int),L_4)))) & (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),L_4)) -> hAPP(int,int,hAPP(int,fun(int,int),z3div,K_4),L_4) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),K_4),L_4)))) # label(fact_2729_z3div__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4715 (all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),hAPP(nat,nat,suc,zero_zero(nat))) = hAPP(nat,nat,suc,zero_zero(nat))) # label(fact_3258_gcd__Suc__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4716 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),hAPP(nat,nat,suc,N))) -> (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hAPP(nat,nat,suc,N) = M))) # label(fact_1248_le__SucE) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4717 (all K (ti(int,K) = pls <-> pls = hAPP(int,int,bit0,K))) # label(fact_120_rel__simps_I44_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4718 (all X_a all A_3 hAPP(fun(X_a,bool),fun(X_a,bool),collect(X_a),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(bool,bool),fun(fun(X_a,bool),fun(X_a,bool)),combb(bool,bool,X_a),fNot),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,fun(fun(X_a,bool),bool)),fun(fun(X_a,bool),fun(X_a,bool)),combc(X_a,fun(X_a,bool),bool),member(X_a)),A_3))) = hAPP(fun(X_a,bool),fun(X_a,bool),uminus_uminus(fun(X_a,bool)),A_3)) # label(fact_2192_Compl__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4719 (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_416_power__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4720 (all X_a (group_add(X_a) -> (all A_2 all B_1 (ti(X_a,B_1) = hAPP(X_a,X_a,uminus_uminus(X_a),A_2) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2))))) # label(fact_2043_minus__equation__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4721 (all N_1 all K all Ma (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),Ma)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K),N_1)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),Ma),N_1)) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),Ma),K)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),K))))))) # label(fact_675_le__diff__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4722 (all M all D all R_4 (R_4 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),M),D) -> (exists Q_4 hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),R_4),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Q_4),D)) = M))) # label(fact_1182_mod__eqD) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4723 (all X_a (metric_space(X_a) -> (all X all Z_1 all Y all E_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Z_1)),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),Y),Z_1))),E_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(X_a,real,hAPP(X_a,fun(X_a,real),dist_dist(X_a),X),Y)),E_1)))))) # label(fact_3508_dist__triangle__le) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4724 (all N hAPP(complex,real,im,hAPP(nat,complex,semiring_1_of_nat(complex),N)) = zero_zero(real)) # label(fact_2982_complex__Im__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4725 (all B all A_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(real,int,archim2085082626_floor(real),A_1)),hAPP(real,int,archim2085082626_floor(real),B))),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A_1),B))))))) # label(fact_2891_le__mult__floor) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4726 (all X all Y hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),hAPP(complex,complex,inverse_inverse(complex),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),X),Y)) # label(fact_2755_complex__divide__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4727 (all Z_1 hAPP(complex,real,im,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),Z_1),hAPP(complex,complex,cnj,Z_1))) = zero_zero(real)) # label(fact_2984_complex__In__mult__cnj__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4728 (all Ma all N_1 all K (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1))))) # label(fact_741_nat__mult__dvd__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4729 (all N all A_1 hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N)),A_1)) = hAPP(complex,real,re,hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,cis,A_1)),N))) # label(fact_3025_cos__n__Re__cis__pow__n) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4730 (all N hAPP(nat,nat,suc,hAPP(nat,nat,suc,N)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1429_add__2__eq__Suc_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4731 (all X all Y hAPP(complex,complex,cnj,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),X),Y)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,cnj,X)),hAPP(complex,complex,cnj,Y))) # label(fact_2933_complex__cnj__mult) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4732 (all X hAPP(real,real,hAPP(real,fun(real,real),powr,X),zero_zero(real)) = one_one(real)) # label(fact_3351_powr__zero__eq__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4733 (all N all M hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,suc,N)))),hAPP(nat,int,semiring_1_of_nat(int),M)))) # label(fact_2134_negative__zless) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4734 (all N_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),N_1)),hAPP(int,real,real_1(int),Ma))) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),N_1)),Ma)))) # label(fact_3388_number__of__less__real__of__int__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4735 (all A_1 all Q_3 all R_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),A_1),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),Q_3),R_4))) -> (zero_zero(int) != ti(int,A_1) -> ti(int,R_4) = zero_zero(int)))) # label(fact_1188_self__remainder) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4736 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,number_number_of(X_a),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2895_one__less__floor) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4737 (all X_a all X_b all A_3 all B_2 all P_1 (hBOOL(hAPP(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool,hAPP(product_prod(fun(X_a,bool),fun(X_b,bool)),fun(fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bool),member(product_prod(fun(X_a,bool),fun(X_b,bool))),hAPP(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool)),hAPP(fun(X_a,bool),fun(fun(X_b,bool),product_prod(fun(X_a,bool),fun(X_b,bool))),product_Pair(fun(X_a,bool),fun(X_b,bool)),A_3),B_2)),hAPP(fun(X_a,fun(X_b,bool)),fun(product_prod(fun(X_a,bool),fun(X_b,bool)),bool),bijR(X_a,X_b),P_1))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)))) # label(fact_4876_fin__bijRl) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4738 (all X_5 all Y_4 hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) = hAPP(real,real,sin,hAPP(real,real,arccos,hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),X_5),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X_5),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y_4),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))))) # label(fact_2404_sin__arccos__lemma1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4739 (all L (hAPP(int,int,bit1,L) = min_1 <-> min_1 = ti(int,L))) # label(fact_286_rel__simps_I43_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4740 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z_1),zero_zero(int))) -> hAPP(int,nat,nat_1,Z_1) = zero_zero(nat))) # label(fact_1123_nat__le__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4741 (all P_4 ((all M_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M_2),P_4)) -> M_2 = one_one(nat) | P_4 = M_2)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),P_4)) <-> hBOOL(hAPP(nat,bool,prime,P_4)))) # label(fact_3067_prime__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4742 (all A_1 all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),P_5)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(int,nat,nat_1,P_5)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(int,nat,nat_1,P_5)),one_one(nat)))))) # label(fact_1149_Euler_Oaux__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4743 (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_4811_min__max_Oinf__left__commute) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4744 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,cauchy(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,cauchy(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4723_scaleR__left_OCauchy) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4745 (all Ma all X_3 ((all Y1 all Y2 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),Y1),X_3)) & hBOOL(hAPP(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_3)) -> ti(int,Y1) = ti(int,Y2))) <-> hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),resSet,Ma),X_3)))) # label(fact_2916_ResSet__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4746 (all Y all X (hBOOL(hAPP(int,bool,even_odd_even(int),X)) -> (hBOOL(hAPP(int,bool,even_odd_even(int),Y)) -> hBOOL(hAPP(int,bool,even_odd_even(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),X),Y)))))) # label(fact_1264_Parity_Oeven__plus__even) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4747 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A_2),B_1)) -> -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),B_1),hAPP(int,fun(int,bool),d22set,A_2))))) # label(fact_864_d22set__le__swap) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4748 (all X_a (comm_semiring_1(X_a) -> (all A_1 all C all D hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),D))))) # label(fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4749 (all M all K_4 all N (one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),K_4),N) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),M),N))) # label(fact_3268_gcd__mult__cancel__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4750 (all X_a (ring_1(X_a) -> (all K_4 ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),K_4),zero_zero(int))) -> hAPP(int,X_a,ring_1_of_int(X_a),K_4) = hAPP(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))))) & (-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_3559_of__int__of__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4751 (all L all U_1 hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,U_1)),L) = hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1))) # label(fact_4571_card__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4752 (all X_a (linordered_idom(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),A_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,abs_abs(X_a),A_1)),hAPP(X_a,X_a,abs_abs(X_a),A_1))))) # label(fact_1855_abs__mult__self) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4753 (all M all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))),M)),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,hAPP(nat,nat,suc,hAPP(nat,nat,suc,M)))),N)) # label(fact_1440_Suc__mod__eq__add3__mod) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4754 (all X_a (semiring_div(X_a) -> (all A_1 all C all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),C),B)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),B),C)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_div(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)),C))))) # label(fact_1003_div__mult__swap) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4755 (all X_a (linorder(X_a) -> (all T_5 exists Z_2 all X_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_2),X_2)) -> -hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),X_2),T_5)))))) # label(fact_2824_pinf_I6_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4756 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3))))) # label(fact_3797_mlex__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4757 (all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),X_1),Y_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),X_1)),hAPP(nat,int,semiring_1_of_nat(int),Y_1))))) # label(fact_1299_Nat__Transfer_Otransfer__int__nat__relations_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4758 (all X_a all R_3 all F all X_1 all Y_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(X_a,nat,F,X_1)),hAPP(X_a,nat,F,Y_1))) -> (hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),R_3)) -> hBOOL(hAPP(fun(product_prod(X_a,X_a),bool),bool,hAPP(product_prod(X_a,X_a),fun(fun(product_prod(X_a,X_a),bool),bool),member(product_prod(X_a,X_a)),hAPP(X_a,product_prod(X_a,X_a),hAPP(X_a,fun(X_a,product_prod(X_a,X_a)),product_Pair(X_a,X_a),X_1),Y_1)),hAPP(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool),hAPP(fun(X_a,nat),fun(fun(product_prod(X_a,X_a),bool),fun(product_prod(X_a,X_a),bool)),mlex_prod(X_a),F),R_3)))))) # label(fact_3796_mlex__leq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4759 (all X_a (linordered_idom(X_a) & number_ring(X_a) -> one_one(X_a) = hAPP(X_a,X_a,abs_abs(X_a),hAPP(int,X_a,number_number_of(X_a),min_1)))) # label(fact_1885_abs__minus__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4760 (all X_a (real_normed_field(X_a) -> (all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (ti(X_a,D_2) = ti(X_a,E_3) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),E_3))))))) # label(fact_2635_Deriv_Olemma__DERIV__subst) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4761 (all T_1 order(filter(T_1))) # label(arity_Limits_Ofilter___Orderings_Oorder) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4762 (all M all N all K_4 (hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,N),K_4) = one_one(int) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),M),N))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),K_4),M))))) # label(fact_3462_zrelprime__zdvd__zmult) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4763 (all K_4 hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),K_4),one_one(int)) = hAPP(int,int,succ,K_4)) # label(fact_1528_succ__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4764 (all A_1 all B all Qr_1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,hAPP(int,int,uminus_uminus(int),A_1)),hAPP(int,int,uminus_uminus(int),B)),Qr_1)) -> hBOOL(hAPP(product_prod(int,int),bool,hAPP(int,fun(product_prod(int,int),bool),hAPP(int,fun(int,fun(product_prod(int,int),bool)),divmod_int_rel,A_1),B),hAPP(product_prod(int,int),product_prod(int,int),negateSnd,Qr_1))))) # label(fact_3073_divmod__int__rel__neg) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4765 (all P_1 all A_2 all B_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))))))) # label(fact_3131_Bolzano__bisect__le) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4766 (all M (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),M)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),one_one(int))) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),M),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))))) # label(fact_1476_inv__is__inv__aux) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4767 (all X_a (real_normed_field(X_a) -> (all Y_3 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),Y_3)) -> hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),X_3)),Y_3)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),hAPP(fun(nat,X_a),X_a,suminf(X_a),Y_3))))))) # label(fact_3982_suminf__diff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4768 (all D all A_1 all B (hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)) = one_one(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),D),B) = one_one(int))) # label(fact_4382_coprime__rmult__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4769 (all X all Y ((Y = zero_zero(nat) -> X = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)) & (zero_zero(nat) != 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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),nat_gcd,X),Y)))) # label(fact_3665_nat__gcd_Osimps) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4770 (all X_a (comm_monoid_add(X_a) & topological_space(X_a) -> (all Sa all F (hAPP(nat,X_a,F,zero_zero(nat)) = zero_zero(X_a) -> (hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),F),suc)),Sa)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(nat,X_a),fun(X_a,bool),sums(X_a),F),Sa))))))) # label(fact_4094_sums__Suc__imp) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4771 (all A_1 hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,one_one(nat)),A_1))) # label(fact_2854_coprime__1_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4772 (all X_a (field_inverse_zero(X_a) & number_ring(X_a) -> (all X hAPP(X_a,X_a,uminus_uminus(X_a),X) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),hAPP(int,X_a,number_number_of(X_a),min_1))))) # label(fact_2105_divide__minus1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4773 (all L all U_1 hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1) = hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),L),hAPP(nat,nat,suc,U_1))) # label(fact_4542_atLeastLessThanSuc__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4774 (all X_1 all Y_1 (X_1 = Y_1 <-> hAPP(quickcheck_code_int,int,quickcheck_int_of,Y_1) = hAPP(quickcheck_code_int,int,quickcheck_int_of,X_1))) # label(fact_3161_code__int_Oint__of__inject) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4775 (all X hAPP(real,real,sqrt,hAPP(real,real,inverse_inverse(real),X)) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,sqrt,X))) # label(fact_2533_real__sqrt__inverse) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4776 (all F all G all N_1 hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(nat,fun(real,fun(real,real))),fun(fun(nat,real),fun(nat,fun(real,real))),combs(nat,real,fun(real,real)),hAPP(fun(nat,bool),fun(nat,fun(real,fun(real,real))),hAPP(fun(bool,fun(real,fun(real,real))),fun(fun(nat,bool),fun(nat,fun(real,fun(real,real)))),combb(bool,fun(real,fun(real,real)),nat),if(real)),even_odd_even(nat))),F)),G)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_1))) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),G),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_1)))) # label(fact_4235_sum__split__even__odd) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4777 (all Y all X all U (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),U)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),Y),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),U),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sqrt,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),Y),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),U)))))))) # label(fact_1650_lemma__sqrt__hcomplex__capprox) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4778 (all A_2 all B_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_1)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_2),zero_zero(int))) <-> hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_2),B_1)),zero_zero(rat)))))) # label(fact_3791_Fract__le__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4779 (all N all I_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),I_1)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),I_1),N))))) # label(fact_1394_nat__one__le__power) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4780 (all X_a (real_normed_field(X_a) -> (all G all Db all F all X_1 all Da (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),Da)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),Db)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),times_times(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Da),hAPP(X_a,X_a,G,X_1))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Db),hAPP(X_a,X_a,F,X_1)))))))))) # label(fact_3817_DERIV__mult) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4781 (all B all A_1 all A_6 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A_1),A_6)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_1),B)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A_6),B)))))) # label(fact_1015_zdiv__mono1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4782 (all X_b all X_a (comm_monoid_mult(X_a) & semiring_1(X_a) -> (all F all A_3 hAPP(nat,X_a,semiring_1_of_nat(X_a),hAPP(fun(X_b,bool),nat,hAPP(fun(X_b,nat),fun(fun(X_b,bool),nat),big_co302546470etprod(X_b,nat),F),A_3)) = hAPP(fun(X_b,bool),X_a,hAPP(fun(X_b,X_a),fun(fun(X_b,bool),X_a),big_co302546470etprod(X_b,X_a),hAPP(fun(X_b,nat),fun(X_b,X_a),hAPP(fun(nat,X_a),fun(fun(X_b,nat),fun(X_b,X_a)),combb(nat,X_a,X_b),semiring_1_of_nat(X_a)),F)),A_3)))) # label(fact_3928_of__nat__setprod) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4783 (all L all U_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),L),U_1)))) # label(fact_4533_finite__atLeastAtMost) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4784 (all X_1 ((exists N_2 (X_1 = hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)))) | (exists N_2 (hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2)) & X_1 = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) <-> hAPP(real,real,sin,X_1) = zero_zero(real))) # label(fact_2411_sin__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4785 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,cos,X)))))) # label(fact_2246_cos__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4786 (all 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)) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,W))) # label(fact_3830_nat__number__of__Bit0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4787 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> hAPP(real,nat,natfloor,hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),X),one_one(real))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(real,nat,natfloor,X)),one_one(nat)))) # label(fact_1907_natfloor__add__one) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4788 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),N),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) -> N = hAPP(nat,nat,suc,zero_zero(nat)) | zero_zero(nat) = N)) # label(fact_1451_less__2__cases) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4789 (all X_a (linord1117847801e_zero(X_a) -> (all A_2 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),B_1),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_2)) | hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),zero_zero(X_a))) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),B_1)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),A_2),B_1)),zero_zero(X_a))))))) # label(fact_1674_divide__le__0__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4790 (all A_1 all B all C all Q_3 all R_4 (hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,B),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),Q_3),R_4))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) -> hBOOL(hAPP(product_prod(nat,nat),bool,hAPP(nat,fun(product_prod(nat,nat),bool),hAPP(nat,fun(nat,fun(product_prod(nat,nat),bool)),divmod_nat_rel,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)),C),hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),Q_3)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),R_4)),C))))))) # label(fact_3095_divmod__nat__rel__mult1__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4791 (all X_a (cancel_semigroup_add(X_a) -> (all B_1 all A_2 all C_1 (ti(X_a,C_1) = ti(X_a,B_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C_1),A_2) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B_1),A_2))))) # label(fact_769_add__right__cancel) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4792 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (zero_zero(X_a) != hAPP(X_a,X_a,F,X_1) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))),D_2)),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,F,X_1))))))))))) # label(fact_3877_DERIV__inverse_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4793 (all Ma all No_1 all F ((all N_2 hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,N_2)),hAPP(nat,real,F,hAPP(nat,nat,suc,N_2))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,F,Ma)),hAPP(nat,real,F,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),Ma),No_1)))))) # label(fact_1833_lemma__f__mono__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4794 (all X_a (ring(X_a) -> (all A_2 all E_2 all C_1 all B_1 all D_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),E_2)),C_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B_1),E_2)),D_1) <-> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_2),B_1)),E_2)),C_1) = ti(X_a,D_1))))) # label(fact_490_eq__add__iff1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4795 (all X_a ti(fun(fun(X_a,bool),fun(fun(X_a,bool),bool)),pow(X_a)) = pow(X_a)) # label(tsy_c_Set_OPow_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4796 (all X_1 hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),X_1))))) # label(fact_3865_bdd__nat__set__l__finite) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4797 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),sequentially))))) # label(fact_4426_summable__Leibniz_I5_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4798 (all X_a (real_normed_field(X_a) -> (all G all E_3 all F all X_1 all D_2 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_2)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),G),X_1),E_3)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,X_a)),combs(X_a,X_a,X_a),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(X_a,X_a),fun(X_a,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),X_a),plus_plus(X_a)),F)),G)),X_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),D_2),E_3)))))))) # label(fact_3823_DERIV__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4799 (all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),M),N)) -> hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),product_Pair(nat,nat),zero_zero(nat)),M) = hAPP(nat,product_prod(nat,nat),hAPP(nat,fun(nat,product_prod(nat,nat)),divmod_nat,M),N))) # label(fact_3093_divmod__nat__base) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4800 (all N hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,suc,N)),hAPP(nat,nat,fact,N)) = hAPP(nat,nat,fact,hAPP(nat,nat,suc,N))) # label(fact_3546_fact_Osimps_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4801 (all X_a all A_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,finite_finite_1(fun(X_a,bool)),A_3)) -> ((all M_3 (hBOOL(hAPP(fun(fun(X_a,bool),bool),bool,hAPP(fun(X_a,bool),fun(fun(fun(X_a,bool),bool),bool),member(fun(X_a,bool)),M_3),A_3)) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),M_3)))) -> hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),hAPP(fun(fun(X_a,bool),bool),fun(X_a,bool),complete_Sup_Sup(fun(X_a,bool)),A_3)))))) # label(fact_1829_finite__Union) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4802 (all X_a (real_normed_vector(X_a) -> (all F all G all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),G),L_2),sequentially)) -> (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),minus_minus(X_a)),F)),G)),zero_zero(X_a)),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),F),L_2),sequentially))))))) # label(fact_4448_LIMSEQ__diff__approach__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4803 (all X_a (comm_ring_1(X_a) -> (all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),one_one(X_a))),X) = hAPP(X_a,X_a,uminus_uminus(X_a),X)))) # label(fact_2071_comm__ring__1__class_Onormalizing__ring__rules_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4804 (all N_1 hAPP(fun(nat,bool),nat,finite_card(nat),hAPP(fun(nat,bool),fun(nat,bool),collect(nat),hAPP(nat,fun(nat,bool),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less(nat)),N_1))) = N_1) # label(fact_3866_card__Collect__less__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4805 (all X_b all X_c all X_a all X_d all X_e all F all G all P_4 hAPP(product_prod(X_b,X_c),X_a,hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F),hAPP(product_prod(X_d,X_e),product_prod(X_b,X_c),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(product_prod(X_d,X_e),product_prod(X_b,X_c)),product_prod_case(X_d,X_e,product_prod(X_b,X_c)),G),P_4)) = hAPP(product_prod(X_d,X_e),X_a,hAPP(fun(X_d,fun(X_e,X_a)),fun(product_prod(X_d,X_e),X_a),product_prod_case(X_d,X_e,X_a),hAPP(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a)),hAPP(fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),fun(fun(X_d,fun(X_e,product_prod(X_b,X_c))),fun(X_d,fun(X_e,X_a))),combb(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a),X_d),hAPP(fun(product_prod(X_b,X_c),X_a),fun(fun(X_e,product_prod(X_b,X_c)),fun(X_e,X_a)),combb(product_prod(X_b,X_c),X_a,X_e),hAPP(fun(X_b,fun(X_c,X_a)),fun(product_prod(X_b,X_c),X_a),product_prod_case(X_b,X_c,X_a),F))),G)),P_4)) # label(fact_4005_split__twice) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4806 (all X_a (linorder(X_a) -> (all X_1 all Y_1 all Z (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),X_1),Z)) & hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Y_1),Z)) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X_1),Y_1)),Z)))))) # label(fact_4949_max__less__iff__conj) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4807 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(real,fun(nat,real),power_power(real),X_1)))))) # label(fact_3833_Bseq__realpow) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4808 (all X hAPP(real,real,cos,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),X)) = 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)))))) # label(fact_2395_cos__double) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4809 (all X_a (ordere1490568538miring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)))))))) # label(fact_371_comm__mult__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4810 (all A_2 all B_1 all P_1 ((all A_4 all B_4 all C_4 (hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),B_4))) & hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),B_4),C_4))) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B_4),C_4)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_4),B_4)) -> hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_4),C_4))))) -> (-hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),A_2),B_1))) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A_2),B_1)) -> (all N_2 -hBOOL(hAPP(product_prod(real,real),bool,P_1,hAPP(real,product_prod(real,real),hAPP(real,fun(real,product_prod(real,real)),product_Pair(real,real),hAPP(product_prod(real,real),real,product_fst(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2))),hAPP(product_prod(real,real),real,product_snd(real,real),hAPP(nat,product_prod(real,real),hAPP(real,fun(nat,product_prod(real,real)),hAPP(real,fun(real,fun(nat,product_prod(real,real))),hAPP(fun(product_prod(real,real),bool),fun(real,fun(real,fun(nat,product_prod(real,real)))),bolzano_bisect,P_1),A_2),B_1),N_2)))))))))) # label(fact_3145_not__P__Bolzano__bisect_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4811 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (zero_zero(real) = hAPP(real,real,sin,X) -> (exists N_2 (hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,real_1(nat),N_2)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),pi),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = X & hBOOL(hAPP(nat,bool,even_odd_even(nat),N_2))))))) # label(fact_2475_sin__zero__lemma) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4812 (all X_a all X_b (real_normed_vector(X_b) -> (all X_3 all L_2 all S ((all N_2 (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),N_2),S)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(X_a,fun(nat,X_b),X_3,N_2)),hAPP(X_a,X_b,L_2,N_2)),sequentially)))) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_b,fun(filter(nat),bool),hAPP(fun(nat,X_b),fun(X_b,fun(filter(nat),bool)),tendsto(nat,X_b),hAPP(fun(X_a,bool),fun(nat,X_b),hAPP(fun(nat,fun(fun(X_a,bool),X_b)),fun(fun(X_a,bool),fun(nat,X_b)),combc(nat,fun(X_a,bool),X_b),hAPP(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b)),hAPP(fun(fun(X_a,X_b),fun(fun(X_a,bool),X_b)),fun(fun(nat,fun(X_a,X_b)),fun(nat,fun(fun(X_a,bool),X_b))),combb(fun(X_a,X_b),fun(fun(X_a,bool),X_b),nat),big_co1399186613setsum(X_a,X_b)),hAPP(fun(X_a,fun(nat,X_b)),fun(nat,fun(X_a,X_b)),combc(X_a,nat,X_b),X_3))),S)),hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co1399186613setsum(X_a,X_b),L_2),S)),sequentially)))))) # label(fact_4658_LIMSEQ__setsum) # label(axiom) # label(non_clause). [assumption]. 10.93/10.92 4813 (all A_1 all B all P_5 all Q_3 (hAPP(rat,product_prod(int,int),quotient_of,hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B)) = hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) -> hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3))) # label(fact_3735_quotient__of__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4814 (all Z_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Z_1)) -> hAPP(int,nat,nat_1,hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),Z_1)) = hAPP(nat,nat,suc,hAPP(int,nat,nat_1,Z_1)))) # label(fact_1435_Suc__nat__eq__nat__zadd1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4815 (all X_a (real_normed_algebra(X_a) -> (all Xa_1 all R_4 all X hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),X)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),Xa_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),X))))) # label(fact_4676_mult__right_OscaleR) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4816 (all N_1 (zero_zero(nat) = N_1 <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),N_1)),zero_zero(int))))) # label(fact_1372_int__le__0__conv) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4817 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))))))) # label(fact_1737_pos__le__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4818 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> Y = hAPP(real,real,sin,hAPP(real,real,arcsin,Y))))) # label(fact_2361_sin__arcsin) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4819 (all X_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),X_1)) | zero_zero(nat) = N_1 <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),X_1),N_1))))) # label(fact_348_nat__zero__less__power__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4820 (all X_a (archim1727834104eiling(X_a) -> (all Z all X_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),Z),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(int,X_a,ring_1_of_int(X_a),Z)),X_1)))))) # label(fact_3593_le__floor__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4821 (all K_4 hAPP(int,rat,hAPP(int,fun(int,rat),fract,K_4),zero_zero(int)) = zero_zero(rat)) # label(fact_3740_rat__number__collapse_I4_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4822 (all Ma all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),Ma),N_1))) <-> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),N_1)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,suc,zero_zero(nat))),Ma)))) # label(fact_1390_one__le__mult__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4823 (all X_a (divisi14063676e_zero(X_a) -> (all A_1 all B (hAPP(X_a,X_a,inverse_inverse(X_a),B) = hAPP(X_a,X_a,inverse_inverse(X_a),A_1) -> ti(X_a,A_1) = ti(X_a,B))))) # label(fact_2523_inverse__eq__imp__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4824 (all X_a (topological_space(X_a) -> (all F all A_2 (hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),F),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))) <-> hBOOL(hAPP(filter(X_a),bool,hAPP(real,fun(filter(X_a),bool),hAPP(fun(X_a,real),fun(real,fun(filter(X_a),bool)),tendsto(X_a,real),hAPP(fun(X_a,real),fun(X_a,real),hAPP(fun(real,real),fun(fun(X_a,real),fun(X_a,real)),combb(real,real,X_a),abs_abs(real)),F)),zero_zero(real)),hAPP(X_a,filter(X_a),at(X_a),A_2))))))) # label(fact_4594_LIM__rabs__zero__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4825 (all F all B_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B_1),X_1)) -> ((all X_2 (hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_gr676655987ssThan(real),B_1),X_1))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_2))))) -> (hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),F),X_1)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,F,X_1))))))) # label(fact_4924_LIM__less__bound) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4826 (all X_a (group_add(X_a) -> (all A_2 all B_1 (hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_2),B_1) = zero_zero(X_a) <-> hAPP(X_a,X_a,uminus_uminus(X_a),B_1) = ti(X_a,A_2))))) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4827 (all Q_3 ((all A_4 all B_4 (hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_4),B_4) = Q_3 -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B_4)) -> (ti(int,A_4) != zero_zero(int) -> hAPP(int,int,hAPP(int,fun(int,int),gcd_gcd(int),A_4),B_4) != one_one(int))))) -> Q_3 = zero_zero(rat))) # label(fact_4411_Rat__cases__nonzero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4828 (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]. 10.93/10.93 4829 (all X_a all A_2 all R_1 all B_1 (hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),B_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),R_1,A_2),B_1)) -> hBOOL(hAPP(X_a,bool,hAPP(fun(X_a,fun(X_a,bool)),fun(X_a,bool),accp(X_a),R_1),A_2))))) # label(fact_2919_accp__downward) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4830 (all X_a (ordered_ab_group_add(X_a) -> (all X all Y all Z_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),X),Y)),Z_1) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_max(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),Z_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),Y),Z_1))))) # label(fact_4958_max__diff__distrib__left) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4831 (all X_a (linordered_semidom(X_a) -> (all M all N all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),one_one(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),M)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N))))))) # label(fact_442_power__le__imp__le__exp) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4832 (all X_a (field(X_a) -> (all Z all N_1 all H (ti(X_a,H) != zero_zero(X_a) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),H),hAPP(fun(nat,bool),X_a,hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,fun(nat,bool)),fun(nat,X_a),hAPP(fun(fun(nat,bool),X_a),fun(fun(nat,fun(nat,bool)),fun(nat,X_a)),combb(fun(nat,bool),X_a,nat),hAPP(fun(nat,X_a),fun(fun(nat,bool),X_a),big_co1399186613setsum(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,X_a)),combs(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H)))),hAPP(fun(nat,nat),fun(nat,X_a),hAPP(fun(nat,X_a),fun(fun(nat,nat),fun(nat,X_a)),combb(nat,X_a,nat),hAPP(X_a,fun(nat,X_a),power_power(X_a),Z)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))))),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,bool)),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combb(nat,fun(nat,bool),nat),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat))),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat))))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),Z),H)),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),N_1))),H)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(nat,X_a,semiring_1_of_nat(X_a),N_1)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),Z),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N_1),hAPP(nat,nat,suc,zero_zero(nat)))))))))) # label(fact_4238_lemma__termdiff2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4833 (all X_a (real_normed_vector(X_a) -> (all X_1 all X_3 (hBOOL(hAPP(fun(nat,real),bool,summable(real),X_3)) -> hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,real),fun(nat,fun(X_a,X_a)),hAPP(fun(real,fun(X_a,X_a)),fun(fun(nat,real),fun(nat,fun(X_a,X_a))),combb(real,fun(X_a,X_a),nat),scaleR_scaleR(X_a)),X_3)),X_1))))))) # label(fact_4671_scaleR__left_Osummable) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4834 (all N_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),N_1),Ma)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,real_1(int),N_1)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,real_1(int),Ma)),one_one(real)))))) # label(fact_3393_int__le__real__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4835 (all X_a all X_b (comm_monoid_mult(X_b) -> (all F all A_3 (-hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> hAPP(fun(X_a,bool),X_b,hAPP(fun(X_a,X_b),fun(fun(X_a,bool),X_b),big_co302546470etprod(X_a,X_b),F),A_3) = one_one(X_b))))) # label(fact_3951_setprod__infinite) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4836 (all X_a (archim1727834104eiling(X_a) -> (all X_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),one_one(X_a)),X_1)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(X_a,int,archim2085082626_floor(X_a),X_1))))))) # label(fact_2881_zero__less__floor) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4837 (all X_a ti(fun(X_a,fun(fun(X_a,bool),bool)),member(X_a)) = member(X_a)) # label(tsy_c_member_res) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4838 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),A_2),sequentially)) -> hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),hAPP(fun(nat,X_a),fun(nat,X_a),hAPP(fun(X_a,X_a),fun(fun(nat,X_a),fun(nat,X_a)),combb(X_a,X_a,nat),hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1)),X_3)),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_1),A_2)),sequentially)))))) # label(fact_4729_scaleR__right_OLIMSEQ) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4839 (all M all N (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),M),N)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,fact_fact(int),M)),hAPP(int,int,fact_fact(int),N))))) # label(fact_3181_fact__mono__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4840 (all X_a (linordered_field(X_a) -> (all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),X),Y)))))))) # label(fact_1679_divide__pos__pos) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4841 (all X_b all X_a all B_2 all A_3 (hBOOL(hAPP(fun(X_a,bool),bool,finite_finite_1(X_a),A_3)) -> (hBOOL(hAPP(fun(X_b,bool),bool,finite_finite_1(X_b),B_2)) -> hAPP(fun(sum_sum(X_a,X_b),bool),nat,finite_card(sum_sum(X_a,X_b)),hAPP(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool),hAPP(fun(X_a,bool),fun(fun(X_b,bool),fun(sum_sum(X_a,X_b),bool)),sum_Plus(X_a,X_b),A_3),B_2)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(fun(X_a,bool),nat,finite_card(X_a),A_3)),hAPP(fun(X_b,bool),nat,finite_card(X_b),B_2))))) # label(fact_3198_card__Plus) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4842 (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_1438_div__Suc__eq__div__add3) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4843 (all X_a all Q_1 all P_1 all X_1 (hBOOL(hAPP(X_a,bool,P_1,X_1)) -> (hBOOL(hAPP(fun(X_a,bool),bool,hAPP(fun(X_a,bool),fun(fun(X_a,bool),bool),ord_less_eq(fun(X_a,bool)),P_1),Q_1)) -> hBOOL(hAPP(X_a,bool,Q_1,X_1))))) # label(fact_4337_rev__predicate1D) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4844 (all X_a (ab_group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),A_1)))) # label(fact_2053_minus__diff__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4845 (all A_2 (hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A_2),zero_zero(real)),sequentially)) -> (hBOOL(hAPP(fun(nat,real),bool,monoseq(real),A_2)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,A_2,zero_zero(nat)))) -> (all N_2 hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2))),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_atLeastAtMost(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),A_2)),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),N_2)),one_one(nat)))))))))))) # label(fact_4523_summable__Leibniz_I2_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4846 (all P_1 all P1 all D_1 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),D_1)) -> ((all X_2 all K_1 (hBOOL(hAPP(int,bool,P1,hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),X_2),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),K_1),D_1)))) <-> hBOOL(hAPP(int,bool,P1,X_2)))) -> ((exists Z_2 all X_2 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),X_2),Z_2)) -> (hBOOL(hAPP(int,bool,P1,X_2)) <-> hBOOL(hAPP(int,bool,P_1,X_2))))) -> ((exists X1 hBOOL(hAPP(int,bool,P1,X1))) -> (exists X1 hBOOL(hAPP(int,bool,P_1,X1)))))))) # label(fact_2844_minusinfinity) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4847 (all X_a (comm_semiring_1(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),dvd_dvd(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),B),C)))))))) # label(fact_340_dvd__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4848 (all X_a (linorder(X_a) -> (all B all A_1 all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),X)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),A_1),B)),X)))))) # label(fact_4825_min__max_Ole__infI1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4849 (all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),min_1)),Y)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),Y),one_one(real))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,arccos,Y)))))) # label(fact_2262_arccos__lbound) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4850 (all A_2 all B_1 (A_2 = zero_zero(real) & zero_zero(real) = B_1 <-> hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_2),B_1) = zero_zero(complex))) # label(fact_2740_Complex__eq__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4851 (all X_a (linordered_semiring(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B))))))) # label(fact_428_mult__left__less__imp__less) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4852 (all X_a (comm_monoid_add(X_a) & t2_space(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))) = zero_zero(X_a))) # label(fact_3968_suminf__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4853 (all X_a (comm_ring_1(X_a) -> (all X all N ((-hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N)) & (hBOOL(hAPP(nat,bool,even_odd_even(nat),N)) -> hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)),N) = hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),X),N)))))) # label(fact_2423_neg__power__if) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4854 (all K all N_2 all F_3 hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),F_3),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),K))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),N_2))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),K))) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),F_3),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N_2),K)))) # label(fact_4183_sumr__offset4) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4855 (all X_a (linordered_field(X_a) -> (all A_2 all B_1 all C_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_2),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),inverse_divide(X_a),B_1),C_1))) <-> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_2),C_1)),B_1))))))) # label(fact_1710_pos__less__divide__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4856 (all U_1 hAPP(fun(int,bool),nat,finite_card(int),hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),ord_atLeastLessThan(int),zero_zero(int)),U_1)) = hAPP(int,nat,nat_1,U_1)) # label(fact_4258_card__atLeastZeroLessThan__int) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4857 (all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),zero_zero(int)),P_5)))))) # label(fact_845_MultInv__prop3) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4858 (all N hAPP(nat,nat,suc,N) != N) # label(fact_1217_n__not__Suc__n) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4859 (all C all N all A_1 all B (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,A_1),B)) -> (hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),N) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B) -> (exists R_2 exists S_1 (A_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),R_2),N) & hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),S_1),N) = B))))) # label(fact_3425_coprime__pow) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4860 (all Y all X (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),Y)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),X),Y)))))) # label(fact_985_Divides_Otransfer__nat__int__function__closures_I1_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4861 (all C_1 all D_1 all A_2 all B_1 all Ma (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_2),B_1),Ma)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),A_2)),Ma)) <-> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,C_1),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D_1),B_1)),Ma))))) # label(fact_357_zcong__zmult__prop2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4862 (all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),X_1)),one_one(real))) -> hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),inverse_divide(real),one_one(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat)))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),X_1)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),one_one(nat))))))))) # label(fact_3979_summable__arctan__series) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4863 (all X_a (real_normed_vector(X_a) -> (all X hAPP(X_a,X_a,sgn_sgn(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),X)) = hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,sgn_sgn(X_a),X))))) # label(fact_2207_sgn__minus) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4864 (all N hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),N))))) # label(fact_2430_real__of__nat__fact__ge__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4865 (all X_a (real_algebra(X_a) -> (all A_1 all X all Y hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),X),Y)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),A_1),X)),Y)))) # label(fact_4677_mult__scaleR__left) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4866 (all G all X_1 all Ma (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),G),X_1),Ma)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),sin),G)),X_1),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,cos,hAPP(real,real,G,X_1))),Ma))))) # label(fact_3859_DERIV__fun__sin) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4867 (all X_a (archim1727834104eiling(X_a) -> (all X all V hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(X_a,int,archimedean_ceiling(X_a),X)),hAPP(int,int,number_number_of(int),V)) = hAPP(X_a,int,archimedean_ceiling(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),X),hAPP(int,X_a,number_number_of(X_a),V)))))) # label(fact_3308_ceiling__diff__number__of) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4868 (all N all M hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),N),M)),N) = M) # label(fact_667_diff__add__inverse) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4869 (all A_2 hAPP(int,int,zfact,A_2) = hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),combi(int)),hAPP(int,fun(int,bool),d22set,A_2))) # label(fact_3930_d22set__prod__zfact) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4870 (all N (N != zero_zero(nat) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)))) # label(fact_540_gr0I) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4871 (all X_a (real_normed_algebra(X_a) -> (all Y_1 all X_3 (hBOOL(hAPP(fun(nat,X_a),bool,summable(X_a),X_3)) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),hAPP(fun(nat,X_a),X_a,suminf(X_a),X_3)),Y_1) = hAPP(fun(nat,X_a),X_a,suminf(X_a),hAPP(X_a,fun(nat,X_a),hAPP(fun(nat,fun(X_a,X_a)),fun(X_a,fun(nat,X_a)),combc(nat,X_a,X_a),hAPP(fun(nat,X_a),fun(nat,fun(X_a,X_a)),hAPP(fun(X_a,fun(X_a,X_a)),fun(fun(nat,X_a),fun(nat,fun(X_a,X_a))),combb(X_a,fun(X_a,X_a),nat),times_times(X_a)),X_3)),Y_1)))))) # label(fact_3987_mult__left_Osuminf) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4872 (all X_a all G all A_2 all A_3 (hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),G),A_2),A_3)) -> hBOOL(hAPP(filter(X_a),bool,hAPP(complex,fun(filter(X_a),bool),hAPP(fun(X_a,complex),fun(complex,fun(filter(X_a),bool)),tendsto(X_a,complex),hAPP(fun(X_a,complex),fun(X_a,complex),hAPP(fun(complex,complex),fun(fun(X_a,complex),fun(X_a,complex)),combb(complex,complex,X_a),cnj),G)),hAPP(complex,complex,cnj,A_2)),A_3)))) # label(fact_4507_cnj_Otendsto) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4873 (all X_a (order(X_a) -> (all Z_1 all Y all X (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Y),X)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),Y)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),Z_1),X))))))) # label(fact_1602_xt1_I8_J) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4874 (all X_a (semiring_div(X_a) -> (all C all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),div_mod(X_a),A_1),B))))) # label(fact_931_mod__mult__mult1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4875 (all I_1 all K_4 all J_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),K_4),J_2)) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),I_1),K_4)),J_2) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),I_1),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),J_2),K_4)))) # label(fact_699_diff__diff__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4876 (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),one_one(X_a)),A_1) = ti(X_a,A_1)))) # label(fact_802_mult__1__left) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4877 (all D all A_1 all B (hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A_1),B)) = one_one(nat) -> hAPP(nat,nat,hAPP(nat,fun(nat,nat),gcd_gcd(nat),D),A_1) = one_one(nat))) # label(fact_3271_coprime__lmult__nat) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4878 (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_878_mult_Ozero__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4879 (all X_1 all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),Y_1)) -> (exists X_2 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_2),Y_1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),X_1),X_2)) & hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),X_2),field_char_0_Rats(real))))))) # label(fact_3703_Rats__dense__in__real) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4880 (all K_4 all N all M (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),M)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),K_4),M)))))) # label(fact_1117_div__le__mono2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4881 (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)) = hAPP(int,real,number_number_of(real),V)) & (hBOOL(hAPP(int,bool,nat_neg,hAPP(int,int,number_number_of(int),V))) -> zero_zero(real) = hAPP(nat,real,real_1(nat),hAPP(int,nat,number_number_of(nat),V))))) # label(fact_2358_real__of__nat__number__of) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4882 (all I all P_1 all K (hBOOL(hAPP(nat,bool,P_1,K)) -> ((all N_2 (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,suc,N_2))) -> hBOOL(hAPP(nat,bool,P_1,N_2)))) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),K),I)))))) # label(fact_1522_zero__induct__lemma) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4883 (all X all Y (-hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),coprime,X),Y)) -> (exists P_6 (hBOOL(hAPP(nat,bool,prime,P_6)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),Y)) & hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_6),X)))))) # label(fact_3086_coprime__prime__dvd__ex) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4884 (all K_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),M)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K_4),N))) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),K_4)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),M),N))))) # label(fact_498_dvd__mult__cancel) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4885 (all X_a (mult_zero(X_a) -> (all A_1 hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),zero_zero(X_a)) = zero_zero(X_a)))) # label(fact_322_mult__zero__right) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4886 (all X_a all C_1 all A_3 all B_2 (-hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),B_2)) & hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),A_3)) <-> hBOOL(hAPP(fun(X_a,bool),bool,hAPP(X_a,fun(fun(X_a,bool),bool),member(X_a),C_1),hAPP(fun(X_a,bool),fun(X_a,bool),hAPP(fun(X_a,bool),fun(fun(X_a,bool),fun(X_a,bool)),minus_minus(fun(X_a,bool)),A_3),B_2))))) # label(fact_1962_Diff__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4887 (all X_a (linord20386208strict(X_a) -> (all C all D all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),A_1),B)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),C),D)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),C)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),B),D)))))))))) # label(fact_433_mult__strict__mono_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4888 (all K all F (zero_zero(nat) = hAPP(nat,nat,F,zero_zero(nat)) -> hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),F),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),hAPP(nat,nat,suc,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),zero_zero(nat)),K)))) # label(fact_4589_setsum__shift__lb__Suc0__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4889 (all X_a (real_normed_field(X_a) -> (all F all X_1 all D_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),F),X_1),D_1)) -> (hAPP(X_a,X_a,F,X_1) != zero_zero(X_a) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),hAPP(fun(X_a,X_a),fun(X_a,fun(X_a,bool)),deriv(X_a),hAPP(fun(X_a,X_a),fun(X_a,X_a),hAPP(fun(X_a,X_a),fun(fun(X_a,X_a),fun(X_a,X_a)),combb(X_a,X_a,X_a),inverse_inverse(X_a)),F)),X_1),hAPP(X_a,X_a,uminus_uminus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),D_1),hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),hAPP(X_a,X_a,F,X_1)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))))))))))))) # label(fact_3901_DERIV__inverse__fun) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4890 (all X_a (real_normed_vector(X_a) -> (all R_1 all X_3 all L_2 (hBOOL(hAPP(filter(nat),bool,hAPP(X_a,fun(filter(nat),bool),hAPP(fun(nat,X_a),fun(X_a,fun(filter(nat),bool)),tendsto(nat,X_a),X_3),L_2),sequentially)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),R_1)) -> (exists No all N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),No),N_2)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(X_a,real,norm_norm(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(nat,X_a,X_3,N_2)),L_2))),R_1))))))))) # label(fact_4519_LIMSEQ__D) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4891 (all D2 all D1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),D2)) -> (exists E (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),E)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D1)) & hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),E),D2))))))) # label(fact_1605_real__lbound__gt__zero) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4892 (all X_a (group_add(X_a) -> (all A_1 all B hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,uminus_uminus(X_a),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)) = ti(X_a,B)))) # label(fact_2048_minus__add__cancel) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4893 (all X_a (real_vector(X_a) -> (all A_1 all B all X hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),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)) = 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)))) # label(fact_4714_scaleR__left__diff__distrib) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4894 (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_2050_minus__add) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4895 (all X_a (ordere142940540dd_abs(X_a) -> (all A_1 all B all C all D hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),A_1),B)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),C),D)))),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),plus_plus(X_a),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),A_1),C))),hAPP(X_a,X_a,abs_abs(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),minus_minus(X_a),B),D)))))))) # label(fact_1881_abs__diff__triangle__ineq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4896 (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]. 10.93/10.93 4897 (all X_a (linordered_semidom(X_a) -> (all A_1 all N all N_5 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),N),N_5)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),zero_zero(X_a)),A_1)) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),one_one(X_a))) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N_5)),hAPP(nat,X_a,hAPP(X_a,fun(nat,X_a),power_power(X_a),A_1),N))))))))) # label(fact_441_power__decreasing) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4898 (all P_1 all N_1 all K (hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),N_1),K))) <-> (zero_zero(nat) != K -> (all I_2 all J_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),J_1),K)) -> (N_1 = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),I_2)),J_1) -> hBOOL(hAPP(nat,bool,P_1,I_2)))))) & (K = zero_zero(nat) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat)))))) # label(fact_1131_split__div) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4899 (all A_2 all A_3 all Ma (hBOOL(hAPP(int,bool,hAPP(fun(int,bool),fun(int,bool),is_RRset,A_3),Ma)) -> (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A_2),A_3)) -> hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,A_2),Ma) = one_one(int)))) # label(fact_3619_RRset__gcd) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4900 (all X ((zero_zero(real) = X -> zero_zero(real) = hAPP(real,real,sgn_sgn(real),X)) & (X != zero_zero(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)) & (-hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X)) -> hAPP(real,real,uminus_uminus(real),one_one(real)) = hAPP(real,real,sgn_sgn(real),X))))) # label(fact_2227_real__sgn__def) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4901 (all Y all X all P_5 (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),P_5)) -> (hBOOL(hAPP(int,bool,zprime,P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),zero_zero(int)),P_5)) -> (-hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,Y),zero_zero(int)),P_5)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),X)),hAPP(int,int,hAPP(int,fun(int,int),multInv,P_5),Y)),P_5)) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,X),Y),P_5)))))))) # label(fact_847_MultInv__prop5) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4902 (all P_1 all A0 all A1 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A0),A1))) -> ((all A_4 all B_4 (hBOOL(hAPP(product_prod(int,int),bool,hAPP(fun(product_prod(int,int),fun(product_prod(int,int),bool)),fun(product_prod(int,int),bool),accp(product_prod(int,int)),norm_frac_rel),hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),A_4),B_4))) -> ((hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B_4),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,hAPP(int,int,uminus_uminus(int),A_4)),hAPP(int,int,uminus_uminus(int),B_4)))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A_4),B_4))))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),P_1,A0),A1))))) # label(fact_3553_norm__frac_Opinduct) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4903 (all K all Ma all N_1 (K = zero_zero(nat) | N_1 = Ma <-> hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),Ma) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),K),N_1))) # label(fact_552_mult__cancel1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4904 (all L_4 all M all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M),N)) -> hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),N)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),L_4),M))))) # label(fact_670_diff__le__mono2) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4905 (all X_1 all Y_1 all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N_1)) -> (hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),X_1) = hAPP(real,real,hAPP(nat,fun(real,real),root,N_1),Y_1) <-> X_1 = Y_1))) # label(fact_2672_real__root__eq__iff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4906 (all X_1 (hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),X_1),zEven)) -> (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),X_1)) -> hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),hAPP(int,nat,nat_1,X_1)) = one_one(int)))) # label(fact_1203_EvenOdd_Oneg__one__even__power) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4907 (all A_1 all B (hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) -> hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A_1),B))))) # label(fact_987_neg__mod__bound) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4908 (all Ma all K all N_1 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),Ma),N_1)) | 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),N_1),K))))) # label(fact_724_nat__mult__dvd__cancel__disj_H) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4909 (all S ((all M_2 exists N_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),M_2),N_2)) & hBOOL(hAPP(fun(nat,bool),bool,hAPP(nat,fun(fun(nat,bool),bool),member(nat),N_2),S)))) <-> -hBOOL(hAPP(fun(nat,bool),bool,finite_finite_1(nat),S)))) # label(fact_3656_infinite__nat__iff__unbounded__le) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4910 (all I all P_1 all P_4 ((all I_2 (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I_2),P_4)) -> (hBOOL(hAPP(nat,bool,P_1,I_2)) -> hBOOL(hAPP(nat,bool,P_1,hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,suc,I_2)),P_4)))))) -> (hBOOL(hAPP(nat,bool,P_1,I)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),I),P_4)) -> hBOOL(hAPP(nat,bool,P_1,zero_zero(nat))))))) # label(fact_1478_mod__induct__0) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4911 (all A_1 all B all C hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A_1),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))),C)) # label(fact_954_zmod__zmult1__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4912 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),hAPP(nat,nat,suc,zero_zero(nat)))) = N)) # label(fact_1389_Suc__pred) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4913 (all Q_3 all P_5 (hBOOL(hAPP(nat,bool,prime,P_5)) -> (hBOOL(hAPP(nat,bool,prime,Q_3)) -> (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),P_5),Q_3)) -> P_5 = Q_3)))) # label(fact_3048_primes__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4914 (all K_4 all M all N hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),M)),N) = hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,K_4),hAPP(int,int,hAPP(int,fun(int,int),legacy_zgcd,M),N))) # label(fact_3438_zgcd__assoc) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4915 (all N (hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),N)) -> N = hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),N),one_one(nat))))) # label(fact_1414_Suc__diff__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4916 (all A_1 all B all P_5 all Q_3 (hAPP(int,product_prod(int,int),hAPP(int,fun(int,product_prod(int,int)),product_Pair(int,int),P_5),Q_3) = hAPP(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,rat,hAPP(int,fun(int,rat),fract,P_5),Q_3) = hAPP(int,rat,hAPP(int,fun(int,rat),fract,A_1),B))) # label(fact_3758_normalize__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4917 (all X_a all X_b all X_c all X_1 all P_1 ((all A_4 all B_4 all C_4 hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,hAPP(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c)),hAPP(X_a,fun(product_prod(X_b,X_c),product_prod(X_a,product_prod(X_b,X_c))),product_Pair(X_a,product_prod(X_b,X_c)),A_4),hAPP(X_c,product_prod(X_b,X_c),hAPP(X_b,fun(X_c,product_prod(X_b,X_c)),product_Pair(X_b,X_c),B_4),C_4))))) -> hBOOL(hAPP(product_prod(X_a,product_prod(X_b,X_c)),bool,P_1,X_1)))) # label(fact_3148_prod__induct3) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4918 (all A_1 all B hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),hAPP(int,fun(int,fun(int,bool)),zcong,A_1),B),one_one(int)))) # label(fact_354_zcong__1) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4919 (all A_1 all B all C all D hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A_1),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,A_1),B)),hAPP(real,complex,hAPP(real,fun(real,complex),complex_1,C),D))) # label(fact_2747_complex__diff) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4920 (all X (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),X)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),X)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),X),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,ln,hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),X))))))) # label(fact_2127_ln__one__minus__pos__lower__bound) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4921 (all X_a (division_ring(X_a) -> (all A_1 (ti(X_a,A_1) != zero_zero(X_a) -> hAPP(X_a,X_a,inverse_inverse(X_a),hAPP(X_a,X_a,inverse_inverse(X_a),A_1)) = ti(X_a,A_1))))) # label(fact_2529_nonzero__inverse__inverse__eq) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4922 (all X_a (linord20386208strict(X_a) -> (all C all A_1 all B (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),A_1)),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),C),B))) -> (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),C)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),A_1),B))))))) # label(fact_425_mult__left__le__imp__le) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4923 (all X_a (linordered_field(X_a) -> (all A_1 (hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),A_1)) -> hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less(X_a),zero_zero(X_a)),hAPP(X_a,X_a,inverse_inverse(X_a),A_1))))))) # label(fact_2543_positive__imp__inverse__positive) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4924 (all Z_1 all X all Y (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X),Y)) -> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),X)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),Z_1),Y))))) # label(fact_653_real__add__left__mono) # label(axiom) # label(non_clause). [assumption]. 10.93/10.93 4925 (all X_a (ord(X_a) -> (all X all Least ((all X_2 hBOOL(hAPP(X_a,bool,hAPP(X_a,fun(X_a,bool),ord_less_eq(X_a),Least),X_2))) -> hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),ord_min(X_a),Least),X) = ti(X_a,Least))))) # label(fact_4836_min__leastL) # label(axiom) # label(non_clause). [assumption]. 11.84/11.82 4926 (all X_a (real_normed_algebra(X_a) -> (all A_1 all R_4 all B hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),B)) = hAPP(X_a,X_a,hAPP(X_a,fun(X_a,X_a),times_times(X_a),A_1),hAPP(X_a,X_a,hAPP(real,fun(X_a,X_a),scaleR_scaleR(X_a),R_4),B))))) # label(fact_4674_mult_OscaleR__right) # label(axiom) # label(non_clause). [assumption]. 11.84/11.82 4927 (all Y_1 all X_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),X_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),Y_1)) -> (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),X_1),Y_1)) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,ln,X_1)),hAPP(real,real,ln,Y_1))))))) # label(fact_1944_ln__le__cancel__iff) # label(axiom) # label(non_clause). [assumption]. 11.84/11.82 4928 (all Y_1 (hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,sqrt,Y_1))) <-> hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),Y_1)))) # label(fact_1624_real__sqrt__ge__0__iff) # label(axiom) # label(non_clause). [assumption]. 11.84/11.82 11.84/11.82 ============================== end of process non-clausal formulas === 11.84/11.82 11.84/11.82 ============================== PROCESS INITIAL CLAUSES =============== 11.84/11.82 11.84/11.82 ============================== PREDICATE ELIMINATION ================= 11.84/11.82 4929 linord581940658strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 11.84/11.82 4930 -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),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),C),D)) # label(fact_395_mult__less__cancel__left__pos) # label(axiom). [clausify(1)]. 11.84/11.82 4931 -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),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),C),D)) # label(fact_395_mult__less__cancel__left__pos) # label(axiom). [clausify(1)]. 11.84/11.82 4932 -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))) | ti(A,C) = zero_zero(A) # label(fact_45_sum__squares__le__zero__iff) # label(axiom). [clausify(6)]. 11.84/11.82 4933 -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))) | ti(A,B) = zero_zero(A) # label(fact_45_sum__squares__le__zero__iff) # label(axiom). [clausify(6)]. 11.84/11.82 4934 -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))) | ti(A,C) != zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_45_sum__squares__le__zero__iff) # label(axiom). [clausify(6)]. 11.84/11.82 4935 -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_396_mult__less__cancel__left__disj) # label(axiom). [clausify(171)]. 11.84/11.82 4936 -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_396_mult__less__cancel__left__disj) # label(axiom). [clausify(171)]. 11.84/11.82 4937 -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),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom). [clausify(171)]. 11.84/11.82 4938 -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),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom). [clausify(171)]. 11.84/11.82 4939 -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),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))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom). [clausify(171)]. 11.84/11.82 4940 -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),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_396_mult__less__cancel__left__disj) # label(axiom). [clausify(171)]. 11.84/11.82 4941 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_380_zero__le__mult__iff) # label(axiom). [clausify(486)]. 11.84/11.82 4942 -linord581940658strict(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_380_zero__le__mult__iff) # label(axiom). [clausify(486)]. 11.84/11.82 4943 -linord581940658strict(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),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_380_zero__le__mult__iff) # label(axiom). [clausify(486)]. 11.84/11.82 4944 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_380_zero__le__mult__iff) # label(axiom). [clausify(486)]. 11.84/11.82 4945 -linord581940658strict(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_380_zero__le__mult__iff) # label(axiom). [clausify(486)]. 11.84/11.82 4946 -linord581940658strict(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),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_380_zero__le__mult__iff) # label(axiom). [clausify(486)]. 11.84/11.82 4947 -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_383_mult__strict__right__mono__neg) # label(axiom). [clausify(1352)]. 11.84/11.83 4948 -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_436_mult__le__cancel__left__pos) # label(axiom). [clausify(1388)]. 11.84/11.83 4949 -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_436_mult__le__cancel__left__pos) # label(axiom). [clausify(1388)]. 11.84/11.83 4950 -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)),C)) # label(fact_379_mult__le__0__iff) # label(axiom). [clausify(1603)]. 11.84/11.83 4951 -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),B),zero_zero(A))) # label(fact_379_mult__le__0__iff) # label(axiom). [clausify(1603)]. 11.84/11.83 4952 -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)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_379_mult__le__0__iff) # label(axiom). [clausify(1603)]. 11.84/11.83 4953 -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)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_379_mult__le__0__iff) # label(axiom). [clausify(1603)]. 11.84/11.83 4954 -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_379_mult__le__0__iff) # label(axiom). [clausify(1603)]. 11.84/11.83 4955 -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_379_mult__le__0__iff) # label(axiom). [clausify(1603)]. 11.84/11.83 4956 -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_389_mult__less__cancel__left__neg) # label(axiom). [clausify(2175)]. 11.84/11.83 4957 -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_389_mult__less__cancel__left__neg) # label(axiom). [clausify(2175)]. 11.84/11.83 4958 -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),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom). [clausify(2268)]. 11.84/11.84 4959 -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),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom). [clausify(2268)]. 11.84/11.84 4960 -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),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom). [clausify(2268)]. 11.84/11.84 4961 -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),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom). [clausify(2268)]. 11.84/11.84 4962 -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),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom). [clausify(2268)]. 11.84/11.84 4963 -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),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_397_mult__less__cancel__right__disj) # label(axiom). [clausify(2268)]. 11.84/11.84 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),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),B),C)). [resolve(4929,a,4930,a)]. 11.84/11.84 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))) | ti(real,B) = zero_zero(real). [resolve(4929,a,4932,a)]. 11.84/11.84 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))) | ti(real,A) = zero_zero(real). [resolve(4929,a,4933,a)]. 11.84/11.84 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))) | ti(real,B) != zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(4929,a,4934,a)]. 11.84/11.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4929,a,4936,a)]. 11.84/11.85 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(4929,a,4937,a)]. 11.84/11.85 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),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),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(4929,a,4938,a)]. 11.84/11.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(4929,a,4939,a)]. 11.84/11.85 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),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4929,a,4940,a)]. 11.84/11.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(4929,a,4941,a)]. 11.84/11.85 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4929,a,4942,a)]. 11.84/11.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(4929,a,4943,a)]. 11.84/11.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(4929,a,4944,a)]. 11.84/11.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4929,a,4945,a)]. 11.84/11.85 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4929,a,4946,a)]. 11.84/11.85 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(4929,a,4947,a)]. 11.84/11.87 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)),B)). [resolve(4929,a,4950,a)]. 11.84/11.87 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),A),zero_zero(real))). [resolve(4929,a,4951,a)]. 11.84/11.87 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)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)). [resolve(4929,a,4952,a)]. 11.84/11.87 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)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(4929,a,4953,a)]. 11.84/11.87 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(4929,a,4954,a)]. 11.84/11.87 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(4929,a,4955,a)]. 11.84/11.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(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(4929,a,4956,a)]. 11.84/11.87 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),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(4929,a,4959,a)]. 11.84/11.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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),B),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(4929,a,4960,a)]. 11.84/11.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(4929,a,4961,a)]. 11.84/11.87 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),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),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(4929,a,4962,a)]. 11.84/11.87 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),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),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(4929,a,4963,a)]. 11.93/11.90 4964 linord581940658strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 11.93/11.90 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),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),B),C)). [resolve(4964,a,4930,a)]. 11.93/11.90 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),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),B),C)). [resolve(4964,a,4931,a)]. 11.93/11.90 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))) | ti(rat,B) = zero_zero(rat). [resolve(4964,a,4932,a)]. 11.93/11.90 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))) | ti(rat,A) = zero_zero(rat). [resolve(4964,a,4933,a)]. 11.93/11.90 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))) | ti(rat,B) != zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(4964,a,4934,a)]. 11.93/11.90 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),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4964,a,4936,a)]. 11.93/11.90 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(4964,a,4937,a)]. 11.93/11.90 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(4964,a,4938,a)]. 11.93/11.90 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),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))). [resolve(4964,a,4939,a)]. 11.93/11.90 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),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),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4964,a,4940,a)]. 11.93/11.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(4964,a,4941,a)]. 11.93/11.92 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4964,a,4942,a)]. 11.93/11.92 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(4964,a,4943,a)]. 11.93/11.92 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(4964,a,4944,a)]. 11.93/11.92 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4964,a,4945,a)]. 11.93/11.92 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4964,a,4946,a)]. 11.93/11.92 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),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(4964,a,4947,a)]. 11.93/11.92 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(4964,a,4948,a)]. 11.93/11.92 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(4964,a,4949,a)]. 11.93/11.92 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)),B)). [resolve(4964,a,4950,a)]. 11.93/11.92 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),A),zero_zero(rat))). [resolve(4964,a,4951,a)]. 11.93/11.92 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)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)). [resolve(4964,a,4952,a)]. 11.93/11.92 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)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(4964,a,4953,a)]. 12.13/12.11 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(4964,a,4954,a)]. 12.13/12.11 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(4964,a,4955,a)]. 12.13/12.11 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(4964,a,4956,a)]. 12.13/12.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),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),C))). [resolve(4964,a,4959,a)]. 12.13/12.11 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),B),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(4964,a,4960,a)]. 12.13/12.11 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),B),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(4964,a,4961,a)]. 12.13/12.11 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(4964,a,4962,a)]. 12.13/12.11 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(4964,a,4963,a)]. 12.13/12.11 4965 -linord581940658strict(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)) = zero_zero(A) # label(fact_94_sum__squares__eq__zero__iff) # label(axiom). [clausify(2650)]. 12.13/12.11 Derived: ti(real,A) != zero_zero(real) | ti(real,B) != 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),B),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)) = zero_zero(real). [resolve(4965,a,4929,a)]. 12.13/12.11 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,B) != 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),B),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)) = zero_zero(rat). [resolve(4965,a,4964,a)]. 12.13/12.11 4966 -linord581940658strict(A) | ti(A,B) = 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),C),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)) != zero_zero(A) # label(fact_94_sum__squares__eq__zero__iff) # label(axiom). [clausify(2650)]. 12.44/12.43 Derived: ti(real,A) = 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),B),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)) != zero_zero(real). [resolve(4966,a,4929,a)]. 12.44/12.43 Derived: ti(rat,A) = 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),B),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)) != zero_zero(rat). [resolve(4966,a,4964,a)]. 12.44/12.43 4967 -linord581940658strict(A) | ti(A,B) = 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) # label(fact_94_sum__squares__eq__zero__iff) # label(axiom). [clausify(2650)]. 12.44/12.43 Derived: ti(real,A) = 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). [resolve(4967,a,4929,a)]. 12.44/12.43 Derived: ti(rat,A) = 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). [resolve(4967,a,4964,a)]. 12.44/12.43 4968 -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_387_mult__neg__neg) # label(axiom). [clausify(3038)]. 12.44/12.43 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(4968,a,4929,a)]. 12.44/12.43 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(4968,a,4964,a)]. 12.44/12.43 4969 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_435_mult__le__cancel__left__neg) # label(axiom). [clausify(3091)]. 12.44/12.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4969,a,4929,a)]. 12.44/12.43 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),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4969,a,4964,a)]. 12.44/12.43 4970 -linord581940658strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_435_mult__le__cancel__left__neg) # label(axiom). [clausify(3091)]. 12.44/12.43 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(4970,a,4929,a)]. 13.64/13.68 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),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(4970,a,4964,a)]. 13.64/13.68 4971 -linord581940658strict(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,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)))) # label(fact_108_sum__squares__gt__zero__iff) # label(axiom). [clausify(3146)]. 13.64/13.68 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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)))). [resolve(4971,a,4929,a)]. 13.64/13.68 Derived: ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),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)))). [resolve(4971,a,4964,a)]. 13.64/13.68 4972 -linord581940658strict(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)))) # label(fact_108_sum__squares__gt__zero__iff) # label(axiom). [clausify(3146)]. 13.64/13.68 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)))). [resolve(4972,a,4929,a)]. 13.64/13.68 Derived: ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)))). [resolve(4972,a,4964,a)]. 13.64/13.68 4973 -linord581940658strict(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,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)))) # label(fact_108_sum__squares__gt__zero__iff) # label(axiom). [clausify(3146)]. 13.64/13.68 Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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)))). [resolve(4973,a,4929,a)]. 13.64/13.68 Derived: ti(rat,A) != zero_zero(rat) | ti(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),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)))). [resolve(4973,a,4964,a)]. 13.64/13.68 4974 -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_382_mult__strict__left__mono__neg) # label(axiom). [clausify(4179)]. 14.55/14.57 4975 linord581940658strict(int) # label(arity_Int_Oint___Rings_Olinordered__ring__strict) # label(axiom). [assumption]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,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),B),C)). [resolve(4975,a,4930,a)]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,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),B),C)). [resolve(4975,a,4931,a)]. 14.55/14.57 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))) | ti(int,B) = zero_zero(int). [resolve(4975,a,4932,a)]. 14.55/14.57 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))) | ti(int,A) = zero_zero(int). [resolve(4975,a,4933,a)]. 14.55/14.57 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))) | ti(int,B) != zero_zero(int) | ti(int,A) != zero_zero(int). [resolve(4975,a,4934,a)]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(4975,a,4936,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(4975,a,4937,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(4975,a,4938,a)]. 14.55/14.57 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),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))). [resolve(4975,a,4939,a)]. 14.55/14.57 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),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(4975,a,4940,a)]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))). [resolve(4975,a,4941,a)]. 14.55/14.57 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),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(4975,a,4942,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),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),B),A))). [resolve(4975,a,4943,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A))). [resolve(4975,a,4944,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(4975,a,4945,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),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(4975,a,4946,a)]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(4975,a,4947,a)]. 14.55/14.57 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(4975,a,4948,a)]. 14.55/14.57 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(4975,a,4949,a)]. 14.55/14.57 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)),B)). [resolve(4975,a,4950,a)]. 14.55/14.57 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),A),zero_zero(int))). [resolve(4975,a,4951,a)]. 14.55/14.57 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)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)). [resolve(4975,a,4952,a)]. 14.55/14.57 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)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))). [resolve(4975,a,4953,a)]. 14.55/14.57 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(4975,a,4954,a)]. 14.55/14.57 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(4975,a,4955,a)]. 14.55/14.57 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(4975,a,4956,a)]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(4975,a,4959,a)]. 14.55/14.57 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),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(4975,a,4960,a)]. 14.55/14.57 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),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(4975,a,4961,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(4975,a,4962,a)]. 14.55/14.57 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),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),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(4975,a,4963,a)]. 14.55/14.57 Derived: ti(int,A) != zero_zero(int) | ti(int,B) != 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),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)) = zero_zero(int). [resolve(4975,a,4965,a)]. 14.55/14.57 Derived: ti(int,A) = 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),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)) != zero_zero(int). [resolve(4975,a,4966,a)]. 14.55/14.57 Derived: ti(int,A) = 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). [resolve(4975,a,4967,a)]. 14.55/14.57 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(4975,a,4968,a)]. 14.55/14.57 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(4975,a,4969,a)]. 15.55/15.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B))). [resolve(4975,a,4970,a)]. 15.55/15.52 Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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)))). [resolve(4975,a,4971,a)]. 15.55/15.52 Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)))). [resolve(4975,a,4972,a)]. 15.55/15.52 Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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)))). [resolve(4975,a,4973,a)]. 15.55/15.52 4976 real_vector(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__vector) # label(axiom). [assumption]. 15.55/15.52 4977 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),zero_zero(real)),B) = zero_zero(A) # label(fact_4709_scaleR__left_Ozero) # label(axiom). [clausify(2)]. 15.55/15.52 4978 -real_vector(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(int,real,number_number_of(real),min_1)),B) # label(fact_4724_scaleR__minus1__left) # label(axiom). [clausify(63)]. 15.55/15.52 4979 -real_vector(A) | ti(A,B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),one_one(real)),B) # label(fact_4706_real__vector_Oscale__one) # label(axiom). [clausify(158)]. 15.55/15.52 4980 -real_vector(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) | C = D # label(fact_4705_scaleR__right__imp__eq) # label(axiom). [clausify(182)]. 15.55/15.52 4981 -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_4713_scaleR__left_Oadd) # label(axiom). [clausify(543)]. 15.55/15.52 4982 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),zero_zero(A)) = zero_zero(A) # label(fact_4702_scaleR__right_Ozero) # label(axiom). [clausify(592)]. 15.55/15.52 4983 -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_4711_real__vector_Oscale__left__distrib) # label(axiom). [clausify(625)]. 15.55/15.52 4984 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) # label(fact_4686_scaleR__minus__left) # label(axiom). [clausify(734)]. 15.55/15.52 4985 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | zero_zero(real) = B | ti(A,C) = ti(A,D) # label(fact_4700_scaleR__cancel__left) # label(axiom). [clausify(998)]. 15.55/15.52 4986 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | zero_zero(real) != B # label(fact_4700_scaleR__cancel__left) # label(axiom). [clausify(998)]. 15.55/15.52 4987 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) != ti(A,D) # label(fact_4700_scaleR__cancel__left) # label(axiom). [clausify(998)]. 16.25/16.28 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),zero_zero(real)),A) = zero_zero(complex). [resolve(4976,a,4977,a)]. 16.25/16.28 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(4976,a,4978,a)]. 16.25/16.28 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),one_one(real)),A). [resolve(4976,a,4979,a)]. 16.25/16.28 Derived: ti(complex,A) = zero_zero(complex) | 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) | B = C. [resolve(4976,a,4980,a)]. 16.25/16.28 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(4976,a,4981,a)]. 16.25/16.28 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(4976,a,4982,a)]. 16.25/16.28 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(4976,a,4984,a)]. 16.25/16.28 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) != hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | zero_zero(real) = A | ti(complex,B) = ti(complex,C). [resolve(4976,a,4985,a)]. 16.25/16.28 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | zero_zero(real) != A. [resolve(4976,a,4986,a)]. 16.25/16.28 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),C) | ti(complex,B) != ti(complex,C). [resolve(4976,a,4987,a)]. 16.25/16.28 4988 -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_4720_scaleR__right_Odiff) # label(axiom). [clausify(1989)]. 16.25/16.28 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(4988,a,4976,a)]. 16.25/16.28 4989 -real_vector(A) | zero_zero(real) = B | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) != hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D) | ti(A,C) = ti(A,D) # label(fact_4701_scaleR__left__imp__eq) # label(axiom). [clausify(2334)]. 16.25/16.28 4990 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4688_scaleR__minus__right) # label(axiom). [clausify(2431)]. 16.25/16.28 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(4990,a,4976,a)]. 16.25/16.28 4991 -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_4718_scaleR__right_Oadd) # label(axiom). [clausify(2944)]. 16.64/16.61 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(4991,a,4976,a)]. 16.64/16.61 4992 -real_vector(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) = zero_zero(A) # label(fact_4708_scaleR__eq__0__iff) # label(axiom). [clausify(3019)]. 16.64/16.61 Derived: ti(complex,A) != zero_zero(complex) | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),A) = zero_zero(complex). [resolve(4992,a,4976,a)]. 16.64/16.61 4993 -real_vector(A) | zero_zero(real) != B | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = zero_zero(A) # label(fact_4708_scaleR__eq__0__iff) # label(axiom). [clausify(3019)]. 16.64/16.61 Derived: zero_zero(real) != A | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = zero_zero(complex). [resolve(4993,a,4976,a)]. 16.64/16.61 4994 -real_vector(A) | ti(A,B) = zero_zero(A) | zero_zero(real) = C | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) != zero_zero(A) # label(fact_4708_scaleR__eq__0__iff) # label(axiom). [clausify(3019)]. 16.64/16.61 Derived: ti(complex,A) = zero_zero(complex) | zero_zero(real) = B | hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),B),A) != zero_zero(complex). [resolve(4994,a,4976,a)]. 16.64/16.61 4995 -real_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,real),fun(B,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(B,real),fun(B,fun(A,A))),combb(real,fun(A,A),B),scaleR_scaleR(A)),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),E)),D) # label(fact_4731_scaleR__left_Osetsum) # label(axiom). [clausify(3067)]. 16.64/16.61 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(4995,a,4976,a)]. 16.64/16.61 4996 -real_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(real,fun(A,A),scaleR_scaleR(A),C)),D)),E) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4730_scaleR__right_Osetsum) # label(axiom). [clausify(3172)]. 16.64/16.61 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(4996,a,4976,a)]. 16.64/16.61 4997 real_vector(real) # label(arity_RealDef_Oreal___RealVector_Oreal__vector) # label(axiom). [assumption]. 16.64/16.61 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),zero_zero(real)),A) = zero_zero(real). [resolve(4997,a,4977,a)]. 16.64/16.62 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(int,real,number_number_of(real),min_1)),A). [resolve(4997,a,4978,a)]. 16.64/16.62 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),one_one(real)),A). [resolve(4997,a,4979,a)]. 16.64/16.62 Derived: ti(real,A) = zero_zero(real) | 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) | B = C. [resolve(4997,a,4980,a)]. 16.64/16.62 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(4997,a,4981,a)]. 16.64/16.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),zero_zero(real)) = zero_zero(real). [resolve(4997,a,4982,a)]. 16.64/16.62 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(4997,a,4984,a)]. 16.64/16.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | zero_zero(real) = A | ti(real,B) = ti(real,C). [resolve(4997,a,4985,a)]. 16.64/16.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | zero_zero(real) != A. [resolve(4997,a,4986,a)]. 16.64/16.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),C) | ti(real,B) != ti(real,C). [resolve(4997,a,4987,a)]. 16.64/16.62 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(4997,a,4988,a)]. 16.64/16.62 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(4997,a,4990,a)]. 16.64/16.62 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(4997,a,4991,a)]. 16.64/16.62 Derived: ti(real,A) != zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),A) = zero_zero(real). [resolve(4997,a,4992,a)]. 16.64/16.62 Derived: zero_zero(real) != A | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = zero_zero(real). [resolve(4997,a,4993,a)]. 16.64/16.62 Derived: ti(real,A) = zero_zero(real) | zero_zero(real) = B | hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),A) != zero_zero(real). [resolve(4997,a,4994,a)]. 16.64/16.62 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(4997,a,4995,a)]. 16.64/16.62 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(4997,a,4996,a)]. 17.13/17.09 4998 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),D)) # label(fact_4694_scaleR__left__commute) # label(axiom). [clausify(3410)]. 17.13/17.09 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(4998,a,4976,a)]. 17.13/17.09 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(4998,a,4997,a)]. 17.13/17.09 4999 -real_vector(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,uminus_uminus(real),B)),C) # label(fact_4687_scaleR__left_Ominus) # label(axiom). [clausify(3590)]. 17.13/17.09 5000 -real_vector(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),D) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),D)) # label(fact_4672_real__vector_Oscale__scale) # label(axiom). [clausify(3600)]. 17.13/17.09 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(5000,a,4976,a)]. 17.13/17.09 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(5000,a,4997,a)]. 17.13/17.09 5001 -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_4704_scaleR__cancel__right) # label(axiom). [clausify(3618)]. 17.13/17.09 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(5001,a,4976,a)]. 17.13/17.09 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(5001,a,4997,a)]. 17.13/17.09 5002 -real_vector(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),C),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),D),B) # label(fact_4704_scaleR__cancel__right) # label(axiom). [clausify(3618)]. 17.13/17.09 Derived: ti(complex,A) != zero_zero(complex) | 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(5002,a,4976,a)]. 17.13/17.09 Derived: ti(real,A) != zero_zero(real) | 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(5002,a,4997,a)]. 17.13/17.09 5003 -real_vector(A) | B = C | ti(A,D) = zero_zero(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_4704_scaleR__cancel__right) # label(axiom). [clausify(3618)]. 17.13/17.09 5004 -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_4716_scaleR__left_Odiff) # label(axiom). [clausify(3766)]. 19.25/19.21 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(5004,a,4976,a)]. 19.25/19.21 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(5004,a,4997,a)]. 19.25/19.21 5005 -real_vector(A) | ti(fun(real,fun(A,A)),scaleR_scaleR(A)) = scaleR_scaleR(A) # label(tsy_c_RealVector_OscaleR__class_OscaleR_1_res) # label(axiom). [clausify(4324)]. 19.25/19.21 Derived: ti(fun(real,fun(complex,complex)),scaleR_scaleR(complex)) = scaleR_scaleR(complex). [resolve(5005,a,4976,a)]. 19.25/19.21 Derived: ti(fun(real,fun(real,real)),scaleR_scaleR(real)) = scaleR_scaleR(real). [resolve(5005,a,4997,a)]. 19.25/19.21 5006 -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_4714_scaleR__left__diff__distrib) # label(axiom). [clausify(4893)]. 19.25/19.21 5007 comm_monoid_mult(nat) # label(arity_Nat_Onat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 19.25/19.21 5008 -comm_monoid_mult(A) | -comm_monoid_add(A) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),C) # label(fact_4264_transfer__nat__int__sum__prod_I1_J) # label(axiom). [clausify(4)]. 19.25/19.21 5009 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),D)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_3959_setprod__constant) # label(axiom). [clausify(64)]. 19.25/19.21 Derived: -comm_monoid_add(nat) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),A),B). [resolve(5007,a,5008,a)]. 19.25/19.21 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(5007,a,5009,a)]. 19.25/19.21 5010 -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),f72(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3960_setprod__mono__one__left) # label(axiom). [clausify(364)]. 19.34/19.33 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),f72(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(5010,a,5007,a)]. 19.34/19.33 5011 -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,f72(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3960_setprod__mono__one__left) # label(axiom). [clausify(364)]. 19.34/19.33 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,f72(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(5011,a,5007,a)]. 19.34/19.33 5012 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f95(B,A,C,D)),D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_4772_setprod__1_H) # label(axiom). [clausify(454)]. 19.34/19.33 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5012,a,5007,a)]. 19.34/19.33 5013 -comm_monoid_mult(A) | one_one(A) != hAPP(B,A,C,f95(B,A,C,D)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D) # label(fact_4772_setprod__1_H) # label(axiom). [clausify(454)]. 19.34/19.33 Derived: one_one(nat) != hAPP(A,nat,B,f95(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(5013,a,5007,a)]. 19.34/19.33 5014 -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_3929_of__int__setprod) # label(axiom). [clausify(685)]. 19.34/19.33 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(5014,b,5007,a)]. 19.34/19.33 5015 -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)),f158(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),C) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(820)]. 19.34/19.33 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)),f158(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(5015,a,5007,a)]. 19.43/19.44 5016 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f158(A,E,D,C,B)) != hAPP(int,A,E,f158(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),E),C) # label(fact_3962_transfer__nat__int__sum__prod__cong_I2_J) # label(axiom). [clausify(820)]. 19.43/19.44 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f158(nat,D,C,B,A)) != hAPP(int,nat,D,f158(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(5016,a,5007,a)]. 19.43/19.44 5017 -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(1043)]. 19.43/19.44 Derived: big_co302546470etprod(A,nat) = ti(fun(fun(A,nat),fun(fun(A,bool),nat)),big_co302546470etprod(A,nat)). [resolve(5017,a,5007,a)]. 19.43/19.44 5018 -comm_monoid_mult(A) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),combk(A,B),one_one(A))),C) # label(fact_3947_setprod__1) # label(axiom). [clausify(1108)]. 19.43/19.44 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(5018,a,5007,a)]. 19.43/19.44 5019 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) # label(fact_3956_setprod__delta) # label(axiom). [clausify(1133)]. 19.43/19.44 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(5019,a,5007,a)]. 19.43/19.44 5020 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_3956_setprod__delta) # label(axiom). [clausify(1133)]. 19.65/19.62 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(5020,a,5007,a)]. 19.65/19.62 5021 -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),f269(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3961_setprod__mono__one__right) # label(axiom). [clausify(1382)]. 19.65/19.62 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),f269(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(5021,a,5007,a)]. 19.65/19.62 5022 -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,f269(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D) # label(fact_3961_setprod__mono__one__right) # label(axiom). [clausify(1382)]. 19.65/19.62 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,f269(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(5022,a,5007,a)]. 19.65/19.62 5023 -dvd(A) | -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(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C))) # label(fact_3958_setprod__dvd__setprod__subset) # label(axiom). [clausify(1421)]. 19.65/19.62 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(5023,b,5007,a)]. 19.65/19.62 5024 comm_monoid_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 19.65/19.62 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),A),B). [resolve(5024,a,5008,a)]. 19.65/19.63 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(5024,a,5009,a)]. 19.65/19.63 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),f72(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(5024,a,5010,a)]. 19.65/19.63 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,f72(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(5024,a,5011,a)]. 19.65/19.63 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5024,a,5012,a)]. 19.65/19.63 Derived: one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,B,f95(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(5024,a,5013,a)]. 19.65/19.63 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(5024,a,5014,b)]. 19.65/19.63 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)),f158(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(5024,a,5015,a)]. 19.65/19.64 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,f158(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f158(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(5024,a,5016,a)]. 19.65/19.64 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(5024,a,5017,a)]. 19.65/19.64 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(5024,a,5018,a)]. 19.65/19.64 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(5024,a,5019,a)]. 19.65/19.64 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(5024,a,5020,a)]. 19.84/19.82 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),f269(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(5024,a,5021,a)]. 19.84/19.82 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(quickcheck_code_int) != hAPP(A,quickcheck_code_int,D,f269(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(5024,a,5022,a)]. 19.84/19.82 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(5024,a,5023,b)]. 19.84/19.82 5025 -comm_monoid_mult(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)) # label(fact_3946_setprod__timesf) # label(axiom). [clausify(1866)]. 19.84/19.82 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(5025,a,5007,a)]. 19.84/19.82 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(5025,a,5024,a)]. 20.04/20.03 5026 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D)),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C)) # label(fact_3954_setprod_Odistrib) # label(axiom). [clausify(1964)]. 20.04/20.03 5027 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_799_mult_Ocomm__neutral) # label(axiom). [clausify(2077)]. 20.04/20.03 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),one_one(nat)). [resolve(5027,a,5007,a)]. 20.04/20.03 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(5027,a,5024,a)]. 20.04/20.03 5028 comm_monoid_mult(rat) # label(arity_Rat_Orat___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 20.04/20.03 Derived: -comm_monoid_add(rat) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),B). [resolve(5028,a,5008,a)]. 20.04/20.03 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(5028,a,5009,a)]. 20.04/20.03 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),f72(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(5028,a,5010,a)]. 20.04/20.03 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,f72(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(5028,a,5011,a)]. 20.04/20.03 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5028,a,5012,a)]. 20.04/20.03 Derived: one_one(rat) != hAPP(A,rat,B,f95(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(5028,a,5013,a)]. 20.04/20.03 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(5028,a,5014,b)]. 20.04/20.04 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)),f158(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(5028,a,5015,a)]. 20.04/20.04 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f158(rat,D,C,B,A)) != hAPP(int,rat,D,f158(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(5028,a,5016,a)]. 20.04/20.04 Derived: big_co302546470etprod(A,rat) = ti(fun(fun(A,rat),fun(fun(A,bool),rat)),big_co302546470etprod(A,rat)). [resolve(5028,a,5017,a)]. 20.04/20.04 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(5028,a,5018,a)]. 20.04/20.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5028,a,5019,a)]. 20.04/20.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5028,a,5020,a)]. 20.04/20.04 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),f269(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(5028,a,5021,a)]. 20.04/20.04 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,f269(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(5028,a,5022,a)]. 20.04/20.04 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(5028,a,5023,b)]. 20.04/20.07 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(5028,a,5025,a)]. 20.04/20.07 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),one_one(rat)). [resolve(5028,a,5027,a)]. 20.04/20.07 5029 -dvd(A) | -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f421(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4427_setprod__dvd__setprod) # label(axiom). [clausify(2231)]. 20.04/20.07 Derived: -dvd(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(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(5029,b,5007,a)]. 20.04/20.07 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(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(5029,b,5024,a)]. 20.04/20.07 Derived: -dvd(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(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(5029,b,5028,a)]. 20.04/20.07 5030 -dvd(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,C,f421(B,A,C,D,E))),hAPP(B,A,D,f421(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4427_setprod__dvd__setprod) # label(axiom). [clausify(2231)]. 20.04/20.07 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(A,nat,B,f421(A,nat,B,C,D))),hAPP(A,nat,C,f421(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(5030,b,5007,a)]. 20.04/20.07 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,f421(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f421(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(5030,b,5024,a)]. 20.35/20.38 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,B,f421(A,rat,B,C,D))),hAPP(A,rat,C,f421(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(5030,b,5028,a)]. 20.35/20.38 5031 -comm_monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_801_mult__1) # label(axiom). [clausify(2271)]. 20.35/20.38 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),one_one(nat)),A). [resolve(5031,a,5007,a)]. 20.35/20.38 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(5031,a,5024,a)]. 20.35/20.38 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),one_one(rat)),A). [resolve(5031,a,5028,a)]. 20.35/20.38 5032 -comm_monoid_mult(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),C),B) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) # label(fact_4266_transfer__int__nat__sum__prod_I1_J) # label(axiom). [clausify(2480)]. 20.35/20.38 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co1399186613setsum(int,nat),B),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5032,a,5007,a)]. 20.35/20.38 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co1399186613setsum(int,quickcheck_code_int),B),A) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5032,a,5024,a)]. 20.35/20.38 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co1399186613setsum(int,rat),B),A) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5032,a,5028,a)]. 20.35/20.38 5033 -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),f488(B,A,D,C)),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_4148_setprod_Oneutral) # label(axiom). [clausify(2644)]. 20.55/20.53 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),f488(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(5033,a,5007,a)]. 20.55/20.53 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),f488(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(5033,a,5024,a)]. 20.55/20.53 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),f488(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(5033,a,5028,a)]. 20.55/20.53 5034 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) != hAPP(B,A,D,f488(B,A,D,C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_4148_setprod_Oneutral) # label(axiom). [clausify(2644)]. 20.55/20.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(nat) != hAPP(A,nat,C,f488(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(5034,a,5007,a)]. 20.55/20.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(quickcheck_code_int) != hAPP(A,quickcheck_code_int,C,f488(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(5034,a,5024,a)]. 20.55/20.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(rat) != hAPP(A,rat,C,f488(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(5034,a,5028,a)]. 20.55/20.53 5035 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) = hAPP(B,A,E,D) # label(fact_3955_setprod__delta_H) # label(axiom). [clausify(2836)]. 20.55/20.53 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(5035,a,5007,a)]. 20.55/20.53 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(5035,a,5024,a)]. 20.55/20.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(fun(A,bool),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(5035,a,5028,a)]. 20.55/20.54 5036 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),fequal(B),D))),E)),one_one(A))),C) # label(fact_3955_setprod__delta_H) # label(axiom). [clausify(2836)]. 20.55/20.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5036,a,5007,a)]. 20.55/20.54 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5036,a,5024,a)]. 20.65/20.63 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(rat) = hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(A,fun(rat,fun(rat,rat))),fun(fun(A,rat),fun(A,fun(rat,rat))),combs(A,rat,fun(rat,rat)),hAPP(fun(A,bool),fun(A,fun(rat,fun(rat,rat))),hAPP(fun(bool,fun(rat,fun(rat,rat))),fun(fun(A,bool),fun(A,fun(rat,fun(rat,rat)))),combb(bool,fun(rat,fun(rat,rat)),A),if(rat)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(rat))),B). [resolve(5036,a,5028,a)]. 20.65/20.63 5037 -comm_monoid_add(A) | -comm_monoid_mult(A) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),hAPP(fun(int,nat),fun(int,A),hAPP(fun(nat,A),fun(fun(int,nat),fun(int,A)),combb(nat,A,int),B),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),C)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),B),C) # label(fact_3944_transfer__nat__int__sum__prod_I2_J) # label(axiom). [clausify(2903)]. 20.65/20.63 Derived: -comm_monoid_add(nat) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),hAPP(fun(int,nat),fun(int,nat),hAPP(fun(nat,nat),fun(fun(int,nat),fun(int,nat)),combb(nat,nat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),A),B). [resolve(5037,b,5007,a)]. 20.65/20.63 Derived: -comm_monoid_add(quickcheck_code_int) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),hAPP(fun(int,nat),fun(int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(int,nat),fun(int,quickcheck_code_int)),combb(nat,quickcheck_code_int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),A),B). [resolve(5037,b,5024,a)]. 20.65/20.63 Derived: -comm_monoid_add(rat) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),hAPP(fun(int,nat),fun(int,rat),hAPP(fun(nat,rat),fun(fun(int,nat),fun(int,rat)),combb(nat,rat,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),A),B). [resolve(5037,b,5028,a)]. 20.65/20.63 5038 -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)),f538(A,D,E,C,B))) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),C) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(2957)]. 20.65/20.63 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)),f538(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(5038,a,5007,a)]. 20.65/20.63 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)),f538(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(5038,a,5024,a)]. 20.74/20.76 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)),f538(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(5038,a,5028,a)]. 20.74/20.76 5039 -comm_monoid_mult(A) | -comm_monoid_add(A) | B != C | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(int,A,D,f538(A,E,D,C,B)) != hAPP(int,A,E,f538(A,E,D,C,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),D),B) = hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co1399186613setsum(int,A),E),C) # label(fact_4297_transfer__nat__int__sum__prod__cong_I1_J) # label(axiom). [clausify(2957)]. 20.74/20.76 Derived: -comm_monoid_add(nat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,nat,C,f538(nat,D,C,B,A)) != hAPP(int,nat,D,f538(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(5039,a,5007,a)]. 20.74/20.76 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,f538(quickcheck_code_int,D,C,B,A)) != hAPP(int,quickcheck_code_int,D,f538(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(5039,a,5024,a)]. 20.74/20.76 Derived: -comm_monoid_add(rat) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,rat,C,f538(rat,D,C,B,A)) != hAPP(int,rat,D,f538(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(5039,a,5028,a)]. 20.74/20.76 5040 -comm_monoid_add(A) | -comm_monoid_mult(A) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,B)) | hAPP(fun(int,bool),A,hAPP(fun(int,A),fun(fun(int,bool),A),big_co302546470etprod(int,A),C),B) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co302546470etprod(nat,A),hAPP(fun(nat,int),fun(nat,A),hAPP(fun(int,A),fun(fun(nat,int),fun(nat,A)),combb(int,A,nat),C),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),B)) # label(fact_3945_transfer__int__nat__sum__prod_I2_J) # label(axiom). [clausify(3099)]. 20.74/20.76 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),nat,hAPP(fun(int,nat),fun(fun(int,bool),nat),big_co302546470etprod(int,nat),B),A) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co302546470etprod(nat,nat),hAPP(fun(nat,int),fun(nat,nat),hAPP(fun(int,nat),fun(fun(nat,int),fun(nat,nat)),combb(int,nat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5040,b,5007,a)]. 20.74/20.76 Derived: -comm_monoid_add(quickcheck_code_int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),quickcheck_code_int,hAPP(fun(int,quickcheck_code_int),fun(fun(int,bool),quickcheck_code_int),big_co302546470etprod(int,quickcheck_code_int),B),A) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co302546470etprod(nat,quickcheck_code_int),hAPP(fun(nat,int),fun(nat,quickcheck_code_int),hAPP(fun(int,quickcheck_code_int),fun(fun(nat,int),fun(nat,quickcheck_code_int)),combb(int,quickcheck_code_int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5040,b,5024,a)]. 21.33/21.34 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),rat,hAPP(fun(int,rat),fun(fun(int,bool),rat),big_co302546470etprod(int,rat),B),A) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co302546470etprod(nat,rat),hAPP(fun(nat,int),fun(nat,rat),hAPP(fun(int,rat),fun(fun(nat,int),fun(nat,rat)),combb(int,rat,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5040,b,5028,a)]. 21.33/21.34 5041 comm_monoid_mult(int) # label(arity_Int_Oint___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 21.33/21.34 Derived: -comm_monoid_add(int) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),B). [resolve(5041,a,5008,a)]. 21.33/21.34 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(5041,a,5009,a)]. 21.33/21.34 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),f72(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(5041,a,5010,a)]. 21.33/21.34 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,f72(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(5041,a,5011,a)]. 21.33/21.34 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5041,a,5012,a)]. 21.33/21.34 Derived: one_one(int) != hAPP(A,int,B,f95(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(5041,a,5013,a)]. 21.33/21.34 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(5041,a,5014,b)]. 21.33/21.34 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)),f158(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(5041,a,5015,a)]. 21.33/21.35 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f158(int,D,C,B,A)) != hAPP(int,int,D,f158(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(5041,a,5016,a)]. 21.33/21.35 Derived: big_co302546470etprod(A,int) = ti(fun(fun(A,int),fun(fun(A,bool),int)),big_co302546470etprod(A,int)). [resolve(5041,a,5017,a)]. 21.33/21.35 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(5041,a,5018,a)]. 21.33/21.35 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(5041,a,5019,a)]. 21.33/21.35 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(5041,a,5020,a)]. 21.33/21.35 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),f269(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(5041,a,5021,a)]. 21.33/21.35 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,f269(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(5041,a,5022,a)]. 21.33/21.35 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(5041,a,5023,b)]. 21.33/21.35 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),D)). [resolve(5041,a,5025,a)]. 21.33/21.35 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),one_one(int)). [resolve(5041,a,5027,a)]. 21.33/21.35 Derived: -dvd(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(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(5041,a,5029,b)]. 21.33/21.35 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(A,int,B,f421(A,int,B,C,D))),hAPP(A,int,C,f421(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(5041,a,5030,b)]. 21.33/21.35 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),one_one(int)),A). [resolve(5041,a,5031,a)]. 21.33/21.35 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co1399186613setsum(int,int),B),A) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5041,a,5032,a)]. 21.33/21.35 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),f488(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(5041,a,5033,a)]. 21.33/21.35 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(int) != hAPP(A,int,C,f488(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(5041,a,5034,a)]. 21.33/21.35 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(5041,a,5035,a)]. 21.33/21.35 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(5041,a,5036,a)]. 21.33/21.35 Derived: -comm_monoid_add(int) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),hAPP(fun(int,nat),fun(int,int),hAPP(fun(nat,int),fun(fun(int,nat),fun(int,int)),combb(nat,int,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),A),B). [resolve(5041,a,5037,b)]. 21.45/21.42 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)),f538(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(5041,a,5038,a)]. 21.45/21.42 Derived: -comm_monoid_add(int) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,int,C,f538(int,D,C,B,A)) != hAPP(int,int,D,f538(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(5041,a,5039,a)]. 21.45/21.42 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),int,hAPP(fun(int,int),fun(fun(int,bool),int),big_co302546470etprod(int,int),B),A) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co302546470etprod(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(int,int),fun(fun(nat,int),fun(nat,int)),combb(int,int,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5041,a,5040,b)]. 21.45/21.42 5042 -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),f627(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_4769_setprod_Ocong) # label(axiom). [clausify(3581)]. 21.45/21.42 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),f627(A,nat,C,D,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),D),B) = hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B). [resolve(5042,a,5007,a)]. 21.45/21.42 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),f627(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(5042,a,5024,a)]. 21.45/21.42 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),f627(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(5042,a,5028,a)]. 21.45/21.42 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),f627(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(5042,a,5041,a)]. 21.45/21.42 5043 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f627(B,A,E,D,C)) != hAPP(B,A,E,f627(B,A,E,D,C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C) # label(fact_4769_setprod_Ocong) # label(axiom). [clausify(3581)]. 21.55/21.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f627(A,nat,D,C,B)) != hAPP(A,nat,D,f627(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(5043,a,5007,a)]. 21.55/21.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f627(A,quickcheck_code_int,D,C,B)) != hAPP(A,quickcheck_code_int,D,f627(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(5043,a,5024,a)]. 21.55/21.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f627(A,rat,D,C,B)) != hAPP(A,rat,D,f627(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(5043,a,5028,a)]. 21.55/21.53 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f627(A,int,D,C,B)) != hAPP(A,int,D,f627(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(5043,a,5041,a)]. 21.55/21.53 5044 -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,f638(C,A,D,E,F,B)),f640(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),f642(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(3686)]. 21.55/21.53 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,f638(B,nat,C,D,E,A)),f640(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),f642(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(5044,a,5007,a)]. 21.55/21.53 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,f638(B,quickcheck_code_int,C,D,E,A)),f640(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),f642(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(5044,a,5024,a)]. 21.55/21.53 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,f638(B,rat,C,D,E,A)),f640(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),f642(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(5044,a,5028,a)]. 21.55/21.53 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,f638(B,int,C,D,E,A)),f640(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),f642(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(5044,a,5041,a)]. 21.55/21.53 5045 -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,f638(C,A,D,E,F,B)),f640(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,f642(C,A,D,E,F,B))),hAPP(C,A,E,f642(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(3686)]. 21.55/21.53 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,f638(B,nat,C,D,E,A)),f640(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,f642(B,nat,C,D,E,A))),hAPP(B,nat,D,f642(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(5045,a,5007,a)]. 21.55/21.53 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,f638(B,quickcheck_code_int,C,D,E,A)),f640(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,f642(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f642(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(5045,a,5024,a)]. 21.55/21.53 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,f638(B,rat,C,D,E,A)),f640(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,f642(B,rat,C,D,E,A))),hAPP(B,rat,D,f642(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(5045,a,5028,a)]. 21.55/21.53 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,f638(B,int,C,D,E,A)),f640(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,f642(B,int,C,D,E,A))),hAPP(B,int,D,f642(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(5045,a,5041,a)]. 21.55/21.54 5046 -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,f639(C,A,D,E,F,B)),f641(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),f642(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(3686)]. 21.55/21.54 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,f639(B,nat,C,D,E,A)),f641(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),f642(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(5046,a,5007,a)]. 21.55/21.54 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,f639(B,quickcheck_code_int,C,D,E,A)),f641(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),f642(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(5046,a,5024,a)]. 21.55/21.54 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,f639(B,rat,C,D,E,A)),f641(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),f642(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(5046,a,5028,a)]. 21.55/21.54 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,f639(B,int,C,D,E,A)),f641(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),f642(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(5046,a,5041,a)]. 21.55/21.54 5047 -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,f639(C,A,D,E,F,B)),f641(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,f642(C,A,D,E,F,B))),hAPP(C,A,E,f642(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(3686)]. 21.55/21.54 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,f639(B,nat,C,D,E,A)),f641(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,f642(B,nat,C,D,E,A))),hAPP(B,nat,D,f642(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(5047,a,5007,a)]. 21.55/21.54 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,f639(B,quickcheck_code_int,C,D,E,A)),f641(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,f642(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f642(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(5047,a,5024,a)]. 21.55/21.54 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,f639(B,rat,C,D,E,A)),f641(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,f642(B,rat,C,D,E,A))),hAPP(B,rat,D,f642(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(5047,a,5028,a)]. 21.55/21.54 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,f639(B,int,C,D,E,A)),f641(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,f642(B,int,C,D,E,A))),hAPP(B,int,D,f642(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(5047,a,5041,a)]. 21.55/21.54 5048 -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),f638(C,A,D,E,F,B)),f639(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f640(C,A,D,E,F,B)),f641(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),f642(C,A,D,E,F,B)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(3686)]. 21.55/21.54 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),f638(B,nat,C,D,E,A)),f639(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f640(B,nat,C,D,E,A)),f641(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),f642(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(5048,a,5007,a)]. 21.55/21.55 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),f638(B,quickcheck_code_int,C,D,E,A)),f639(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),f640(B,quickcheck_code_int,C,D,E,A)),f641(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),f642(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(5048,a,5024,a)]. 21.55/21.55 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),f638(B,rat,C,D,E,A)),f639(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f640(B,rat,C,D,E,A)),f641(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),f642(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(5048,a,5028,a)]. 21.55/21.55 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),f638(B,int,C,D,E,A)),f639(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f640(B,int,C,D,E,A)),f641(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),f642(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(5048,a,5041,a)]. 21.55/21.55 5049 -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),f638(C,A,D,E,F,B)),f639(C,A,D,E,F,B))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),f640(C,A,D,E,F,B)),f641(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,f642(C,A,D,E,F,B))),hAPP(C,A,E,f642(C,A,D,E,F,B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),B,hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),D),F)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co302546470etprod(C,A),E),F))) # label(fact_4779_setprod_Orelated) # label(axiom). [clausify(3686)]. 21.55/21.55 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),f638(B,nat,C,D,E,A)),f639(B,nat,C,D,E,A))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),f640(B,nat,C,D,E,A)),f641(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,f642(B,nat,C,D,E,A))),hAPP(B,nat,D,f642(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(5049,a,5007,a)]. 21.74/21.71 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),f638(B,quickcheck_code_int,C,D,E,A)),f639(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),f640(B,quickcheck_code_int,C,D,E,A)),f641(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,f642(B,quickcheck_code_int,C,D,E,A))),hAPP(B,quickcheck_code_int,D,f642(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(5049,a,5024,a)]. 21.74/21.71 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),f638(B,rat,C,D,E,A)),f639(B,rat,C,D,E,A))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),f640(B,rat,C,D,E,A)),f641(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,f642(B,rat,C,D,E,A))),hAPP(B,rat,D,f642(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(5049,a,5028,a)]. 21.74/21.71 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),f638(B,int,C,D,E,A)),f639(B,int,C,D,E,A))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),f640(B,int,C,D,E,A)),f641(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,f642(B,int,C,D,E,A))),hAPP(B,int,D,f642(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(5049,a,5041,a)]. 21.74/21.71 5050 -comm_monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(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(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_330_power__mult__distrib) # label(axiom). [clausify(3827)]. 21.74/21.71 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(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),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C)). [resolve(5050,a,5007,a)]. 21.94/21.97 Derived: 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),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(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(5050,a,5024,a)]. 21.94/21.97 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(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(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(5050,a,5028,a)]. 21.94/21.97 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(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(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(5050,a,5041,a)]. 21.94/21.97 5051 comm_monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 21.94/21.97 Derived: -comm_monoid_add(real) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),B). [resolve(5051,a,5008,a)]. 21.94/21.97 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(5051,a,5009,a)]. 21.94/21.97 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),f72(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(5051,a,5010,a)]. 21.94/21.97 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)) | one_one(real) != hAPP(A,real,D,f72(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(5051,a,5011,a)]. 21.94/21.97 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5051,a,5012,a)]. 21.94/21.97 Derived: one_one(real) != hAPP(A,real,B,f95(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(5051,a,5013,a)]. 21.94/21.97 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(5051,a,5014,b)]. 21.94/21.97 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)),f158(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(5051,a,5015,a)]. 21.94/21.97 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f158(real,D,C,B,A)) != hAPP(int,real,D,f158(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(5051,a,5016,a)]. 21.94/21.97 Derived: big_co302546470etprod(A,real) = ti(fun(fun(A,real),fun(fun(A,bool),real)),big_co302546470etprod(A,real)). [resolve(5051,a,5017,a)]. 21.94/21.97 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(5051,a,5018,a)]. 21.94/21.97 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(5051,a,5019,a)]. 21.94/21.97 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(5051,a,5020,a)]. 21.94/21.97 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),f269(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(5051,a,5021,a)]. 21.94/21.97 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)) | one_one(real) != hAPP(A,real,D,f269(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(5051,a,5022,a)]. 21.94/21.97 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(5051,a,5023,b)]. 21.94/21.98 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(5051,a,5025,a)]. 21.94/21.98 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),one_one(real)). [resolve(5051,a,5027,a)]. 21.94/21.98 Derived: -dvd(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(A,real,B,C,D)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),D))). [resolve(5051,a,5029,b)]. 21.94/21.98 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,B,f421(A,real,B,C,D))),hAPP(A,real,C,f421(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(5051,a,5030,b)]. 21.94/21.98 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),one_one(real)),A). [resolve(5051,a,5031,a)]. 21.94/21.98 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co1399186613setsum(int,real),B),A) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5051,a,5032,a)]. 21.94/21.98 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),f488(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(5051,a,5033,a)]. 21.94/21.98 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(real) != hAPP(A,real,C,f488(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(5051,a,5034,a)]. 21.94/21.98 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)) | 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(5051,a,5035,a)]. 21.94/21.98 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)) | 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(5051,a,5036,a)]. 21.94/21.98 Derived: -comm_monoid_add(real) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),hAPP(fun(int,nat),fun(int,real),hAPP(fun(nat,real),fun(fun(int,nat),fun(int,real)),combb(nat,real,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),A),B). [resolve(5051,a,5037,b)]. 21.94/21.98 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)),f538(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(5051,a,5038,a)]. 21.94/21.98 Derived: -comm_monoid_add(real) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,real,C,f538(real,D,C,B,A)) != hAPP(int,real,D,f538(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(5051,a,5039,a)]. 21.94/21.98 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),real,hAPP(fun(int,real),fun(fun(int,bool),real),big_co302546470etprod(int,real),B),A) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co302546470etprod(nat,real),hAPP(fun(nat,int),fun(nat,real),hAPP(fun(int,real),fun(fun(nat,int),fun(nat,real)),combb(int,real,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5051,a,5040,b)]. 21.94/21.98 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),f627(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(5051,a,5042,a)]. 21.94/21.98 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f627(A,real,D,C,B)) != hAPP(A,real,D,f627(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(5051,a,5043,a)]. 21.94/21.98 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,f638(B,real,C,D,E,A)),f640(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),f642(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(5051,a,5044,a)]. 21.94/21.98 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,f638(B,real,C,D,E,A)),f640(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,f642(B,real,C,D,E,A))),hAPP(B,real,D,f642(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(5051,a,5045,a)]. 22.45/22.43 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,f639(B,real,C,D,E,A)),f641(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),f642(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(5051,a,5046,a)]. 22.45/22.43 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,f639(B,real,C,D,E,A)),f641(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,f642(B,real,C,D,E,A))),hAPP(B,real,D,f642(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(5051,a,5047,a)]. 22.45/22.43 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),f638(B,real,C,D,E,A)),f639(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f640(B,real,C,D,E,A)),f641(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),f642(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(5051,a,5048,a)]. 22.45/22.43 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),f638(B,real,C,D,E,A)),f639(B,real,C,D,E,A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),f640(B,real,C,D,E,A)),f641(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,f642(B,real,C,D,E,A))),hAPP(B,real,D,f642(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(5051,a,5049,a)]. 22.45/22.43 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(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(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(5051,a,5050,a)]. 22.45/22.43 5052 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_3952_setprod_Oinfinite) # label(axiom). [clausify(4408)]. 22.45/22.43 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(5052,a,5007,a)]. 22.54/22.59 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(5052,a,5024,a)]. 22.54/22.59 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(5052,a,5028,a)]. 22.54/22.59 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(5052,a,5041,a)]. 22.54/22.59 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(5052,a,5051,a)]. 22.54/22.59 5053 comm_monoid_mult(complex) # label(arity_Complex_Ocomplex___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 22.54/22.59 Derived: -comm_monoid_add(complex) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),B). [resolve(5053,a,5008,a)]. 22.54/22.59 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(5053,a,5009,a)]. 22.54/22.59 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),f72(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(5053,a,5010,a)]. 22.54/22.59 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)) | one_one(complex) != hAPP(A,complex,D,f72(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(5053,a,5011,a)]. 22.54/22.59 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5053,a,5012,a)]. 22.54/22.59 Derived: one_one(complex) != hAPP(A,complex,B,f95(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(5053,a,5013,a)]. 22.54/22.59 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(5053,a,5014,b)]. 22.54/22.59 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)),f158(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(5053,a,5015,a)]. 22.63/22.59 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f158(complex,D,C,B,A)) != hAPP(int,complex,D,f158(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(5053,a,5016,a)]. 22.63/22.59 Derived: big_co302546470etprod(A,complex) = ti(fun(fun(A,complex),fun(fun(A,bool),complex)),big_co302546470etprod(A,complex)). [resolve(5053,a,5017,a)]. 22.63/22.59 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(5053,a,5018,a)]. 22.63/22.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5053,a,5019,a)]. 22.63/22.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5053,a,5020,a)]. 22.63/22.59 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),f269(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(5053,a,5021,a)]. 22.63/22.59 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)) | one_one(complex) != hAPP(A,complex,D,f269(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(5053,a,5022,a)]. 22.63/22.59 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(5053,a,5023,b)]. 22.63/22.59 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(5053,a,5025,a)]. 22.63/22.59 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),one_one(complex)). [resolve(5053,a,5027,a)]. 22.63/22.59 Derived: -dvd(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(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(5053,a,5029,b)]. 22.63/22.59 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(A,complex,B,f421(A,complex,B,C,D))),hAPP(A,complex,C,f421(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(5053,a,5030,b)]. 22.63/22.59 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),one_one(complex)),A). [resolve(5053,a,5031,a)]. 22.63/22.59 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co1399186613setsum(int,complex),B),A) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5053,a,5032,a)]. 22.63/22.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f488(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(5053,a,5033,a)]. 22.63/22.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(complex) != hAPP(A,complex,C,f488(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(5053,a,5034,a)]. 22.63/22.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(5053,a,5035,a)]. 22.63/22.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | one_one(complex) = hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(A,fun(complex,fun(complex,complex))),fun(fun(A,complex),fun(A,fun(complex,complex))),combs(A,complex,fun(complex,complex)),hAPP(fun(A,bool),fun(A,fun(complex,fun(complex,complex))),hAPP(fun(bool,fun(complex,fun(complex,complex))),fun(fun(A,bool),fun(A,fun(complex,fun(complex,complex)))),combb(bool,fun(complex,fun(complex,complex)),A),if(complex)),hAPP(A,fun(A,bool),fequal(A),C))),D)),one_one(complex))),B). [resolve(5053,a,5036,a)]. 22.63/22.60 Derived: -comm_monoid_add(complex) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),hAPP(fun(int,nat),fun(int,complex),hAPP(fun(nat,complex),fun(fun(int,nat),fun(int,complex)),combb(nat,complex,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),A),B). [resolve(5053,a,5037,b)]. 22.63/22.60 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)),f538(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(5053,a,5038,a)]. 22.63/22.60 Derived: -comm_monoid_add(complex) | A != B | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(int,complex,C,f538(complex,D,C,B,A)) != hAPP(int,complex,D,f538(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(5053,a,5039,a)]. 22.63/22.60 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),complex,hAPP(fun(int,complex),fun(fun(int,bool),complex),big_co302546470etprod(int,complex),B),A) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co302546470etprod(nat,complex),hAPP(fun(nat,int),fun(nat,complex),hAPP(fun(int,complex),fun(fun(nat,int),fun(nat,complex)),combb(int,complex,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5053,a,5040,b)]. 22.63/22.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f627(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(5053,a,5042,a)]. 22.63/22.60 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f627(A,complex,D,C,B)) != hAPP(A,complex,D,f627(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(5053,a,5043,a)]. 22.64/22.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f638(B,complex,C,D,E,A)),f640(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),f642(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(5053,a,5044,a)]. 22.64/22.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f638(B,complex,C,D,E,A)),f640(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,f642(B,complex,C,D,E,A))),hAPP(B,complex,D,f642(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(5053,a,5045,a)]. 22.64/22.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f639(B,complex,C,D,E,A)),f641(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),f642(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(5053,a,5046,a)]. 22.64/22.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,f639(B,complex,C,D,E,A)),f641(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,f642(B,complex,C,D,E,A))),hAPP(B,complex,D,f642(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(5053,a,5047,a)]. 22.64/22.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f638(B,complex,C,D,E,A)),f639(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f640(B,complex,C,D,E,A)),f641(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),f642(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(5053,a,5048,a)]. 22.64/22.60 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,one_one(complex)),one_one(complex))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f638(B,complex,C,D,E,A)),f639(B,complex,C,D,E,A))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),f640(B,complex,C,D,E,A)),f641(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,f642(B,complex,C,D,E,A))),hAPP(B,complex,D,f642(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(5053,a,5049,a)]. 22.76/22.72 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(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(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(5053,a,5050,a)]. 22.76/22.72 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(5053,a,5052,a)]. 22.76/22.72 5054 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(fun(B,bool),nat,finite_card(B),C)) # label(fact_3936_setprod__gen__delta) # label(axiom). [clausify(4622)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5054,a,5007,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5054,a,5024,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5054,a,5028,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5054,a,5041,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5054,a,5051,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5054,a,5053,a)]. 22.76/22.72 5055 -comm_monoid_mult(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(B,fun(A,fun(A,A))),fun(fun(B,A),fun(B,fun(A,A))),combs(B,A,fun(A,A)),hAPP(fun(B,bool),fun(B,fun(A,fun(A,A))),hAPP(fun(bool,fun(A,fun(A,A))),fun(fun(B,bool),fun(B,fun(A,fun(A,A)))),combb(bool,fun(A,fun(A,A)),B),if(A)),hAPP(B,fun(B,bool),hAPP(fun(B,fun(B,bool)),fun(B,fun(B,bool)),combc(B,B,bool),fequal(B)),D))),E)),F)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(B,A,E,D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),F),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(fun(B,bool),nat,finite_card(B),C)),one_one(nat)))) # label(fact_3936_setprod__gen__delta) # label(axiom). [clausify(4622)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5055,a,5007,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5055,a,5024,a)]. 22.76/22.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(5055,a,5028,a)]. 22.76/22.76 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)) | 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(5055,a,5041,a)]. 22.76/22.76 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)) | 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(5055,a,5051,a)]. 22.76/22.76 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)) | 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(5055,a,5053,a)]. 22.76/22.76 5056 comm_monoid_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocomm__monoid__mult) # label(axiom). [assumption]. 22.76/22.76 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),A),B). [resolve(5056,a,5008,a)]. 22.76/22.76 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(5056,a,5009,a)]. 22.76/22.76 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),f72(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(5056,a,5010,a)]. 22.76/22.76 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,f72(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(5056,a,5011,a)]. 22.76/22.76 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f95(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(5056,a,5012,a)]. 22.76/22.76 Derived: one_one(code_code_numeral) != hAPP(A,code_code_numeral,B,f95(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(5056,a,5013,a)]. 22.76/22.76 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(5056,a,5014,b)]. 22.76/22.76 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)),f158(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(5056,a,5015,a)]. 22.76/22.76 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,f158(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f158(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(5056,a,5016,a)]. 22.76/22.76 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(5056,a,5017,a)]. 22.76/22.76 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(5056,a,5018,a)]. 22.76/22.76 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)) | 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(5056,a,5019,a)]. 22.76/22.76 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)) | 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(5056,a,5020,a)]. 22.76/22.76 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),f269(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(5056,a,5021,a)]. 22.76/22.76 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,f269(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(5056,a,5022,a)]. 22.76/22.76 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(5056,a,5023,b)]. 22.76/22.76 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(5056,a,5025,a)]. 22.76/22.76 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(5056,a,5027,a)]. 22.76/22.76 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f421(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(5056,a,5029,b)]. 22.76/22.76 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,f421(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f421(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(5056,a,5030,b)]. 22.76/22.76 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(5056,a,5031,a)]. 22.76/22.76 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co1399186613setsum(int,code_code_numeral),B),A) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5056,a,5032,a)]. 22.76/22.76 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),f488(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(5056,a,5033,a)]. 22.76/22.76 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | one_one(code_code_numeral) != hAPP(A,code_code_numeral,C,f488(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(5056,a,5034,a)]. 22.76/22.76 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)) | 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(5056,a,5035,a)]. 22.76/22.76 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)) | 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(5056,a,5036,a)]. 22.76/22.76 Derived: -comm_monoid_add(code_code_numeral) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),hAPP(fun(int,nat),fun(int,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(int,nat),fun(int,code_code_numeral)),combb(nat,code_code_numeral,int),A),nat_1)),hAPP(fun(nat,bool),fun(int,bool),hAPP(fun(nat,int),fun(fun(nat,bool),fun(int,bool)),image(nat,int),semiring_1_of_nat(int)),B)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),A),B). [resolve(5056,a,5037,b)]. 22.76/22.77 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)),f538(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(5056,a,5038,a)]. 22.76/22.77 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,f538(code_code_numeral,D,C,B,A)) != hAPP(int,code_code_numeral,D,f538(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(5056,a,5039,a)]. 22.76/22.77 Derived: -comm_monoid_add(code_code_numeral) | -hBOOL(hAPP(fun(int,bool),bool,nat_nat_set,A)) | hAPP(fun(int,bool),code_code_numeral,hAPP(fun(int,code_code_numeral),fun(fun(int,bool),code_code_numeral),big_co302546470etprod(int,code_code_numeral),B),A) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co302546470etprod(nat,code_code_numeral),hAPP(fun(nat,int),fun(nat,code_code_numeral),hAPP(fun(int,code_code_numeral),fun(fun(nat,int),fun(nat,code_code_numeral)),combb(int,code_code_numeral,nat),B),semiring_1_of_nat(int))),hAPP(fun(int,bool),fun(nat,bool),hAPP(fun(int,nat),fun(fun(int,bool),fun(nat,bool)),image(int,nat),nat_1),A)). [resolve(5056,a,5040,b)]. 22.76/22.77 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),f627(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(5056,a,5042,a)]. 22.76/22.77 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f627(A,code_code_numeral,D,C,B)) != hAPP(A,code_code_numeral,D,f627(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(5056,a,5043,a)]. 22.76/22.77 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,f638(B,code_code_numeral,C,D,E,A)),f640(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),f642(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(5056,a,5044,a)]. 22.76/22.77 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,f638(B,code_code_numeral,C,D,E,A)),f640(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,f642(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f642(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(5056,a,5045,a)]. 22.76/22.77 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,f639(B,code_code_numeral,C,D,E,A)),f641(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),f642(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(5056,a,5046,a)]. 22.76/22.77 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,f639(B,code_code_numeral,C,D,E,A)),f641(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,f642(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f642(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(5056,a,5047,a)]. 22.76/22.77 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),f638(B,code_code_numeral,C,D,E,A)),f639(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),f640(B,code_code_numeral,C,D,E,A)),f641(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),f642(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(5056,a,5048,a)]. 22.76/22.77 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),f638(B,code_code_numeral,C,D,E,A)),f639(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),f640(B,code_code_numeral,C,D,E,A)),f641(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,f642(B,code_code_numeral,C,D,E,A))),hAPP(B,code_code_numeral,D,f642(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(5056,a,5049,a)]. 22.76/22.77 Derived: 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),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(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(5056,a,5050,a)]. 22.76/22.77 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(5056,a,5052,a)]. 22.76/22.77 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(5056,a,5054,a)]. 22.76/22.77 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(5056,a,5055,a)]. 22.94/22.94 5057 -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_3928_of__nat__setprod) # label(axiom). [clausify(4782)]. 22.94/22.94 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(5057,a,5007,a)]. 22.94/22.94 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(5057,a,5024,a)]. 22.94/22.94 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(5057,a,5028,a)]. 22.94/22.94 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(5057,a,5041,a)]. 22.94/22.94 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(5057,a,5051,a)]. 25.45/25.40 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(5057,a,5053,a)]. 25.45/25.40 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(5057,a,5056,a)]. 25.45/25.40 5058 -comm_monoid_mult(A) | hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | one_one(A) = hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) # label(fact_3951_setprod__infinite) # label(axiom). [clausify(4835)]. 25.45/25.40 5059 cancel_semigroup_add(complex) # label(arity_Complex_Ocomplex___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 25.45/25.40 5060 -cancel_semigroup_add(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_3_res) # label(axiom). [clausify(8)]. 25.45/25.40 5061 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_768_add__left__imp__eq) # label(axiom). [clausify(11)]. 25.45/25.40 Derived: plus_plus(complex) = ti(fun(complex,fun(complex,complex)),plus_plus(complex)). [resolve(5059,a,5060,a)]. 25.45/25.40 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C) | ti(complex,B) = ti(complex,C). [resolve(5059,a,5061,a)]. 25.45/25.40 5062 cancel_semigroup_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 25.45/25.40 Derived: plus_plus(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),plus_plus(code_code_numeral)). [resolve(5062,a,5060,a)]. 25.45/25.40 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C) | ti(code_code_numeral,B) = ti(code_code_numeral,C). [resolve(5062,a,5061,a)]. 25.45/25.40 5063 cancel_semigroup_add(real) # label(arity_RealDef_Oreal___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 25.45/25.40 Derived: plus_plus(real) = ti(fun(real,fun(real,real)),plus_plus(real)). [resolve(5063,a,5060,a)]. 25.45/25.40 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) = ti(real,C). [resolve(5063,a,5061,a)]. 25.45/25.40 5064 cancel_semigroup_add(rat) # label(arity_Rat_Orat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 25.45/25.40 Derived: plus_plus(rat) = ti(fun(rat,fun(rat,rat)),plus_plus(rat)). [resolve(5064,a,5060,a)]. 25.45/25.40 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C) | ti(rat,B) = ti(rat,C). [resolve(5064,a,5061,a)]. 25.45/25.40 5065 cancel_semigroup_add(nat) # label(arity_Nat_Onat___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 25.45/25.40 Derived: plus_plus(nat) = ti(fun(nat,fun(nat,nat)),plus_plus(nat)). [resolve(5065,a,5060,a)]. 25.45/25.40 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) = ti(nat,C). [resolve(5065,a,5061,a)]. 25.45/25.40 5066 cancel_semigroup_add(int) # label(arity_Int_Oint___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 26.35/26.31 Derived: plus_plus(int) = ti(fun(int,fun(int,int)),plus_plus(int)). [resolve(5066,a,5060,a)]. 26.35/26.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) = ti(int,C). [resolve(5066,a,5061,a)]. 26.35/26.31 5067 cancel_semigroup_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ocancel__semigroup__add) # label(axiom). [assumption]. 26.35/26.31 Derived: plus_plus(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),plus_plus(quickcheck_code_int)). [resolve(5067,a,5060,a)]. 26.35/26.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C) | ti(quickcheck_code_int,B) = ti(quickcheck_code_int,C). [resolve(5067,a,5061,a)]. 26.35/26.31 5068 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C) | ti(A,B) = ti(A,D) # label(fact_766_add__right__imp__eq) # label(axiom). [clausify(4203)]. 26.35/26.31 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),B) | ti(complex,A) = ti(complex,C). [resolve(5068,a,5059,a)]. 26.35/26.31 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(5068,a,5062,a)]. 26.35/26.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B) | ti(real,A) = ti(real,C). [resolve(5068,a,5063,a)]. 26.35/26.31 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B) | ti(rat,A) = ti(rat,C). [resolve(5068,a,5064,a)]. 26.35/26.31 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B) | ti(nat,A) = ti(nat,C). [resolve(5068,a,5065,a)]. 26.35/26.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B) | ti(int,A) = ti(int,C). [resolve(5068,a,5066,a)]. 26.35/26.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(5068,a,5067,a)]. 26.35/26.31 5069 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) = ti(A,D) # label(fact_770_add__left__cancel) # label(axiom). [clausify(4244)]. 26.35/26.31 5070 -cancel_semigroup_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) | ti(A,C) != ti(A,D) # label(fact_770_add__left__cancel) # label(axiom). [clausify(4244)]. 26.35/26.31 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C) | ti(complex,B) != ti(complex,C). [resolve(5070,a,5059,a)]. 26.35/26.31 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C) | ti(code_code_numeral,B) != ti(code_code_numeral,C). [resolve(5070,a,5062,a)]. 26.35/26.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C) | ti(real,B) != ti(real,C). [resolve(5070,a,5063,a)]. 29.97/29.91 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C) | ti(rat,B) != ti(rat,C). [resolve(5070,a,5064,a)]. 29.97/29.91 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C) | ti(nat,B) != ti(nat,C). [resolve(5070,a,5065,a)]. 29.97/29.91 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C) | ti(int,B) != ti(int,C). [resolve(5070,a,5066,a)]. 29.97/29.91 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,C). [resolve(5070,a,5067,a)]. 29.97/29.91 5071 -cancel_semigroup_add(A) | ti(A,B) != ti(A,C) | 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_769_add__right__cancel) # label(axiom). [clausify(4791)]. 29.97/29.91 Derived: ti(complex,A) != ti(complex,B) | 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),C). [resolve(5071,a,5059,a)]. 29.97/29.91 Derived: 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),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(5071,a,5062,a)]. 29.97/29.91 Derived: ti(real,A) != ti(real,B) | 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(5071,a,5063,a)]. 29.97/29.91 Derived: ti(rat,A) != ti(rat,B) | 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(5071,a,5064,a)]. 29.97/29.91 Derived: ti(nat,A) != ti(nat,B) | 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(5071,a,5065,a)]. 29.97/29.91 Derived: ti(int,A) != ti(int,B) | 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(5071,a,5066,a)]. 29.97/29.91 Derived: 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),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(5071,a,5067,a)]. 29.97/29.91 5072 -cancel_semigroup_add(A) | ti(A,B) = ti(A,C) | 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_769_add__right__cancel) # label(axiom). [clausify(4791)]. 29.97/29.91 5073 real_algebra_1(real) # label(arity_RealDef_Oreal___RealVector_Oreal__algebra__1) # label(axiom). [assumption]. 29.97/29.91 5074 -real_algebra_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(real,A,of_real(A),B)),C) = hAPP(real,A,of_real(A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)) # label(fact_2789_of__real__power) # label(axiom). [clausify(9)]. 29.97/29.91 5075 -real_algebra_1(A) | hAPP(int,A,ring_1_of_int(A),B) = hAPP(real,A,of_real(A),hAPP(int,real,ring_1_of_int(real),B)) # label(fact_3573_of__real__of__int__eq) # label(axiom). [clausify(34)]. 29.97/29.91 5076 -real_normed_vector(A) | -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),B),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(real,A,of_real(A),C)) # label(fact_4693_of__real_OscaleR) # label(axiom). [clausify(62)]. 29.97/29.91 5077 -topological_space(A) | -real_normed_vector(B) | -real_algebra_1(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),zero_zero(real)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,real),fun(A,B),hAPP(fun(real,B),fun(fun(A,real),fun(A,B)),combb(real,B,A),of_real(B)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4613_of__real_OLIM__zero) # label(axiom). [clausify(79)]. 29.97/29.91 5078 -real_normed_vector(A) | -real_algebra_1(A) | -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B))) # label(fact_4077_of__real_OCauchy) # label(axiom). [clausify(94)]. 29.97/29.91 5079 -real_algebra_1(A) | hAPP(nat,A,hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)),C) = hAPP(real,A,of_real(A),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),B),C)) # label(fact_4111_diffs__of__real) # label(axiom). [clausify(99)]. 29.97/29.91 5080 -real_algebra_1(A) | -real_normed_vector(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(real,fun(filter(B),bool),hAPP(fun(B,real),fun(real,fun(filter(B),bool)),tendsto(B,real),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,real),fun(B,A),hAPP(fun(real,A),fun(fun(B,real),fun(B,A)),combb(real,A,B),of_real(A)),C)),hAPP(real,A,of_real(A),D)),hAPP(B,filter(B),at(B),E))) # label(fact_4595_LIM__of__real) # label(axiom). [clausify(166)]. 29.97/29.91 5081 -real_normed_vector(A) | -real_algebra_1(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B))) # label(fact_4006_of__real_Osummable) # label(axiom). [clausify(219)]. 29.97/29.91 5082 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2788_of__real__add) # label(axiom). [clausify(300)]. 29.97/29.91 5083 -real_algebra_1(A) | one_one(A) = hAPP(real,A,of_real(A),one_one(real)) # label(fact_2786_of__real__1) # label(axiom). [clausify(494)]. 29.97/29.91 5084 -real_normed_vector(A) | -real_algebra_1(A) | hBOOL(hAPP(real,bool,hAPP(fun(real,A),fun(real,bool),isCont(real,A),of_real(A)),B)) # label(fact_4903_of__real_OisCont) # label(axiom). [clausify(741)]. 29.97/29.91 5085 -real_normed_vector(A) | -real_algebra_1(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)) = hAPP(real,A,of_real(A),hAPP(fun(nat,real),real,suminf(real),B)) # label(fact_4020_of__real_Osuminf) # label(axiom). [clausify(778)]. 29.97/29.91 5086 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f198(A))) # label(fact_2818_of__real_Ononneg__bounded) # label(axiom). [clausify(990)]. 29.97/29.91 5087 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f198(A)))) # label(fact_2818_of__real_Ononneg__bounded) # label(axiom). [clausify(990)]. 29.97/29.91 5088 -real_normed_vector(A) | -real_algebra_1(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),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)),hAPP(real,A,of_real(A),C)),sequentially)) # label(fact_4468_of__real_OLIMSEQ) # label(axiom). [clausify(1183)]. 29.97/29.91 5089 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2793_of__real__diff) # label(axiom). [clausify(1247)]. 29.97/29.91 5090 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),one_one(A)) # label(fact_4699_of__real__def) # label(axiom). [clausify(1342)]. 29.97/29.91 5091 -real_algebra_1(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(real,A,of_real(A),B)),C) # label(fact_4680_scaleR__conv__of__real) # label(axiom). [clausify(1710)]. 29.97/29.91 5092 -real_algebra_1(A) | of_real(A) = ti(fun(real,A),of_real(A)) # label(tsy_c_RealVector_Oof__real_res) # label(axiom). [clausify(1836)]. 29.97/29.91 5093 -real_algebra_1(A) | -real_normed_vector(A) | -hBOOL(hAPP(filter(B),bool,hAPP(real,fun(filter(B),bool),hAPP(fun(B,real),fun(real,fun(filter(B),bool)),tendsto(B,real),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,real),fun(B,A),hAPP(fun(real,A),fun(fun(B,real),fun(B,A)),combb(real,A,B),of_real(A)),C)),hAPP(real,A,of_real(A),D)),E)) # label(fact_4458_of__real_Otendsto) # label(axiom). [clausify(1870)]. 29.97/29.91 5094 -real_algebra_1(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(real,A,of_real(A),hAPP(nat,real,semiring_1_of_nat(real),B)) # label(fact_2800_of__real__of__nat__eq) # label(axiom). [clausify(2272)]. 29.97/29.91 5095 -real_normed_vector(A) | -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(A,A,uminus_uminus(A),hAPP(real,A,of_real(A),B)) # label(fact_2796_of__real_Ominus) # label(axiom). [clausify(2412)]. 29.97/29.91 5096 -real_normed_vector(A) | -real_algebra_1(A) | hAPP(real,A,of_real(A),zero_zero(real)) = zero_zero(A) # label(fact_2782_of__real_Ozero) # label(axiom). [clausify(2537)]. 29.97/29.91 5097 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f464(A)))) # label(fact_2817_of__real_Opos__bounded) # label(axiom). [clausify(2580)]. 29.97/29.91 5098 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f464(A))) # label(fact_2817_of__real_Opos__bounded) # label(axiom). [clausify(2580)]. 29.97/29.91 5099 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2794_of__real_Odiff) # label(axiom). [clausify(2939)]. 29.97/29.91 5100 -real_normed_vector(A) | -real_algebra_1(A) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,real),fun(nat,A),hAPP(fun(real,A),fun(fun(nat,real),fun(nat,A)),combb(real,A,nat),of_real(A)),B)),hAPP(real,A,of_real(A),C))) # label(fact_4084_of__real_Osums) # label(axiom). [clausify(3059)]. 29.97/29.91 5101 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,uminus_uminus(real),B)) = hAPP(A,A,uminus_uminus(A),hAPP(real,A,of_real(A),B)) # label(fact_2795_of__real__minus) # label(axiom). [clausify(3062)]. 29.97/29.91 5102 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,real),fun(B,A),hAPP(fun(real,A),fun(fun(B,real),fun(B,A)),combb(real,A,B),of_real(A)),C)),D) = hAPP(real,A,of_real(A),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),C),D)) # label(fact_4189_of__real_Osetsum) # label(axiom). [clausify(3079)]. 29.97/29.91 5103 -real_normed_vector(A) | -real_algebra_1(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f551(A)))) # label(fact_2822_of__real_Obounded) # label(axiom). [clausify(3096)]. 29.97/29.92 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,of_real(real),A)),B) = hAPP(real,real,of_real(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5073,a,5074,a)]. 29.97/29.92 Derived: hAPP(int,real,ring_1_of_int(real),A) = hAPP(real,real,of_real(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5073,a,5075,a)]. 29.97/29.92 Derived: -real_normed_vector(real) | hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,of_real(real),B)). [resolve(5073,a,5076,b)]. 29.97/29.92 Derived: -topological_space(A) | -real_normed_vector(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5073,a,5077,c)]. 29.97/29.92 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A))). [resolve(5073,a,5078,b)]. 29.97/29.92 Derived: 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),of_real(real)),A)),B) = hAPP(real,real,of_real(real),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B)). [resolve(5073,a,5079,a)]. 29.97/29.92 Derived: -real_normed_vector(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(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),hAPP(real,real,of_real(real),C)),hAPP(A,filter(A),at(A),D))). [resolve(5073,a,5080,a)]. 29.97/29.92 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A))). [resolve(5073,a,5081,b)]. 29.97/29.92 Derived: hAPP(real,real,of_real(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,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(5073,a,5082,a)]. 29.97/29.92 Derived: one_one(real) = hAPP(real,real,of_real(real),one_one(real)). [resolve(5073,a,5083,a)]. 29.97/29.92 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),of_real(real)),A)). [resolve(5073,a,5084,b)]. 29.97/29.92 Derived: -real_normed_vector(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A)) = hAPP(real,real,of_real(real),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5073,a,5085,b)]. 29.97/29.92 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f198(real))). [resolve(5073,a,5086,a)]. 29.97/29.92 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f198(real)))). [resolve(5073,a,5087,a)]. 30.35/30.34 Derived: -real_normed_vector(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(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A)),hAPP(real,real,of_real(real),B)),sequentially)). [resolve(5073,a,5088,b)]. 30.35/30.34 Derived: hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(5073,a,5089,a)]. 30.35/30.34 Derived: hAPP(real,real,of_real(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),one_one(real)). [resolve(5073,a,5090,a)]. 30.35/30.34 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,of_real(real),A)),B). [resolve(5073,a,5091,a)]. 30.35/30.34 Derived: of_real(real) = ti(fun(real,real),of_real(real)). [resolve(5073,a,5092,a)]. 30.35/30.34 Derived: -real_normed_vector(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),hAPP(real,real,of_real(real),C)),D)). [resolve(5073,a,5093,a)]. 30.35/30.34 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(real,real,of_real(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5073,a,5094,a)]. 30.35/30.34 Derived: -real_normed_vector(real) | hAPP(real,real,of_real(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,of_real(real),A)). [resolve(5073,a,5095,b)]. 30.35/30.34 Derived: -real_normed_vector(real) | hAPP(real,real,of_real(real),zero_zero(real)) = zero_zero(real). [resolve(5073,a,5096,b)]. 30.35/30.34 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f464(real)))). [resolve(5073,a,5097,a)]. 30.35/30.34 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f464(real))). [resolve(5073,a,5098,a)]. 30.35/30.34 Derived: -real_normed_vector(real) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),of_real(real)),A)),hAPP(real,real,of_real(real),B))). [resolve(5073,a,5100,b)]. 30.35/30.34 Derived: hAPP(real,real,of_real(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,of_real(real),A)). [resolve(5073,a,5101,a)]. 30.35/30.34 Derived: -real_normed_vector(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),of_real(real)),B)),C) = hAPP(real,real,of_real(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(5073,a,5102,a)]. 30.35/30.34 Derived: -real_normed_vector(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f551(real)))). [resolve(5073,a,5103,b)]. 30.35/30.34 5104 real_algebra_1(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__algebra__1) # label(axiom). [assumption]. 30.35/30.34 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(real,complex,of_real(complex),A)),B) = hAPP(real,complex,of_real(complex),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5104,a,5074,a)]. 30.35/30.35 Derived: hAPP(int,complex,ring_1_of_int(complex),A) = hAPP(real,complex,of_real(complex),hAPP(int,real,ring_1_of_int(real),A)). [resolve(5104,a,5075,a)]. 30.35/30.35 Derived: -real_normed_vector(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(real,complex,of_real(complex),B)). [resolve(5104,a,5076,b)]. 30.35/30.35 Derived: -topological_space(A) | -real_normed_vector(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5104,a,5077,c)]. 30.35/30.35 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A))). [resolve(5104,a,5078,b)]. 30.35/30.35 Derived: hAPP(nat,complex,hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)),B) = hAPP(real,complex,of_real(complex),hAPP(nat,real,hAPP(fun(nat,real),fun(nat,real),diffs(real),A),B)). [resolve(5104,a,5079,a)]. 30.35/30.35 Derived: -real_normed_vector(complex) | -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(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),hAPP(real,complex,of_real(complex),C)),hAPP(A,filter(A),at(A),D))). [resolve(5104,a,5080,a)]. 30.35/30.35 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A))). [resolve(5104,a,5081,b)]. 30.35/30.35 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(5104,a,5082,a)]. 30.35/30.35 Derived: one_one(complex) = hAPP(real,complex,of_real(complex),one_one(real)). [resolve(5104,a,5083,a)]. 30.35/30.35 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(fun(real,complex),fun(real,bool),isCont(real,complex),of_real(complex)),A)). [resolve(5104,a,5084,b)]. 30.35/30.35 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)) = hAPP(real,complex,of_real(complex),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5104,a,5085,b)]. 30.35/30.35 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f198(complex))). [resolve(5104,a,5086,a)]. 30.35/30.35 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f198(complex)))). [resolve(5104,a,5087,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | -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(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(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)),hAPP(real,complex,of_real(complex),B)),sequentially)). [resolve(5104,a,5088,b)]. 30.35/30.36 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(5104,a,5089,a)]. 30.35/30.36 Derived: hAPP(real,complex,of_real(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),one_one(complex)). [resolve(5104,a,5090,a)]. 30.35/30.36 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),A)),B). [resolve(5104,a,5091,a)]. 30.35/30.36 Derived: of_real(complex) = ti(fun(real,complex),of_real(complex)). [resolve(5104,a,5092,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),hAPP(real,complex,of_real(complex),C)),D)). [resolve(5104,a,5093,a)]. 30.35/30.36 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(real,complex,of_real(complex),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5104,a,5094,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),A)). [resolve(5104,a,5095,b)]. 30.35/30.36 Derived: -real_normed_vector(complex) | hAPP(real,complex,of_real(complex),zero_zero(real)) = zero_zero(complex). [resolve(5104,a,5096,b)]. 30.35/30.36 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f464(complex)))). [resolve(5104,a,5097,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f464(complex))). [resolve(5104,a,5098,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,real),fun(nat,complex),hAPP(fun(real,complex),fun(fun(nat,real),fun(nat,complex)),combb(real,complex,nat),of_real(complex)),A)),hAPP(real,complex,of_real(complex),B))). [resolve(5104,a,5100,b)]. 30.35/30.36 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,uminus_uminus(real),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(real,complex,of_real(complex),A)). [resolve(5104,a,5101,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),C) = hAPP(real,complex,of_real(complex),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(5104,a,5102,a)]. 30.35/30.36 Derived: -real_normed_vector(complex) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f551(complex)))). [resolve(5104,a,5103,b)]. 30.78/30.76 5105 -real_algebra_1(A) | -real_normed_vector(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2787_of__real_Oadd) # label(axiom). [clausify(4089)]. 30.78/30.76 5106 -real_algebra_1(A) | zero_zero(real) != B | hAPP(real,A,of_real(A),B) = zero_zero(A) # label(fact_2781_of__real__eq__0__iff) # label(axiom). [clausify(4178)]. 30.78/30.76 Derived: zero_zero(real) != A | hAPP(real,real,of_real(real),A) = zero_zero(real). [resolve(5106,a,5073,a)]. 30.78/30.76 Derived: zero_zero(real) != A | hAPP(real,complex,of_real(complex),A) = zero_zero(complex). [resolve(5106,a,5104,a)]. 30.78/30.76 5107 -real_algebra_1(A) | zero_zero(real) = B | hAPP(real,A,of_real(A),B) != zero_zero(A) # label(fact_2781_of__real__eq__0__iff) # label(axiom). [clausify(4178)]. 30.78/30.76 Derived: zero_zero(real) = A | hAPP(real,real,of_real(real),A) != zero_zero(real). [resolve(5107,a,5073,a)]. 30.78/30.76 Derived: zero_zero(real) = A | hAPP(real,complex,of_real(complex),A) != zero_zero(complex). [resolve(5107,a,5104,a)]. 30.78/30.76 5108 -real_algebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2784_of__real__mult) # label(axiom). [clausify(4243)]. 30.78/30.76 Derived: hAPP(real,real,of_real(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,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(5108,a,5073,a)]. 30.78/30.76 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(5108,a,5104,a)]. 30.78/30.76 5109 -real_algebra_1(A) | -real_normed_vector(A) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),of_real(A)),hAPP(real,A,of_real(A),B)),hAPP(real,filter(real),at(real),B))) # label(fact_4555_of__real_Ocont) # label(axiom). [clausify(4261)]. 30.78/30.76 Derived: -real_normed_vector(real) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),of_real(real)),hAPP(real,real,of_real(real),A)),hAPP(real,filter(real),at(real),A))). [resolve(5109,a,5073,a)]. 30.78/30.76 Derived: -real_normed_vector(complex) | hBOOL(hAPP(filter(real),bool,hAPP(complex,fun(filter(real),bool),hAPP(fun(real,complex),fun(complex,fun(filter(real),bool)),tendsto(real,complex),of_real(complex)),hAPP(real,complex,of_real(complex),A)),hAPP(real,filter(real),at(real),A))). [resolve(5109,a,5104,a)]. 30.78/30.76 5110 -real_algebra_1(A) | hAPP(real,A,of_real(A),zero_zero(real)) = zero_zero(A) # label(fact_2783_of__real__0) # label(axiom). [clausify(4305)]. 30.78/30.76 Derived: hAPP(real,real,of_real(real),zero_zero(real)) = zero_zero(real). [resolve(5110,a,5073,a)]. 30.78/30.76 Derived: hAPP(real,complex,of_real(complex),zero_zero(real)) = zero_zero(complex). [resolve(5110,a,5104,a)]. 30.78/30.76 5111 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) != hAPP(real,A,of_real(A),C) | B = C # label(fact_2777_of__real__eq__iff) # label(axiom). [clausify(4402)]. 30.78/30.76 Derived: hAPP(real,real,of_real(real),A) != hAPP(real,real,of_real(real),B) | A = B. [resolve(5111,a,5073,a)]. 30.78/30.76 Derived: hAPP(real,complex,of_real(complex),A) != hAPP(real,complex,of_real(complex),B) | A = B. [resolve(5111,a,5104,a)]. 30.78/30.76 5112 -real_algebra_1(A) | hAPP(real,A,of_real(A),B) = hAPP(real,A,of_real(A),C) | B != C # label(fact_2777_of__real__eq__iff) # label(axiom). [clausify(4402)]. 30.78/30.76 Derived: hAPP(real,real,of_real(real),A) = hAPP(real,real,of_real(real),B) | A != B. [resolve(5112,a,5073,a)]. 34.74/34.70 Derived: hAPP(real,complex,of_real(complex),A) = hAPP(real,complex,of_real(complex),B) | A != B. [resolve(5112,a,5104,a)]. 34.74/34.70 5113 -number_ring(A) | -real_algebra_1(A) | hAPP(int,A,number_number_of(A),B) = hAPP(real,A,of_real(A),hAPP(int,real,number_number_of(real),B)) # label(fact_2785_of__real__number__of__eq) # label(axiom). [clausify(4551)]. 34.74/34.70 Derived: -number_ring(real) | hAPP(int,real,number_number_of(real),A) = hAPP(real,real,of_real(real),hAPP(int,real,number_number_of(real),A)). [resolve(5113,b,5073,a)]. 34.74/34.70 Derived: -number_ring(complex) | hAPP(int,complex,number_number_of(complex),A) = hAPP(real,complex,of_real(complex),hAPP(int,real,number_number_of(real),A)). [resolve(5113,b,5104,a)]. 34.74/34.70 5114 -comm_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_327_comm__semiring__class_Odistrib) # label(axiom). [clausify(1100)]. 34.74/34.70 5115 comm_semiring(int) # label(arity_Int_Oint___Rings_Ocomm__semiring) # label(axiom). [assumption]. 34.74/34.70 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(5114,a,5115,a)]. 34.74/34.70 5116 comm_semiring(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__semiring) # label(axiom). [assumption]. 34.74/34.70 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B). [resolve(5116,a,5114,a)]. 34.74/34.70 5117 comm_semiring(rat) # label(arity_Rat_Orat___Rings_Ocomm__semiring) # label(axiom). [assumption]. 34.74/34.70 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C)),B). [resolve(5117,a,5114,a)]. 34.74/34.70 5118 comm_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ocomm__semiring) # label(axiom). [assumption]. 34.74/34.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C)),B). [resolve(5118,a,5114,a)]. 34.74/34.70 5119 comm_semiring(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring) # label(axiom). [assumption]. 34.74/34.70 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),B). [resolve(5119,a,5114,a)]. 34.74/34.70 5120 comm_semiring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ocomm__semiring) # label(axiom). [assumption]. 34.74/34.70 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C)),B). [resolve(5120,a,5114,a)]. 41.84/41.84 5121 comm_semiring(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring) # label(axiom). [assumption]. 41.84/41.84 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B). [resolve(5121,a,5114,a)]. 41.84/41.84 5122 real_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__algebra) # label(axiom). [assumption]. 41.84/41.84 5123 -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_4675_mult__scaleR__right) # label(axiom). [clausify(10)]. 41.84/41.84 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(5122,a,5123,a)]. 41.84/41.84 5124 real_algebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__algebra) # label(axiom). [assumption]. 41.84/41.84 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(5124,a,5123,a)]. 41.84/41.84 5125 -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_4677_mult__scaleR__left) # label(axiom). [clausify(4865)]. 41.84/41.84 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(5125,a,5122,a)]. 41.84/41.84 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(5125,a,5124,a)]. 41.84/41.84 5126 field_char_0(rat) # label(arity_Rat_Orat___Rat_Ofield__char__0) # label(axiom). [assumption]. 41.84/41.84 5127 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),field_char_0_Rats(A))) # label(fact_3697_Rats__power) # label(axiom). [clausify(15)]. 41.84/41.84 5128 -field_char_0(A) | -number_ring(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,number_number_of(A),B)),field_char_0_Rats(A))) # label(fact_3694_Rats__number__of) # label(axiom). [clausify(754)]. 41.84/41.84 5129 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),one_one(A)),field_char_0_Rats(A))) # label(fact_3695_Rats__1) # label(axiom). [clausify(905)]. 41.84/41.84 5130 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(nat,A,semiring_1_of_nat(A),B)),field_char_0_Rats(A))) # label(fact_3700_Rats__of__nat) # label(axiom). [clausify(1761)]. 42.15/42.14 5131 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),field_char_0_Rats(A))) # label(fact_3689_nonzero__Rats__divide) # label(axiom). [clausify(2305)]. 42.15/42.14 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),field_char_0_Rats(rat))). [resolve(5126,a,5127,a)]. 42.15/42.14 Derived: -number_ring(rat) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,number_number_of(rat),A)),field_char_0_Rats(rat))). [resolve(5126,a,5128,a)]. 42.15/42.14 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),one_one(rat)),field_char_0_Rats(rat))). [resolve(5126,a,5129,a)]. 42.15/42.14 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),field_char_0_Rats(rat))). [resolve(5126,a,5130,a)]. 42.15/42.14 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | ti(rat,B) = zero_zero(rat) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),field_char_0_Rats(rat))). [resolve(5126,a,5131,a)]. 42.15/42.14 5132 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,inverse_inverse(A),B)),field_char_0_Rats(A))) # label(fact_3688_nonzero__Rats__inverse) # label(axiom). [clausify(2678)]. 42.15/42.14 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,inverse_inverse(rat),A)),field_char_0_Rats(rat))). [resolve(5132,a,5126,a)]. 42.15/42.14 5133 -field_inverse_zero(A) | -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),field_char_0_Rats(A))) # label(fact_3699_Rats__divide) # label(axiom). [clausify(2825)]. 42.15/42.14 Derived: -field_inverse_zero(rat) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),field_char_0_Rats(rat))). [resolve(5133,b,5126,a)]. 42.15/42.14 5134 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),field_char_0_Rats(A))) # label(fact_3693_Rats__add) # label(axiom). [clausify(2960)]. 42.15/42.14 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),field_char_0_Rats(rat))). [resolve(5134,a,5126,a)]. 43.06/43.01 5135 field_char_0(real) # label(arity_RealDef_Oreal___Rat_Ofield__char__0) # label(axiom). [assumption]. 43.06/43.01 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),field_char_0_Rats(real))). [resolve(5135,a,5127,a)]. 43.06/43.01 Derived: -number_ring(real) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,number_number_of(real),A)),field_char_0_Rats(real))). [resolve(5135,a,5128,a)]. 43.06/43.01 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),one_one(real)),field_char_0_Rats(real))). [resolve(5135,a,5129,a)]. 43.06/43.01 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(nat,real,semiring_1_of_nat(real),A)),field_char_0_Rats(real))). [resolve(5135,a,5130,a)]. 43.06/43.01 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | ti(real,B) = zero_zero(real) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),field_char_0_Rats(real))). [resolve(5135,a,5131,a)]. 43.06/43.01 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | ti(real,A) = zero_zero(real) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,inverse_inverse(real),A)),field_char_0_Rats(real))). [resolve(5135,a,5132,a)]. 43.06/43.01 Derived: -field_inverse_zero(real) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),field_char_0_Rats(real))). [resolve(5135,a,5133,b)]. 43.06/43.01 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),field_char_0_Rats(real))). [resolve(5135,a,5134,a)]. 43.06/43.01 5136 -field_char_0(A) | field_char_0_Rats(A) = ti(fun(A,bool),field_char_0_Rats(A)) # label(tsy_c_Rat_Ofield__char__0__class_ORats_res) # label(axiom). [clausify(3330)]. 43.06/43.01 Derived: field_char_0_Rats(rat) = ti(fun(rat,bool),field_char_0_Rats(rat)). [resolve(5136,a,5126,a)]. 43.06/43.01 Derived: field_char_0_Rats(real) = ti(fun(real,bool),field_char_0_Rats(real)). [resolve(5136,a,5135,a)]. 43.06/43.01 5137 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),zero_zero(A)),field_char_0_Rats(A))) # label(fact_3691_Rats__0) # label(axiom). [clausify(3450)]. 43.06/43.01 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),zero_zero(rat)),field_char_0_Rats(rat))). [resolve(5137,a,5126,a)]. 43.06/43.01 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),zero_zero(real)),field_char_0_Rats(real))). [resolve(5137,a,5135,a)]. 43.06/43.01 5138 -field_inverse_zero(A) | -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,inverse_inverse(A),B)),field_char_0_Rats(A))) # label(fact_3701_Rats__inverse) # label(axiom). [clausify(3886)]. 43.06/43.01 Derived: -field_inverse_zero(rat) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,inverse_inverse(rat),A)),field_char_0_Rats(rat))). [resolve(5138,b,5126,a)]. 43.48/43.43 Derived: -field_inverse_zero(real) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,inverse_inverse(real),A)),field_char_0_Rats(real))). [resolve(5138,b,5135,a)]. 43.48/43.43 5139 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,uminus_uminus(A),B)),field_char_0_Rats(A))) # label(fact_3698_Rats__minus) # label(axiom). [clausify(3944)]. 43.48/43.43 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,uminus_uminus(rat),A)),field_char_0_Rats(rat))). [resolve(5139,a,5126,a)]. 43.48/43.43 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,uminus_uminus(real),A)),field_char_0_Rats(real))). [resolve(5139,a,5135,a)]. 43.48/43.43 5140 -field_char_0(A) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(int,A,ring_1_of_int(A),B)),field_char_0_Rats(A))) # label(fact_3702_Rats__of__int) # label(axiom). [clausify(4214)]. 43.48/43.43 Derived: hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(int,rat,ring_1_of_int(rat),A)),field_char_0_Rats(rat))). [resolve(5140,a,5126,a)]. 43.48/43.43 Derived: hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(int,real,ring_1_of_int(real),A)),field_char_0_Rats(real))). [resolve(5140,a,5135,a)]. 43.48/43.43 5141 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),field_char_0_Rats(A))) # label(fact_3692_Rats__mult) # label(axiom). [clausify(4259)]. 43.48/43.43 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),field_char_0_Rats(rat))). [resolve(5141,a,5126,a)]. 43.48/43.43 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),field_char_0_Rats(real))). [resolve(5141,a,5135,a)]. 43.48/43.43 5142 -field_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),field_char_0_Rats(A))) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),field_char_0_Rats(A))) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),field_char_0_Rats(A))) # label(fact_3696_Rats__diff) # label(axiom). [clausify(4301)]. 43.48/43.43 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),field_char_0_Rats(rat))) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),B),field_char_0_Rats(rat))) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),field_char_0_Rats(rat))). [resolve(5142,a,5126,a)]. 43.48/43.43 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),field_char_0_Rats(real))) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),B),field_char_0_Rats(real))) | hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),field_char_0_Rats(real))). [resolve(5142,a,5135,a)]. 43.96/43.91 5143 field_char_0(complex) # label(arity_Complex_Ocomplex___Rat_Ofield__char__0) # label(axiom). [assumption]. 43.96/43.91 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),field_char_0_Rats(complex))). [resolve(5143,a,5127,a)]. 43.96/43.91 Derived: -number_ring(complex) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,number_number_of(complex),A)),field_char_0_Rats(complex))). [resolve(5143,a,5128,a)]. 43.96/43.91 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),one_one(complex)),field_char_0_Rats(complex))). [resolve(5143,a,5129,a)]. 43.96/43.91 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)),field_char_0_Rats(complex))). [resolve(5143,a,5130,a)]. 43.96/43.91 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | ti(complex,B) = zero_zero(complex) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),field_char_0_Rats(complex))). [resolve(5143,a,5131,a)]. 43.96/43.91 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | ti(complex,A) = zero_zero(complex) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,inverse_inverse(complex),A)),field_char_0_Rats(complex))). [resolve(5143,a,5132,a)]. 43.96/43.91 Derived: -field_inverse_zero(complex) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)),field_char_0_Rats(complex))). [resolve(5143,a,5133,b)]. 43.96/43.91 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),field_char_0_Rats(complex))). [resolve(5143,a,5134,a)]. 43.96/43.91 Derived: field_char_0_Rats(complex) = ti(fun(complex,bool),field_char_0_Rats(complex)). [resolve(5143,a,5136,a)]. 43.96/43.91 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),zero_zero(complex)),field_char_0_Rats(complex))). [resolve(5143,a,5137,a)]. 43.96/43.91 Derived: -field_inverse_zero(complex) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,inverse_inverse(complex),A)),field_char_0_Rats(complex))). [resolve(5143,a,5138,b)]. 43.96/43.91 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,uminus_uminus(complex),A)),field_char_0_Rats(complex))). [resolve(5143,a,5139,a)]. 45.34/45.28 Derived: hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(int,complex,ring_1_of_int(complex),A)),field_char_0_Rats(complex))). [resolve(5143,a,5140,a)]. 45.34/45.28 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),field_char_0_Rats(complex))). [resolve(5143,a,5141,a)]. 45.34/45.28 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),field_char_0_Rats(complex))) | -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),B),field_char_0_Rats(complex))) | hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),field_char_0_Rats(complex))). [resolve(5143,a,5142,a)]. 45.34/45.28 5144 linord20386208strict(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 45.34/45.28 5145 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_394_mult__pos__pos) # label(axiom). [clausify(16)]. 45.34/45.28 5146 -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_393_mult__pos__neg) # label(axiom). [clausify(475)]. 45.34/45.28 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(5144,a,5145,a)]. 45.34/45.28 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(5144,a,5146,a)]. 45.34/45.28 5147 -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_388_mult__neg__pos) # label(axiom). [clausify(711)]. 45.34/45.28 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(5147,a,5144,a)]. 45.86/45.80 5148 linord20386208strict(int) # label(arity_Int_Oint___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 45.86/45.80 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(5148,a,5145,a)]. 45.86/45.80 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(5148,a,5146,a)]. 45.86/45.80 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),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(5148,a,5147,a)]. 45.86/45.80 5149 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_431_mult__le__less__imp__less) # label(axiom). [clausify(1292)]. 45.86/45.80 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(5149,a,5144,a)]. 45.86/45.80 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(5149,a,5148,a)]. 45.86/45.80 5150 -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_434_mult__strict__mono) # label(axiom). [clausify(2106)]. 46.16/46.15 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(5150,a,5144,a)]. 46.16/46.15 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(5150,a,5148,a)]. 46.16/46.15 5151 -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_426_mult__right__le__imp__le) # label(axiom). [clausify(2130)]. 46.16/46.15 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(5151,a,5144,a)]. 46.16/46.15 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(5151,a,5148,a)]. 46.16/46.15 5152 linord20386208strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 46.16/46.15 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(5152,a,5145,a)]. 46.16/46.15 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(5152,a,5146,a)]. 46.16/46.15 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(5152,a,5147,a)]. 46.38/46.35 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(5152,a,5149,a)]. 46.38/46.35 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(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(5152,a,5150,a)]. 46.38/46.35 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(5152,a,5151,a)]. 46.38/46.35 5153 -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_429_mult__less__imp__less__right) # label(axiom). [clausify(2828)]. 46.38/46.35 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(5153,a,5144,a)]. 46.38/46.35 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(5153,a,5148,a)]. 46.38/46.35 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(5153,a,5152,a)]. 46.38/46.35 5154 -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_386_mult__strict__right__mono) # label(axiom). [clausify(2995)]. 46.38/46.35 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(5154,a,5144,a)]. 47.16/47.10 5155 -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_392_mult__pos__neg2) # label(axiom). [clausify(3014)]. 47.16/47.10 5156 linord20386208strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 47.16/47.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5156,a,5145,a)]. 47.16/47.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),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(5156,a,5146,a)]. 47.16/47.10 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(5156,a,5147,a)]. 47.16/47.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5156,a,5149,a)]. 47.16/47.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),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(5156,a,5150,a)]. 47.16/47.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5156,a,5151,a)]. 47.16/47.10 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(5156,a,5153,a)]. 47.16/47.10 5157 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_385_mult__strict__left__mono) # label(axiom). [clausify(3683)]. 47.36/47.36 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(5157,a,5144,a)]. 47.36/47.37 5158 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_391_zero__less__mult__pos) # label(axiom). [clausify(3728)]. 47.36/47.37 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(5158,a,5144,a)]. 47.36/47.37 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(5158,a,5148,a)]. 47.36/47.37 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(5158,a,5152,a)]. 47.36/47.37 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(5158,a,5156,a)]. 47.36/47.37 5159 linord20386208strict(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 47.36/47.37 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(5159,a,5145,a)]. 47.36/47.37 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(5159,a,5146,a)]. 47.36/47.37 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(5159,a,5147,a)]. 47.36/47.37 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(5159,a,5149,a)]. 47.36/47.37 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(5159,a,5150,a)]. 47.36/47.37 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(5159,a,5151,a)]. 47.36/47.37 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(5159,a,5153,a)]. 47.48/47.41 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(5159,a,5154,a)]. 47.48/47.41 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(5159,a,5157,a)]. 47.48/47.41 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(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(5159,a,5158,a)]. 47.48/47.41 5160 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_390_zero__less__mult__pos2) # label(axiom). [clausify(3971)]. 47.48/47.41 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(5160,a,5144,a)]. 47.48/47.41 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(5160,a,5148,a)]. 47.48/47.41 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(5160,a,5152,a)]. 47.48/47.41 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(5160,a,5156,a)]. 47.97/47.97 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(5160,a,5159,a)]. 47.97/47.97 5161 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_427_mult__less__imp__less__left) # label(axiom). [clausify(4069)]. 47.97/47.97 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(5161,a,5144,a)]. 47.97/47.97 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(5161,a,5148,a)]. 47.97/47.97 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(5161,a,5152,a)]. 47.97/47.97 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(5161,a,5156,a)]. 47.97/47.97 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(5161,a,5159,a)]. 47.97/47.97 5162 linord20386208strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__semiring__strict) # label(axiom). [assumption]. 47.97/47.97 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(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(5162,a,5145,a)]. 48.05/48.06 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(5162,a,5149,a)]. 48.05/48.06 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(5162,a,5150,a)]. 48.05/48.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(5162,a,5151,a)]. 48.05/48.06 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(5162,a,5153,a)]. 48.05/48.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))). [resolve(5162,a,5154,a)]. 48.05/48.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B))). [resolve(5162,a,5157,a)]. 48.05/48.06 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(5162,a,5158,a)]. 48.05/48.06 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(5162,a,5160,a)]. 48.05/48.06 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)). [resolve(5162,a,5161,a)]. 48.05/48.06 5163 -linord20386208strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_432_mult__less__le__imp__less) # label(axiom). [clausify(4525)]. 48.05/48.07 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(5163,a,5144,a)]. 48.05/48.07 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_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(5163,a,5148,a)]. 48.05/48.07 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(5163,a,5152,a)]. 48.05/48.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(5163,a,5156,a)]. 48.05/48.07 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(5163,a,5159,a)]. 48.05/48.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_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(5163,a,5162,a)]. 48.57/48.51 5164 -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_433_mult__strict__mono_H) # label(axiom). [clausify(4887)]. 48.57/48.51 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(5164,a,5144,a)]. 48.57/48.51 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(5164,a,5148,a)]. 48.57/48.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5164,a,5152,a)]. 48.57/48.51 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(5164,a,5156,a)]. 48.57/48.51 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(5164,a,5159,a)]. 49.95/49.88 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(5164,a,5162,a)]. 49.95/49.88 5165 -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_425_mult__left__le__imp__le) # label(axiom). [clausify(4922)]. 49.95/49.88 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),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(5165,a,5144,a)]. 49.95/49.88 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5165,a,5156,a)]. 49.95/49.88 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(5165,a,5159,a)]. 49.95/49.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5165,a,5162,a)]. 49.95/49.88 5166 real_normed_field(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__field) # label(axiom). [assumption]. 49.95/49.88 5167 -real_normed_field(A) | -field_inverse_zero(A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)) = hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) # label(fact_1783_norm__divide) # label(axiom). [clausify(22)]. 49.95/49.88 5168 -topological_space(A) | -real_normed_field(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),inverse_divide(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4586_divide_OLIM__zero) # label(axiom). [clausify(130)]. 49.95/49.88 5169 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f27(A,B))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom). [clausify(139)]. 49.95/49.88 5170 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f27(A,C)))) # label(fact_1806_divide_Ononneg__bounded) # label(axiom). [clausify(139)]. 49.95/49.88 5171 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),hAPP(A,fun(A,A),times_times(A),E)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),D))) # label(fact_3863_DERIV__cmult) # label(axiom). [clausify(287)]. 49.95/49.88 5172 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,E) != ti(A,D) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2634_DERIV__cong) # label(axiom). [clausify(343)]. 49.95/49.88 5173 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),B),C)) # label(fact_4886_DERIV__isCont) # label(axiom). [clausify(349)]. 49.95/49.88 5174 -real_normed_field(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4184_divide_Osetsum) # label(axiom). [clausify(363)]. 49.95/49.88 5175 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) # label(fact_4601_DERIV__iff2) # label(axiom). [clausify(513)]. 49.95/49.88 5176 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),hAPP(A,A,B,C)))),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),minus_minus(A)),C))),D),hAPP(A,filter(A),at(A),C))) # label(fact_4601_DERIV__iff2) # label(axiom). [clausify(513)]. 49.95/49.88 5177 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),times_times(A),B)),C),B)) # label(fact_2636_DERIV__cmult__Id) # label(axiom). [clausify(529)]. 49.95/49.88 5178 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D)))) # label(fact_4024_powser__inside) # label(axiom). [clausify(558)]. 49.95/49.88 5179 -real_normed_field(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),inverse_inverse(A)),B),hAPP(A,A,uminus_uminus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3888_DERIV__inverse) # label(axiom). [clausify(672)]. 49.95/49.88 5180 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) | ti(A,E) = ti(A,D) # label(fact_2633_DERIV__unique) # label(axiom). [clausify(735)]. 49.95/49.88 5181 -real_normed_field(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4564_divide_Ocont) # label(axiom). [clausify(791)]. 49.95/49.88 5182 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),C))),C)))),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4231_sums__group) # label(axiom). [clausify(839)]. 49.95/49.88 5183 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),power_power(A)))),D),hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,A),fun(nat,A),diffs(A),B))),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_4124_termdiffs) # label(axiom). [clausify(842)]. 49.95/49.89 5184 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hAPP(A,A,E,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,E,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))) # label(fact_3899_DERIV__quotient) # label(axiom). [clausify(1042)]. 49.95/49.89 5185 -real_normed_field(A) | deriv(A) = ti(fun(fun(A,A),fun(A,fun(A,bool))),deriv(A)) # label(tsy_c_Deriv_Oderiv_res) # label(axiom). [clausify(1061)]. 49.95/49.89 5186 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)),hAPP(A,A,uminus_uminus(A),C))) # label(fact_4083_sums__minus) # label(axiom). [clausify(1197)]. 49.95/49.89 Derived: -field_inverse_zero(complex) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)). [resolve(5166,a,5167,a)]. 49.95/49.89 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5166,a,5168,b)]. 49.95/49.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f27(complex,A))). [resolve(5166,a,5169,a)]. 49.95/49.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f27(complex,B)))). [resolve(5166,a,5170,a)]. 49.95/49.90 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),D)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),C))). [resolve(5166,a,5171,a)]. 49.95/49.90 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,D) != ti(complex,C) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)). [resolve(5166,a,5172,a)]. 49.95/49.90 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),A),B)). [resolve(5166,a,5173,a)]. 49.95/49.90 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(5166,a,5174,a)]. 49.95/49.90 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))). [resolve(5166,a,5175,a)]. 49.95/49.90 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),hAPP(complex,complex,A,B)))),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),minus_minus(complex)),B))),C),hAPP(complex,filter(complex),at(complex),B))). [resolve(5166,a,5176,a)]. 49.97/49.91 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B),A)). [resolve(5166,a,5177,a)]. 49.97/49.91 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C)))). [resolve(5166,a,5178,b)]. 49.97/49.91 Derived: ti(complex,A) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),inverse_inverse(complex)),A),hAPP(complex,complex,uminus_uminus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5166,a,5179,a)]. 49.97/49.91 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),D)) | ti(complex,D) = ti(complex,C). [resolve(5166,a,5180,a)]. 49.97/49.91 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5166,a,5181,a)]. 49.97/49.91 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(fun(nat,bool),complex),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combb(fun(nat,bool),complex,nat),hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,complex),complex,suminf(complex),A))). [resolve(5166,a,5182,a)]. 49.97/49.92 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),power_power(complex)))),C),hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A))),hAPP(complex,fun(nat,complex),power_power(complex),C))))). [resolve(5166,a,5183,b)]. 49.97/49.92 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hAPP(complex,complex,D,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5166,a,5184,a)]. 49.99/49.98 Derived: deriv(complex) = ti(fun(fun(complex,complex),fun(complex,fun(complex,bool))),deriv(complex)). [resolve(5166,a,5185,a)]. 49.99/49.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)),hAPP(complex,complex,uminus_uminus(complex),B))). [resolve(5166,a,5186,a)]. 49.99/49.98 5187 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4620_DERIV__D) # label(axiom). [clausify(1390)]. 49.99/49.98 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5187,a,5166,a)]. 49.99/49.98 5188 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),combk(A,A),B)),C),zero_zero(A))) # label(fact_3840_DERIV__const) # label(axiom). [clausify(1493)]. 50.08/50.06 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),combk(complex,complex),A)),B),zero_zero(complex))). [resolve(5188,a,5166,a)]. 50.08/50.06 5189 -real_normed_field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D))),hAPP(A,A,inverse_inverse(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))),D) # label(fact_2620_DERIV__inverse__lemma) # label(axiom). [clausify(1560)]. 50.08/50.06 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C))),hAPP(complex,complex,inverse_inverse(complex),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B))),C). [resolve(5189,a,5166,a)]. 50.08/50.06 5190 real_normed_field(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__field) # label(axiom). [assumption]. 50.08/50.06 Derived: -field_inverse_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)) = hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)). [resolve(5190,a,5167,a)]. 50.08/50.06 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5190,a,5168,b)]. 50.08/50.06 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f27(real,A))). [resolve(5190,a,5169,a)]. 50.08/50.06 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f27(real,B)))). [resolve(5190,a,5170,a)]. 50.08/50.06 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),hAPP(real,fun(real,real),times_times(real),D)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),C))). [resolve(5190,a,5171,a)]. 50.08/50.06 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,D) != ti(real,C) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)). [resolve(5190,a,5172,a)]. 50.08/50.06 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),A),B)). [resolve(5190,a,5173,a)]. 50.08/50.07 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),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(5190,a,5174,a)]. 50.08/50.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))). [resolve(5190,a,5175,a)]. 50.08/50.07 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),hAPP(real,real,A,B)))),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),minus_minus(real)),B))),C),hAPP(real,filter(real),at(real),B))). [resolve(5190,a,5176,a)]. 50.08/50.07 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),times_times(real),A)),B),A)). [resolve(5190,a,5177,a)]. 50.08/50.07 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C)))). [resolve(5190,a,5178,b)]. 50.08/50.07 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),inverse_inverse(real)),A),hAPP(real,real,uminus_uminus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5190,a,5179,a)]. 50.08/50.08 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),D)) | ti(real,D) = ti(real,C). [resolve(5190,a,5180,a)]. 50.08/50.08 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),hAPP(real,filter(real),at(real),B))). [resolve(5190,a,5181,a)]. 50.08/50.08 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(fun(nat,bool),real),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combb(fun(nat,bool),real,nat),hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A)),hAPP(fun(nat,nat),fun(nat,fun(nat,bool)),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,bool))),combs(nat,nat,fun(nat,bool)),hAPP(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool))),hAPP(fun(nat,fun(nat,fun(nat,bool))),fun(fun(nat,nat),fun(nat,fun(nat,fun(nat,bool)))),combb(nat,fun(nat,fun(nat,bool)),nat),ord_atLeastLessThan(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),plus_plus(nat)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),times_times(nat)),B))),B)))),hAPP(fun(nat,real),real,suminf(real),A))). [resolve(5190,a,5182,a)]. 50.08/50.08 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),power_power(real)))),C),hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),A))),hAPP(real,fun(nat,real),power_power(real),C))))). [resolve(5190,a,5183,b)]. 50.08/50.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hAPP(real,real,D,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,D,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))). [resolve(5190,a,5184,a)]. 50.08/50.09 Derived: deriv(real) = ti(fun(fun(real,real),fun(real,fun(real,bool))),deriv(real)). [resolve(5190,a,5185,a)]. 50.08/50.09 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)),hAPP(real,real,uminus_uminus(real),B))). [resolve(5190,a,5186,a)]. 50.08/50.09 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5190,a,5187,a)]. 50.08/50.09 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),combk(real,real),A)),B),zero_zero(real))). [resolve(5190,a,5188,a)]. 50.08/50.09 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C))),hAPP(real,real,inverse_inverse(real),B))) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))),C). [resolve(5190,a,5189,a)]. 50.16/50.11 5191 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),f326(A,B,C,D)),C)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1695)]. 50.16/50.11 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),f326(complex,A,B,C)),B)). [resolve(5191,a,5166,a)]. 50.16/50.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),f326(real,A,B,C)),B)). [resolve(5191,a,5190,a)]. 50.16/50.11 5192 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,D) = hAPP(A,A,f326(A,B,C,D),C) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1695)]. 50.16/50.11 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | ti(complex,C) = hAPP(complex,complex,f326(complex,A,B,C),B). [resolve(5192,a,5166,a)]. 50.16/50.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | ti(real,C) = hAPP(real,real,f326(real,A,B,C),B). [resolve(5192,a,5190,a)]. 50.16/50.11 5193 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,E)),hAPP(A,A,B,C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,f326(A,B,C,D),E)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),C)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1695)]. 50.16/50.11 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,D)),hAPP(complex,complex,A,B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,f326(complex,A,B,C),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),B)). [resolve(5193,a,5166,a)]. 50.16/50.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,D)),hAPP(real,real,A,B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,f326(real,A,B,C),D)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),B)). [resolve(5193,a,5190,a)]. 50.16/50.11 5194 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),E),C)) | ti(A,D) != hAPP(A,A,E,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,B,f327(A,B,C,D,E))),hAPP(A,A,B,C)) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,f327(A,B,C,D,E))),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),f327(A,B,C,D,E)),C)) # label(fact_4882_CARAT__DERIV) # label(axiom). [clausify(1695)]. 50.16/50.11 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),D),B)) | ti(complex,C) != hAPP(complex,complex,D,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,A,f327(complex,A,B,C,D))),hAPP(complex,complex,A,B)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,f327(complex,A,B,C,D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),f327(complex,A,B,C,D)),B)). [resolve(5194,a,5166,a)]. 50.28/50.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),D),B)) | ti(real,C) != hAPP(real,real,D,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,A,f327(real,A,B,C,D))),hAPP(real,real,A,B)) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,f327(real,A,B,C,D))),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),f327(real,A,B,C,D)),B)). [resolve(5194,a,5190,a)]. 50.28/50.28 5195 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),power_power(A),B))) # label(fact_4026_summable__geometric) # label(axiom). [clausify(1777)]. 50.28/50.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),power_power(complex),A))). [resolve(5195,a,5166,a)]. 50.28/50.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),power_power(real),A))). [resolve(5195,a,5190,a)]. 50.28/50.28 5196 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),E))),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,uminus_uminus(A),F)))) # label(fact_3816_DERIV__add__minus) # label(axiom). [clausify(2032)]. 50.28/50.28 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),hAPP(complex,complex,uminus_uminus(complex),E)))). [resolve(5196,a,5166,a)]. 50.28/50.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),D))),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),hAPP(real,real,uminus_uminus(real),E)))). [resolve(5196,a,5190,a)]. 50.45/50.42 5197 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3984_suminf__divide) # label(axiom). [clausify(2055)]. 50.45/50.42 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B). [resolve(5197,a,5166,a)]. 50.45/50.42 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(fun(nat,real),real,suminf(real),A)),B). [resolve(5197,a,5190,a)]. 50.45/50.42 5198 -real_normed_field(A) | hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),B),C)),D) # label(fact_4707_divide_OscaleR) # label(axiom). [clausify(2294)]. 50.45/50.42 Derived: hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),A),B)),C). [resolve(5198,a,5166,a)]. 50.45/50.42 Derived: hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),A),B)),C). [resolve(5198,a,5190,a)]. 50.45/50.42 5199 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f434(A,B))) # label(fact_1802_divide_Opos__bounded) # label(axiom). [clausify(2322)]. 50.45/50.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f434(complex,A))). [resolve(5199,a,5166,a)]. 50.45/50.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f434(real,A))). [resolve(5199,a,5190,a)]. 50.45/50.42 5200 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f434(A,C)))) # label(fact_1802_divide_Opos__bounded) # label(axiom). [clausify(2322)]. 50.45/50.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f434(complex,B)))). [resolve(5200,a,5166,a)]. 50.45/50.42 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f434(real,B)))). [resolve(5200,a,5190,a)]. 50.45/50.44 5201 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),E))) # label(fact_3836_DERIV__cdivide) # label(axiom). [clausify(2340)]. 50.45/50.44 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),D))). [resolve(5201,a,5166,a)]. 50.45/50.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),D))). [resolve(5201,a,5190,a)]. 50.45/50.44 5202 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))))) # label(fact_3818_DERIV__mult_H) # label(axiom). [clausify(2341)]. 50.45/50.44 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))))). [resolve(5202,a,5166,a)]. 50.45/50.44 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))))). [resolve(5202,a,5190,a)]. 50.45/50.45 5203 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4619_DERIV__iff) # label(axiom). [clausify(2342)]. 50.45/50.45 5204 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),hAPP(A,fun(A,A),plus_plus(A),C)))),hAPP(A,A,B,C)))),combi(A))),D),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4619_DERIV__iff) # label(axiom). [clausify(2342)]. 50.45/50.45 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),hAPP(complex,fun(complex,complex),plus_plus(complex),B)))),hAPP(complex,complex,A,B)))),combi(complex))),C),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5204,a,5166,a)]. 50.45/50.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),hAPP(real,fun(real,real),plus_plus(real),B)))),hAPP(real,real,A,B)))),combi(real))),C),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5204,a,5190,a)]. 50.58/50.54 5205 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),hAPP(A,A,C,D)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),C),D),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),B),C)),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),F))) # label(fact_3861_DERIV__chain2) # label(axiom). [clausify(2362)]. 50.58/50.54 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),hAPP(complex,complex,B,C)),D)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),B),C),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),A),B)),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),E))). [resolve(5205,a,5166,a)]. 50.58/50.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),hAPP(real,real,B,C)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),B),C),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),A),B)),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),E))). [resolve(5205,a,5190,a)]. 50.58/50.54 5206 -real_normed_field(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),one_one(real))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),one_one(A)),B)))) # label(fact_4098_geometric__sums) # label(axiom). [clausify(2485)]. 50.58/50.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),one_one(complex)),A)))). [resolve(5206,a,5166,a)]. 50.58/50.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),one_one(real)),A)))). [resolve(5206,a,5190,a)]. 50.58/50.54 5207 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) = zero_zero(A) # label(fact_1656_divide_Ozero) # label(axiom). [clausify(2496)]. 50.58/50.59 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5207,a,5166,a)]. 50.58/50.59 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),zero_zero(real)),A) = zero_zero(real). [resolve(5207,a,5190,a)]. 50.58/50.59 5208 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hAPP(A,A,E,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),inverse_divide(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,B,C)),F))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,E,C)),hAPP(A,A,E,C))))) # label(fact_3811_DERIV__divide) # label(axiom). [clausify(2510)]. 50.58/50.59 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hAPP(complex,complex,D,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),inverse_divide(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,A,B)),E))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,D,B)),hAPP(complex,complex,D,B))))). [resolve(5208,a,5166,a)]. 50.58/50.59 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hAPP(real,real,D,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),inverse_divide(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,A,B)),E))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,D,B)),hAPP(real,real,D,B))))). [resolve(5208,a,5190,a)]. 50.58/50.59 5209 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4009_summable__divide) # label(axiom). [clausify(2575)]. 50.58/50.60 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))). [resolve(5209,a,5166,a)]. 50.58/50.60 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))). [resolve(5209,a,5190,a)]. 50.58/50.60 5210 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | ti(A,f465(B,A,E,D,C)) != zero_zero(A) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom). [clausify(2582)]. 50.58/50.60 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | ti(complex,f465(A,complex,D,C,B)) != zero_zero(complex) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5210,a,5166,a)]. 50.58/50.60 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | ti(real,f465(A,real,D,C,B)) != zero_zero(real) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5210,a,5190,a)]. 50.58/50.60 5211 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),f465(B,A,E,D,C))),C)) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom). [clausify(2582)]. 50.58/50.60 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f465(A,complex,D,C,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5211,a,5166,a)]. 50.58/50.60 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f465(A,real,D,C,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5211,a,5190,a)]. 50.68/50.68 5212 -real_normed_field(A) | -banach(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(B,real,norm_norm(B),hAPP(nat,B,hAPP(A,fun(nat,B),E,f465(B,A,E,D,C)),f466(B,A,E,D,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,D,f466(B,A,E,D,C))),hAPP(A,real,norm_norm(A),f465(B,A,E,D,C))))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,fun(nat,B)),fun(A,B),hAPP(fun(fun(nat,B),B),fun(fun(A,fun(nat,B)),fun(A,B)),combb(fun(nat,B),B,A),suminf(B)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4625_lemma__termdiff5) # label(axiom). [clausify(2582)]. 50.68/50.68 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(complex,fun(nat,A),D,f465(A,complex,D,C,B)),f466(A,complex,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f466(A,complex,D,C,B))),hAPP(complex,real,norm_norm(complex),f465(A,complex,D,C,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(fun(complex,fun(nat,A)),fun(complex,A),hAPP(fun(fun(nat,A),A),fun(fun(complex,fun(nat,A)),fun(complex,A)),combb(fun(nat,A),A,complex),suminf(A)),D)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5212,a,5166,a)]. 50.68/50.68 Derived: -banach(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(real,fun(nat,A),D,f465(A,real,D,C,B)),f466(A,real,D,C,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,C,f466(A,real,D,C,B))),hAPP(real,real,norm_norm(real),f465(A,real,D,C,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(fun(real,fun(nat,A)),fun(real,A),hAPP(fun(fun(nat,A),A),fun(fun(real,fun(nat,A)),fun(real,A)),combb(fun(nat,A),A,real),suminf(A)),D)),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5212,a,5190,a)]. 50.68/50.68 5213 -real_normed_vector(A) | -real_normed_field(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | ti(B,f497(A,B,D,E,C)) != zero_zero(B) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4626_lemma__termdiff4) # label(axiom). [clausify(2689)]. 50.68/50.68 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | ti(complex,f497(A,complex,C,D,B)) != zero_zero(complex) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5213,b,5166,a)]. 50.68/50.68 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | ti(real,f497(A,real,C,D,B)) != zero_zero(real) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5213,b,5190,a)]. 50.76/50.74 5214 -real_normed_vector(A) | -real_normed_field(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(B,real,norm_norm(B),f497(A,B,D,E,C))),C)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4626_lemma__termdiff4) # label(axiom). [clausify(2689)]. 50.76/50.74 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),f497(A,complex,C,D,B))),B)) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5214,b,5166,a)]. 50.76/50.74 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),f497(A,real,C,D,B))),B)) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5214,b,5190,a)]. 50.76/50.74 5215 -real_normed_vector(A) | -real_normed_field(B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(B,A,D,f497(A,B,D,E,C)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(B,real,norm_norm(B),f497(A,B,D,E,C))))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),zero_zero(A)),hAPP(B,filter(B),at(B),zero_zero(B)))) # label(fact_4626_lemma__termdiff4) # label(axiom). [clausify(2689)]. 50.76/50.74 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(complex,A,C,f497(A,complex,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(complex,real,norm_norm(complex),f497(A,complex,C,D,B))))) | hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),C),zero_zero(A)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5215,b,5166,a)]. 50.76/50.74 Derived: -real_normed_vector(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(real,A,C,f497(A,real,C,D,B)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),hAPP(real,real,norm_norm(real),f497(A,real,C,D,B))))) | hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),C),zero_zero(A)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5215,b,5190,a)]. 50.76/50.74 5216 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_4002_summable__minus) # label(axiom). [clausify(2780)]. 50.76/50.74 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A))). [resolve(5216,a,5166,a)]. 50.76/50.74 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A))). [resolve(5216,a,5190,a)]. 50.87/50.82 5217 -banach(A) | -real_normed_field(A) | one_one(A) = hAPP(A,A,exp(A),zero_zero(A)) # label(fact_2583_exp__zero) # label(axiom). [clausify(2793)]. 50.87/50.82 Derived: -banach(complex) | one_one(complex) = hAPP(complex,complex,exp(complex),zero_zero(complex)). [resolve(5217,b,5166,a)]. 50.87/50.82 Derived: -banach(real) | one_one(real) = hAPP(real,real,exp(real),zero_zero(real)). [resolve(5217,b,5190,a)]. 50.87/50.82 5218 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),C))) # label(fact_4011_summable__add) # label(axiom). [clausify(2805)]. 50.87/50.82 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B))). [resolve(5218,a,5166,a)]. 50.87/50.82 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B))). [resolve(5218,a,5190,a)]. 50.87/50.82 5219 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2586_mult__exp__exp) # label(axiom). [clausify(2823)]. 50.87/50.82 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)). [resolve(5219,a,5166,a)]. 50.87/50.82 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)). [resolve(5219,a,5190,a)]. 50.87/50.82 5220 -real_normed_field(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),F)),hAPP(B,filter(B),at(B),E))) # label(fact_4563_divide_OLIM) # label(axiom). [clausify(2905)]. 50.87/50.82 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5220,a,5166,a)]. 50.87/50.88 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5220,a,5190,a)]. 50.87/50.88 5221 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2589_exp__diff) # label(axiom). [clausify(2926)]. 50.87/50.88 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,exp(complex),A)),hAPP(complex,complex,exp(complex),B)). [resolve(5221,a,5166,a)]. 50.87/50.88 Derived: -banach(real) | hAPP(real,real,exp(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,exp(real),A)),hAPP(real,real,exp(real),B)). [resolve(5221,a,5190,a)]. 50.87/50.88 5222 -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_2632_DERIV__exp) # label(axiom). [clausify(2927)]. 50.87/50.88 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),exp(complex)),A),hAPP(complex,complex,exp(complex),A))). [resolve(5222,a,5166,a)]. 50.87/50.88 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),exp(real)),A),hAPP(real,real,exp(real),A))). [resolve(5222,a,5190,a)]. 50.87/50.88 5223 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1664_divide_Odiff) # label(axiom). [clausify(2943)]. 50.87/50.88 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)). [resolve(5223,a,5166,a)]. 50.87/50.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)). [resolve(5223,a,5190,a)]. 50.87/50.88 5224 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4008_divide_Osummable) # label(axiom). [clausify(2952)]. 50.87/50.88 5225 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f543(B,A,D,E,F,C)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom). [clausify(3000)]. 50.87/50.89 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,complex,C,D,E,B)),B)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))). [resolve(5225,a,5166,a)]. 50.87/50.89 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f543(A,real,C,D,E,B)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))). [resolve(5225,a,5190,a)]. 50.87/50.89 5226 -real_normed_field(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(B,fun(A,A),hAPP(fun(A,fun(B,A)),fun(B,fun(A,A)),combc(A,B,A),D),f543(B,A,D,E,F,C))),E),hAPP(B,A,hAPP(A,fun(B,A),F,E),f543(B,A,D,E,F,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(B,bool),fun(A,A),hAPP(fun(A,fun(fun(B,bool),A)),fun(fun(B,bool),fun(A,A)),combc(A,fun(B,bool),A),hAPP(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(A,fun(B,A)),fun(A,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),A),big_co1399186613setsum(B,A)),D)),C)),E),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),F,E)),C))) # label(fact_4304_DERIV__setsum) # label(axiom). [clausify(3000)]. 50.87/50.89 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(A,fun(complex,complex),hAPP(fun(complex,fun(A,complex)),fun(A,fun(complex,complex)),combc(complex,A,complex),C),f543(A,complex,C,D,E,B))),D),hAPP(A,complex,hAPP(complex,fun(A,complex),E,D),f543(A,complex,C,D,E,B)))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(A,bool),fun(complex,complex),hAPP(fun(complex,fun(fun(A,bool),complex)),fun(fun(A,bool),fun(complex,complex)),combc(complex,fun(A,bool),complex),hAPP(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex)),hAPP(fun(fun(A,complex),fun(fun(A,bool),complex)),fun(fun(complex,fun(A,complex)),fun(complex,fun(fun(A,bool),complex))),combb(fun(A,complex),fun(fun(A,bool),complex),complex),big_co1399186613setsum(A,complex)),C)),B)),D),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),E,D)),B))). [resolve(5226,a,5166,a)]. 50.97/50.98 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(A,fun(real,real),hAPP(fun(real,fun(A,real)),fun(A,fun(real,real)),combc(real,A,real),C),f543(A,real,C,D,E,B))),D),hAPP(A,real,hAPP(real,fun(A,real),E,D),f543(A,real,C,D,E,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(A,bool),fun(real,real),hAPP(fun(real,fun(fun(A,bool),real)),fun(fun(A,bool),fun(real,real)),combc(real,fun(A,bool),real),hAPP(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real)),hAPP(fun(fun(A,real),fun(fun(A,bool),real)),fun(fun(real,fun(A,real)),fun(real,fun(fun(A,bool),real))),combb(fun(A,real),fun(fun(A,bool),real),real),big_co1399186613setsum(A,real)),C)),B)),D),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),E,D)),B))). [resolve(5226,a,5190,a)]. 50.97/50.98 5227 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),hAPP(A,A,B,C)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),E),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D))) # label(fact_3862_DERIV__chain_H) # label(axiom). [clausify(3005)]. 50.97/50.98 5228 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | ti(A,V6) = zero_zero(A) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),V6)),E)) # label(fact_4452_tendsto__divide) # label(axiom). [clausify(3136)]. 50.97/50.98 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | ti(complex,F) = zero_zero(complex) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),F)),D)). [resolve(5228,a,5166,a)]. 50.97/50.98 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | ti(real,F) = zero_zero(real) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),F)),D)). [resolve(5228,a,5190,a)]. 51.18/51.14 5229 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),zero_zero(A)),sequentially)) # label(fact_4435_summable__LIMSEQ__zero) # label(axiom). [clausify(3174)]. 51.18/51.14 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),zero_zero(complex)),sequentially)). [resolve(5229,a,5166,a)]. 51.18/51.14 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),zero_zero(real)),sequentially)). [resolve(5229,a,5190,a)]. 51.18/51.14 5230 -real_normed_field(A) | -banach(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_2799_exp__of__real) # label(axiom). [clausify(3238)]. 51.18/51.14 Derived: -banach(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(5230,a,5166,a)]. 51.18/51.14 Derived: -banach(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(5230,a,5190,a)]. 51.18/51.14 5231 -real_normed_field(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),C)),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B))),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),E))),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),E)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(A,real,norm_norm(A),B)))) # label(fact_1773_lemma__termdiff3) # label(axiom). [clausify(3335)]. 51.18/51.14 Derived: ti(complex,A) = zero_zero(complex) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),D))),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(complex,real,norm_norm(complex),A)))). [resolve(5231,a,5166,a)]. 51.37/51.35 Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A))),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A)),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),D))),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))),hAPP(real,real,norm_norm(real),A)))). [resolve(5231,a,5190,a)]. 51.37/51.35 5232 -real_normed_field(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1661_divide_Oadd) # label(axiom). [clausify(3374)]. 51.37/51.35 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)). [resolve(5232,a,5166,a)]. 51.37/51.35 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)). [resolve(5232,a,5190,a)]. 51.37/51.35 5233 -real_normed_field(A) | -banach(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,exp(A),B)) = hAPP(A,A,exp(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2535_exp__minus) # label(axiom). [clausify(3418)]. 51.37/51.35 Derived: -banach(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,exp(complex),A)) = hAPP(complex,complex,exp(complex),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(5233,a,5166,a)]. 51.37/51.35 Derived: -banach(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,exp(real),A)) = hAPP(real,real,exp(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(5233,a,5190,a)]. 51.45/51.41 5234 -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_4750_lemma__exp__ext) # label(axiom). [clausify(3441)]. 51.45/51.41 Derived: -banach(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))) = hAPP(complex,complex,exp(complex),A). [resolve(5234,b,5166,a)]. 51.45/51.41 Derived: -banach(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))) = hAPP(real,real,exp(real),A). [resolve(5234,b,5190,a)]. 51.45/51.41 5235 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),combi(A)),B),one_one(A))) # label(fact_3839_DERIV__ident) # label(axiom). [clausify(3446)]. 51.45/51.41 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),combi(complex)),A),one_one(complex))). [resolve(5235,a,5166,a)]. 51.45/51.41 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),combi(real)),A),one_one(real))). [resolve(5235,a,5190,a)]. 51.45/51.41 5236 -real_normed_field(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f607(A,C)))) # label(fact_1810_divide_Obounded) # label(axiom). [clausify(3454)]. 51.45/51.41 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f607(complex,B)))). [resolve(5236,a,5166,a)]. 51.45/51.41 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f607(real,B)))). [resolve(5236,a,5190,a)]. 51.45/51.41 5237 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),minus_minus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F))) # label(fact_3822_DERIV__diff) # label(axiom). [clausify(3495)]. 51.55/51.49 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),minus_minus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),E))). [resolve(5237,a,5166,a)]. 51.55/51.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),minus_minus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),E))). [resolve(5237,a,5190,a)]. 51.55/51.49 5238 -banach(A) | -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),exp(A)),B)) # label(fact_4891_isCont__exp) # label(axiom). [clausify(3569)]. 51.55/51.49 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),exp(complex)),A)). [resolve(5238,b,5166,a)]. 51.55/51.49 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),exp(real)),A)). [resolve(5238,b,5190,a)]. 51.55/51.49 5239 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4086_sums__divide) # label(axiom). [clausify(3580)]. 51.55/51.49 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C))). [resolve(5239,a,5166,a)]. 51.55/51.49 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5239,a,5190,a)]. 51.58/51.54 5240 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3983_suminf__add) # label(axiom). [clausify(3610)]. 51.58/51.54 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5240,a,5166,a)]. 51.58/51.54 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5240,a,5190,a)]. 51.58/51.54 5241 -real_normed_field(A) | -banach(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),exp(A)),B)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),hAPP(A,A,B,C))),D))) # label(fact_3864_DERIV__fun__exp) # label(axiom). [clausify(3633)]. 51.58/51.54 Derived: -banach(complex) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),exp(complex)),A)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,exp(complex),hAPP(complex,complex,A,B))),C))). [resolve(5241,a,5166,a)]. 51.58/51.54 Derived: -banach(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),exp(real)),A)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,exp(real),hAPP(real,real,A,B))),C))). [resolve(5241,a,5190,a)]. 51.58/51.54 5242 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C))) # label(fact_4012_summable__diff) # label(axiom). [clausify(3640)]. 51.58/51.54 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B))). [resolve(5242,a,5166,a)]. 51.67/51.66 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B))). [resolve(5242,a,5190,a)]. 51.67/51.66 5243 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),uminus_uminus(A)),B)),C),hAPP(A,A,uminus_uminus(A),D))) # label(fact_3856_DERIV__minus) # label(axiom). [clausify(3736)]. 51.67/51.66 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),uminus_uminus(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),C))). [resolve(5243,a,5166,a)]. 51.67/51.66 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),uminus_uminus(real)),A)),B),hAPP(real,real,uminus_uminus(real),C))). [resolve(5243,a,5190,a)]. 51.67/51.66 5244 -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)),hAPP(fun(nat,A),fun(nat,A),diffs(A),hAPP(fun(nat,A),fun(nat,A),diffs(A),B)))),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(fun(A,fun(nat,A)),fun(A,A),hAPP(fun(fun(nat,A),A),fun(fun(A,fun(nat,A)),fun(A,A)),combb(fun(nat,A),A,A),suminf(A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(A,fun(nat,A)),fun(A,fun(nat,A))),combb(fun(nat,A),fun(nat,A),A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(A,fun(nat,A))),fun(fun(A,A),fun(A,fun(nat,A))),combs(A,A,fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(A,fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(A,fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(A,fun(nat,A)),A),combc(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A))),hAPP(fun(nat,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(fun(nat,A),fun(nat,A))),fun(fun(nat,A),fun(A,fun(nat,A))),combc(A,fun(nat,A),fun(nat,A)),hAPP(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A))),hAPP(fun(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A))),fun(fun(A,fun(nat,fun(A,A))),fun(A,fun(fun(nat,A),fun(nat,A)))),combb(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),A),combs(nat,A,A)),hAPP(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A))),hAPP(fun(fun(nat,A),fun(nat,fun(A,A))),fun(fun(A,fun(nat,A)),fun(A,fun(nat,fun(A,A)))),combb(fun(nat,A),fun(nat,fun(A,A)),A),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A))),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),hAPP(A,fun(A,A),plus_plus(A),D))))),hAPP(A,fun(nat,A),power_power(A),D))))),combi(A))))),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),semiring_1_of_nat(A))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(A)),hAPP(A,filter(A),at(A),zero_zero(A)))) # label(fact_4532_termdiffs__aux) # label(axiom). [clausify(3785)]. 51.67/51.66 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),hAPP(fun(nat,complex),fun(nat,complex),diffs(complex),A)))),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(complex,complex),hAPP(fun(fun(nat,complex),complex),fun(fun(complex,fun(nat,complex)),fun(complex,complex)),combb(fun(nat,complex),complex,complex),suminf(complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(complex,fun(nat,complex))),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combs(complex,complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(complex,fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),complex),combc(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex))),hAPP(fun(nat,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(fun(nat,complex),fun(nat,complex))),fun(fun(nat,complex),fun(complex,fun(nat,complex))),combc(complex,fun(nat,complex),fun(nat,complex)),hAPP(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex))),hAPP(fun(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex))),fun(fun(complex,fun(nat,fun(complex,complex))),fun(complex,fun(fun(nat,complex),fun(nat,complex)))),combb(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),complex),combs(nat,complex,complex)),hAPP(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex))),hAPP(fun(fun(nat,complex),fun(nat,fun(complex,complex))),fun(fun(complex,fun(nat,complex)),fun(complex,fun(nat,fun(complex,complex)))),combb(fun(nat,complex),fun(nat,fun(complex,complex)),complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex))),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),hAPP(complex,fun(complex,complex),plus_plus(complex),C))))),hAPP(complex,fun(nat,complex),power_power(complex),C))))),combi(complex))))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),semiring_1_of_nat(complex))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(complex)),hAPP(complex,filter(complex),at(complex),zero_zero(complex)))). [resolve(5244,a,5166,a)]. 51.67/51.66 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,real),fun(nat,real),diffs(real),hAPP(fun(nat,real),fun(nat,real),diffs(real),A)))),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(fun(real,fun(nat,real)),fun(real,real),hAPP(fun(fun(nat,real),real),fun(fun(real,fun(nat,real)),fun(real,real)),combb(fun(nat,real),real,real),suminf(real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(real,fun(nat,real)),fun(real,fun(nat,real))),combb(fun(nat,real),fun(nat,real),real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(real,fun(nat,real))),fun(fun(real,real),fun(real,fun(nat,real))),combs(real,real,fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(real,fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(real,fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(real,fun(nat,real)),real),combc(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real))),hAPP(fun(nat,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(fun(nat,real),fun(nat,real))),fun(fun(nat,real),fun(real,fun(nat,real))),combc(real,fun(nat,real),fun(nat,real)),hAPP(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real))),hAPP(fun(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real))),fun(fun(real,fun(nat,fun(real,real))),fun(real,fun(fun(nat,real),fun(nat,real)))),combb(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),real),combs(nat,real,real)),hAPP(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real))),hAPP(fun(fun(nat,real),fun(nat,fun(real,real))),fun(fun(real,fun(nat,real)),fun(real,fun(nat,fun(real,real)))),combb(fun(nat,real),fun(nat,fun(real,real)),real),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real))),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),hAPP(real,fun(real,real),plus_plus(real),C))))),hAPP(real,fun(nat,real),power_power(real),C))))),combi(real))))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),semiring_1_of_nat(real))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),minus_minus(nat)),hAPP(nat,nat,suc,zero_zero(nat))))))))),zero_zero(real)),hAPP(real,filter(real),at(real),zero_zero(real)))). [resolve(5244,a,5190,a)]. 51.88/51.88 5245 -real_normed_field(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),inverse_divide(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),F)),E)) # label(fact_4456_divide_Otendsto) # label(axiom). [clausify(3860)]. 51.88/51.88 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),inverse_divide(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),E)),D)). [resolve(5245,a,5166,a)]. 51.88/51.88 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),inverse_divide(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),E)),D)). [resolve(5245,a,5190,a)]. 51.88/51.88 5246 -real_normed_field(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2017_divide_Ominus) # label(axiom). [clausify(3864)]. 51.88/51.88 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B). [resolve(5246,a,5166,a)]. 51.88/51.88 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(5246,a,5190,a)]. 51.88/51.88 5247 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),sequentially)) # label(fact_4449_divide_OLIMSEQ) # label(axiom). [clausify(4003)]. 51.88/51.88 5248 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),hAPP(nat,nat,suc,E))),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(nat,A,semiring_1_of_nat(A),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),E))))) # label(fact_3887_DERIV__power__Suc) # label(axiom). [clausify(4021)]. 52.05/52.07 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),hAPP(nat,nat,suc,D))),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(nat,complex,semiring_1_of_nat(complex),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),D))))). [resolve(5248,a,5166,a)]. 52.05/52.07 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),hAPP(nat,nat,suc,D))),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(nat,real,semiring_1_of_nat(real),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),D))))). [resolve(5248,a,5190,a)]. 52.05/52.07 5249 -banach(A) | -real_normed_field(A) | hAPP(A,A,exp(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,exp(A),B)),hAPP(A,A,exp(A),C)) # label(fact_2585_exp__add) # label(axiom). [clausify(4105)]. 52.05/52.07 5250 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_4088_sums__diff) # label(axiom). [clausify(4217)]. 52.05/52.07 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))). [resolve(5250,a,5166,a)]. 52.05/52.07 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))). [resolve(5250,a,5190,a)]. 52.18/52.19 5251 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),plus_plus(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_4087_sums__add) # label(axiom). [clausify(4254)]. 52.18/52.19 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),C),D)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),plus_plus(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),D))). [resolve(5251,a,5166,a)]. 52.18/52.19 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),plus_plus(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),D))). [resolve(5251,a,5190,a)]. 52.18/52.19 5252 -banach(A) | -real_normed_field(A) | exp(A) = ti(fun(A,A),exp(A)) # label(tsy_c_Transcendental_Oexp_res) # label(axiom). [clausify(4272)]. 52.18/52.19 Derived: -banach(complex) | exp(complex) = ti(fun(complex,complex),exp(complex)). [resolve(5252,b,5166,a)]. 52.18/52.19 Derived: -banach(real) | exp(real) = ti(fun(real,real),exp(real)). [resolve(5252,b,5190,a)]. 52.18/52.19 5253 -real_normed_field(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),inverse_divide(A)),B)),C)) # label(fact_4897_divide_OisCont) # label(axiom). [clausify(4279)]. 52.18/52.19 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),inverse_divide(complex)),A)),B)). [resolve(5253,a,5166,a)]. 52.18/52.19 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),inverse_divide(real)),A)),B)). [resolve(5253,a,5190,a)]. 52.18/52.19 5254 -real_normed_field(A) | ti(A,B) = zero_zero(A) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(A,real,norm_norm(A),C)),hAPP(A,real,norm_norm(A),B)) = hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) # label(fact_1790_nonzero__norm__divide) # label(axiom). [clausify(4316)]. 52.18/52.19 Derived: ti(complex,A) = zero_zero(complex) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(complex,real,norm_norm(complex),B)),hAPP(complex,real,norm_norm(complex),A)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)). [resolve(5254,a,5166,a)]. 52.18/52.19 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,norm_norm(real),B)),hAPP(real,real,norm_norm(real),A)) = hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)). [resolve(5254,a,5190,a)]. 52.27/52.27 5255 -real_normed_field(A) | -banach(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(A,A,exp(A),B))) # label(fact_4752_exp__converges) # label(axiom). [clausify(4332)]. 52.27/52.27 Derived: -banach(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,real),fun(nat,fun(complex,complex)),hAPP(fun(real,fun(complex,complex)),fun(fun(nat,real),fun(nat,fun(complex,complex))),combb(real,fun(complex,complex),nat),scaleR_scaleR(complex)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(complex,complex,exp(complex),A))). [resolve(5255,a,5166,a)]. 52.27/52.27 Derived: -banach(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),scaleR_scaleR(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(real,real,exp(real),A))). [resolve(5255,a,5190,a)]. 52.27/52.27 5256 -real_normed_field(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | ti(A,E) = zero_zero(A) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),E)),sequentially)) # label(fact_4451_LIMSEQ__divide) # label(axiom). [clausify(4364)]. 52.27/52.27 5257 -real_normed_field(A) | -banach(A) | hAPP(A,A,exp(A),B) != zero_zero(A) # label(fact_2537_exp__not__eq__zero) # label(axiom). [clausify(4379)]. 52.27/52.27 Derived: -banach(complex) | hAPP(complex,complex,exp(complex),A) != zero_zero(complex). [resolve(5257,a,5166,a)]. 52.27/52.27 Derived: -banach(real) | hAPP(real,real,exp(real),A) != zero_zero(real). [resolve(5257,a,5190,a)]. 52.27/52.27 5258 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3985_divide_Osuminf) # label(axiom). [clausify(4395)]. 52.36/52.33 5259 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),C))) # label(fact_4102_divide_OCauchy) # label(axiom). [clausify(4422)]. 52.36/52.33 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),inverse_divide(complex)),A)),B))). [resolve(5259,a,5166,a)]. 52.36/52.33 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),A)),B))). [resolve(5259,a,5190,a)]. 52.36/52.33 5260 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(nat,fun(A,A),hAPP(fun(A,fun(nat,A)),fun(nat,fun(A,A)),combc(A,nat,A),hAPP(fun(A,A),fun(A,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(A,A),fun(A,fun(nat,A))),combb(A,fun(nat,A),A),power_power(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),hAPP(nat,nat,suc,zero_zero(nat)))))))) # label(fact_3889_DERIV__power) # label(axiom). [clausify(4431)]. 52.36/52.33 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(nat,fun(complex,complex),hAPP(fun(complex,fun(nat,complex)),fun(nat,fun(complex,complex)),combc(complex,nat,complex),hAPP(fun(complex,complex),fun(complex,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(complex,complex),fun(complex,fun(nat,complex))),combb(complex,fun(nat,complex),complex),power_power(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,semiring_1_of_nat(complex),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))). [resolve(5260,a,5166,a)]. 52.36/52.33 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(nat,fun(real,real),hAPP(fun(real,fun(nat,real)),fun(nat,fun(real,real)),combc(real,nat,real),hAPP(fun(real,real),fun(real,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(real,real),fun(real,fun(nat,real))),combb(real,fun(nat,real),real),power_power(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),D),hAPP(nat,nat,suc,zero_zero(nat)))))))). [resolve(5260,a,5190,a)]. 52.36/52.33 5261 -real_normed_field(A) | -banach(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,real),fun(nat,fun(A,A)),hAPP(fun(real,fun(A,A)),fun(fun(nat,real),fun(nat,fun(A,A))),combb(real,fun(A,A),nat),scaleR_scaleR(A)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat))))),hAPP(A,fun(nat,A),power_power(A),B))) = hAPP(A,A,exp(A),B) # label(fact_4751_exp__def) # label(axiom). [clausify(4456)]. 52.59/52.56 5262 -banach(A) | -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),hAPP(A,real,norm_norm(A),C))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),hAPP(A,fun(nat,A),power_power(A),D))))) # label(fact_3996_powser__insidea) # label(axiom). [clausify(4492)]. 52.59/52.56 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),hAPP(complex,real,norm_norm(complex),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),hAPP(complex,fun(nat,complex),power_power(complex),C))))). [resolve(5262,b,5166,a)]. 52.59/52.56 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),hAPP(real,real,norm_norm(real),B))) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),hAPP(real,fun(nat,real),power_power(real),C))))). [resolve(5262,b,5190,a)]. 52.59/52.56 5263 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B)) = hAPP(A,A,uminus_uminus(A),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3986_suminf__minus) # label(axiom). [clausify(4675)]. 52.67/52.67 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),uminus_uminus(complex)),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)). [resolve(5263,a,5166,a)]. 52.67/52.67 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),uminus_uminus(real)),A)) = hAPP(real,real,uminus_uminus(real),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5263,a,5190,a)]. 52.67/52.67 5264 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),inverse_divide(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_4085_divide_Osums) # label(axiom). [clausify(4679)]. 52.67/52.67 5265 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | ti(A,E) != ti(A,D) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),E)) # label(fact_2635_Deriv_Olemma__DERIV__subst) # label(axiom). [clausify(4760)]. 52.67/52.67 5266 -real_normed_field(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),C)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_3982_suminf__diff) # label(axiom). [clausify(4767)]. 52.67/52.67 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),B)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5266,a,5166,a)]. 52.67/52.67 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),B)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5266,a,5190,a)]. 52.67/52.67 5267 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),times_times(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,E,C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),hAPP(A,A,B,C))))) # label(fact_3817_DERIV__mult) # label(axiom). [clausify(4780)]. 52.75/52.69 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),times_times(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,D,B))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),hAPP(complex,complex,A,B))))). [resolve(5267,a,5166,a)]. 52.75/52.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),times_times(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,D,B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),hAPP(real,real,A,B))))). [resolve(5267,a,5190,a)]. 52.75/52.69 5268 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,B,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C))),D)),hAPP(A,A,inverse_inverse(A),hAPP(A,A,B,C)))))) # label(fact_3877_DERIV__inverse_H) # label(axiom). [clausify(4792)]. 52.75/52.69 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,A,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B))),C)),hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,A,B)))))). [resolve(5268,a,5166,a)]. 52.75/52.69 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,A,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B))),C)),hAPP(real,real,inverse_inverse(real),hAPP(real,real,A,B)))))). [resolve(5268,a,5190,a)]. 52.80/52.79 5269 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),E),C),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,A)),combs(A,A,A),hAPP(fun(A,A),fun(A,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(A,A),fun(A,fun(A,A))),combb(A,fun(A,A),A),plus_plus(A)),B)),E)),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F))) # label(fact_3823_DERIV__add) # label(axiom). [clausify(4798)]. 52.80/52.79 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),D),B),E)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,complex)),combs(complex,complex,complex),hAPP(fun(complex,complex),fun(complex,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(complex,complex),fun(complex,fun(complex,complex))),combb(complex,fun(complex,complex),complex),plus_plus(complex)),A)),D)),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),E))). [resolve(5269,a,5166,a)]. 52.80/52.79 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),D),B),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,real)),combs(real,real,real),hAPP(fun(real,real),fun(real,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(real,real),fun(real,fun(real,real))),combb(real,fun(real,real),real),plus_plus(real)),A)),D)),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),E))). [resolve(5269,a,5190,a)]. 52.80/52.79 5270 -real_normed_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),B),C),D)) | hAPP(A,A,B,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),hAPP(fun(A,A),fun(A,fun(A,bool)),deriv(A),hAPP(fun(A,A),fun(A,A),hAPP(fun(A,A),fun(fun(A,A),fun(A,A)),combb(A,A,A),inverse_inverse(A)),B)),C),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,B,C)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))) # label(fact_3901_DERIV__inverse__fun) # label(axiom). [clausify(4889)]. 52.80/52.79 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),A),B),C)) | hAPP(complex,complex,A,B) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),hAPP(fun(complex,complex),fun(complex,fun(complex,bool)),deriv(complex),hAPP(fun(complex,complex),fun(complex,complex),hAPP(fun(complex,complex),fun(fun(complex,complex),fun(complex,complex)),combb(complex,complex,complex),inverse_inverse(complex)),A)),B),hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))). [resolve(5270,a,5166,a)]. 54.86/54.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),A),B),C)) | hAPP(real,real,A,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),hAPP(fun(real,real),fun(real,fun(real,bool)),deriv(real),hAPP(fun(real,real),fun(real,real),hAPP(fun(real,real),fun(fun(real,real),fun(real,real)),combb(real,real,real),inverse_inverse(real)),A)),B),hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,A,B)),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat))))))))). [resolve(5270,a,5190,a)]. 54.86/54.81 5271 division_ring(real) # label(arity_RealDef_Oreal___Fields_Odivision__ring) # label(axiom). [assumption]. 54.86/54.81 5272 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom). [clausify(24)]. 54.86/54.81 5273 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_1688_nonzero__divide__eq__eq) # label(axiom). [clausify(24)]. 54.86/54.81 5274 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2551_nonzero__inverse__mult__distrib) # label(axiom). [clausify(208)]. 54.86/54.81 5275 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),zero_zero(A)),B) = zero_zero(A) # label(fact_1658_divide__zero__left) # label(axiom). [clausify(242)]. 54.86/54.81 5276 -division_ring(A) | ti(A,B) = zero_zero(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,inverse_inverse(A),B)),C) = hAPP(A,A,inverse_inverse(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_2553_nonzero__power__inverse) # label(axiom). [clausify(254)]. 54.86/54.81 5277 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1659_times__divide__eq__right) # label(axiom). [clausify(282)]. 54.86/54.81 5278 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,inverse_inverse(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2611_inverse__diff__inverse) # label(axiom). [clausify(414)]. 54.86/54.81 5279 -division_ring(A) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) | ti(A,C) = hAPP(A,A,inverse_inverse(A),B) # label(fact_2552_inverse__unique) # label(axiom). [clausify(899)]. 54.86/54.81 5280 -division_ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2019_minus__divide__left) # label(axiom). [clausify(1082)]. 54.86/54.81 5281 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1692_divide__eq__imp) # label(axiom). [clausify(1359)]. 54.86/54.81 5282 -division_ring(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),one_one(A)) # label(fact_1663_divide__1) # label(axiom). [clausify(1366)]. 54.86/54.81 5283 -division_ring(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),B) # label(fact_2581_left__inverse) # label(axiom). [clausify(1449)]. 54.86/54.81 5284 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,B) != ti(A,C) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1696_right__inverse__eq) # label(axiom). [clausify(1511)]. 55.08/55.01 5285 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,B) = ti(A,C) | one_one(A) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1696_right__inverse__eq) # label(axiom). [clausify(1511)]. 55.08/55.01 5286 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1665_diff__divide__distrib) # label(axiom). [clausify(1607)]. 55.08/55.01 5287 -division_ring(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,inverse_inverse(A),B) != zero_zero(A) # label(fact_2528_nonzero__imp__inverse__nonzero) # label(axiom). [clausify(1655)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A) | ti(real,C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A). [resolve(5271,a,5272,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A) | ti(real,C) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A). [resolve(5271,a,5273,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),B)),hAPP(real,real,inverse_inverse(real),A)). [resolve(5271,a,5274,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,inverse_inverse(real),A)),B) = hAPP(real,real,inverse_inverse(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5271,a,5276,a)]. 55.08/55.01 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)). [resolve(5271,a,5277,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B))),hAPP(real,real,inverse_inverse(real),B))) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)). [resolve(5271,a,5278,a)]. 55.08/55.01 Derived: one_one(real) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B) | ti(real,B) = hAPP(real,real,inverse_inverse(real),A). [resolve(5271,a,5279,a)]. 55.08/55.01 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),one_one(real)). [resolve(5271,a,5282,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),A). [resolve(5271,a,5283,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | ti(real,A) != ti(real,B) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A). [resolve(5271,a,5284,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | ti(real,A) = ti(real,B) | one_one(real) != hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A). [resolve(5271,a,5285,a)]. 55.08/55.01 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,inverse_inverse(real),A) != zero_zero(real). [resolve(5271,a,5287,a)]. 55.08/55.01 5288 -division_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)) # label(fact_1662_add__divide__distrib) # label(axiom). [clausify(2114)]. 55.08/55.01 5289 -division_ring(A) | inverse_inverse(A) = ti(fun(A,A),inverse_inverse(A)) # label(tsy_c_Fields_Oinverse__class_Oinverse_res) # label(axiom). [clausify(2131)]. 55.86/55.80 Derived: inverse_inverse(real) = ti(fun(real,real),inverse_inverse(real)). [resolve(5289,a,5271,a)]. 55.86/55.80 5290 -division_ring(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_2557_divide__inverse) # label(axiom). [clausify(2244)]. 55.86/55.80 Derived: hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,inverse_inverse(real),B)). [resolve(5290,a,5271,a)]. 55.86/55.80 5291 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom). [clausify(2253)]. 55.86/55.80 5292 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1687_nonzero__eq__divide__eq) # label(axiom). [clausify(2253)]. 55.86/55.80 5293 -division_ring(A) | -number(A) | hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_2588_inverse__eq__divide__number__of) # label(axiom). [clausify(2297)]. 55.86/55.80 Derived: -number(real) | hAPP(real,real,inverse_inverse(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),A)). [resolve(5293,a,5271,a)]. 55.86/55.80 5294 -division_ring(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),B) # label(fact_1695_divide__self) # label(axiom). [clausify(2583)]. 55.86/55.80 Derived: ti(real,A) = zero_zero(real) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),A). [resolve(5294,a,5271,a)]. 55.86/55.80 5295 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),B) # label(fact_2560_inverse__eq__divide) # label(axiom). [clausify(2769)]. 55.86/55.80 Derived: hAPP(real,real,inverse_inverse(real),A) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),A). [resolve(5295,a,5271,a)]. 55.86/55.80 5296 -division_ring(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2077_nonzero__minus__divide__right) # label(axiom). [clausify(2782)]. 55.86/55.80 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),hAPP(real,real,uminus_uminus(real),A)). [resolve(5296,a,5271,a)]. 55.86/55.80 5297 -division_ring(A) | inverse_divide(A) = ti(fun(A,fun(A,A)),inverse_divide(A)) # label(tsy_c_Fields_Oinverse__class_Odivide_1_res) # label(axiom). [clausify(2932)]. 55.86/55.80 Derived: inverse_divide(real) = ti(fun(real,fun(real,real)),inverse_divide(real)). [resolve(5297,a,5271,a)]. 55.86/55.80 5298 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_1693_eq__divide__imp) # label(axiom). [clausify(2994)]. 55.86/55.80 5299 -division_ring(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2579_right__inverse) # label(axiom). [clausify(3166)]. 55.86/55.80 Derived: ti(real,A) = zero_zero(real) | one_one(real) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,inverse_inverse(real),A)). [resolve(5299,a,5271,a)]. 55.86/55.80 5300 -division_ring(A) | ti(A,B) = zero_zero(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_2584_nonzero__inverse__eq__divide) # label(axiom). [clausify(3229)]. 55.86/55.80 5301 -division_ring(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B) # label(fact_2078_nonzero__minus__divide__divide) # label(axiom). [clausify(3245)]. 55.90/55.84 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A). [resolve(5301,a,5271,a)]. 55.90/55.84 5302 division_ring(complex) # label(arity_Complex_Ocomplex___Fields_Odivision__ring) # label(axiom). [assumption]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A) | ti(complex,C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A). [resolve(5302,a,5272,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),C),A) | ti(complex,C) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A). [resolve(5302,a,5273,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),B)),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5302,a,5274,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,inverse_inverse(complex),A)),B) = hAPP(complex,complex,inverse_inverse(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(5302,a,5276,a)]. 55.90/55.84 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),C)). [resolve(5302,a,5277,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B))),hAPP(complex,complex,inverse_inverse(complex),B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(5302,a,5278,a)]. 55.90/55.84 Derived: one_one(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B) | ti(complex,B) = hAPP(complex,complex,inverse_inverse(complex),A). [resolve(5302,a,5279,a)]. 55.90/55.84 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),one_one(complex)). [resolve(5302,a,5282,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),A). [resolve(5302,a,5283,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,A) != ti(complex,B) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A). [resolve(5302,a,5284,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,A) = ti(complex,B) | one_one(complex) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A). [resolve(5302,a,5285,a)]. 55.90/55.84 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,complex,inverse_inverse(complex),A) != zero_zero(complex). [resolve(5302,a,5287,a)]. 55.90/55.84 Derived: inverse_inverse(complex) = ti(fun(complex,complex),inverse_inverse(complex)). [resolve(5302,a,5289,a)]. 56.97/56.97 Derived: -number(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(int,complex,number_number_of(complex),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)). [resolve(5302,a,5293,a)]. 56.97/56.97 Derived: ti(complex,A) = zero_zero(complex) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),A),A). [resolve(5302,a,5294,a)]. 56.97/56.97 Derived: hAPP(complex,complex,inverse_inverse(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),one_one(complex)),A). [resolve(5302,a,5295,a)]. 56.97/56.97 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(5302,a,5296,a)]. 56.97/56.97 Derived: inverse_divide(complex) = ti(fun(complex,fun(complex,complex)),inverse_divide(complex)). [resolve(5302,a,5297,a)]. 56.97/56.97 Derived: ti(complex,A) = zero_zero(complex) | one_one(complex) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5302,a,5299,a)]. 56.97/56.97 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,uminus_uminus(complex),B)),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),B),A). [resolve(5302,a,5301,a)]. 56.97/56.97 5303 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B))),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2582_division__ring__inverse__diff) # label(axiom). [clausify(3578)]. 56.97/56.97 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A))),hAPP(real,real,inverse_inverse(real),B)). [resolve(5303,a,5271,a)]. 56.97/56.97 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,inverse_inverse(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A))),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(5303,a,5302,a)]. 56.97/56.97 5304 -division_ring(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2556_nonzero__inverse__minus__eq) # label(axiom). [clausify(4126)]. 56.97/56.97 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5304,a,5271,a)]. 56.97/56.97 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,uminus_uminus(complex),A)) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5304,a,5302,a)]. 56.97/56.97 5305 division_ring(rat) # label(arity_Rat_Orat___Fields_Odivision__ring) # label(axiom). [assumption]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A) | ti(rat,C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A). [resolve(5305,a,5272,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A) | ti(rat,C) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A). [resolve(5305,a,5273,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5305,a,5274,a)]. 57.05/56.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(5305,a,5275,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,inverse_inverse(rat),A)),B) = hAPP(rat,rat,inverse_inverse(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(5305,a,5276,a)]. 57.05/56.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)). [resolve(5305,a,5277,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B))),hAPP(rat,rat,inverse_inverse(rat),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(5305,a,5278,a)]. 57.05/56.99 Derived: one_one(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B) | ti(rat,B) = hAPP(rat,rat,inverse_inverse(rat),A). [resolve(5305,a,5279,a)]. 57.05/56.99 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B). [resolve(5305,a,5280,a)]. 57.05/56.99 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),one_one(rat)). [resolve(5305,a,5282,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),A). [resolve(5305,a,5283,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,A) != ti(rat,B) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A). [resolve(5305,a,5284,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,A) = ti(rat,B) | one_one(rat) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A). [resolve(5305,a,5285,a)]. 57.05/56.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(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(5305,a,5286,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,inverse_inverse(rat),A) != zero_zero(rat). [resolve(5305,a,5287,a)]. 57.05/56.99 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)). [resolve(5305,a,5288,a)]. 57.05/56.99 Derived: inverse_inverse(rat) = ti(fun(rat,rat),inverse_inverse(rat)). [resolve(5305,a,5289,a)]. 57.05/56.99 Derived: -number(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)). [resolve(5305,a,5293,a)]. 57.05/56.99 Derived: ti(rat,A) = zero_zero(rat) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),A). [resolve(5305,a,5294,a)]. 57.36/57.30 Derived: hAPP(rat,rat,inverse_inverse(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),A). [resolve(5305,a,5295,a)]. 57.36/57.30 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(5305,a,5296,a)]. 57.36/57.30 Derived: inverse_divide(rat) = ti(fun(rat,fun(rat,rat)),inverse_divide(rat)). [resolve(5305,a,5297,a)]. 57.36/57.30 Derived: ti(rat,A) = zero_zero(rat) | one_one(rat) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5305,a,5299,a)]. 57.36/57.30 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A). [resolve(5305,a,5301,a)]. 57.36/57.30 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A))),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(5305,a,5303,a)]. 57.36/57.30 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5305,a,5304,a)]. 57.36/57.30 5306 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2577_division__ring__inverse__add) # label(axiom). [clausify(4360)]. 57.36/57.30 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | 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)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(real,real,inverse_inverse(real),B)). [resolve(5306,a,5271,a)]. 57.36/57.30 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | 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)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(complex,complex,inverse_inverse(complex),B)). [resolve(5306,a,5302,a)]. 57.36/57.30 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | 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)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,inverse_inverse(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(rat,rat,inverse_inverse(rat),B)). [resolve(5306,a,5305,a)]. 57.36/57.30 5307 -division_ring(A) | one_one(A) = hAPP(A,A,inverse_inverse(A),one_one(A)) # label(fact_2516_inverse__1) # label(axiom). [clausify(4495)]. 57.36/57.30 Derived: one_one(real) = hAPP(real,real,inverse_inverse(real),one_one(real)). [resolve(5307,a,5271,a)]. 57.36/57.30 Derived: one_one(complex) = hAPP(complex,complex,inverse_inverse(complex),one_one(complex)). [resolve(5307,a,5302,a)]. 59.30/59.27 Derived: one_one(rat) = hAPP(rat,rat,inverse_inverse(rat),one_one(rat)). [resolve(5307,a,5305,a)]. 59.30/59.27 5308 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_2530_inverse__zero__imp__zero) # label(axiom). [clausify(4541)]. 59.30/59.27 5309 -division_ring(A) | hAPP(A,A,inverse_inverse(A),B) != hAPP(A,A,inverse_inverse(A),C) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | ti(A,B) = ti(A,C) # label(fact_2531_nonzero__inverse__eq__imp__eq) # label(axiom). [clausify(4654)]. 59.30/59.27 Derived: hAPP(real,real,inverse_inverse(real),A) != hAPP(real,real,inverse_inverse(real),B) | ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | ti(real,A) = ti(real,B). [resolve(5309,a,5271,a)]. 59.30/59.27 Derived: hAPP(complex,complex,inverse_inverse(complex),A) != hAPP(complex,complex,inverse_inverse(complex),B) | ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | ti(complex,A) = ti(complex,B). [resolve(5309,a,5302,a)]. 59.30/59.27 Derived: hAPP(rat,rat,inverse_inverse(rat),A) != hAPP(rat,rat,inverse_inverse(rat),B) | ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | ti(rat,A) = ti(rat,B). [resolve(5309,a,5305,a)]. 59.30/59.27 5310 -division_ring(A) | ti(A,B) = zero_zero(A) | ti(A,B) = hAPP(A,A,inverse_inverse(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2529_nonzero__inverse__inverse__eq) # label(axiom). [clausify(4921)]. 59.30/59.27 Derived: ti(real,A) = zero_zero(real) | ti(real,A) = hAPP(real,real,inverse_inverse(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5310,a,5271,a)]. 59.30/59.27 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,A) = hAPP(complex,complex,inverse_inverse(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5310,a,5302,a)]. 59.30/59.27 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,A) = hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5310,a,5305,a)]. 59.30/59.27 5311 linorder(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Orderings_Olinorder) # label(axiom). [assumption]. 59.30/59.27 5312 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_4977_min__max_Osup__least) # label(axiom). [clausify(38)]. 59.30/59.27 5313 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C))) # label(fact_4986_le__maxI1) # label(axiom). [clausify(104)]. 59.30/59.27 5314 -plus(A) | -dvd(A) | -linorder(A) | plus_plus(A) = ti(fun(A,fun(A,A)),plus_plus(A)) # label(tsy_c_Groups_Oplus__class_Oplus_0_res) # label(axiom). [clausify(118)]. 59.30/59.27 5315 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),B)) # label(fact_4829_min__max_Oinf__le1) # label(axiom). [clausify(207)]. 59.30/59.27 5316 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4830_min__le__iff__disj) # label(axiom). [clausify(231)]. 59.30/59.27 5317 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4830_min__le__iff__disj) # label(axiom). [clausify(231)]. 59.30/59.27 5318 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4830_min__le__iff__disj) # label(axiom). [clausify(231)]. 59.30/59.27 5319 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B))) # label(fact_4985_le__maxI2) # label(axiom). [clausify(252)]. 59.30/59.27 5320 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),E))) # label(fact_4976_min__max_Osup__mono) # label(axiom). [clausify(270)]. 59.30/59.27 5321 -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_1583_linorder__not__le) # label(axiom). [clausify(284)]. 59.30/59.27 5322 -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_1583_linorder__not__le) # label(axiom). [clausify(284)]. 59.30/59.27 5323 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_4820_min__max_Oinf__greatest) # label(axiom). [clausify(448)]. 59.30/59.27 5324 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_4822_min__max_Oinf__absorb2) # label(axiom). [clausify(480)]. 59.30/59.27 5325 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1582_linorder__not__less) # label(axiom). [clausify(489)]. 59.30/59.27 5326 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1582_linorder__not__less) # label(axiom). [clausify(489)]. 59.30/59.27 5327 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4809_min__max_Oinf__assoc) # label(axiom). [clausify(505)]. 59.30/59.27 5328 -linorder(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom). [clausify(539)]. 59.30/59.27 5329 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_4984_min__max_Ole__iff__sup) # label(axiom). [clausify(539)]. 59.30/59.27 5330 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_4824_min__max_Ole__infI2) # label(axiom). [clausify(554)]. 59.30/59.27 5331 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4975_min__max_Ole__supE) # label(axiom). [clausify(707)]. 59.30/59.27 5332 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4975_min__max_Ole__supE) # label(axiom). [clausify(707)]. 59.30/59.27 5333 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_4964_min__max_Osup__assoc) # label(axiom). [clausify(782)]. 59.30/59.27 5334 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4818_min__max_Ole__infE) # label(axiom). [clausify(788)]. 59.30/59.27 5335 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4818_min__max_Ole__infE) # label(axiom). [clausify(788)]. 59.30/59.27 5336 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | ti(A,D) != ti(A,B) | ti(A,E) != ti(A,C) | 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) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom). [clausify(885)]. 59.30/59.29 5337 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | ti(A,D) = ti(A,B) | 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) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom). [clausify(885)]. 59.30/59.29 5338 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | ti(A,E) = ti(A,C) | 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) # label(fact_4197_atLeastLessThan__eq__iff) # label(axiom). [clausify(885)]. 59.30/59.29 5339 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_4823_min__max_Oinf__absorb1) # label(axiom). [clausify(893)]. 59.30/59.29 5340 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_1544_linorder__le__cases) # label(axiom). [clausify(999)]. 59.30/59.29 5341 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1563_linorder__less__linear) # label(axiom). [clausify(1044)]. 59.30/59.29 5342 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) # label(fact_4821_min__max_Ole__infI) # label(axiom). [clausify(1069)]. 59.30/59.29 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)),B)). [resolve(5311,a,5312,a)]. 59.30/59.29 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B))). [resolve(5311,a,5313,a)]. 59.30/59.29 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(5311,a,5315,a)]. 59.30/59.29 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(5311,a,5316,a)]. 59.30/59.29 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(5311,a,5317,a)]. 59.30/59.29 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(5311,a,5318,a)]. 59.30/59.31 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),A))). [resolve(5311,a,5319,a)]. 59.30/59.31 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),D))). [resolve(5311,a,5320,a)]. 59.30/59.31 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(5311,a,5321,a)]. 59.30/59.31 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(5311,a,5322,a)]. 59.30/59.31 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(5311,a,5323,a)]. 59.30/59.31 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(5311,a,5324,a)]. 59.30/59.31 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(5311,a,5327,a)]. 59.30/59.31 Derived: ti(code_code_numeral,A) != hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(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),B),A)). [resolve(5311,a,5328,a)]. 59.30/59.31 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(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),B),A)). [resolve(5311,a,5329,a)]. 59.30/59.31 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(5311,a,5331,a)]. 59.40/59.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(5311,a,5332,a)]. 59.40/59.33 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)). [resolve(5311,a,5333,a)]. 59.40/59.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5311,a,5334,a)]. 59.40/59.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(5311,a,5335,a)]. 59.40/59.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | ti(code_code_numeral,C) != ti(code_code_numeral,A) | ti(code_code_numeral,D) != ti(code_code_numeral,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) = 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). [resolve(5311,a,5336,a)]. 59.40/59.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | ti(code_code_numeral,C) = ti(code_code_numeral,A) | 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). [resolve(5311,a,5337,a)]. 59.40/59.33 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | ti(code_code_numeral,D) = ti(code_code_numeral,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) != 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). [resolve(5311,a,5338,a)]. 59.48/59.40 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),A),B). [resolve(5311,a,5339,a)]. 59.48/59.40 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(5311,a,5340,a)]. 59.48/59.40 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) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)). [resolve(5311,a,5341,a)]. 59.48/59.40 5343 -linorder(A) | ord_min(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),max(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_4834_dual__max) # label(axiom). [clausify(1149)]. 59.48/59.40 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(5343,a,5311,a)]. 59.48/59.40 5344 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_4978_min__max_Ole__supI) # label(axiom). [clausify(1170)]. 59.48/59.40 5345 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_4802_Min_Oidem) # label(axiom). [clausify(1259)]. 59.48/59.40 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(5345,a,5311,a)]. 59.48/59.40 5346 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4987_le__max__iff__disj) # label(axiom). [clausify(1280)]. 59.48/59.40 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5346,a,5311,a)]. 59.48/59.40 5347 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4987_le__max__iff__disj) # label(axiom). [clausify(1280)]. 59.48/59.40 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(5347,a,5311,a)]. 59.48/59.40 5348 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4987_le__max__iff__disj) # label(axiom). [clausify(1280)]. 59.48/59.40 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)). [resolve(5348,a,5311,a)]. 59.48/59.44 5349 -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_4320_lessThan__strict__subset__iff) # label(axiom). [clausify(1295)]. 59.48/59.44 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(5349,a,5311,a)]. 59.48/59.44 5350 -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_4320_lessThan__strict__subset__iff) # label(axiom). [clausify(1295)]. 59.48/59.44 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(5350,a,5311,a)]. 59.48/59.44 5351 -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_4195_atLeastLessThan__inj_I2_J) # label(axiom). [clausify(1326)]. 59.48/59.44 5352 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_4812_min__max_Oinf_Oleft__commute) # label(axiom). [clausify(1327)]. 59.48/59.44 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(5352,a,5311,a)]. 59.48/59.44 5353 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom). [clausify(1356)]. 59.48/59.44 5354 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom). [clausify(1356)]. 59.48/59.44 5355 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4826_min__max_Ole__inf__iff) # label(axiom). [clausify(1356)]. 59.61/59.55 5356 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) # label(fact_4965_min__max_Osup_Oassoc) # label(axiom). [clausify(1371)]. 59.61/59.55 5357 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_4951_min__max_Oless__supI1) # label(axiom). [clausify(1395)]. 59.61/59.55 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(5357,a,5311,a)]. 59.61/59.55 5358 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_4938_min__max_Osup__inf__distrib2) # label(axiom). [clausify(1407)]. 59.61/59.55 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),B). [resolve(5358,a,5311,a)]. 59.61/59.55 5359 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4810_min__max_Oinf_Oassoc) # label(axiom). [clausify(1458)]. 59.61/59.55 5360 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f303(A,B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2829_pinf_I8_J) # label(axiom). [clausify(1542)]. 59.61/59.55 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),f303(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(5360,a,5311,a)]. 59.61/59.55 5361 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_4967_min__max_Osup_Oleft__commute) # label(axiom). [clausify(1586)]. 59.61/59.55 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)). [resolve(5361,a,5311,a)]. 59.61/59.55 5362 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),E))) # label(fact_4819_min__max_Oinf__mono) # label(axiom). [clausify(1636)]. 59.61/59.55 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(5362,a,5311,a)]. 59.70/59.67 5363 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)))) # label(fact_4946_min__max_Odistrib__sup__le) # label(axiom). [clausify(1750)]. 59.70/59.67 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(5363,a,5311,a)]. 59.70/59.67 5364 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_1588_leI) # label(axiom). [clausify(1767)]. 59.70/59.67 5365 -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_4799_min__less__iff__conj) # label(axiom). [clausify(1906)]. 59.70/59.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),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(5365,a,5311,a)]. 59.70/59.67 5366 -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_4799_min__less__iff__conj) # label(axiom). [clausify(1906)]. 59.70/59.67 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),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(5366,a,5311,a)]. 59.70/59.67 5367 -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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_4799_min__less__iff__conj) # label(axiom). [clausify(1906)]. 59.70/59.67 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),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)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(5367,a,5311,a)]. 59.86/59.78 5368 -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_4798_min__less__iff__disj) # label(axiom). [clausify(1942)]. 59.86/59.78 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(5368,a,5311,a)]. 59.86/59.78 5369 -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_4798_min__less__iff__disj) # label(axiom). [clausify(1942)]. 59.86/59.78 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(5369,a,5311,a)]. 59.86/59.78 5370 -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_4798_min__less__iff__disj) # label(axiom). [clausify(1942)]. 59.86/59.78 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(5370,a,5311,a)]. 59.86/59.78 5371 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) # label(fact_1590_linorder__antisym__conv1) # label(axiom). [clausify(1975)]. 59.86/59.78 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) = ti(code_code_numeral,A). [resolve(5371,a,5311,a)]. 59.86/59.78 5372 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_1590_linorder__antisym__conv1) # label(axiom). [clausify(1975)]. 59.86/59.78 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) != ti(code_code_numeral,A). [resolve(5372,a,5311,a)]. 59.86/59.78 5373 -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),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom). [clausify(2135)]. 59.86/59.78 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),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),C),A)). [resolve(5373,a,5311,a)]. 59.99/59.96 5374 -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),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),E)) # label(fact_4199_atLeastLessThan__subset__iff) # label(axiom). [clausify(2135)]. 59.99/59.96 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),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),D)). [resolve(5374,a,5311,a)]. 59.99/59.96 5375 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f430(A,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2828_minf_I6_J) # label(axiom). [clausify(2291)]. 59.99/59.96 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),f430(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(5375,a,5311,a)]. 59.99/59.96 5376 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4968_min__max_Osup__left__idem) # label(axiom). [clausify(2347)]. 59.99/59.96 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B). [resolve(5376,a,5311,a)]. 59.99/59.96 5377 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_1558_linorder__linear) # label(axiom). [clausify(2357)]. 59.99/59.96 5378 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_4979_min__max_Osup__absorb1) # label(axiom). [clausify(2391)]. 59.99/59.96 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),A). [resolve(5378,a,5311,a)]. 59.99/59.96 5379 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),D),B)),C)) # label(fact_4801_min__max_Oless__infI2) # label(axiom). [clausify(2467)]. 59.99/59.96 5380 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4980_min__max_Osup__absorb2) # label(axiom). [clausify(2474)]. 60.21/60.15 5381 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1593_leD) # label(axiom). [clausify(2488)]. 60.21/60.15 5382 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),C)) # label(fact_4828_min__max_Oinf__le2) # label(axiom). [clausify(2509)]. 60.21/60.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),B)). [resolve(5382,a,5311,a)]. 60.21/60.15 5383 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1581_linorder__cases) # label(axiom). [clausify(2524)]. 60.21/60.15 5384 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4950_less__max__iff__disj) # label(axiom). [clausify(2598)]. 60.21/60.15 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B))). [resolve(5384,a,5311,a)]. 60.21/60.15 5385 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_4950_less__max__iff__disj) # label(axiom). [clausify(2598)]. 60.21/60.15 5386 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4950_less__max__iff__disj) # label(axiom). [clausify(2598)]. 60.21/60.15 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),C),B))). [resolve(5386,a,5311,a)]. 60.21/60.15 5387 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) # label(fact_4969_min__max_Osup_Oleft__idem) # label(axiom). [clausify(2691)]. 60.21/60.15 5388 linorder(nat) # label(arity_Nat_Onat___Orderings_Olinorder) # label(axiom). [assumption]. 60.21/60.15 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B)). [resolve(5388,a,5312,a)]. 60.21/60.15 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B))). [resolve(5388,a,5313,a)]. 60.21/60.15 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(5388,a,5315,a)]. 60.21/60.15 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(5388,a,5316,a)]. 60.21/60.15 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(5388,a,5317,a)]. 60.21/60.17 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(5388,a,5318,a)]. 60.21/60.17 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A))). [resolve(5388,a,5319,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),D))). [resolve(5388,a,5320,a)]. 60.21/60.17 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(5388,a,5321,a)]. 60.21/60.17 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(5388,a,5322,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(5388,a,5323,a)]. 60.21/60.17 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(5388,a,5324,a)]. 60.21/60.17 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(5388,a,5327,a)]. 60.21/60.17 Derived: ti(nat,A) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5388,a,5328,a)]. 60.21/60.17 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5388,a,5329,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(5388,a,5331,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(5388,a,5332,a)]. 60.21/60.17 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)). [resolve(5388,a,5333,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5388,a,5334,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(5388,a,5335,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | ti(nat,C) != ti(nat,A) | ti(nat,D) != ti(nat,B) | 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). [resolve(5388,a,5336,a)]. 60.21/60.17 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | ti(nat,C) = ti(nat,A) | 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). [resolve(5388,a,5337,a)]. 60.21/60.21 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | ti(nat,D) = ti(nat,B) | 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). [resolve(5388,a,5338,a)]. 60.21/60.21 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),A),B). [resolve(5388,a,5339,a)]. 60.21/60.21 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),B),A)). [resolve(5388,a,5340,a)]. 60.21/60.21 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,A) = ti(nat,B) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)). [resolve(5388,a,5341,a)]. 60.21/60.21 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(5388,a,5343,a)]. 60.21/60.21 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),A). [resolve(5388,a,5345,a)]. 60.21/60.21 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5388,a,5346,a)]. 60.21/60.21 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(5388,a,5347,a)]. 60.21/60.21 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5388,a,5348,a)]. 60.21/60.21 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(5388,a,5349,a)]. 60.21/60.21 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(5388,a,5350,a)]. 60.21/60.21 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(5388,a,5352,a)]. 60.21/60.21 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C))). [resolve(5388,a,5357,a)]. 60.21/60.21 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(5388,a,5358,a)]. 60.21/60.21 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f303(nat,A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5388,a,5360,a)]. 60.21/60.21 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)). [resolve(5388,a,5361,a)]. 60.21/60.21 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),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),D))). [resolve(5388,a,5362,a)]. 60.29/60.23 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(5388,a,5363,a)]. 60.29/60.23 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(5388,a,5365,a)]. 60.29/60.23 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(5388,a,5366,a)]. 60.29/60.23 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)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(5388,a,5367,a)]. 60.29/60.23 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(5388,a,5368,a)]. 60.29/60.23 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(5388,a,5369,a)]. 60.29/60.23 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(5388,a,5370,a)]. 60.29/60.23 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = ti(nat,A). [resolve(5388,a,5371,a)]. 60.29/60.23 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(5388,a,5372,a)]. 60.29/60.23 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),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),A)). [resolve(5388,a,5373,a)]. 60.29/60.23 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),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),D)). [resolve(5388,a,5374,a)]. 60.29/60.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f430(nat,B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(5388,a,5375,a)]. 60.29/60.23 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B). [resolve(5388,a,5376,a)]. 60.29/60.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(5388,a,5378,a)]. 60.29/60.23 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(5388,a,5382,a)]. 60.29/60.23 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(5388,a,5384,a)]. 60.38/60.37 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),C),B))). [resolve(5388,a,5386,a)]. 60.38/60.37 5389 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) # label(fact_4942_min__max_Osup__inf__absorb) # label(axiom). [clausify(2781)]. 60.38/60.37 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(5389,a,5311,a)]. 60.38/60.37 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(5389,a,5388,a)]. 60.38/60.37 5390 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),f516(A,C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2830_minf_I8_J) # label(axiom). [clausify(2799)]. 60.38/60.37 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),f516(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(5390,a,5311,a)]. 60.38/60.37 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),f516(nat,B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5390,a,5388,a)]. 60.38/60.37 5391 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4940_min__max_Osup__inf__distrib1) # label(axiom). [clausify(2831)]. 60.38/60.37 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C)). [resolve(5391,a,5311,a)]. 60.38/60.37 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(5391,a,5388,a)]. 60.38/60.37 5392 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) # label(fact_4941_min__max_Oinf__sup__absorb) # label(axiom). [clausify(2881)]. 60.38/60.37 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(5392,a,5311,a)]. 60.38/60.37 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(5392,a,5388,a)]. 60.38/60.37 5393 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_4939_min__max_Oinf__sup__distrib1) # label(axiom). [clausify(2998)]. 60.38/60.37 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)). [resolve(5393,a,5311,a)]. 60.67/60.61 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)). [resolve(5393,a,5388,a)]. 60.67/60.61 5394 -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_4196_atLeastLessThan__inj_I1_J) # label(axiom). [clausify(3098)]. 60.67/60.61 5395 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom). [clausify(3108)]. 60.67/60.61 5396 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom). [clausify(3108)]. 60.67/60.61 5397 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_4983_min__max_Ole__sup__iff) # label(axiom). [clausify(3108)]. 60.67/60.61 5398 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4981_min__max_Ole__supI2) # label(axiom). [clausify(3206)]. 60.67/60.61 5399 -linorder(A) | ti(A,B) != hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom). [clausify(3227)]. 60.67/60.61 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(5399,a,5311,a)]. 60.67/60.61 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(5399,a,5388,a)]. 60.67/60.61 5400 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_4827_min__max_Ole__iff__inf) # label(axiom). [clausify(3227)]. 60.67/60.61 5401 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D))) # label(fact_4982_min__max_Ole__supI1) # label(axiom). [clausify(3302)]. 60.67/60.61 5402 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) = ti(A,C) # label(fact_1564_linorder__antisym__conv3) # label(axiom). [clausify(3315)]. 60.67/60.61 5403 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | ti(A,B) != ti(A,C) # label(fact_1564_linorder__antisym__conv3) # label(axiom). [clausify(3315)]. 60.67/60.61 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),A)) | ti(code_code_numeral,A) != ti(code_code_numeral,B). [resolve(5403,a,5311,a)]. 61.09/61.03 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),A)) | ti(nat,A) != ti(nat,B). [resolve(5403,a,5388,a)]. 61.09/61.03 5404 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom). [clausify(3368)]. 61.09/61.03 5405 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | ti(A,C) != ti(A,B) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom). [clausify(3368)]. 61.09/61.03 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(5405,a,5311,a)]. 61.09/61.03 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | ti(nat,B) != ti(nat,A). [resolve(5405,a,5388,a)]. 61.09/61.03 5406 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1562_not__less__iff__gr__or__eq) # label(axiom). [clausify(3368)]. 61.09/61.03 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(5406,a,5311,a)]. 61.09/61.03 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(5406,a,5388,a)]. 61.09/61.03 5407 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),B) # label(fact_4817_min__max_Oinf_Oidem) # label(axiom). [clausify(3407)]. 61.09/61.03 5408 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_4815_min__max_Oinf__commute) # label(axiom). [clausify(3647)]. 61.09/61.03 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(5408,a,5311,a)]. 61.09/61.03 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(5408,a,5388,a)]. 61.09/61.03 5409 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),B) # label(fact_4816_min__max_Oinf_Ocommute) # label(axiom). [clausify(3655)]. 61.09/61.03 5410 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) # label(fact_4937_min__max_Oinf__sup__distrib2) # label(axiom). [clausify(3691)]. 61.09/61.03 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B)),C) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),A),C)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_min(code_code_numeral),B),C)). [resolve(5410,a,5311,a)]. 61.09/61.03 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B)),C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),B),C)). [resolve(5410,a,5388,a)]. 61.28/61.26 5411 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_1584_linorder__le__less__linear) # label(axiom). [clausify(3771)]. 61.28/61.26 5412 -linorder(A) | ord_max(A) = hAPP(fun(A,fun(A,bool)),fun(A,fun(A,A)),min(A),hAPP(fun(A,fun(A,bool)),fun(A,fun(A,bool)),combc(A,A,bool),ord_less_eq(A))) # label(fact_4991_dual__min) # label(axiom). [clausify(3835)]. 61.28/61.26 Derived: ord_max(code_code_numeral) = hAPP(fun(code_code_numeral,fun(code_code_numeral,bool)),fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),min(code_code_numeral),hAPP(fun(code_code_numeral,fun(code_code_numeral,bool)),fun(code_code_numeral,fun(code_code_numeral,bool)),combc(code_code_numeral,code_code_numeral,bool),ord_less_eq(code_code_numeral))). [resolve(5412,a,5311,a)]. 61.28/61.26 Derived: ord_max(nat) = hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,nat)),min(nat),hAPP(fun(nat,fun(nat,bool)),fun(nat,fun(nat,bool)),combc(nat,nat,bool),ord_less_eq(nat))). [resolve(5412,a,5388,a)]. 61.28/61.26 5413 linorder(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Orderings_Olinorder) # label(axiom). [assumption]. 61.28/61.26 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)),B)). [resolve(5413,a,5312,a)]. 61.28/61.26 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B))). [resolve(5413,a,5313,a)]. 61.28/61.26 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(5413,a,5315,a)]. 61.28/61.26 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(5413,a,5316,a)]. 61.28/61.26 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(5413,a,5317,a)]. 61.28/61.26 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(5413,a,5318,a)]. 61.28/61.26 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),A))). [resolve(5413,a,5319,a)]. 61.28/61.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),D))). [resolve(5413,a,5320,a)]. 61.28/61.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5413,a,5321,a)]. 61.28/61.27 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),A)). [resolve(5413,a,5322,a)]. 61.28/61.27 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(5413,a,5323,a)]. 61.28/61.27 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(5413,a,5324,a)]. 61.28/61.27 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(5413,a,5327,a)]. 61.28/61.27 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),B),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(5413,a,5328,a)]. 61.28/61.27 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),B),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(5413,a,5329,a)]. 61.28/61.27 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(5413,a,5331,a)]. 61.28/61.28 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(5413,a,5332,a)]. 61.28/61.28 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)). [resolve(5413,a,5333,a)]. 61.28/61.28 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5413,a,5334,a)]. 61.28/61.28 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(5413,a,5335,a)]. 61.28/61.28 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | ti(quickcheck_code_int,C) != ti(quickcheck_code_int,A) | ti(quickcheck_code_int,D) != ti(quickcheck_code_int,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) = 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). [resolve(5413,a,5336,a)]. 61.28/61.28 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | ti(quickcheck_code_int,C) = ti(quickcheck_code_int,A) | 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). [resolve(5413,a,5337,a)]. 61.28/61.28 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),C),D)) | ti(quickcheck_code_int,D) = ti(quickcheck_code_int,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) != 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). [resolve(5413,a,5338,a)]. 61.37/61.29 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),A),B). [resolve(5413,a,5339,a)]. 61.37/61.29 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(5413,a,5340,a)]. 61.37/61.29 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) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)). [resolve(5413,a,5341,a)]. 61.37/61.29 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(5413,a,5343,a)]. 61.37/61.29 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(5413,a,5345,a)]. 61.37/61.29 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5413,a,5346,a)]. 61.37/61.29 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(5413,a,5347,a)]. 61.37/61.29 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)). [resolve(5413,a,5348,a)]. 61.37/61.29 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(5413,a,5349,a)]. 61.37/61.29 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(5413,a,5350,a)]. 61.37/61.30 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(5413,a,5352,a)]. 61.37/61.30 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(5413,a,5357,a)]. 61.37/61.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),B). [resolve(5413,a,5358,a)]. 61.37/61.30 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),f303(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(5413,a,5360,a)]. 61.37/61.30 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)). [resolve(5413,a,5361,a)]. 61.37/61.30 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(5413,a,5362,a)]. 61.37/61.30 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(5413,a,5363,a)]. 61.39/61.30 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(5413,a,5365,a)]. 61.39/61.30 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(5413,a,5366,a)]. 61.39/61.30 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)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(5413,a,5367,a)]. 61.39/61.30 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(5413,a,5368,a)]. 61.39/61.30 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(5413,a,5369,a)]. 61.39/61.30 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(5413,a,5370,a)]. 61.39/61.30 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = ti(quickcheck_code_int,A). [resolve(5413,a,5371,a)]. 61.39/61.30 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) != ti(quickcheck_code_int,A). [resolve(5413,a,5372,a)]. 61.40/61.31 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),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),A)). [resolve(5413,a,5373,a)]. 61.40/61.31 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),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),D)). [resolve(5413,a,5374,a)]. 61.40/61.31 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),f430(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(5413,a,5375,a)]. 61.40/61.31 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B). [resolve(5413,a,5376,a)]. 61.40/61.31 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),A). [resolve(5413,a,5378,a)]. 61.40/61.31 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(5413,a,5382,a)]. 61.40/61.31 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(5413,a,5384,a)]. 61.40/61.31 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),C),B))). [resolve(5413,a,5386,a)]. 61.40/61.33 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(5413,a,5389,a)]. 61.40/61.33 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),f516(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(5413,a,5390,a)]. 61.40/61.33 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C)). [resolve(5413,a,5391,a)]. 61.40/61.33 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(5413,a,5392,a)]. 61.40/61.33 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)). [resolve(5413,a,5393,a)]. 61.40/61.33 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(5413,a,5399,a)]. 61.40/61.33 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),A)) | ti(quickcheck_code_int,A) != ti(quickcheck_code_int,B). [resolve(5413,a,5403,a)]. 61.40/61.33 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(5413,a,5405,a)]. 61.40/61.33 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(5413,a,5406,a)]. 61.40/61.41 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(5413,a,5408,a)]. 61.40/61.41 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B)),C) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_min(quickcheck_code_int),B),C)). [resolve(5413,a,5410,a)]. 61.40/61.41 Derived: ord_max(quickcheck_code_int) = hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),min(quickcheck_code_int),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),fun(quickcheck_code_int,fun(quickcheck_code_int,bool)),combc(quickcheck_code_int,quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int))). [resolve(5413,a,5412,a)]. 61.40/61.41 5414 -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_4316_lessThan__eq__iff) # label(axiom). [clausify(3972)]. 61.40/61.41 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(5414,a,5311,a)]. 61.40/61.41 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(5414,a,5388,a)]. 61.40/61.41 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(5414,a,5413,a)]. 61.40/61.41 5415 -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_4316_lessThan__eq__iff) # label(axiom). [clausify(3972)]. 61.40/61.41 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(5415,a,5311,a)]. 61.40/61.41 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(5415,a,5388,a)]. 61.40/61.41 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(5415,a,5413,a)]. 61.40/61.41 5416 linorder(rat) # label(arity_Rat_Orat___Orderings_Olinorder) # label(axiom). [assumption]. 61.40/61.41 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B)). [resolve(5416,a,5312,a)]. 61.40/61.41 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B))). [resolve(5416,a,5313,a)]. 61.40/61.41 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(5416,a,5315,a)]. 61.40/61.41 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(5416,a,5316,a)]. 61.50/61.42 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(5416,a,5317,a)]. 61.50/61.42 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(5416,a,5318,a)]. 61.50/61.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A))). [resolve(5416,a,5319,a)]. 61.50/61.42 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),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),D))). [resolve(5416,a,5320,a)]. 61.50/61.42 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(5416,a,5321,a)]. 61.50/61.42 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(5416,a,5322,a)]. 61.50/61.42 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),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(5416,a,5323,a)]. 61.50/61.42 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(5416,a,5324,a)]. 61.50/61.42 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(5416,a,5327,a)]. 61.50/61.42 Derived: ti(rat,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5416,a,5328,a)]. 61.50/61.42 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5416,a,5329,a)]. 61.50/61.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5416,a,5331,a)]. 61.50/61.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(5416,a,5332,a)]. 61.50/61.42 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)). [resolve(5416,a,5333,a)]. 61.50/61.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5416,a,5334,a)]. 61.50/61.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5416,a,5335,a)]. 61.50/61.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | ti(rat,C) != ti(rat,A) | ti(rat,D) != ti(rat,B) | 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). [resolve(5416,a,5336,a)]. 61.50/61.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | ti(rat,C) = ti(rat,A) | 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). [resolve(5416,a,5337,a)]. 61.50/61.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | ti(rat,D) = ti(rat,B) | 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). [resolve(5416,a,5338,a)]. 61.50/61.44 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),A),B). [resolve(5416,a,5339,a)]. 61.50/61.44 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(5416,a,5340,a)]. 61.50/61.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,A) = ti(rat,B) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5416,a,5341,a)]. 61.50/61.44 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(5416,a,5343,a)]. 61.50/61.44 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),A). [resolve(5416,a,5345,a)]. 61.50/61.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5416,a,5346,a)]. 61.50/61.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5416,a,5347,a)]. 61.50/61.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5416,a,5348,a)]. 61.50/61.44 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(5416,a,5349,a)]. 61.50/61.44 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(5416,a,5350,a)]. 61.50/61.44 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(5416,a,5352,a)]. 61.50/61.44 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(5416,a,5357,a)]. 61.50/61.44 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B). [resolve(5416,a,5358,a)]. 61.50/61.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f303(rat,A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5416,a,5360,a)]. 61.50/61.44 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)). [resolve(5416,a,5361,a)]. 61.50/61.45 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(5416,a,5362,a)]. 61.50/61.45 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(5416,a,5363,a)]. 61.50/61.45 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(5416,a,5365,a)]. 61.50/61.45 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(5416,a,5366,a)]. 61.50/61.45 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)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(5416,a,5367,a)]. 61.50/61.45 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(5416,a,5368,a)]. 61.50/61.45 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(5416,a,5369,a)]. 61.50/61.45 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(5416,a,5370,a)]. 61.50/61.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) = ti(rat,A). [resolve(5416,a,5371,a)]. 61.50/61.45 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) != ti(rat,A). [resolve(5416,a,5372,a)]. 61.50/61.45 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),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5416,a,5373,a)]. 61.50/61.45 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),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),D)). [resolve(5416,a,5374,a)]. 61.50/61.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f430(rat,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5416,a,5375,a)]. 61.50/61.45 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B). [resolve(5416,a,5376,a)]. 61.50/61.45 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A). [resolve(5416,a,5378,a)]. 61.59/61.51 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(5416,a,5382,a)]. 61.59/61.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B))). [resolve(5416,a,5384,a)]. 61.59/61.51 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),C),B))). [resolve(5416,a,5386,a)]. 61.59/61.51 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(5416,a,5389,a)]. 61.59/61.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),f516(rat,B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5416,a,5390,a)]. 61.59/61.51 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C)). [resolve(5416,a,5391,a)]. 61.59/61.51 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(5416,a,5392,a)]. 61.59/61.51 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)). [resolve(5416,a,5393,a)]. 61.59/61.51 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(5416,a,5399,a)]. 61.59/61.51 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | ti(rat,A) != ti(rat,B). [resolve(5416,a,5403,a)]. 61.59/61.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | ti(rat,B) != ti(rat,A). [resolve(5416,a,5405,a)]. 61.59/61.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)). [resolve(5416,a,5406,a)]. 61.59/61.51 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(5416,a,5408,a)]. 61.59/61.51 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),B),C)). [resolve(5416,a,5410,a)]. 61.59/61.51 Derived: ord_max(rat) = hAPP(fun(rat,fun(rat,bool)),fun(rat,fun(rat,rat)),min(rat),hAPP(fun(rat,fun(rat,bool)),fun(rat,fun(rat,bool)),combc(rat,rat,bool),ord_less_eq(rat))). [resolve(5416,a,5412,a)]. 61.59/61.51 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(5416,a,5414,a)]. 61.59/61.51 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(5416,a,5415,a)]. 61.59/61.51 5417 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_4970_min__max_Osup__commute) # label(axiom). [clausify(4046)]. 61.59/61.51 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),B),A). [resolve(5417,a,5311,a)]. 61.59/61.51 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),B),A). [resolve(5417,a,5388,a)]. 61.59/61.51 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),B),A). [resolve(5417,a,5413,a)]. 61.59/61.53 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),B),A). [resolve(5417,a,5416,a)]. 61.59/61.53 5418 linorder(int) # label(arity_Int_Oint___Orderings_Olinorder) # label(axiom). [assumption]. 61.59/61.53 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B)). [resolve(5418,a,5312,a)]. 61.59/61.53 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B))). [resolve(5418,a,5313,a)]. 61.59/61.53 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(5418,a,5315,a)]. 61.59/61.53 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(5418,a,5316,a)]. 61.59/61.53 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(5418,a,5317,a)]. 61.59/61.53 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(5418,a,5318,a)]. 61.59/61.53 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A))). [resolve(5418,a,5319,a)]. 61.59/61.53 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),D))). [resolve(5418,a,5320,a)]. 61.59/61.53 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(5418,a,5321,a)]. 61.59/61.53 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(5418,a,5322,a)]. 61.59/61.53 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(5418,a,5323,a)]. 61.59/61.53 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(5418,a,5324,a)]. 61.59/61.53 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(5418,a,5327,a)]. 61.59/61.53 Derived: ti(int,A) != hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5418,a,5328,a)]. 61.59/61.53 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5418,a,5329,a)]. 61.59/61.53 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(5418,a,5331,a)]. 61.59/61.53 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(5418,a,5332,a)]. 61.59/61.54 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)). [resolve(5418,a,5333,a)]. 61.59/61.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5418,a,5334,a)]. 61.59/61.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(5418,a,5335,a)]. 61.59/61.54 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),C),D)) | ti(int,C) != ti(int,A) | ti(int,D) != ti(int,B) | 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). [resolve(5418,a,5336,a)]. 61.59/61.54 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),C),D)) | ti(int,C) = ti(int,A) | 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). [resolve(5418,a,5337,a)]. 61.59/61.54 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),C),D)) | ti(int,D) = ti(int,B) | 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). [resolve(5418,a,5338,a)]. 61.59/61.54 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),A),B). [resolve(5418,a,5339,a)]. 61.59/61.54 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5418,a,5340,a)]. 61.59/61.54 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | ti(int,A) = ti(int,B) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(5418,a,5341,a)]. 61.59/61.54 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(5418,a,5343,a)]. 61.59/61.54 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),A). [resolve(5418,a,5345,a)]. 61.59/61.54 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5418,a,5346,a)]. 61.59/61.54 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(5418,a,5347,a)]. 61.59/61.54 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5418,a,5348,a)]. 61.59/61.54 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(5418,a,5349,a)]. 61.59/61.54 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(5418,a,5350,a)]. 61.59/61.56 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(5418,a,5352,a)]. 61.59/61.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C))). [resolve(5418,a,5357,a)]. 61.59/61.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(5418,a,5358,a)]. 61.59/61.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f303(int,A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5418,a,5360,a)]. 61.59/61.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)). [resolve(5418,a,5361,a)]. 61.59/61.56 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(5418,a,5362,a)]. 61.59/61.56 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(5418,a,5363,a)]. 61.59/61.56 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(5418,a,5365,a)]. 61.59/61.56 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(5418,a,5366,a)]. 61.59/61.56 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)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(5418,a,5367,a)]. 61.59/61.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B)). [resolve(5418,a,5368,a)]. 61.59/61.56 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),C),A)),B)). [resolve(5418,a,5369,a)]. 61.59/61.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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(5418,a,5370,a)]. 61.59/61.56 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) != ti(int,A). [resolve(5418,a,5372,a)]. 61.59/61.56 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),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),A)). [resolve(5418,a,5373,a)]. 61.68/61.59 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),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),D)). [resolve(5418,a,5374,a)]. 61.68/61.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f430(int,B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)). [resolve(5418,a,5375,a)]. 61.68/61.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B). [resolve(5418,a,5376,a)]. 61.68/61.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(5418,a,5378,a)]. 61.68/61.59 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(5418,a,5382,a)]. 61.68/61.59 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(5418,a,5384,a)]. 61.68/61.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),B))). [resolve(5418,a,5386,a)]. 61.68/61.59 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(5418,a,5389,a)]. 61.68/61.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),f516(int,B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5418,a,5390,a)]. 61.68/61.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(5418,a,5391,a)]. 61.68/61.59 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(5418,a,5392,a)]. 61.68/61.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)). [resolve(5418,a,5393,a)]. 61.68/61.59 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(5418,a,5399,a)]. 61.68/61.59 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(5418,a,5406,a)]. 61.68/61.59 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(5418,a,5408,a)]. 61.68/61.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),B),C)). [resolve(5418,a,5410,a)]. 61.68/61.59 Derived: ord_max(int) = hAPP(fun(int,fun(int,bool)),fun(int,fun(int,int)),min(int),hAPP(fun(int,fun(int,bool)),fun(int,fun(int,bool)),combc(int,int,bool),ord_less_eq(int))). [resolve(5418,a,5412,a)]. 61.68/61.59 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(5418,a,5414,a)]. 61.68/61.59 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(5418,a,5415,a)]. 61.68/61.59 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),B),A). [resolve(5418,a,5417,a)]. 61.80/61.74 5419 -linorder(A) | ti(A,B) != ti(A,C) | hAPP(A,fun(A,bool),ord_atMost(A),B) = hAPP(A,fun(A,bool),ord_atMost(A),C) # label(fact_4962_atMost__eq__iff) # label(axiom). [clausify(4055)]. 61.80/61.74 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(5419,a,5311,a)]. 61.80/61.74 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(5419,a,5388,a)]. 61.80/61.74 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(5419,a,5413,a)]. 61.80/61.74 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(5419,a,5416,a)]. 61.80/61.74 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(5419,a,5418,a)]. 61.80/61.74 5420 -linorder(A) | ti(A,B) = ti(A,C) | hAPP(A,fun(A,bool),ord_atMost(A),B) != hAPP(A,fun(A,bool),ord_atMost(A),C) # label(fact_4962_atMost__eq__iff) # label(axiom). [clausify(4055)]. 61.80/61.74 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(5420,a,5311,a)]. 61.80/61.74 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(5420,a,5388,a)]. 61.80/61.74 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(5420,a,5413,a)]. 61.80/61.74 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(5420,a,5416,a)]. 61.80/61.74 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(5420,a,5418,a)]. 61.80/61.74 5421 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_4319_lessThan__subset__iff) # label(axiom). [clausify(4212)]. 61.80/61.74 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less_eq(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B))). [resolve(5421,a,5311,a)]. 61.80/61.74 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))). [resolve(5421,a,5388,a)]. 61.80/61.74 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less_eq(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B))). [resolve(5421,a,5413,a)]. 61.80/61.74 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))). [resolve(5421,a,5416,a)]. 61.80/61.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))). [resolve(5421,a,5418,a)]. 61.80/61.78 5422 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),hAPP(A,fun(A,bool),ord_lessThan(A),B)),hAPP(A,fun(A,bool),ord_lessThan(A),C))) # label(fact_4319_lessThan__subset__iff) # label(axiom). [clausify(4212)]. 61.80/61.78 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(fun(code_code_numeral,bool),bool,hAPP(fun(code_code_numeral,bool),fun(fun(code_code_numeral,bool),bool),ord_less_eq(fun(code_code_numeral,bool)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),A)),hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_lessThan(code_code_numeral),B))). [resolve(5422,a,5311,a)]. 61.80/61.78 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(fun(nat,bool),bool,hAPP(fun(nat,bool),fun(fun(nat,bool),bool),ord_less_eq(fun(nat,bool)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A)),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))). [resolve(5422,a,5388,a)]. 61.80/61.78 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(fun(quickcheck_code_int,bool),bool,hAPP(fun(quickcheck_code_int,bool),fun(fun(quickcheck_code_int,bool),bool),ord_less_eq(fun(quickcheck_code_int,bool)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),A)),hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_lessThan(quickcheck_code_int),B))). [resolve(5422,a,5413,a)]. 61.80/61.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(fun(rat,bool),bool,hAPP(fun(rat,bool),fun(fun(rat,bool),bool),ord_less_eq(fun(rat,bool)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),A)),hAPP(rat,fun(rat,bool),ord_lessThan(rat),B))). [resolve(5422,a,5416,a)]. 61.80/61.78 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(fun(int,bool),bool,hAPP(fun(int,bool),fun(fun(int,bool),bool),ord_less_eq(fun(int,bool)),hAPP(int,fun(int,bool),ord_lessThan(int),A)),hAPP(int,fun(int,bool),ord_lessThan(int),B))). [resolve(5422,a,5418,a)]. 61.80/61.78 5423 -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_50_le__number__of__eq__not__less) # label(axiom). [clausify(4215)]. 61.80/61.78 5424 -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_50_le__number__of__eq__not__less) # label(axiom). [clausify(4215)]. 61.80/61.78 5425 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),D)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastLessThan(A),C),D) # label(fact_4205_ivl__diff) # label(axiom). [clausify(4234)]. 61.80/61.78 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(5425,a,5311,a)]. 61.89/61.80 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(5425,a,5388,a)]. 61.89/61.80 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(5425,a,5413,a)]. 61.89/61.80 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hAPP(fun(rat,bool),fun(rat,bool),hAPP(fun(rat,bool),fun(fun(rat,bool),fun(rat,bool)),minus_minus(fun(rat,bool)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),C)),hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),A),B)) = hAPP(rat,fun(rat,bool),hAPP(rat,fun(rat,fun(rat,bool)),ord_atLeastLessThan(rat),B),C). [resolve(5425,a,5416,a)]. 61.89/61.80 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(5425,a,5418,a)]. 61.89/61.80 5426 linorder(real) # label(arity_RealDef_Oreal___Orderings_Olinorder) # label(axiom). [assumption]. 61.89/61.80 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B)). [resolve(5426,a,5312,a)]. 61.89/61.80 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B))). [resolve(5426,a,5313,a)]. 61.89/61.80 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(5426,a,5315,a)]. 61.89/61.80 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(5426,a,5316,a)]. 61.89/61.81 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(5426,a,5317,a)]. 61.89/61.81 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(5426,a,5318,a)]. 61.89/61.81 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A))). [resolve(5426,a,5319,a)]. 61.89/61.81 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_max(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),D))). [resolve(5426,a,5320,a)]. 61.89/61.81 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(5426,a,5321,a)]. 61.89/61.81 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(5426,a,5322,a)]. 61.89/61.81 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(5426,a,5323,a)]. 61.89/61.81 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(5426,a,5324,a)]. 61.89/61.81 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(5426,a,5327,a)]. 61.89/61.81 Derived: ti(real,A) != hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5426,a,5328,a)]. 61.89/61.81 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5426,a,5329,a)]. 61.89/61.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5426,a,5331,a)]. 61.89/61.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(5426,a,5332,a)]. 61.89/61.81 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)). [resolve(5426,a,5333,a)]. 61.89/61.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5426,a,5334,a)]. 61.89/61.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5426,a,5335,a)]. 61.89/61.81 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | ti(real,C) != ti(real,A) | ti(real,D) != ti(real,B) | 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). [resolve(5426,a,5336,a)]. 61.89/61.83 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | ti(real,C) = ti(real,A) | 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). [resolve(5426,a,5337,a)]. 61.89/61.83 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | ti(real,D) = ti(real,B) | 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). [resolve(5426,a,5338,a)]. 61.89/61.83 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),A),B). [resolve(5426,a,5339,a)]. 61.89/61.83 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(5426,a,5340,a)]. 61.89/61.83 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,A) = ti(real,B) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)). [resolve(5426,a,5341,a)]. 61.89/61.83 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(5426,a,5343,a)]. 61.89/61.83 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),A). [resolve(5426,a,5345,a)]. 61.89/61.83 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5426,a,5346,a)]. 61.89/61.83 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5426,a,5347,a)]. 61.89/61.83 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5426,a,5348,a)]. 61.89/61.83 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(5426,a,5349,a)]. 61.89/61.83 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(5426,a,5350,a)]. 61.89/61.83 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(5426,a,5352,a)]. 61.89/61.83 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(5426,a,5357,a)]. 61.89/61.83 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B). [resolve(5426,a,5358,a)]. 61.89/61.84 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f303(real,A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5426,a,5360,a)]. 61.89/61.84 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)). [resolve(5426,a,5361,a)]. 61.89/61.84 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(5426,a,5362,a)]. 61.89/61.84 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(5426,a,5363,a)]. 61.89/61.84 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(5426,a,5365,a)]. 61.89/61.84 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(5426,a,5366,a)]. 61.89/61.84 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)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(5426,a,5367,a)]. 61.89/61.84 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(5426,a,5368,a)]. 61.89/61.84 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(5426,a,5369,a)]. 61.89/61.84 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(5426,a,5370,a)]. 61.89/61.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) = ti(real,A). [resolve(5426,a,5371,a)]. 61.89/61.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) != ti(real,A). [resolve(5426,a,5372,a)]. 61.89/61.84 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_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),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5426,a,5373,a)]. 61.89/61.84 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_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),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),D)). [resolve(5426,a,5374,a)]. 61.89/61.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f430(real,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5426,a,5375,a)]. 61.89/61.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B). [resolve(5426,a,5376,a)]. 61.89/61.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A). [resolve(5426,a,5378,a)]. 61.89/61.87 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(5426,a,5382,a)]. 61.89/61.87 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),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B))). [resolve(5426,a,5384,a)]. 61.89/61.87 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),A),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),B))). [resolve(5426,a,5386,a)]. 61.89/61.87 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(5426,a,5389,a)]. 61.89/61.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),f516(real,B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5426,a,5390,a)]. 61.89/61.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C)). [resolve(5426,a,5391,a)]. 61.89/61.87 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(5426,a,5392,a)]. 61.89/61.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)). [resolve(5426,a,5393,a)]. 61.89/61.87 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(5426,a,5399,a)]. 61.89/61.87 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),B),A)) | ti(real,A) != ti(real,B). [resolve(5426,a,5403,a)]. 61.89/61.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | ti(real,B) != ti(real,A). [resolve(5426,a,5405,a)]. 61.89/61.87 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),B),A)). [resolve(5426,a,5406,a)]. 61.89/61.87 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(5426,a,5408,a)]. 61.89/61.87 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),B),C)). [resolve(5426,a,5410,a)]. 61.89/61.87 Derived: ord_max(real) = hAPP(fun(real,fun(real,bool)),fun(real,fun(real,real)),min(real),hAPP(fun(real,fun(real,bool)),fun(real,fun(real,bool)),combc(real,real,bool),ord_less_eq(real))). [resolve(5426,a,5412,a)]. 61.89/61.87 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(5426,a,5414,a)]. 62.11/62.03 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(5426,a,5415,a)]. 62.11/62.03 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),B),A). [resolve(5426,a,5417,a)]. 62.11/62.03 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(5426,a,5419,a)]. 62.11/62.03 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(5426,a,5420,a)]. 62.11/62.03 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))). [resolve(5426,a,5421,a)]. 62.11/62.03 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(fun(real,bool),bool,hAPP(fun(real,bool),fun(fun(real,bool),bool),ord_less_eq(fun(real,bool)),hAPP(real,fun(real,bool),ord_lessThan(real),A)),hAPP(real,fun(real,bool),ord_lessThan(real),B))). [resolve(5426,a,5422,a)]. 62.11/62.03 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(5426,a,5425,a)]. 62.11/62.03 5427 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_4972_min__max_Osup_Oidem) # label(axiom). [clausify(4258)]. 62.11/62.03 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),ord_max(code_code_numeral),A),A). [resolve(5427,a,5311,a)]. 62.11/62.03 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),A). [resolve(5427,a,5388,a)]. 62.11/62.03 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),ord_max(quickcheck_code_int),A),A). [resolve(5427,a,5413,a)]. 62.11/62.03 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),A). [resolve(5427,a,5416,a)]. 62.11/62.03 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),A). [resolve(5427,a,5418,a)]. 62.11/62.03 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),A). [resolve(5427,a,5426,a)]. 62.11/62.03 5428 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D))),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)))) # label(fact_4945_min__max_Odistrib__inf__le) # label(axiom). [clausify(4410)]. 62.11/62.03 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(5428,a,5311,a)]. 62.11/62.03 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(5428,a,5388,a)]. 62.11/62.05 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(5428,a,5413,a)]. 62.11/62.05 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(5428,a,5416,a)]. 62.11/62.05 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(5428,a,5418,a)]. 62.11/62.05 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(5428,a,5426,a)]. 62.11/62.05 5429 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1589_not__leE) # label(axiom). [clausify(4419)]. 62.11/62.05 5430 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_4814_min__max_Oinf_Oleft__idem) # label(axiom). [clausify(4433)]. 62.11/62.05 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(5430,a,5311,a)]. 62.11/62.05 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(5430,a,5388,a)]. 62.11/62.05 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(5430,a,5413,a)]. 62.11/62.05 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(5430,a,5416,a)]. 62.11/62.05 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(5430,a,5418,a)]. 62.41/62.36 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(5430,a,5426,a)]. 62.41/62.36 5431 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),C))) # label(fact_4952_min__max_Oless__supI2) # label(axiom). [clausify(4463)]. 62.41/62.36 5432 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) != ti(A,B) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_1595_linorder__antisym__conv2) # label(axiom). [clausify(4483)]. 62.41/62.36 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(5432,a,5418,a)]. 62.41/62.36 5433 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | ti(A,C) = ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_1595_linorder__antisym__conv2) # label(axiom). [clausify(4483)]. 62.41/62.36 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(5433,a,5418,a)]. 62.41/62.36 5434 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),B) # label(fact_4971_min__max_Osup_Ocommute) # label(axiom). [clausify(4528)]. 62.41/62.36 5435 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_4800_min__max_Oless__infI1) # label(axiom). [clausify(4556)]. 62.41/62.36 5436 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)) # label(fact_4966_min__max_Osup__left__commute) # label(axiom). [clausify(4576)]. 62.41/62.36 5437 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1561_linorder__neq__iff) # label(axiom). [clausify(4624)]. 62.41/62.36 5438 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_1561_linorder__neq__iff) # label(axiom). [clausify(4624)]. 62.41/62.36 Derived: ti(code_code_numeral,A) != ti(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(5438,a,5311,a)]. 62.41/62.36 Derived: ti(nat,A) != ti(nat,B) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)). [resolve(5438,a,5388,a)]. 62.41/62.36 Derived: ti(quickcheck_code_int,A) != ti(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(5438,a,5413,a)]. 62.41/62.36 Derived: ti(rat,A) != ti(rat,B) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(5438,a,5416,a)]. 62.41/62.36 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(5438,a,5418,a)]. 62.41/62.36 Derived: ti(real,A) != ti(real,B) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(5438,a,5426,a)]. 62.41/62.36 5439 -linorder(A) | ti(A,B) != ti(A,C) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_1561_linorder__neq__iff) # label(axiom). [clausify(4624)]. 62.41/62.36 Derived: ti(int,A) != ti(int,B) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),A)). [resolve(5439,a,5418,a)]. 62.41/62.36 5440 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C) # label(fact_4813_min__max_Oinf__left__idem) # label(axiom). [clausify(4699)]. 62.41/62.36 5441 -linorder(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_1565_linorder__neqE) # label(axiom). [clausify(4700)]. 62.49/62.47 5442 -linorder(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),B) # label(fact_4956_Max_Oidem) # label(axiom). [clausify(4712)]. 62.49/62.47 5443 -linorder(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),C),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)) # label(fact_4811_min__max_Oinf__left__commute) # label(axiom). [clausify(4743)]. 62.49/62.47 5444 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f807(A,B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2824_pinf_I6_J) # label(axiom). [clausify(4755)]. 62.49/62.47 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),f807(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(5444,a,5311,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f807(nat,A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),A)). [resolve(5444,a,5388,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),f807(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(5444,a,5413,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f807(rat,A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5444,a,5416,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),f807(int,A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),A)). [resolve(5444,a,5418,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f807(real,A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5444,a,5426,a)]. 62.49/62.47 5445 -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_4949_max__less__iff__conj) # label(axiom). [clausify(4806)]. 62.49/62.47 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(5445,a,5311,a)]. 62.49/62.47 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(5445,a,5388,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),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(5445,a,5413,a)]. 62.49/62.47 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5445,a,5416,a)]. 62.49/62.48 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(5445,a,5418,a)]. 62.49/62.48 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(5445,a,5426,a)]. 62.49/62.48 5446 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C)) # label(fact_4949_max__less__iff__conj) # label(axiom). [clausify(4806)]. 62.49/62.48 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(5446,a,5311,a)]. 62.49/62.48 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(5446,a,5388,a)]. 62.49/62.48 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(5446,a,5413,a)]. 62.49/62.48 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(5446,a,5416,a)]. 62.49/62.48 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(5446,a,5418,a)]. 62.49/62.48 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(5446,a,5426,a)]. 62.49/62.48 5447 -linorder(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),D),B)),C)) # label(fact_4949_max__less__iff__conj) # label(axiom). [clausify(4806)]. 62.49/62.48 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(5447,a,5311,a)]. 62.49/62.48 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(5447,a,5388,a)]. 62.49/62.48 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(5447,a,5413,a)]. 62.49/62.48 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(5447,a,5416,a)]. 65.19/65.10 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),C),A)),B)). [resolve(5447,a,5418,a)]. 65.19/65.10 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),C),A)),B)). [resolve(5447,a,5426,a)]. 65.19/65.10 5448 -linorder(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C)) # label(fact_4825_min__max_Ole__infI1) # label(axiom). [clausify(4848)]. 65.19/65.10 5449 real_normed_algebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 65.19/65.10 5450 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f5(A,B))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom). [clausify(42)]. 65.19/65.10 5451 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f5(A,B)))) # label(fact_1804_mult__right_Opos__bounded) # label(axiom). [clausify(42)]. 65.19/65.10 5452 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f13(A,B))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom). [clausify(65)]. 65.19/65.10 5453 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f13(A,C)))) # label(fact_1803_mult__left_Opos__bounded) # label(axiom). [clausify(65)]. 65.19/65.10 5454 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)))) # label(fact_1788_norm__mult__ineq) # label(axiom). [clausify(87)]. 65.19/65.10 5455 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))) # label(fact_875_mult_Oprod__diff__prod) # label(axiom). [clausify(101)]. 65.19/65.10 5456 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_3999_mult__right_Osummable) # label(axiom). [clausify(111)]. 65.19/65.10 5457 -real_normed_algebra(A) | -metric_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),E),zero_zero(A)),hAPP(B,filter(B),at(B),D))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),E)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4577_LIM__mult__zero) # label(axiom). [clausify(181)]. 65.19/65.10 5458 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_880_mult_Oadd__right) # label(axiom). [clausify(265)]. 65.19/65.10 5459 -real_normed_algebra(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4191_mult__right_Osetsum) # label(axiom). [clausify(293)]. 65.19/65.10 5460 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),times_times(A),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,filter(A),at(A),C))) # label(fact_4552_mult__right_Ocont) # label(axiom). [clausify(330)]. 65.19/65.10 5461 -real_normed_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_4678_mult_OscaleR__left) # label(axiom). [clausify(338)]. 65.19/65.10 5462 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f116(A,B)))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom). [clausify(584)]. 65.19/65.10 5463 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f116(A,B))) # label(fact_1808_mult__right_Ononneg__bounded) # label(axiom). [clausify(584)]. 65.19/65.10 5464 -real_normed_algebra(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4190_mult__left_Osetsum) # label(axiom). [clausify(668)]. 65.19/65.10 5465 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4081_mult__right_Osums) # label(axiom). [clausify(702)]. 65.19/65.10 5466 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4576_mult__left_OLIM__zero) # label(axiom). [clausify(730)]. 65.19/65.10 5467 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),V6)),E)) # label(fact_4474_mult_Otendsto) # label(axiom). [clausify(793)]. 65.19/65.10 5468 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_876_mult_Ozero__left) # label(axiom). [clausify(891)]. 65.19/65.10 5469 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4082_mult__left_Osums) # label(axiom). [clausify(970)]. 65.19/65.10 5470 -real_normed_algebra(A) | -power(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(nat,fun(nat,A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),combc(nat,nat,A),hAPP(fun(nat,A),fun(nat,fun(nat,A)),hAPP(fun(A,fun(nat,A)),fun(fun(nat,A),fun(nat,fun(nat,A))),combb(A,fun(nat,A),nat),power_power(A)),B)),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D)),sequentially)) # label(fact_4467_LIMSEQ__pow) # label(axiom). [clausify(1006)]. 65.19/65.10 5471 -comm_ring_1(A) | -real_normed_algebra(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f234(B,A,C,D,E)),E)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4657_LIMSEQ__setprod) # label(axiom). [clausify(1156)]. 65.19/65.10 5472 -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,f234(B,A,C,D,E))),hAPP(B,A,D,f234(B,A,C,D,E))),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(B,bool),fun(nat,A),hAPP(fun(nat,fun(fun(B,bool),A)),fun(fun(B,bool),fun(nat,A)),combc(nat,fun(B,bool),A),hAPP(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A)),hAPP(fun(fun(B,A),fun(fun(B,bool),A)),fun(fun(nat,fun(B,A)),fun(nat,fun(fun(B,bool),A))),combb(fun(B,A),fun(fun(B,bool),A),nat),big_co302546470etprod(B,A)),hAPP(fun(B,fun(nat,A)),fun(nat,fun(B,A)),combc(B,nat,A),C))),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),sequentially)) # label(fact_4657_LIMSEQ__setprod) # label(axiom). [clausify(1156)]. 65.19/65.10 5473 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3990_suminf__mult) # label(axiom). [clausify(1184)]. 65.19/65.10 5474 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_3997_summable__mult) # label(axiom). [clausify(1225)]. 65.19/65.10 5475 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),times_times(A),B)),C)) # label(fact_4907_mult__right_OisCont) # label(axiom). [clausify(1315)]. 65.19/65.10 5476 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),E)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4573_LIM__mult__right__zero) # label(axiom). [clausify(1491)]. 65.20/65.11 5477 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_881_mult__right_Oadd) # label(axiom). [clausify(1598)]. 65.20/65.11 5478 -topological_space(A) | -real_normed_algebra(B) | -power(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),E)),D)) # label(fact_4902_isCont__power) # label(axiom). [clausify(1672)]. 65.20/65.11 5479 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),F)),hAPP(B,B,hAPP(B,fun(B,B),times_times(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4549_mult__left_OLIM) # label(axiom). [clausify(1679)]. 65.20/65.11 5480 -real_normed_algebra(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),D)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E))) # label(fact_1789_norm__mult__less) # label(axiom). [clausify(1758)]. 65.20/65.11 5481 -real_normed_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_4679_mult__left_OscaleR) # label(axiom). [clausify(1781)]. 65.20/65.11 5482 -topological_space(A) | -power(B) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(nat,fun(A,B),hAPP(fun(A,fun(nat,B)),fun(nat,fun(A,B)),combc(A,nat,B),hAPP(fun(A,B),fun(A,fun(nat,B)),hAPP(fun(B,fun(nat,B)),fun(fun(A,B),fun(A,fun(nat,B))),combb(B,fun(nat,B),A),power_power(B)),C)),F)),hAPP(nat,B,hAPP(B,fun(nat,B),power_power(B),D),F)),hAPP(A,filter(A),at(A),E))) # label(fact_4556_LIM__power) # label(axiom). [clausify(1900)]. 65.20/65.11 5483 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_886_mult__right_Odiff) # label(axiom). [clausify(2015)]. 65.20/65.11 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f5(complex,A))). [resolve(5449,a,5450,a)]. 65.20/65.11 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f5(complex,A)))). [resolve(5449,a,5451,a)]. 65.20/65.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f13(complex,A))). [resolve(5449,a,5452,a)]. 65.20/65.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f13(complex,B)))). [resolve(5449,a,5453,a)]. 65.20/65.12 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)))). [resolve(5449,a,5454,a)]. 65.20/65.12 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))). [resolve(5449,a,5455,a)]. 65.20/65.12 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))). [resolve(5449,a,5456,a)]. 65.20/65.12 Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),D),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5449,a,5457,a)]. 65.20/65.12 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),C)). [resolve(5449,a,5458,a)]. 65.20/65.12 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(5449,a,5459,a)]. 65.20/65.14 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5449,a,5460,a)]. 65.20/65.14 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f116(complex,A)))). [resolve(5449,a,5462,a)]. 65.20/65.14 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f116(complex,A))). [resolve(5449,a,5463,a)]. 65.20/65.14 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),C). [resolve(5449,a,5464,a)]. 65.20/65.14 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),C)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B))). [resolve(5449,a,5465,a)]. 65.20/65.14 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5449,a,5466,b)]. 65.20/65.14 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),F)),D)). [resolve(5449,a,5467,a)]. 65.20/65.14 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(5449,a,5468,a)]. 65.20/65.14 Derived: -hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(5449,a,5469,a)]. 65.20/65.15 Derived: -power(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(nat,fun(nat,complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),combc(nat,nat,complex),hAPP(fun(nat,complex),fun(nat,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(nat,complex),fun(nat,fun(nat,complex))),combb(complex,fun(nat,complex),nat),power_power(complex)),A)),C)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),C)),sequentially)). [resolve(5449,a,5470,a)]. 65.20/65.15 Derived: -comm_ring_1(complex) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f234(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(5449,a,5471,b)]. 65.20/65.15 Derived: -comm_ring_1(complex) | -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(A,fun(nat,complex),B,f234(A,complex,B,C,D))),hAPP(A,complex,C,f234(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(5449,a,5472,b)]. 65.20/65.15 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,complex),complex,suminf(complex),A)). [resolve(5449,a,5473,a)]. 65.20/65.15 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),times_times(complex),A)),B)). [resolve(5449,a,5475,a)]. 65.20/65.15 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),zero_zero(complex)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),D)),B)),zero_zero(complex)),hAPP(A,filter(A),at(A),C))). [resolve(5449,a,5476,b)]. 65.29/65.27 Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),D)),C)). [resolve(5449,a,5478,b)]. 65.29/65.27 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5449,a,5479,b)]. 65.29/65.27 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5449,a,5480,a)]. 65.29/65.27 Derived: -topological_space(A) | -power(complex) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(nat,fun(A,complex),hAPP(fun(A,fun(nat,complex)),fun(nat,fun(A,complex)),combc(A,nat,complex),hAPP(fun(A,complex),fun(A,fun(nat,complex)),hAPP(fun(complex,fun(nat,complex)),fun(fun(A,complex),fun(A,fun(nat,complex))),combb(complex,fun(nat,complex),A),power_power(complex)),B)),E)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5449,a,5482,c)]. 65.29/65.27 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)). [resolve(5449,a,5483,a)]. 65.29/65.27 5484 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f426(A,C)))) # label(fact_1812_mult__left_Obounded) # label(axiom). [clausify(2252)]. 65.29/65.27 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f426(complex,B)))). [resolve(5484,a,5449,a)]. 65.29/65.27 5485 -real_normed_algebra(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,filter(A),at(A),C))) # label(fact_4551_mult__left_Ocont) # label(axiom). [clausify(2301)]. 65.47/65.38 Derived: hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)),hAPP(complex,filter(complex),at(complex),B))). [resolve(5485,a,5449,a)]. 65.47/65.38 5486 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_3998_summable__mult2) # label(axiom). [clausify(2304)]. 65.47/65.38 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))). [resolve(5486,a,5449,a)]. 65.47/65.38 5487 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_879_mult__right_Ozero) # label(axiom). [clausify(2363)]. 65.47/65.38 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),zero_zero(complex)) = zero_zero(complex). [resolve(5487,a,5449,a)]. 65.47/65.38 5488 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),E)),C)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4574_mult__right_OLIM__zero) # label(axiom). [clausify(2375)]. 65.47/65.38 5489 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f449(A)))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom). [clausify(2411)]. 65.47/65.38 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f449(complex)))). [resolve(5489,a,5449,a)]. 65.47/65.38 5490 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f449(A))) # label(fact_1807_mult_Ononneg__bounded) # label(axiom). [clausify(2411)]. 65.47/65.38 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f449(complex))). [resolve(5490,a,5449,a)]. 65.47/65.38 5491 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),E)) # label(fact_4475_mult__left_Otendsto) # label(axiom). [clausify(2455)]. 65.51/65.45 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(complex,fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(complex,fun(A,complex)),combc(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),E)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),E)),D)). [resolve(5491,a,5449,a)]. 65.51/65.45 5492 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_4101_mult__left_OCauchy) # label(axiom). [clausify(2464)]. 65.51/65.45 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B))). [resolve(5492,a,5449,a)]. 65.51/65.45 5493 -real_normed_algebra(A) | hBOOL(hAPP(A,bool,hAPP(fun(A,A),fun(A,bool),isCont(A,A),hAPP(A,fun(A,A),hAPP(fun(A,fun(A,A)),fun(A,fun(A,A)),combc(A,A,A),times_times(A)),B)),C)) # label(fact_4908_mult__left_OisCont) # label(axiom). [clausify(2478)]. 65.51/65.45 Derived: hBOOL(hAPP(complex,bool,hAPP(fun(complex,complex),fun(complex,bool),isCont(complex,complex),hAPP(complex,fun(complex,complex),hAPP(fun(complex,fun(complex,complex)),fun(complex,fun(complex,complex)),combc(complex,complex,complex),times_times(complex)),A)),B)). [resolve(5493,a,5449,a)]. 65.51/65.45 5494 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2036_mult_Ominus__left) # label(axiom). [clausify(2502)]. 65.51/65.45 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B). [resolve(5494,a,5449,a)]. 65.51/65.45 5495 real_normed_algebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra) # label(axiom). [assumption]. 65.51/65.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f5(real,A))). [resolve(5495,a,5450,a)]. 65.51/65.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f5(real,A)))). [resolve(5495,a,5451,a)]. 65.51/65.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f13(real,A))). [resolve(5495,a,5452,a)]. 65.51/65.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f13(real,B)))). [resolve(5495,a,5453,a)]. 65.51/65.45 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)))). [resolve(5495,a,5454,a)]. 65.51/65.47 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))). [resolve(5495,a,5455,a)]. 65.51/65.47 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))). [resolve(5495,a,5456,a)]. 65.51/65.47 Derived: -metric_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),D),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5495,a,5457,a)]. 65.51/65.47 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),C)). [resolve(5495,a,5458,a)]. 65.51/65.47 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(5495,a,5459,a)]. 65.51/65.47 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),times_times(real),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,filter(real),at(real),B))). [resolve(5495,a,5460,a)]. 65.51/65.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f116(real,A)))). [resolve(5495,a,5462,a)]. 65.51/65.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f116(real,A))). [resolve(5495,a,5463,a)]. 65.51/65.47 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),C). [resolve(5495,a,5464,a)]. 65.51/65.47 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),C)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5495,a,5465,a)]. 65.51/65.48 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5495,a,5466,b)]. 65.51/65.48 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),E),F),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),F)),D)). [resolve(5495,a,5467,a)]. 65.51/65.48 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),zero_zero(real)),A) = zero_zero(real). [resolve(5495,a,5468,a)]. 65.51/65.48 Derived: -hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(5495,a,5469,a)]. 65.51/65.48 Derived: -power(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),hAPP(fun(nat,real),fun(nat,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(nat,real),fun(nat,fun(nat,real))),combb(real,fun(nat,real),nat),power_power(real)),A)),C)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),C)),sequentially)). [resolve(5495,a,5470,a)]. 65.51/65.48 Derived: -comm_ring_1(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f234(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(5495,a,5471,b)]. 65.51/65.48 Derived: -comm_ring_1(real) | -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),hAPP(A,fun(nat,real),B,f234(A,real,B,C,D))),hAPP(A,real,C,f234(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(5495,a,5472,b)]. 65.51/65.49 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,real),real,suminf(real),A)). [resolve(5495,a,5473,a)]. 65.51/65.49 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),times_times(real),A)),B)). [resolve(5495,a,5475,a)]. 65.51/65.49 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),zero_zero(real)),hAPP(A,filter(A),at(A),C))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),D)),B)),zero_zero(real)),hAPP(A,filter(A),at(A),C))). [resolve(5495,a,5476,b)]. 65.51/65.49 Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),D)),C)). [resolve(5495,a,5478,b)]. 65.51/65.49 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5495,a,5479,b)]. 65.51/65.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),C)),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(5495,a,5480,a)]. 65.51/65.49 Derived: -topological_space(A) | -power(real) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(nat,fun(A,real),hAPP(fun(A,fun(nat,real)),fun(nat,fun(A,real)),combc(A,nat,real),hAPP(fun(A,real),fun(A,fun(nat,real)),hAPP(fun(real,fun(nat,real)),fun(fun(A,real),fun(A,fun(nat,real))),combb(real,fun(nat,real),A),power_power(real)),B)),E)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),E)),hAPP(A,filter(A),at(A),D))). [resolve(5495,a,5482,c)]. 65.67/65.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)). [resolve(5495,a,5483,a)]. 65.67/65.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f426(real,B)))). [resolve(5495,a,5484,a)]. 65.67/65.62 Derived: hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),hAPP(real,filter(real),at(real),B))). [resolve(5495,a,5485,a)]. 65.67/65.62 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))). [resolve(5495,a,5486,a)]. 65.67/65.62 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),zero_zero(real)) = zero_zero(real). [resolve(5495,a,5487,a)]. 65.67/65.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f449(real)))). [resolve(5495,a,5489,a)]. 65.67/65.62 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f449(real))). [resolve(5495,a,5490,a)]. 65.67/65.62 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(real,fun(A,real),hAPP(fun(A,fun(real,real)),fun(real,fun(A,real)),combc(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),E)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),E)),D)). [resolve(5495,a,5491,a)]. 65.67/65.62 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B))). [resolve(5495,a,5492,a)]. 65.67/65.62 Derived: hBOOL(hAPP(real,bool,hAPP(fun(real,real),fun(real,bool),isCont(real,real),hAPP(real,fun(real,real),hAPP(fun(real,fun(real,real)),fun(real,fun(real,real)),combc(real,real,real),times_times(real)),A)),B)). [resolve(5495,a,5493,a)]. 65.67/65.62 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),B). [resolve(5495,a,5494,a)]. 65.67/65.62 5496 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_4079_sums__mult) # label(axiom). [clausify(2552)]. 65.67/65.62 5497 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2038_mult_Ominus__right) # label(axiom). [clausify(2695)]. 65.97/65.90 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(5497,a,5449,a)]. 65.97/65.90 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(5497,a,5495,a)]. 65.97/65.90 5498 -real_normed_algebra(A) | -topological_space(B) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),hAPP(B,filter(B),at(B),E))) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),F),V6),hAPP(B,filter(B),at(B),E))) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),F)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),V6)),hAPP(B,filter(B),at(B),E))) # label(fact_4548_LIM__mult) # label(axiom). [clausify(2913)]. 65.97/65.90 5499 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),sequentially)) # label(fact_4478_mult__left_OLIMSEQ) # label(axiom). [clausify(2985)]. 65.97/65.90 5500 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_885_mult_Odiff__left) # label(axiom). [clausify(3042)]. 65.97/65.90 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),B). [resolve(5500,a,5449,a)]. 65.97/65.90 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),B). [resolve(5500,a,5495,a)]. 65.97/65.90 5501 -real_normed_algebra(A) | -banach(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)) # label(fact_4621_Cauchy__product) # label(axiom). [clausify(3105)]. 65.97/65.91 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)). [resolve(5501,a,5449,a)]. 65.97/65.91 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hAPP(fun(nat,real),real,suminf(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)). [resolve(5501,a,5495,a)]. 66.21/66.14 5502 -real_normed_algebra(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),E),D)) | hBOOL(hAPP(B,bool,hAPP(fun(B,A),fun(B,bool),isCont(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),E)),D)) # label(fact_4909_isCont__mult) # label(axiom). [clausify(3148)]. 66.21/66.14 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),B)),D)),C)). [resolve(5502,a,5449,a)]. 66.21/66.14 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),D),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),B)),D)),C)). [resolve(5502,a,5495,a)]. 66.21/66.14 5503 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2035_mult__left_Ominus) # label(axiom). [clausify(3280)]. 66.21/66.14 5504 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_887_mult_Odiff__right) # label(axiom). [clausify(3297)]. 66.21/66.14 5505 -real_normed_algebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),F)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),F),D)),E)) # label(fact_4476_mult__right_Otendsto) # label(axiom). [clausify(3361)]. 66.21/66.14 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),hAPP(complex,fun(complex,complex),times_times(complex),E)),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),E),C)),D)). [resolve(5505,a,5449,a)]. 66.21/66.14 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),hAPP(real,fun(real,real),times_times(real),E)),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),E),C)),D)). [resolve(5505,a,5495,a)]. 66.71/66.70 5506 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,cauchy(A),B)) | hBOOL(hAPP(fun(nat,A),bool,cauchy(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B))) # label(fact_4100_mult__right_OCauchy) # label(axiom). [clausify(3395)]. 66.71/66.70 Derived: -hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),A)) | hBOOL(hAPP(fun(nat,complex),bool,cauchy(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),hAPP(complex,fun(complex,complex),times_times(complex),B)),A))). [resolve(5506,a,5449,a)]. 66.71/66.70 Derived: -hBOOL(hAPP(fun(nat,real),bool,cauchy(real),A)) | hBOOL(hAPP(fun(nat,real),bool,cauchy(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),hAPP(real,fun(real,real),times_times(real),B)),A))). [resolve(5506,a,5495,a)]. 66.71/66.70 5507 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),hAPP(B,fun(B,B),times_times(B),F)),C)),hAPP(B,B,hAPP(B,fun(B,B),times_times(B),F),D)),hAPP(A,filter(A),at(A),E))) # label(fact_4550_mult__right_OLIM) # label(axiom). [clausify(3501)]. 66.71/66.70 5508 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_883_mult__left_Oadd) # label(axiom). [clausify(3547)]. 66.71/66.70 5509 -topological_space(A) | -real_normed_algebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),zero_zero(B)),hAPP(A,filter(A),at(A),D))) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),hAPP(fun(A,fun(B,B)),fun(B,fun(A,B)),combc(A,B,B),hAPP(fun(A,B),fun(A,fun(B,B)),hAPP(fun(B,fun(B,B)),fun(fun(A,B),fun(A,fun(B,B))),combb(B,fun(B,B),A),times_times(B)),C)),E)),zero_zero(B)),hAPP(A,filter(A),at(A),D))) # label(fact_4575_LIM__mult__left__zero) # label(axiom). [clausify(3649)]. 66.71/66.70 5510 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_877_mult__left_Ozero) # label(axiom). [clausify(3664)]. 66.71/66.70 5511 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_882_mult_Oadd__left) # label(axiom). [clausify(3673)]. 66.71/66.70 5512 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_884_mult__left_Odiff) # label(axiom). [clausify(3720)]. 66.71/66.70 5513 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,A),A,suminf(A),B)) # label(fact_3988_mult__right_Osuminf) # label(axiom). [clausify(3757)]. 66.71/66.70 5514 -real_normed_algebra(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),E),D)) | hBOOL(hAPP(B,bool,hAPP(fun(B,A),fun(B,bool),isCont(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),E)),D)) # label(fact_4910_mult_OisCont) # label(axiom). [clausify(3811)]. 67.10/67.08 5515 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),hAPP(A,fun(A,A),times_times(A),D)),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),sequentially)) # label(fact_4479_mult__right_OLIMSEQ) # label(axiom). [clausify(3837)]. 67.10/67.08 5516 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3989_suminf__mult2) # label(axiom). [clausify(3901)]. 67.10/67.08 Derived: -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A)),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),B). [resolve(5516,a,5449,a)]. 67.10/67.08 Derived: -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A)),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),B). [resolve(5516,a,5495,a)]. 67.10/67.08 5517 -real_normed_algebra(A) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_4080_sums__mult2) # label(axiom). [clausify(3969)]. 67.10/67.08 5518 -real_normed_algebra(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2037_mult__right_Ominus) # label(axiom). [clausify(4075)]. 67.10/67.08 5519 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(fun(nat,A),bool,summable(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C))) # label(fact_4000_mult__left_Osummable) # label(axiom). [clausify(4123)]. 67.10/67.08 5520 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),f722(A,C)))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom). [clausify(4154)]. 67.10/67.08 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),f722(complex,B)))). [resolve(5520,a,5449,a)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),f722(real,B)))). [resolve(5520,a,5495,a)]. 67.30/67.24 5521 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f722(A,B))) # label(fact_1809_mult__left_Ononneg__bounded) # label(axiom). [clausify(4154)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f722(complex,A))). [resolve(5521,a,5449,a)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),f722(real,A))). [resolve(5521,a,5495,a)]. 67.30/67.24 5522 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f724(A))) # label(fact_1805_mult_Opos__bounded) # label(axiom). [clausify(4171)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f724(complex))). [resolve(5522,a,5449,a)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f724(real))). [resolve(5522,a,5495,a)]. 67.30/67.24 5523 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f724(A)))) # label(fact_1805_mult_Opos__bounded) # label(axiom). [clausify(4171)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f724(complex)))). [resolve(5523,a,5449,a)]. 67.30/67.24 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f724(real)))). [resolve(5523,a,5495,a)]. 67.30/67.24 5524 -real_normed_algebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),D),E),sequentially)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),sequentially)) # label(fact_4477_LIMSEQ__mult) # label(axiom). [clausify(4193)]. 67.30/67.24 5525 -real_normed_algebra(A) | -banach(A) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),B))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,A),fun(nat,real),hAPP(fun(A,real),fun(fun(nat,A),fun(nat,real)),combb(A,real,nat),norm_norm(A)),C))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(nat,fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combs(nat,fun(nat,bool),A),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A)),hAPP(fun(fun(nat,A),fun(fun(nat,bool),A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(fun(nat,bool),A))),combb(fun(nat,A),fun(fun(nat,bool),A),nat),big_co1399186613setsum(nat,A)),hAPP(fun(nat,fun(nat,A)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,A),fun(nat,A)),fun(fun(nat,fun(nat,A)),fun(nat,fun(nat,A))),combb(fun(nat,A),fun(nat,A),nat),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A)),hAPP(fun(fun(nat,nat),fun(nat,A)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,A))),combb(fun(nat,nat),fun(nat,A),nat),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),C)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),hAPP(fun(nat,A),A,suminf(A),C)))) # label(fact_4623_Cauchy__product__sums) # label(axiom). [clausify(4289)]. 67.30/67.24 Derived: -banach(complex) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),B))) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),hAPP(fun(nat,fun(nat,bool)),fun(nat,complex),hAPP(fun(nat,fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,bool)),fun(nat,complex)),combs(nat,fun(nat,bool),complex),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex)),hAPP(fun(fun(nat,complex),fun(fun(nat,bool),complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(fun(nat,bool),complex))),combb(fun(nat,complex),fun(fun(nat,bool),complex),nat),big_co1399186613setsum(nat,complex)),hAPP(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,complex),fun(nat,complex)),fun(fun(nat,fun(nat,complex)),fun(nat,fun(nat,complex))),combb(fun(nat,complex),fun(nat,complex),nat),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex)),hAPP(fun(fun(nat,nat),fun(nat,complex)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,complex))),combb(fun(nat,nat),fun(nat,complex),nat),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(nat,complex),complex,suminf(complex),A)),hAPP(fun(nat,complex),complex,suminf(complex),B)))). [resolve(5525,a,5449,a)]. 67.30/67.24 Derived: -banach(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),A))) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),B))) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),hAPP(fun(nat,fun(nat,bool)),fun(nat,real),hAPP(fun(nat,fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,bool)),fun(nat,real)),combs(nat,fun(nat,bool),real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real)),hAPP(fun(fun(nat,real),fun(fun(nat,bool),real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(fun(nat,bool),real))),combb(fun(nat,real),fun(fun(nat,bool),real),nat),big_co1399186613setsum(nat,real)),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,real),fun(nat,real)),fun(fun(nat,fun(nat,real)),fun(nat,fun(nat,real))),combb(fun(nat,real),fun(nat,real),nat),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),A))),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real)),hAPP(fun(fun(nat,nat),fun(nat,real)),fun(fun(nat,fun(nat,nat)),fun(nat,fun(nat,real))),combb(fun(nat,nat),fun(nat,real),nat),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),B)),minus_minus(nat))))),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),zero_zero(nat)))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(nat,real),real,suminf(real),A)),hAPP(fun(nat,real),real,suminf(real),B)))). [resolve(5525,a,5495,a)]. 68.00/67.95 5526 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C))),f760(A)))) # label(fact_1811_mult_Obounded) # label(axiom). [clausify(4421)]. 68.00/67.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B))),f760(complex)))). [resolve(5526,a,5449,a)]. 68.00/67.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B))),f760(real)))). [resolve(5526,a,5495,a)]. 68.00/67.95 5527 -real_normed_algebra(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),C)),f795(A,B)))) # label(fact_1813_mult__right_Obounded) # label(axiom). [clausify(4686)]. 68.00/67.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),B)),f795(complex,A)))). [resolve(5527,a,5449,a)]. 68.00/67.95 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),B)),f795(real,A)))). [resolve(5527,a,5495,a)]. 68.00/67.95 5528 -real_normed_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_4676_mult__right_OscaleR) # label(axiom). [clausify(4815)]. 68.00/67.95 5529 -real_normed_algebra(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),B)),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(nat,A),A,suminf(A),B)),C) # label(fact_3987_mult__left_Osuminf) # label(axiom). [clausify(4871)]. 68.00/67.95 5530 -real_normed_algebra(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_878_mult_Ozero__right) # label(axiom). [clausify(4878)]. 68.00/67.95 5531 -real_normed_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_4674_mult_OscaleR__right) # label(axiom). [clausify(4926)]. 70.08/70.00 5532 real_n1866405975lgebra(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption]. 70.08/70.00 5533 -real_n1866405975lgebra(A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,norm_norm(A),B)),hAPP(A,real,norm_norm(A),C)) = hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_1778_norm__mult) # label(axiom). [clausify(43)]. 70.08/70.00 5534 -topological_space(A) | -real_n1866405975lgebra(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),C),D)) | hAPP(A,B,C,D) = zero_zero(B) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),inverse_inverse(B)),C)),D)) # label(fact_4912_isCont__inverse) # label(axiom). [clausify(117)]. 70.08/70.00 5535 -real_n1866405975lgebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(fun(nat,A),bool,bseq(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),inverse_inverse(A)),B))) # label(fact_4489_Bseq__inverse) # label(axiom). [clausify(569)]. 70.08/70.00 5536 -real_n1866405975lgebra(A) | -divisi14063676e_zero(A) | hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B)) = hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2510_norm__inverse) # label(axiom). [clausify(790)]. 70.08/70.00 5537 -real_n1866405975lgebra(A) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(A,real,norm_norm(A),B)),C) = hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_1782_norm__power) # label(axiom). [clausify(902)]. 70.08/70.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,norm_norm(real),A)),hAPP(real,real,norm_norm(real),B)) = hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(5532,a,5533,a)]. 70.08/70.00 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hAPP(A,real,B,C) = zero_zero(real) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),inverse_inverse(real)),B)),C)). [resolve(5532,a,5534,b)]. 70.08/70.00 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(real,fun(filter(nat),bool),hAPP(fun(nat,real),fun(real,fun(filter(nat),bool)),tendsto(nat,real),A),B),sequentially)) | ti(real,B) = zero_zero(real) | hBOOL(hAPP(fun(nat,real),bool,bseq(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),inverse_inverse(real)),A))). [resolve(5532,a,5535,a)]. 70.08/70.00 Derived: -divisi14063676e_zero(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A)) = hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5532,a,5536,a)]. 70.08/70.00 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,norm_norm(real),A)),B) = hAPP(real,real,norm_norm(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5532,a,5537,a)]. 70.08/70.00 5538 -real_n1866405975lgebra(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,sgn_sgn(A),C)) # label(fact_2204_sgn__mult) # label(axiom). [clausify(1284)]. 70.08/70.00 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(5538,a,5532,a)]. 70.08/70.00 5539 -real_n1866405975lgebra(A) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(A,real,norm_norm(A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),C))),hAPP(real,real,inverse_inverse(real),B))) # label(fact_2538_Bseq__inverse__lemma) # label(axiom). [clausify(1507)]. 71.49/71.41 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,norm_norm(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),B))),hAPP(real,real,inverse_inverse(real),A))). [resolve(5539,a,5532,a)]. 71.49/71.41 5540 -topological_space(A) | -real_n1866405975lgebra(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | ti(B,D) = zero_zero(B) | hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(fun(A,B),fun(A,B),hAPP(fun(B,B),fun(fun(A,B),fun(A,B)),combb(B,B,A),inverse_inverse(B)),C)),hAPP(B,B,inverse_inverse(B),D)),hAPP(A,filter(A),at(A),E))) # label(fact_4588_LIM__inverse) # label(axiom). [clausify(2016)]. 71.49/71.41 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),hAPP(A,filter(A),at(A),D))) | ti(real,C) = zero_zero(real) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),inverse_inverse(real)),B)),hAPP(real,real,inverse_inverse(real),C)),hAPP(A,filter(A),at(A),D))). [resolve(5540,b,5532,a)]. 71.49/71.41 5541 -real_n1866405975lgebra(A) | ti(A,B) = zero_zero(A) | hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B)) = hAPP(A,real,norm_norm(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2511_nonzero__norm__inverse) # label(axiom). [clausify(2316)]. 71.49/71.41 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A)) = hAPP(real,real,norm_norm(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5541,a,5532,a)]. 71.49/71.41 5542 -real_n1866405975lgebra(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(filter(A),bool,hAPP(A,fun(filter(A),bool),hAPP(fun(A,A),fun(A,fun(filter(A),bool)),tendsto(A,A),inverse_inverse(A)),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,filter(A),at(A),B))) # label(fact_4547_LIM__inverse__fun) # label(axiom). [clausify(2958)]. 71.49/71.41 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),inverse_inverse(real)),hAPP(real,real,inverse_inverse(real),A)),hAPP(real,filter(real),at(real),A))). [resolve(5542,a,5532,a)]. 71.49/71.41 5543 -real_n1866405975lgebra(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),C),D),E)) | ti(A,D) = zero_zero(A) | hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),inverse_inverse(A)),C)),hAPP(A,A,inverse_inverse(A),D)),E)) # label(fact_4481_tendsto__inverse) # label(axiom). [clausify(3758)]. 71.49/71.41 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),B),C),D)) | ti(real,C) = zero_zero(real) | hBOOL(hAPP(filter(A),bool,hAPP(real,fun(filter(A),bool),hAPP(fun(A,real),fun(real,fun(filter(A),bool)),tendsto(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),inverse_inverse(real)),B)),hAPP(real,real,inverse_inverse(real),C)),D)). [resolve(5543,a,5532,a)]. 71.49/71.41 5544 real_n1866405975lgebra(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__div__algebra) # label(axiom). [assumption]. 71.49/71.41 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,norm_norm(complex),A)),hAPP(complex,real,norm_norm(complex),B)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(5544,a,5533,a)]. 71.61/71.54 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),B),C)) | hAPP(A,complex,B,C) = zero_zero(complex) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),inverse_inverse(complex)),B)),C)). [resolve(5544,a,5534,b)]. 71.61/71.54 Derived: -hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),A),B),sequentially)) | ti(complex,B) = zero_zero(complex) | hBOOL(hAPP(fun(nat,complex),bool,bseq(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(complex,complex),fun(fun(nat,complex),fun(nat,complex)),combb(complex,complex,nat),inverse_inverse(complex)),A))). [resolve(5544,a,5535,a)]. 71.61/71.54 Derived: -divisi14063676e_zero(complex) | hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5544,a,5536,a)]. 71.61/71.54 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),A)),B) = hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(5544,a,5537,a)]. 71.61/71.54 Derived: hAPP(complex,complex,sgn_sgn(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,sgn_sgn(complex),A)),hAPP(complex,complex,sgn_sgn(complex),B)). [resolve(5544,a,5538,a)]. 71.61/71.54 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(complex,real,norm_norm(complex),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),B))),hAPP(real,real,inverse_inverse(real),A))). [resolve(5544,a,5539,a)]. 71.61/71.54 Derived: -topological_space(A) | -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),hAPP(A,filter(A),at(A),D))) | ti(complex,C) = zero_zero(complex) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),inverse_inverse(complex)),B)),hAPP(complex,complex,inverse_inverse(complex),C)),hAPP(A,filter(A),at(A),D))). [resolve(5544,a,5540,b)]. 71.61/71.54 Derived: ti(complex,A) = zero_zero(complex) | hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A)) = hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,inverse_inverse(complex),A)). [resolve(5544,a,5541,a)]. 71.61/71.54 Derived: ti(complex,A) = zero_zero(complex) | hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),inverse_inverse(complex)),hAPP(complex,complex,inverse_inverse(complex),A)),hAPP(complex,filter(complex),at(complex),A))). [resolve(5544,a,5542,a)]. 71.61/71.54 Derived: -hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),B),C),D)) | ti(complex,C) = zero_zero(complex) | hBOOL(hAPP(filter(A),bool,hAPP(complex,fun(filter(A),bool),hAPP(fun(A,complex),fun(complex,fun(filter(A),bool)),tendsto(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),inverse_inverse(complex)),B)),hAPP(complex,complex,inverse_inverse(complex),C)),D)). [resolve(5544,a,5543,a)]. 71.61/71.54 5545 -real_n1866405975lgebra(A) | -hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),B),C),sequentially)) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),inverse_inverse(A)),B)),hAPP(A,A,inverse_inverse(A),C)),sequentially)) # label(fact_4483_LIMSEQ__inverse) # label(axiom). [clausify(3978)]. 75.38/75.29 5546 ordered_ring_abs(real) # label(arity_RealDef_Oreal___Rings_Oordered__ring__abs) # label(axiom). [assumption]. 75.38/75.29 5547 -ordered_ring_abs(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)) | 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)),hAPP(A,A,abs_abs(A),B)) # label(fact_1878_abs__eq__mult) # label(axiom). [clausify(48)]. 75.38/75.29 5548 -ordered_ring_abs(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))) | 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)),hAPP(A,A,abs_abs(A),B)) # label(fact_1878_abs__eq__mult) # label(axiom). [clausify(48)]. 75.38/75.29 5549 -ordered_ring_abs(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)) | 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)),hAPP(A,A,abs_abs(A),B)) # label(fact_1878_abs__eq__mult) # label(axiom). [clausify(48)]. 75.38/75.29 5550 -ordered_ring_abs(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))) | 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)),hAPP(A,A,abs_abs(A),B)) # label(fact_1878_abs__eq__mult) # label(axiom). [clausify(48)]. 75.38/75.29 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)) | 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)),hAPP(real,real,abs_abs(real),A)). [resolve(5546,a,5547,a)]. 75.38/75.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | 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)),hAPP(real,real,abs_abs(real),A)). [resolve(5546,a,5548,a)]. 75.38/75.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | 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)),hAPP(real,real,abs_abs(real),A)). [resolve(5546,a,5549,a)]. 75.38/75.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | 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)),hAPP(real,real,abs_abs(real),A)). [resolve(5546,a,5550,a)]. 75.38/75.29 5551 ordered_ring_abs(rat) # label(arity_Rat_Orat___Rings_Oordered__ring__abs) # label(axiom). [assumption]. 75.38/75.29 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)) | 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)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5551,a,5547,a)]. 79.11/79.08 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | 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)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5551,a,5548,a)]. 79.11/79.08 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | 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)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5551,a,5549,a)]. 79.11/79.08 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | 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)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5551,a,5550,a)]. 79.11/79.08 5552 ordered_ring_abs(int) # label(arity_Int_Oint___Rings_Oordered__ring__abs) # label(axiom). [assumption]. 79.11/79.08 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)) | 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)),hAPP(int,int,abs_abs(int),A)). [resolve(5552,a,5547,a)]. 79.11/79.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | 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)),hAPP(int,int,abs_abs(int),A)). [resolve(5552,a,5548,a)]. 79.11/79.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | 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)),hAPP(int,int,abs_abs(int),A)). [resolve(5552,a,5549,a)]. 79.11/79.08 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | 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)),hAPP(int,int,abs_abs(int),A)). [resolve(5552,a,5550,a)]. 79.11/79.08 5553 monoid_mult(real) # label(arity_RealDef_Oreal___Groups_Omonoid__mult) # label(axiom). [assumption]. 79.11/79.08 5554 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_349_power__mult) # label(axiom). [clausify(49)]. 79.11/79.08 5555 -number(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_168_power2__eq__square__number__of) # label(axiom). [clausify(286)]. 79.11/79.08 5556 -monoid_mult(A) | -comm_semiring_0(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,D)))) # label(fact_4174_lemma__realpow__diff__sumr) # label(axiom). [clausify(697)]. 79.11/79.08 5557 -monoid_mult(A) | -linordered_ring(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2433_zero__le__even__power) # label(axiom). [clausify(752)]. 79.11/79.08 5558 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)) # label(fact_233_power__even__eq) # label(axiom). [clausify(1085)]. 79.11/79.08 5559 -monoid_mult(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3898_power__number__of__odd) # label(axiom). [clausify(1110)]. 79.11/79.08 5560 -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(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))) # label(fact_3898_power__number__of__odd) # label(axiom). [clausify(1110)]. 79.11/79.08 5561 -number(A) | -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),C))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) # label(fact_3872_power__number__of__even__number__of) # label(axiom). [clausify(1282)]. 79.11/79.08 5562 -monoid_mult(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),one_one(A)),B) # label(fact_341_power__one) # label(axiom). [clausify(1306)]. 79.11/79.08 5563 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) = 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) # label(fact_1307_power__Suc2) # label(axiom). [clausify(1530)]. 79.11/79.08 5564 -monoid_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_331_power__commutes) # label(axiom). [clausify(1533)]. 79.11/79.09 5565 -monoid_mult(A) | -number(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom). [clausify(1554)]. 79.11/79.09 5566 -monoid_mult(A) | -number(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),B))) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,B))) # label(fact_3905_power__number__of__odd__number__of) # label(axiom). [clausify(1554)]. 79.11/79.09 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(5553,a,5554,a)]. 79.11/79.09 Derived: -number(real) | 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),A)) = 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,hAPP(int,int,bit1,pls)))). [resolve(5553,a,5555,b)]. 79.11/79.09 Derived: -comm_semiring_0(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5553,a,5556,a)]. 79.11/79.09 Derived: -linordered_ring(real) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5553,a,5557,a)]. 79.11/79.09 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5553,a,5558,a)]. 79.28/79.26 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5553,a,5559,a)]. 79.28/79.26 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5553,a,5560,a)]. 79.28/79.26 Derived: -number(real) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5553,a,5561,b)]. 79.28/79.26 Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),one_one(real)),A). [resolve(5553,a,5562,a)]. 79.28/79.26 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B)) = 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). [resolve(5553,a,5563,a)]. 79.28/79.26 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(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(5553,a,5564,a)]. 79.28/79.26 Derived: -number(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5553,a,5566,a)]. 79.28/79.26 5567 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B)),B) # label(fact_138_power3__eq__cube) # label(axiom). [clausify(1863)]. 79.28/79.26 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A)),A). [resolve(5567,a,5553,a)]. 79.28/79.26 5568 monoid_mult(nat) # label(arity_Nat_Onat___Groups_Omonoid__mult) # label(axiom). [assumption]. 79.28/79.26 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(5568,a,5554,a)]. 79.28/79.26 Derived: -number(nat) | 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),A)) = 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,hAPP(int,int,bit1,pls)))). [resolve(5568,a,5555,b)]. 79.28/79.27 Derived: -comm_semiring_0(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5568,a,5556,a)]. 79.28/79.27 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5568,a,5558,a)]. 79.28/79.27 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5568,a,5559,a)]. 79.28/79.27 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5568,a,5560,a)]. 79.28/79.27 Derived: -number(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5568,a,5561,b)]. 79.28/79.27 Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),one_one(nat)),A). [resolve(5568,a,5562,a)]. 79.28/79.27 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),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),A). [resolve(5568,a,5563,a)]. 79.28/79.27 Derived: -number(nat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(int,nat,number_number_of(nat),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5568,a,5566,a)]. 79.72/79.67 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),A)),A). [resolve(5568,a,5567,a)]. 79.72/79.67 5569 -monoid_mult(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(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_143_power2__eq__square) # label(axiom). [clausify(2115)]. 79.72/79.67 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(real,real,hAPP(real,fun(real,real),times_times(real),A),A). [resolve(5569,a,5553,a)]. 79.72/79.67 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),times_times(nat),A),A). [resolve(5569,a,5568,a)]. 79.72/79.67 5570 -monoid_mult(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),one_one(nat)))),C) # label(fact_717_realpow__minus__mult) # label(axiom). [clausify(2144)]. 79.72/79.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5570,a,5553,a)]. 79.72/79.67 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5570,a,5568,a)]. 79.72/79.67 5571 monoid_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Omonoid__mult) # label(axiom). [assumption]. 79.72/79.67 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(5571,a,5554,a)]. 79.72/79.67 Derived: -number(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5571,a,5555,b)]. 79.72/79.67 Derived: -comm_semiring_0(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5571,a,5556,a)]. 79.72/79.68 Derived: -linordered_ring(code_code_numeral) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A))). [resolve(5571,a,5557,a)]. 79.72/79.68 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5571,a,5558,a)]. 79.72/79.68 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5571,a,5559,a)]. 79.72/79.68 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5571,a,5560,a)]. 79.72/79.69 Derived: -number(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5571,a,5561,b)]. 79.72/79.69 Derived: one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),one_one(code_code_numeral)),A). [resolve(5571,a,5562,a)]. 79.72/79.69 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(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). [resolve(5571,a,5563,a)]. 79.72/79.69 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)). [resolve(5571,a,5564,a)]. 79.72/79.69 Derived: -number(code_code_numeral) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(int,code_code_numeral,number_number_of(code_code_numeral),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5571,a,5566,a)]. 79.72/79.69 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,bit1,hAPP(int,int,bit1,pls)))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A)),A). [resolve(5571,a,5567,a)]. 80.00/79.91 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(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),A). [resolve(5571,a,5569,a)]. 80.00/79.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5571,a,5570,a)]. 80.00/79.91 5572 -monoid_mult(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_351_power__one__right) # label(axiom). [clausify(2991)]. 80.00/79.91 Derived: ti(real,A) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),one_one(nat)). [resolve(5572,a,5553,a)]. 80.00/79.91 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),one_one(nat)). [resolve(5572,a,5568,a)]. 80.00/79.91 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(5572,a,5571,a)]. 80.00/79.91 5573 monoid_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Omonoid__mult) # label(axiom). [assumption]. 80.00/79.91 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(5573,a,5554,a)]. 80.00/79.91 Derived: -number(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(5573,a,5555,b)]. 80.00/79.91 Derived: -comm_semiring_0(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5573,a,5556,a)]. 80.00/79.92 Derived: -linordered_ring(quickcheck_code_int) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A))). [resolve(5573,a,5557,a)]. 80.00/79.92 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5573,a,5558,a)]. 80.00/79.92 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5573,a,5559,a)]. 80.00/79.92 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5573,a,5560,a)]. 80.00/79.92 Derived: -number(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5573,a,5561,b)]. 80.02/79.92 Derived: one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),one_one(quickcheck_code_int)),A). [resolve(5573,a,5562,a)]. 80.02/79.92 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(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). [resolve(5573,a,5563,a)]. 80.02/79.92 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)). [resolve(5573,a,5564,a)]. 80.02/79.92 Derived: -number(quickcheck_code_int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(int,quickcheck_code_int,number_number_of(quickcheck_code_int),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5573,a,5566,a)]. 80.02/79.92 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,bit1,hAPP(int,int,bit1,pls)))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A)),A). [resolve(5573,a,5567,a)]. 80.02/79.92 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(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),A). [resolve(5573,a,5569,a)]. 80.02/79.96 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5573,a,5570,a)]. 80.02/79.96 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(5573,a,5572,a)]. 80.02/79.96 5574 monoid_mult(int) # label(arity_Int_Oint___Groups_Omonoid__mult) # label(axiom). [assumption]. 80.02/79.96 Derived: -number(int) | 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),A)) = 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,hAPP(int,int,bit1,pls)))). [resolve(5574,a,5555,b)]. 80.02/79.96 Derived: -comm_semiring_0(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5574,a,5556,a)]. 80.02/79.96 Derived: -linordered_ring(int) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5574,a,5557,a)]. 80.02/79.96 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5574,a,5558,a)]. 80.02/79.96 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5574,a,5559,a)]. 80.02/79.96 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5574,a,5560,a)]. 80.02/79.98 Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),one_one(int)),A). [resolve(5574,a,5562,a)]. 80.02/79.98 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B)) = 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). [resolve(5574,a,5563,a)]. 80.02/79.98 Derived: -number(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5574,a,5566,a)]. 80.02/79.98 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A)),A). [resolve(5574,a,5567,a)]. 80.02/79.98 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(int,int,hAPP(int,fun(int,int),times_times(int),A),A). [resolve(5574,a,5569,a)]. 80.02/79.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5574,a,5570,a)]. 80.02/79.98 Derived: ti(int,A) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),one_one(nat)). [resolve(5574,a,5572,a)]. 80.02/79.98 5575 -monoid_mult(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))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) # label(fact_1456_power__odd__eq) # label(axiom). [clausify(3210)]. 80.02/79.98 Derived: 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))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5575,a,5553,a)]. 80.02/79.98 Derived: 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))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5575,a,5568,a)]. 80.02/79.98 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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5575,a,5571,a)]. 80.11/80.03 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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5575,a,5573,a)]. 80.11/80.03 Derived: 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))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5575,a,5574,a)]. 80.11/80.03 5576 -monoid_mult(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))) # label(fact_3871_power__number__of__even) # label(axiom). [clausify(3265)]. 80.11/80.03 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5576,a,5553,a)]. 80.11/80.03 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5576,a,5568,a)]. 80.11/80.03 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,B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5576,a,5571,a)]. 80.11/80.03 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,B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5576,a,5573,a)]. 80.79/80.77 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5576,a,5574,a)]. 80.79/80.77 5577 -comm_ring(A) | -monoid_mult(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),D))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(A,fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(A,fun(nat,A)),combc(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(nat,fun(nat,nat),minus_minus(nat),D)))),hAPP(A,fun(nat,A),power_power(A),B)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) # label(fact_4226_lemma__termdiff1) # label(axiom). [clausify(4045)]. 80.79/80.77 Derived: -comm_ring(real) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(real,fun(nat,real),power_power(real),A)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5577,b,5553,a)]. 80.79/80.77 Derived: -comm_ring(nat) | hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),minus_minus(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,nat),power_power(nat),A)))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5577,b,5568,a)]. 80.79/80.77 Derived: -comm_ring(code_code_numeral) | hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),minus_minus(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(code_code_numeral,fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(nat,code_code_numeral)),combc(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),minus_minus(code_code_numeral)),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A)))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5577,b,5571,a)]. 80.79/80.77 Derived: -comm_ring(quickcheck_code_int) | hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),minus_minus(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(nat,quickcheck_code_int)),combc(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),minus_minus(quickcheck_code_int)),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A)))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5577,b,5573,a)]. 80.79/80.77 Derived: -comm_ring(int) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(int,fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(int,fun(nat,int)),combc(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(int,fun(nat,int),power_power(int),A)))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5577,b,5574,a)]. 80.91/80.90 5578 monoid_mult(rat) # label(arity_Rat_Orat___Groups_Omonoid__mult) # label(axiom). [assumption]. 80.91/80.90 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(5578,a,5554,a)]. 80.91/80.90 Derived: -number(rat) | 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),A)) = 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,hAPP(int,int,bit1,pls)))). [resolve(5578,a,5555,b)]. 80.91/80.90 Derived: -comm_semiring_0(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5578,a,5556,a)]. 81.00/80.91 Derived: -linordered_ring(rat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5578,a,5557,a)]. 81.00/80.91 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5578,a,5558,a)]. 81.00/80.91 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5578,a,5559,a)]. 81.00/80.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5578,a,5560,a)]. 81.00/80.91 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5578,a,5561,b)]. 81.00/80.91 Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),one_one(rat)),A). [resolve(5578,a,5562,a)]. 81.00/80.91 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B)) = 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). [resolve(5578,a,5563,a)]. 81.00/80.91 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(5578,a,5564,a)]. 81.00/80.91 Derived: -number(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5578,a,5566,a)]. 81.00/80.91 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A)),A). [resolve(5578,a,5567,a)]. 81.00/80.91 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(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A). [resolve(5578,a,5569,a)]. 81.00/80.91 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5578,a,5570,a)]. 81.08/81.02 Derived: ti(rat,A) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),one_one(nat)). [resolve(5578,a,5572,a)]. 81.08/81.02 Derived: 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))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5578,a,5575,a)]. 81.08/81.02 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5578,a,5576,a)]. 81.08/81.02 Derived: -comm_ring(rat) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(rat,fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(rat,fun(nat,rat)),combc(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(rat,fun(nat,rat),power_power(rat),A)))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5578,a,5577,b)]. 81.08/81.02 5579 monoid_mult(complex) # label(arity_Complex_Ocomplex___Groups_Omonoid__mult) # label(axiom). [assumption]. 81.08/81.02 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(5579,a,5554,a)]. 81.08/81.02 Derived: -number(complex) | 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),A)) = 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,hAPP(int,int,bit1,pls)))). [resolve(5579,a,5555,b)]. 81.08/81.03 Derived: -comm_semiring_0(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),B)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))). [resolve(5579,a,5556,a)]. 81.08/81.03 Derived: -linordered_ring(complex) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),ord_less_eq(complex),zero_zero(complex)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A))). [resolve(5579,a,5557,a)]. 81.08/81.03 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B)). [resolve(5579,a,5558,a)]. 81.08/81.03 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5579,a,5559,a)]. 81.08/81.03 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A))). [resolve(5579,a,5560,a)]. 81.08/81.03 Derived: -number(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),B))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),A)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))). [resolve(5579,a,5561,b)]. 81.08/81.03 Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),one_one(complex)),A). [resolve(5579,a,5562,a)]. 81.08/81.03 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)) = 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). [resolve(5579,a,5563,a)]. 81.08/81.03 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(5579,a,5564,a)]. 81.08/81.03 Derived: -number(complex) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),A))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(int,complex,number_number_of(complex),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,A))). [resolve(5579,a,5566,a)]. 81.08/81.03 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,hAPP(int,int,bit1,pls)))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A)),A). [resolve(5579,a,5567,a)]. 81.08/81.03 Derived: 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(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A). [resolve(5579,a,5569,a)]. 81.08/81.03 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(nat)))),B). [resolve(5579,a,5570,a)]. 81.08/81.03 Derived: ti(complex,A) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),one_one(nat)). [resolve(5579,a,5572,a)]. 81.08/81.03 Derived: 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))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))). [resolve(5579,a,5575,a)]. 81.08/81.03 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(int,nat,number_number_of(nat),B))). [resolve(5579,a,5576,a)]. 81.22/81.13 Derived: -comm_ring(complex) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),A)),hAPP(nat,fun(nat,nat),minus_minus(nat),C))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(complex,fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(complex,fun(nat,complex)),combc(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B))),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(complex,fun(nat,complex),power_power(complex),A)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)). [resolve(5579,a,5577,b)]. 81.22/81.13 5580 -monoid_mult(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,C)),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),C),B))),D) # label(fact_1412_lemma__realpow__diff) # label(axiom). [clausify(4426)]. 81.22/81.13 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5553,a)]. 81.22/81.13 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5568,a)]. 81.31/81.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5571,a)]. 81.31/81.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5573,a)]. 81.31/81.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5574,a)]. 81.31/81.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5578,a)]. 81.31/81.23 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,suc,B)),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),B),A))),C). [resolve(5580,a,5579,a)]. 81.31/81.23 5581 -monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_800_mult__1__right) # label(axiom). [clausify(4480)]. 81.31/81.23 5582 -monoid_mult(A) | -comm_ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),times_times(A)),hAPP(A,fun(nat,A),power_power(A),B))),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),hAPP(A,fun(nat,A),power_power(A),D)),hAPP(nat,fun(nat,nat),minus_minus(nat),C)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,C)))) # label(fact_4227_lemma__realpow__diff__sumr2) # label(axiom). [clausify(4529)]. 81.31/81.23 Derived: -comm_ring(real) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),C),hAPP(nat,nat,suc,B))) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),power_power(real),A))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),hAPP(real,fun(nat,real),power_power(real),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5553,a)]. 81.31/81.24 Derived: -comm_ring(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),hAPP(nat,nat,suc,B))),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),hAPP(nat,nat,suc,B))) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),C)),hAPP(fun(nat,bool),nat,hAPP(fun(nat,nat),fun(fun(nat,bool),nat),big_co1399186613setsum(nat,nat),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,nat)),combs(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),hAPP(nat,fun(nat,nat),power_power(nat),A))),hAPP(fun(nat,nat),fun(nat,nat),hAPP(fun(nat,nat),fun(fun(nat,nat),fun(nat,nat)),combb(nat,nat,nat),hAPP(nat,fun(nat,nat),power_power(nat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5568,a)]. 81.31/81.24 Derived: -comm_ring(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B))),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B))) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),minus_minus(code_code_numeral),A),C)),hAPP(fun(nat,bool),code_code_numeral,hAPP(fun(nat,code_code_numeral),fun(fun(nat,bool),code_code_numeral),big_co1399186613setsum(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,code_code_numeral),hAPP(fun(nat,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,code_code_numeral)),combs(nat,code_code_numeral,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(nat,code_code_numeral),fun(nat,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),nat),times_times(code_code_numeral)),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A))),hAPP(fun(nat,nat),fun(nat,code_code_numeral),hAPP(fun(nat,code_code_numeral),fun(fun(nat,nat),fun(nat,code_code_numeral)),combb(nat,code_code_numeral,nat),hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5571,a)]. 81.31/81.24 Derived: -comm_ring(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(nat,nat,suc,B))),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C),hAPP(nat,nat,suc,B))) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),minus_minus(quickcheck_code_int),A),C)),hAPP(fun(nat,bool),quickcheck_code_int,hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,bool),quickcheck_code_int),big_co1399186613setsum(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int),hAPP(fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,quickcheck_code_int)),combs(nat,quickcheck_code_int,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(nat,quickcheck_code_int),fun(nat,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),nat),times_times(quickcheck_code_int)),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A))),hAPP(fun(nat,nat),fun(nat,quickcheck_code_int),hAPP(fun(nat,quickcheck_code_int),fun(fun(nat,nat),fun(nat,quickcheck_code_int)),combb(nat,quickcheck_code_int,nat),hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5573,a)]. 81.31/81.24 Derived: -comm_ring(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,B))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),C),hAPP(nat,nat,suc,B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),times_times(int)),hAPP(int,fun(nat,int),power_power(int),A))),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),hAPP(int,fun(nat,int),power_power(int),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5574,a)]. 81.31/81.24 Derived: -comm_ring(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,B))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),C),hAPP(nat,nat,suc,B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),times_times(rat)),hAPP(rat,fun(nat,rat),power_power(rat),A))),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),hAPP(rat,fun(nat,rat),power_power(rat),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5578,a)]. 81.51/81.42 Derived: -comm_ring(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),C),hAPP(nat,nat,suc,B))) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),times_times(complex)),hAPP(complex,fun(nat,complex),power_power(complex),A))),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),hAPP(complex,fun(nat,complex),power_power(complex),C)),hAPP(nat,fun(nat,nat),minus_minus(nat),B)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,suc,B)))). [resolve(5582,a,5579,a)]. 81.51/81.42 5583 -monoid_mult(A) | 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)) = 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)) # label(fact_416_power__add) # label(axiom). [clausify(4719)]. 81.51/81.42 Derived: 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)) = 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)). [resolve(5583,a,5553,a)]. 81.51/81.42 Derived: 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)) = 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)). [resolve(5583,a,5568,a)]. 81.51/81.42 Derived: 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)) = 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)). [resolve(5583,a,5571,a)]. 81.51/81.42 Derived: 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)) = 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)). [resolve(5583,a,5573,a)]. 81.51/81.42 Derived: 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)) = 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)). [resolve(5583,a,5574,a)]. 81.51/81.42 Derived: 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)) = 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)). [resolve(5583,a,5578,a)]. 84.32/84.24 Derived: 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)) = 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)). [resolve(5583,a,5579,a)]. 84.32/84.24 5584 -monoid_mult(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_802_mult__1__left) # label(axiom). [clausify(4876)]. 84.32/84.24 5585 linordered_idom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__idom) # label(axiom). [assumption]. 84.32/84.24 5586 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2440_power__mono__even) # label(axiom). [clausify(56)]. 84.32/84.24 5587 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,uminus_uminus(A),B)),C)) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_2084_abs__power__minus) # label(axiom). [clausify(88)]. 84.32/84.24 5588 -linordered_idom(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(A,A,abs_abs(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_1849_abs__of__nat) # label(axiom). [clausify(145)]. 84.32/84.24 5589 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B)) # label(fact_437_mult__left__le__one__le) # label(axiom). [clausify(154)]. 84.32/84.24 5590 -linordered_idom(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(A) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom). [clausify(213)]. 84.32/84.24 5591 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(A) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom). [clausify(213)]. 84.32/84.24 5592 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(A) # label(fact_9_sum__power2__eq__zero__iff) # label(axiom). [clausify(213)]. 84.32/84.24 5593 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2060_less__minus__self__iff) # label(axiom). [clausify(226)]. 84.32/84.24 5594 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2060_less__minus__self__iff) # label(axiom). [clausify(226)]. 84.32/84.24 5595 -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3570_of__int__le__iff) # label(axiom). [clausify(409)]. 84.32/84.24 5596 -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3570_of__int__le__iff) # label(axiom). [clausify(409)]. 84.32/84.24 5597 -linordered_idom(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)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) | 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),D),B))),C)) # label(fact_1883_abs__diff__less__iff) # label(axiom). [clausify(507)]. 84.32/84.24 5598 -linordered_idom(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)),D)) | -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),D),B))),C)) # label(fact_1883_abs__diff__less__iff) # label(axiom). [clausify(507)]. 84.32/84.24 5599 -linordered_idom(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),C),D))) | -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)) # label(fact_1883_abs__diff__less__iff) # label(axiom). [clausify(507)]. 84.32/84.24 5600 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) != hAPP(A,A,uminus_uminus(A),one_one(A)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2230_sgn__1__neg) # label(axiom). [clausify(567)]. 84.32/84.24 5601 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2230_sgn__1__neg) # label(axiom). [clausify(567)]. 84.32/84.24 5602 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B)) # label(fact_438_mult__right__le__one__le) # label(axiom). [clausify(678)]. 84.32/84.24 5603 -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)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) # label(fact_180_less__special_I4_J) # label(axiom). [clausify(743)]. 84.32/84.24 5604 -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)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,bit1,pls))) # label(fact_180_less__special_I4_J) # label(axiom). [clausify(743)]. 84.32/84.24 5605 -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_2435_zero__le__power__eq) # label(axiom). [clausify(744)]. 84.32/84.24 5606 -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_2435_zero__le__power__eq) # label(axiom). [clausify(744)]. 84.32/84.24 5607 -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_2435_zero__le__power__eq) # label(axiom). [clausify(744)]. 84.32/84.24 5608 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | one_one(A) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2223_sgn__pos) # label(axiom). [clausify(811)]. 84.32/84.24 5609 -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_1845_dvd__abs__iff) # label(axiom). [clausify(930)]. 84.32/84.24 5610 -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_1845_dvd__abs__iff) # label(axiom). [clausify(930)]. 84.32/84.24 5611 -linordered_idom(A) | one_one(A) = hAPP(A,A,abs_abs(A),one_one(A)) # label(fact_1853_abs__one) # label(axiom). [clausify(935)]. 84.32/84.24 5612 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_144_even__less__0__iff) # label(axiom). [clausify(1117)]. 84.32/84.24 5613 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_144_even__less__0__iff) # label(axiom). [clausify(1117)]. 84.32/84.24 5614 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))) # label(fact_251_zero__le__even__power_H) # label(axiom). [clausify(1199)]. 84.32/84.24 5615 -linordered_idom(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(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))))) # label(fact_1900_abs__power2) # label(axiom). [clausify(1203)]. 84.32/84.24 5616 -linordered_idom(A) | ti(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_2453_power__le__zero__eq) # label(axiom). [clausify(1212)]. 84.32/84.24 5617 -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_2453_power__le__zero__eq) # label(axiom). [clausify(1212)]. 84.32/84.24 5618 -linordered_idom(A) | ti(A,B) = 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(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),zero_zero(A))) # label(fact_2453_power__le__zero__eq) # label(axiom). [clausify(1212)]. 84.32/84.24 5619 -linordered_idom(A) | ti(A,B) = zero_zero(A) | -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_2453_power__le__zero__eq) # label(axiom). [clausify(1212)]. 84.32/84.24 5620 -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_2453_power__le__zero__eq) # label(axiom). [clausify(1212)]. 84.32/84.24 5621 -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_2453_power__le__zero__eq) # label(axiom). [clausify(1212)]. 84.32/84.24 5622 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_181_less__special_I2_J) # label(axiom). [clausify(1231)]. 84.32/84.24 5623 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,bit1,pls)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_181_less__special_I2_J) # label(axiom). [clausify(1231)]. 84.32/84.24 5624 -linordered_idom(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_1854_abs__mult) # label(axiom). [clausify(1251)]. 84.32/84.24 5625 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_3799_Ints__odd__less__0) # label(axiom). [clausify(1266)]. 84.32/84.24 5626 -linordered_idom(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),B)),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_3799_Ints__odd__less__0) # label(axiom). [clausify(1266)]. 84.32/84.24 5627 -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_3569_of__int__less__iff) # label(axiom). [clausify(1331)]. 84.32/84.24 5628 -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_3569_of__int__less__iff) # label(axiom). [clausify(1331)]. 84.32/84.24 5629 -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_2215_mult__sgn__abs) # label(axiom). [clausify(1363)]. 84.32/84.24 5630 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_11_zero__less__power2) # label(axiom). [clausify(1364)]. 84.32/84.24 5631 -linordered_idom(A) | ti(A,B) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_11_zero__less__power2) # label(axiom). [clausify(1364)]. 84.32/84.24 5632 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) # label(fact_1445_of__nat__less__two__power) # label(axiom). [clausify(1724)]. 84.32/84.24 5633 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2212_sgn__less) # label(axiom). [clausify(1730)]. 84.32/84.24 5634 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,sgn_sgn(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2212_sgn__less) # label(axiom). [clausify(1730)]. 84.32/84.24 5635 -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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_2432_zero__le__odd__power) # label(axiom). [clausify(1851)]. 84.32/84.24 5636 -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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) # label(fact_2432_zero__le__odd__power) # label(axiom). [clausify(1851)]. 84.32/84.26 5637 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_177_less__special_I1_J) # label(axiom). [clausify(1903)]. 84.32/84.26 5638 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_177_less__special_I1_J) # label(axiom). [clausify(1903)]. 84.32/84.26 5639 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_48_le__special_I1_J) # label(axiom). [clausify(1970)]. 84.32/84.26 5640 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) # label(fact_48_le__special_I1_J) # label(axiom). [clausify(1970)]. 84.32/84.26 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(5585,a,5586,a)]. 84.32/84.26 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(5585,a,5587,a)]. 84.32/84.26 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(real,real,abs_abs(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(5585,a,5588,a)]. 84.32/84.26 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(5585,a,5589,a)]. 84.32/84.26 Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(real). [resolve(5585,a,5590,a)]. 84.32/84.26 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real). [resolve(5585,a,5591,a)]. 84.32/84.26 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(real). [resolve(5585,a,5592,a)]. 84.32/84.26 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(5585,a,5593,a)]. 84.32/84.26 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(5585,a,5594,a)]. 84.32/84.28 Derived: -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,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5585,a,5595,a)]. 84.32/84.28 Derived: 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,ring_1_of_int(real),A)),hAPP(int,real,ring_1_of_int(real),B))). [resolve(5585,a,5596,a)]. 84.32/84.28 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)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))) | 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),A))),B)). [resolve(5585,a,5597,a)]. 84.32/84.28 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)),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),A))),B)). [resolve(5585,a,5598,a)]. 84.32/84.28 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),B),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),A),B))),C)). [resolve(5585,a,5599,a)]. 84.32/84.28 Derived: hAPP(real,real,sgn_sgn(real),A) != hAPP(real,real,uminus_uminus(real),one_one(real)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5600,a)]. 84.32/84.28 Derived: hAPP(real,real,sgn_sgn(real),A) = hAPP(real,real,uminus_uminus(real),one_one(real)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5601,a)]. 84.32/84.28 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(5585,a,5602,a)]. 84.32/84.28 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(5585,a,5603,a)]. 84.32/84.28 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(5585,a,5604,a)]. 84.32/84.28 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5585,a,5605,a)]. 84.32/84.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(5585,a,5606,a)]. 84.32/84.28 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5585,a,5607,a)]. 84.32/84.28 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(5585,a,5608,a)]. 84.42/84.31 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(5585,a,5609,a)]. 84.42/84.31 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(5585,a,5610,a)]. 84.42/84.31 Derived: one_one(real) = hAPP(real,real,abs_abs(real),one_one(real)). [resolve(5585,a,5611,a)]. 84.42/84.31 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5612,a)]. 84.42/84.31 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5613,a)]. 84.42/84.31 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(5585,a,5614,a)]. 84.42/84.31 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(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))))). [resolve(5585,a,5615,a)]. 84.42/84.31 Derived: ti(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(5585,a,5616,a)]. 84.42/84.31 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(5585,a,5617,a)]. 84.42/84.31 Derived: ti(real,A) = 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),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),zero_zero(real))). [resolve(5585,a,5618,a)]. 84.42/84.31 Derived: ti(real,A) = zero_zero(real) | -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(5585,a,5619,a)]. 84.42/84.31 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(5585,a,5620,a)]. 84.42/84.31 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(5585,a,5621,a)]. 84.42/84.31 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(5585,a,5622,b)]. 84.42/84.31 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(5585,a,5623,b)]. 84.42/84.31 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(5585,a,5624,a)]. 84.42/84.36 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5625,a)]. 84.42/84.36 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),A)),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5626,a)]. 84.42/84.36 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(5585,a,5627,a)]. 84.42/84.36 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(5585,a,5628,a)]. 84.42/84.36 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(5585,a,5629,a)]. 84.42/84.36 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,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(5585,a,5630,a)]. 84.42/84.36 Derived: ti(real,A) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,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(5585,a,5631,a)]. 84.42/84.36 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(5585,a,5632,b)]. 84.42/84.36 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sgn_sgn(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5633,a)]. 84.42/84.36 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,sgn_sgn(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5585,a,5634,a)]. 84.42/84.36 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))). [resolve(5585,a,5637,b)]. 84.42/84.36 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))). [resolve(5585,a,5638,b)]. 84.42/84.36 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))). [resolve(5585,a,5639,b)]. 84.42/84.36 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))). [resolve(5585,a,5640,b)]. 84.42/84.36 5641 -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))) | ti(A,B) = zero_zero(A) # label(fact_234_even__power__le__0__imp__0) # label(axiom). [clausify(2108)]. 84.50/84.45 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(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))) | ti(real,A) = zero_zero(real). [resolve(5641,a,5585,a)]. 84.50/84.45 5642 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_1901_power2__abs) # label(axiom). [clausify(2146)]. 84.50/84.45 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(5642,a,5585,a)]. 84.50/84.45 5643 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_104_zero__le__power2) # label(axiom). [clausify(2150)]. 84.50/84.45 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(5643,a,5585,a)]. 84.50/84.45 5644 -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_60_le__special_I2_J) # label(axiom). [clausify(2153)]. 84.50/84.45 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(5644,b,5585,a)]. 84.50/84.45 5645 -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_60_le__special_I2_J) # label(axiom). [clausify(2153)]. 84.50/84.45 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(5645,b,5585,a)]. 84.50/84.45 5646 -linordered_idom(A) | ti(A,B) = ti(A,C) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_310_linorder__neqE__linordered__idom) # label(axiom). [clausify(2259)]. 84.50/84.45 5647 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3600_of__int__0__less__iff) # label(axiom). [clausify(2260)]. 84.50/84.45 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(5647,a,5585,a)]. 84.50/84.45 5648 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),B)) # label(fact_3600_of__int__0__less__iff) # label(axiom). [clausify(2260)]. 84.73/84.62 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(5648,a,5585,a)]. 84.73/84.62 5649 -linordered_idom(A) | zero_zero(nat) != B | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom). [clausify(2333)]. 84.73/84.62 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(5649,a,5585,a)]. 84.73/84.62 5650 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom). [clausify(2333)]. 84.73/84.62 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | ti(real,B) = zero_zero(real) | 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(5650,a,5585,a)]. 84.73/84.62 5651 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_2454_zero__less__power__eq) # label(axiom). [clausify(2333)]. 84.73/84.62 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(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(5651,a,5585,a)]. 84.73/84.62 5652 -linordered_idom(A) | zero_zero(nat) = B | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom). [clausify(2333)]. 84.73/84.62 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(5652,a,5585,a)]. 84.73/84.62 5653 -linordered_idom(A) | zero_zero(nat) = B | ti(A,C) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom). [clausify(2333)]. 84.73/84.62 Derived: zero_zero(nat) = A | ti(real,B) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A))). [resolve(5653,a,5585,a)]. 84.73/84.62 5654 -linordered_idom(A) | zero_zero(nat) = B | ti(A,C) != zero_zero(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)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_2454_zero__less__power__eq) # label(axiom). [clausify(2333)]. 84.73/84.62 Derived: zero_zero(nat) = A | ti(real,B) != zero_zero(real) | -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(5654,a,5585,a)]. 84.73/84.62 5655 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,sgn_sgn(A),B)) = hAPP(A,A,sgn_sgn(A),B) # label(fact_2199_sgn__sgn) # label(axiom). [clausify(2348)]. 84.73/84.62 Derived: hAPP(real,real,sgn_sgn(real),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,sgn_sgn(real),A). [resolve(5655,a,5585,a)]. 84.73/84.62 5656 -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_47_le__special_I3_J) # label(axiom). [clausify(2519)]. 84.92/84.84 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(5656,a,5585,a)]. 84.92/84.84 5657 -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_47_le__special_I3_J) # label(axiom). [clausify(2519)]. 84.92/84.84 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(5657,a,5585,a)]. 84.92/84.84 5658 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_27_le__number__of) # label(axiom). [clausify(2615)]. 84.92/84.84 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(5658,b,5585,a)]. 84.92/84.84 5659 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_27_le__number__of) # label(axiom). [clausify(2615)]. 84.92/84.84 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(5659,b,5585,a)]. 84.92/84.84 5660 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3602_of__int__0__le__iff) # label(axiom). [clausify(2729)]. 84.92/84.84 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(5660,a,5585,a)]. 84.92/84.84 5661 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,ring_1_of_int(A),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) # label(fact_3602_of__int__0__le__iff) # label(axiom). [clausify(2729)]. 84.92/84.84 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(5661,a,5585,a)]. 84.92/84.84 5662 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_59_le__special_I4_J) # label(axiom). [clausify(2832)]. 84.92/84.84 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(5662,b,5585,a)]. 84.92/84.84 5663 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,bit1,pls))) # label(fact_59_le__special_I4_J) # label(axiom). [clausify(2832)]. 85.22/85.15 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(5663,b,5585,a)]. 85.22/85.15 5664 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),zero_zero(A))) # label(fact_10_power2__less__0) # label(axiom). [clausify(2851)]. 85.22/85.15 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(5664,a,5585,a)]. 85.22/85.15 5665 -linordered_idom(A) | hAPP(A,A,abs_abs(A),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,sgn_sgn(A),B)) # label(fact_2214_abs__sgn) # label(axiom). [clausify(2893)]. 85.22/85.15 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(5665,a,5585,a)]. 85.22/85.15 5666 -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) # label(fact_3603_of__int__le__0__iff) # label(axiom). [clausify(2965)]. 85.22/85.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))). [resolve(5666,a,5585,a)]. 85.22/85.15 5667 -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),zero_zero(A))) # label(fact_3603_of__int__le__0__iff) # label(axiom). [clausify(2965)]. 85.22/85.15 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),A)),zero_zero(real))). [resolve(5667,a,5585,a)]. 85.22/85.15 5668 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,sgn_sgn(A),B)),hAPP(A,A,sgn_sgn(A),C)) # label(fact_2205_sgn__times) # label(axiom). [clausify(2975)]. 85.22/85.15 5669 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),C)),B) # label(fact_1879_abs__mult__pos) # label(axiom). [clausify(3013)]. 85.22/85.15 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(5669,a,5585,a)]. 85.22/85.15 5670 -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_2211_sgn__greater) # label(axiom). [clausify(3257)]. 85.22/85.15 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(5670,a,5585,a)]. 85.22/85.15 5671 -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_2211_sgn__greater) # label(axiom). [clausify(3257)]. 85.22/85.15 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(5671,a,5585,a)]. 85.32/85.21 5672 linordered_idom(rat) # label(arity_Rat_Orat___Rings_Olinordered__idom) # label(axiom). [assumption]. 85.32/85.21 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(5672,a,5586,a)]. 85.32/85.21 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(5672,a,5587,a)]. 85.32/85.21 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(5672,a,5588,a)]. 85.32/85.21 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(5672,a,5589,a)]. 85.32/85.21 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,B) != zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(rat). [resolve(5672,a,5590,a)]. 85.32/85.21 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(rat). [resolve(5672,a,5591,a)]. 85.32/85.21 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(rat). [resolve(5672,a,5592,a)]. 85.32/85.21 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(5672,a,5593,a)]. 85.32/85.21 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(5672,a,5594,a)]. 85.32/85.21 Derived: -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,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(5672,a,5595,a)]. 85.32/85.21 Derived: 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,ring_1_of_int(rat),A)),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(5672,a,5596,a)]. 85.32/85.21 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)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B))) | 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),C),A))),B)). [resolve(5672,a,5597,a)]. 85.32/85.21 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)),C)) | -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),C),A))),B)). [resolve(5672,a,5598,a)]. 85.32/85.24 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),B),C))) | -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)). [resolve(5672,a,5599,a)]. 85.32/85.24 Derived: hAPP(rat,rat,sgn_sgn(rat),A) != hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5600,a)]. 85.32/85.24 Derived: hAPP(rat,rat,sgn_sgn(rat),A) = hAPP(rat,rat,uminus_uminus(rat),one_one(rat)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5601,a)]. 85.32/85.24 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(5672,a,5602,a)]. 85.32/85.24 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(5672,a,5603,a)]. 85.32/85.24 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(5672,a,5604,a)]. 85.32/85.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5672,a,5605,a)]. 85.32/85.24 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(5672,a,5606,a)]. 85.32/85.24 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5672,a,5607,a)]. 85.32/85.24 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(5672,a,5608,a)]. 85.32/85.24 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(5672,a,5609,a)]. 85.32/85.24 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(5672,a,5610,a)]. 85.32/85.24 Derived: one_one(rat) = hAPP(rat,rat,abs_abs(rat),one_one(rat)). [resolve(5672,a,5611,a)]. 85.32/85.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5612,a)]. 85.32/85.24 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5613,a)]. 85.32/85.24 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(5672,a,5614,a)]. 85.32/85.24 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(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))))). [resolve(5672,a,5615,a)]. 85.32/85.26 Derived: ti(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(5672,a,5616,a)]. 85.32/85.26 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(5672,a,5617,a)]. 85.32/85.26 Derived: ti(rat,A) = 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(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),zero_zero(rat))). [resolve(5672,a,5618,a)]. 85.32/85.26 Derived: ti(rat,A) = zero_zero(rat) | -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(5672,a,5619,a)]. 85.32/85.26 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(5672,a,5620,a)]. 85.32/85.26 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(5672,a,5621,a)]. 85.32/85.26 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(5672,a,5622,b)]. 85.32/85.26 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(5672,a,5623,b)]. 85.32/85.26 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(5672,a,5624,a)]. 85.32/85.26 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5625,a)]. 85.32/85.26 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),A)),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5626,a)]. 85.32/85.26 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(5672,a,5627,a)]. 85.32/85.26 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(5672,a,5628,a)]. 85.32/85.26 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(5672,a,5629,a)]. 85.32/85.26 Derived: ti(rat,A) = zero_zero(rat) | 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(5672,a,5630,a)]. 85.32/85.28 Derived: ti(rat,A) != zero_zero(rat) | -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(5672,a,5631,a)]. 85.32/85.28 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(5672,a,5632,b)]. 85.32/85.28 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,sgn_sgn(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5633,a)]. 85.32/85.28 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,sgn_sgn(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5672,a,5634,a)]. 85.32/85.28 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5672,a,5637,b)]. 85.32/85.28 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5672,a,5638,b)]. 85.32/85.28 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5672,a,5639,b)]. 85.32/85.28 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))). [resolve(5672,a,5640,b)]. 85.32/85.28 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))) | ti(rat,A) = zero_zero(rat). [resolve(5672,a,5641,a)]. 85.32/85.28 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(5672,a,5642,a)]. 85.32/85.28 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(5672,a,5643,a)]. 85.32/85.28 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(5672,a,5644,b)]. 85.32/85.28 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(5672,a,5645,b)]. 85.32/85.28 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(5672,a,5647,a)]. 85.32/85.28 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(5672,a,5648,a)]. 85.32/85.28 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(5672,a,5649,a)]. 85.41/85.30 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | ti(rat,B) = zero_zero(rat) | 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(5672,a,5650,a)]. 85.41/85.30 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(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(5672,a,5651,a)]. 85.41/85.30 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(5672,a,5652,a)]. 85.41/85.30 Derived: zero_zero(nat) = A | ti(rat,B) != zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A))). [resolve(5672,a,5653,a)]. 85.41/85.30 Derived: zero_zero(nat) = A | ti(rat,B) != zero_zero(rat) | -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(5672,a,5654,a)]. 85.41/85.30 Derived: hAPP(rat,rat,sgn_sgn(rat),hAPP(rat,rat,sgn_sgn(rat),A)) = hAPP(rat,rat,sgn_sgn(rat),A). [resolve(5672,a,5655,a)]. 85.41/85.30 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(5672,a,5656,a)]. 85.41/85.30 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(5672,a,5657,a)]. 85.41/85.30 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(5672,a,5658,b)]. 85.41/85.30 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(5672,a,5659,b)]. 85.41/85.30 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(5672,a,5660,a)]. 85.41/85.30 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(5672,a,5661,a)]. 85.41/85.30 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(5672,a,5662,b)]. 85.41/85.30 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(5672,a,5663,b)]. 85.41/85.30 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(5672,a,5664,a)]. 85.41/85.30 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(5672,a,5665,a)]. 85.50/85.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))). [resolve(5672,a,5666,a)]. 85.50/85.40 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),A)),zero_zero(rat))). [resolve(5672,a,5667,a)]. 85.50/85.40 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(5672,a,5668,a)]. 85.50/85.40 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(5672,a,5669,a)]. 85.50/85.40 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(5672,a,5670,a)]. 85.50/85.40 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(5672,a,5671,a)]. 85.50/85.40 5673 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),hAPP(int,nat,number_number_of(nat),B)) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)) # label(fact_2444_power__even__abs__number__of) # label(axiom). [clausify(3324)]. 85.50/85.40 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),B)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)). [resolve(5673,a,5585,a)]. 85.50/85.40 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)). [resolve(5673,a,5672,a)]. 85.50/85.40 5674 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))),zero_zero(A))) # label(fact_7_not__sum__power2__lt__zero) # label(axiom). [clausify(3387)]. 85.50/85.40 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(5674,a,5585,a)]. 85.50/85.40 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(5674,a,5672,a)]. 85.50/85.40 5675 -linordered_idom(A) | -number_ring(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_1896_abs__power__minus__one) # label(axiom). [clausify(3403)]. 85.80/85.77 Derived: -number_ring(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(int,real,number_number_of(real),min_1)),A)). [resolve(5675,a,5585,a)]. 85.80/85.77 Derived: -number_ring(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)). [resolve(5675,a,5672,a)]. 85.80/85.77 5676 -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_2222_sgn__1__pos) # label(axiom). [clausify(3430)]. 85.80/85.77 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(5676,a,5585,a)]. 85.80/85.77 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(5676,a,5672,a)]. 85.80/85.77 5677 -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_2222_sgn__1__pos) # label(axiom). [clausify(3430)]. 85.80/85.77 5678 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C)))),zero_zero(A))) # label(fact_1471_odd__power__less__zero) # label(axiom). [clausify(3516)]. 85.80/85.77 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5678,a,5585,a)]. 85.80/85.77 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5678,a,5672,a)]. 85.80/85.77 5679 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,uminus_uminus(A),one_one(A)) # label(fact_2231_sgn__neg) # label(axiom). [clausify(3521)]. 85.80/85.77 5680 linordered_idom(int) # label(arity_Int_Oint___Rings_Olinordered__idom) # label(axiom). [assumption]. 85.80/85.77 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(5680,a,5586,a)]. 85.80/85.77 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(5680,a,5587,a)]. 85.80/85.77 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(int,int,abs_abs(int),hAPP(nat,int,semiring_1_of_nat(int),A)). [resolve(5680,a,5588,a)]. 85.80/85.77 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(5680,a,5589,a)]. 85.80/85.77 Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) = zero_zero(int). [resolve(5680,a,5590,a)]. 85.80/85.78 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(int). [resolve(5680,a,5591,a)]. 85.80/85.78 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) != zero_zero(int). [resolve(5680,a,5592,a)]. 85.80/85.78 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(5680,a,5593,a)]. 85.80/85.78 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(5680,a,5594,a)]. 85.80/85.78 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,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))). [resolve(5680,a,5595,a)]. 85.80/85.78 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,ring_1_of_int(int),A)),hAPP(int,int,ring_1_of_int(int),B))). [resolve(5680,a,5596,a)]. 85.80/85.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B))) | 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),C),A))),B)). [resolve(5680,a,5597,a)]. 85.80/85.78 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)) | -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),C),A))),B)). [resolve(5680,a,5598,a)]. 85.80/85.78 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),B),C))) | -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)). [resolve(5680,a,5599,a)]. 85.80/85.78 Derived: hAPP(int,int,sgn_sgn(int),A) != hAPP(int,int,uminus_uminus(int),one_one(int)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5600,a)]. 85.80/85.78 Derived: hAPP(int,int,sgn_sgn(int),A) = hAPP(int,int,uminus_uminus(int),one_one(int)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5601,a)]. 85.80/85.78 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(5680,a,5602,a)]. 85.80/85.78 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(5680,a,5603,a)]. 85.80/85.78 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(5680,a,5604,a)]. 85.91/85.80 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),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(5680,a,5605,a)]. 85.91/85.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)). [resolve(5680,a,5606,a)]. 85.91/85.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),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(5680,a,5607,a)]. 85.91/85.80 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(5680,a,5608,a)]. 85.91/85.80 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(5680,a,5609,a)]. 85.91/85.80 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(5680,a,5610,a)]. 85.91/85.80 Derived: one_one(int) = hAPP(int,int,abs_abs(int),one_one(int)). [resolve(5680,a,5611,a)]. 85.91/85.80 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5612,a)]. 85.91/85.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5613,a)]. 85.91/85.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),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(5680,a,5614,a)]. 85.91/85.80 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(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))))). [resolve(5680,a,5615,a)]. 85.91/85.80 Derived: ti(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(5680,a,5616,a)]. 85.91/85.80 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(5680,a,5617,a)]. 85.91/85.80 Derived: ti(int,A) = 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),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),zero_zero(int))). [resolve(5680,a,5618,a)]. 85.91/85.80 Derived: ti(int,A) = zero_zero(int) | -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(5680,a,5619,a)]. 85.91/85.80 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(5680,a,5620,a)]. 85.93/85.82 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(5680,a,5621,a)]. 85.93/85.82 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(5680,a,5622,b)]. 85.93/85.82 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(5680,a,5623,b)]. 85.93/85.82 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(5680,a,5624,a)]. 85.93/85.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | -hBOOL(hAPP(int,bool,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)),A)),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5625,a)]. 85.93/85.82 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hBOOL(hAPP(int,bool,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)),A)),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5626,a)]. 85.93/85.82 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(5680,a,5627,a)]. 85.93/85.82 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(5680,a,5628,a)]. 85.93/85.82 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(5680,a,5629,a)]. 85.93/85.82 Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,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(5680,a,5630,a)]. 85.93/85.82 Derived: ti(int,A) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,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(5680,a,5631,a)]. 85.93/85.82 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(5680,a,5632,b)]. 85.93/85.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,sgn_sgn(int),A)),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5633,a)]. 85.93/85.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,sgn_sgn(int),A)),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))). [resolve(5680,a,5634,a)]. 85.93/85.82 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))). [resolve(5680,a,5637,b)]. 85.93/85.82 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))). [resolve(5680,a,5638,b)]. 85.93/85.84 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))). [resolve(5680,a,5639,b)]. 85.93/85.84 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(int,int,number_number_of(int),A))). [resolve(5680,a,5640,b)]. 85.93/85.84 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))) | ti(int,A) = zero_zero(int). [resolve(5680,a,5641,a)]. 85.93/85.84 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(5680,a,5642,a)]. 85.93/85.84 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(5680,a,5643,a)]. 85.93/85.84 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(5680,a,5644,b)]. 85.93/85.84 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(5680,a,5645,b)]. 85.93/85.84 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(5680,a,5647,a)]. 85.93/85.84 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(5680,a,5648,a)]. 85.93/85.84 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(5680,a,5649,a)]. 85.93/85.84 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | ti(int,B) = zero_zero(int) | 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(5680,a,5650,a)]. 85.93/85.84 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(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(5680,a,5651,a)]. 85.93/85.84 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(5680,a,5652,a)]. 85.93/85.84 Derived: zero_zero(nat) = A | ti(int,B) != 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),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A))). [resolve(5680,a,5653,a)]. 85.93/85.84 Derived: zero_zero(nat) = A | ti(int,B) != zero_zero(int) | -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(5680,a,5654,a)]. 85.93/85.86 Derived: hAPP(int,int,sgn_sgn(int),hAPP(int,int,sgn_sgn(int),A)) = hAPP(int,int,sgn_sgn(int),A). [resolve(5680,a,5655,a)]. 85.93/85.86 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(5680,a,5656,a)]. 85.93/85.86 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(5680,a,5657,a)]. 85.93/85.86 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5680,a,5658,b)]. 85.93/85.86 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5680,a,5659,b)]. 85.93/85.86 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(5680,a,5660,a)]. 85.93/85.86 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(5680,a,5661,a)]. 85.93/85.86 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(5680,a,5662,b)]. 85.93/85.86 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(5680,a,5663,b)]. 85.93/85.86 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(5680,a,5664,a)]. 85.93/85.86 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(5680,a,5665,a)]. 85.93/85.86 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))). [resolve(5680,a,5666,a)]. 85.93/85.86 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,ring_1_of_int(int),A)),zero_zero(int))). [resolve(5680,a,5667,a)]. 85.93/85.86 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(5680,a,5668,a)]. 85.93/85.86 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(5680,a,5669,a)]. 85.93/85.86 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(5680,a,5670,a)]. 85.93/85.86 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(5680,a,5671,a)]. 86.01/85.95 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),A))) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),B)),hAPP(int,nat,number_number_of(nat),A)) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)). [resolve(5680,a,5673,a)]. 86.01/85.95 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(5680,a,5674,a)]. 86.01/85.95 Derived: -number_ring(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,number_number_of(int),min_1)),A)). [resolve(5680,a,5675,a)]. 86.01/85.95 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(5680,a,5676,a)]. 86.01/85.95 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(5680,a,5678,a)]. 86.01/85.95 5681 -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_2456_power__less__zero__eq__number__of) # label(axiom). [clausify(3730)]. 86.01/85.95 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(real),B),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),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(real))). [resolve(5681,a,5585,a)]. 86.01/85.95 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(rat),B),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),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(rat))). [resolve(5681,a,5672,a)]. 86.01/85.95 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(int),B),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),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(int))). [resolve(5681,a,5680,a)]. 86.01/85.95 5682 -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_2456_power__less__zero__eq__number__of) # label(axiom). [clausify(3730)]. 86.01/85.95 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(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(real))). [resolve(5682,a,5585,a)]. 86.01/85.95 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(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(rat))). [resolve(5682,a,5672,a)]. 86.01/85.95 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(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(int))). [resolve(5682,a,5680,a)]. 86.10/85.99 5683 -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_2456_power__less__zero__eq__number__of) # label(axiom). [clausify(3730)]. 86.10/85.99 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B))),zero_zero(real))). [resolve(5683,a,5585,a)]. 86.10/85.99 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(int,nat,number_number_of(nat),B))),zero_zero(rat))). [resolve(5683,a,5672,a)]. 86.10/85.99 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(int,nat,number_number_of(nat),B))),zero_zero(int))). [resolve(5683,a,5680,a)]. 86.10/85.99 5684 -linordered_idom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C) = hAPP(A,A,abs_abs(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)) # label(fact_1844_power__abs) # label(axiom). [clausify(3748)]. 86.10/85.99 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,abs_abs(real),A)),B) = hAPP(real,real,abs_abs(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)). [resolve(5684,a,5585,a)]. 86.10/85.99 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),hAPP(rat,rat,abs_abs(rat),A)),B) = hAPP(rat,rat,abs_abs(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)). [resolve(5684,a,5672,a)]. 86.10/85.99 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),B) = hAPP(int,int,abs_abs(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)). [resolve(5684,a,5680,a)]. 86.10/85.99 5685 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),D)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),D))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_1866_abs__mult__less) # label(axiom). [clausify(3773)]. 86.10/85.99 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(5685,a,5585,a)]. 86.10/85.99 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(5685,a,5672,a)]. 86.10/85.99 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(5685,a,5680,a)]. 86.10/86.04 5686 -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),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_2083_abs__less__iff) # label(axiom). [clausify(3808)]. 86.10/86.04 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),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),B)). [resolve(5686,a,5585,a)]. 86.10/86.04 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),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),B)). [resolve(5686,a,5672,a)]. 86.10/86.04 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),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),B)). [resolve(5686,a,5680,a)]. 86.10/86.04 5687 -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_2083_abs__less__iff) # label(axiom). [clausify(3808)]. 86.10/86.04 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(5687,a,5585,a)]. 86.10/86.04 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(5687,a,5672,a)]. 86.10/86.04 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(5687,a,5680,a)]. 86.10/86.04 5688 -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_2083_abs__less__iff) # label(axiom). [clausify(3808)]. 86.10/86.04 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(5688,a,5585,a)]. 86.10/86.04 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(5688,a,5672,a)]. 86.10/86.04 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(5688,a,5680,a)]. 86.10/86.04 5689 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_150_less__number__of) # label(axiom). [clausify(3813)]. 86.10/86.04 Derived: -number_ring(real) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5689,b,5585,a)]. 86.10/86.04 Derived: -number_ring(rat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5689,b,5672,a)]. 86.10/86.04 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5689,b,5680,a)]. 86.21/86.11 5690 -number_ring(A) | -linordered_idom(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_150_less__number__of) # label(axiom). [clausify(3813)]. 86.21/86.11 Derived: -number_ring(real) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5690,b,5585,a)]. 86.21/86.11 Derived: -number_ring(rat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5690,b,5672,a)]. 86.21/86.11 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B))). [resolve(5690,b,5680,a)]. 86.21/86.11 5691 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom). [clausify(3820)]. 86.21/86.11 5692 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C)))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom). [clausify(3820)]. 86.21/86.11 5693 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2455_zero__le__power__eq__number__of) # label(axiom). [clausify(3820)]. 86.21/86.11 5694 -linordered_idom(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_176_less__special_I3_J) # label(axiom). [clausify(3857)]. 86.21/86.11 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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(5694,a,5585,a)]. 86.21/86.11 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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(5694,a,5672,a)]. 86.21/86.11 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))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(5694,a,5680,a)]. 86.21/86.11 5695 -linordered_idom(A) | -number_ring(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),pls)) # label(fact_176_less__special_I3_J) # label(axiom). [clausify(3857)]. 86.21/86.11 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))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(5695,a,5585,a)]. 86.21/86.11 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))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(5695,a,5672,a)]. 86.23/86.14 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))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),pls)). [resolve(5695,a,5680,a)]. 86.23/86.14 5696 -linordered_idom(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,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_106_sum__power2__le__zero__iff) # label(axiom). [clausify(3880)]. 86.23/86.14 Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,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(5696,a,5585,a)]. 86.23/86.14 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,B) != zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),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(5696,a,5672,a)]. 86.23/86.14 Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,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(5696,a,5680,a)]. 86.23/86.14 5697 -linordered_idom(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,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_106_sum__power2__le__zero__iff) # label(axiom). [clausify(3880)]. 86.23/86.14 Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),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(5697,a,5585,a)]. 86.23/86.14 Derived: ti(rat,A) = zero_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),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(5697,a,5672,a)]. 86.23/86.14 Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),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(5697,a,5680,a)]. 86.31/86.24 5698 -linordered_idom(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,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_106_sum__power2__le__zero__iff) # label(axiom). [clausify(3880)]. 86.31/86.24 Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),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(5698,a,5585,a)]. 86.31/86.24 Derived: ti(rat,A) = zero_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),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(5698,a,5672,a)]. 86.31/86.24 Derived: ti(int,A) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),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(5698,a,5680,a)]. 86.31/86.24 5699 -linordered_idom(A) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_2421_power__mono__odd) # label(axiom). [clausify(3927)]. 86.31/86.24 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(5699,a,5585,a)]. 86.31/86.24 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(5699,a,5672,a)]. 86.31/86.24 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(5699,a,5680,a)]. 86.31/86.24 5700 -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_3601_of__int__less__0__iff) # label(axiom). [clausify(3980)]. 86.31/86.24 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(5700,a,5585,a)]. 86.31/86.24 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(5700,a,5672,a)]. 86.40/86.28 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(5700,a,5680,a)]. 86.40/86.28 5701 -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_3601_of__int__less__0__iff) # label(axiom). [clausify(3980)]. 86.40/86.28 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(5701,a,5585,a)]. 86.40/86.28 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(5701,a,5672,a)]. 86.40/86.28 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(5701,a,5680,a)]. 86.40/86.28 5702 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B)))) # label(fact_2464_zero__less__power__eq__number__of) # label(axiom). [clausify(4002)]. 86.40/86.28 5703 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | 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_2464_zero__less__power__eq__number__of) # label(axiom). [clausify(4002)]. 86.40/86.28 5704 -linordered_idom(A) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | 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_2464_zero__less__power__eq__number__of) # label(axiom). [clausify(4002)]. 86.40/86.28 Derived: hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | 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),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5704,a,5585,a)]. 86.40/86.28 Derived: hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | 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),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5704,a,5672,a)]. 86.40/86.28 Derived: hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5704,a,5680,a)]. 86.40/86.28 5705 -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)) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -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_2464_zero__less__power__eq__number__of) # label(axiom). [clausify(4002)]. 86.40/86.28 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(real),zero_zero(real)),B)) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5705,a,5585,a)]. 86.40/86.28 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(rat),zero_zero(rat)),B)) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5705,a,5672,a)]. 86.40/86.30 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(int),zero_zero(int)),B)) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)))). [resolve(5705,a,5680,a)]. 86.40/86.30 5706 -linordered_idom(A) | ti(A,B) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | -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_2464_zero__less__power__eq__number__of) # label(axiom). [clausify(4002)]. 86.40/86.30 Derived: ti(real,A) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5706,a,5585,a)]. 86.40/86.30 Derived: ti(rat,A) != zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5706,a,5672,a)]. 86.40/86.30 Derived: ti(int,A) != zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5706,a,5680,a)]. 86.40/86.30 5707 -linordered_idom(A) | ti(A,B) != zero_zero(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),C))) | hAPP(int,nat,number_number_of(nat),C) = zero_zero(nat) | -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_2464_zero__less__power__eq__number__of) # label(axiom). [clausify(4002)]. 86.40/86.30 Derived: ti(real,A) != zero_zero(real) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5707,a,5585,a)]. 86.40/86.30 Derived: ti(rat,A) != zero_zero(rat) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5707,a,5672,a)]. 86.40/86.30 Derived: ti(int,A) != zero_zero(int) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(int,nat,number_number_of(nat),B)))). [resolve(5707,a,5680,a)]. 86.40/86.30 5708 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),C))))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_1470_odd__0__le__power__imp__0__le) # label(axiom). [clausify(4013)]. 86.40/86.36 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(5708,a,5585,a)]. 86.40/86.36 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(5708,a,5672,a)]. 86.40/86.36 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(5708,a,5680,a)]. 86.40/86.36 5709 -linordered_idom(A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom). [clausify(4056)]. 86.40/86.36 Derived: hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | 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),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(real))). [resolve(5709,a,5585,a)]. 86.40/86.36 Derived: hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | 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),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(rat))). [resolve(5709,a,5672,a)]. 86.40/86.36 Derived: hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | 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),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(int))). [resolve(5709,a,5680,a)]. 86.40/86.36 5710 -linordered_idom(A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | ti(A,C) != zero_zero(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),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom). [clausify(4056)]. 86.40/86.36 Derived: hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(real,B) != zero_zero(real) | -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),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(real))). [resolve(5710,a,5585,a)]. 86.53/86.48 Derived: hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(rat,B) != zero_zero(rat) | -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),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(rat))). [resolve(5710,a,5672,a)]. 86.53/86.48 Derived: hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(int,B) != zero_zero(int) | -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),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A))),zero_zero(int))). [resolve(5710,a,5680,a)]. 86.53/86.48 5711 -linordered_idom(A) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom). [clausify(4056)]. 86.53/86.48 Derived: hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),A))),zero_zero(real))). [resolve(5711,a,5585,a)]. 86.53/86.48 Derived: hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),A))),zero_zero(rat))). [resolve(5711,a,5672,a)]. 86.53/86.48 Derived: hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | -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),hAPP(int,nat,number_number_of(nat),A))),zero_zero(int))). [resolve(5711,a,5680,a)]. 86.53/86.48 5712 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),C))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom). [clausify(4056)]. 86.53/86.48 5713 -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_2463_power__le__zero__eq__number__of) # label(axiom). [clausify(4056)]. 86.53/86.48 5714 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),hAPP(int,nat,number_number_of(nat),B))) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),B))),zero_zero(A))) # label(fact_2463_power__le__zero__eq__number__of) # label(axiom). [clausify(4056)]. 86.53/86.48 5715 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_1846_abs__dvd__iff) # label(axiom). [clausify(4164)]. 86.53/86.48 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,abs_abs(real),A)),B)). [resolve(5715,a,5585,a)]. 86.53/86.48 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,abs_abs(rat),A)),B)). [resolve(5715,a,5672,a)]. 86.53/86.48 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,abs_abs(int),A)),B)). [resolve(5715,a,5680,a)]. 86.53/86.48 5716 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,abs_abs(A),B)),C)) # label(fact_1846_abs__dvd__iff) # label(axiom). [clausify(4164)]. 86.71/86.64 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,abs_abs(real),A)),B)). [resolve(5716,a,5585,a)]. 86.71/86.64 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,abs_abs(rat),A)),B)). [resolve(5716,a,5672,a)]. 86.71/86.64 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,abs_abs(int),A)),B)). [resolve(5716,a,5680,a)]. 86.71/86.64 5717 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2434_zero__le__power__iff) # label(axiom). [clausify(4168)]. 86.71/86.64 5718 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) # label(fact_2434_zero__le__power__iff) # label(axiom). [clausify(4168)]. 86.71/86.64 5719 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2434_zero__le__power__iff) # label(axiom). [clausify(4168)]. 86.71/86.64 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),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5719,a,5585,a)]. 86.71/86.64 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5719,a,5672,a)]. 86.71/86.64 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(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(5719,a,5680,a)]. 86.71/86.64 5720 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_107_sum__power2__ge__zero) # label(axiom). [clausify(4238)]. 86.71/86.64 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(5720,a,5585,a)]. 86.71/86.64 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(5720,a,5672,a)]. 86.71/86.64 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(5720,a,5680,a)]. 86.71/86.64 5721 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_2202_sgn__0__0) # label(axiom). [clausify(4300)]. 86.71/86.66 Derived: hAPP(real,real,sgn_sgn(real),A) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(5721,a,5585,a)]. 86.71/86.66 Derived: hAPP(rat,rat,sgn_sgn(rat),A) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(5721,a,5672,a)]. 86.71/86.66 Derived: hAPP(int,int,sgn_sgn(int),A) != zero_zero(int) | ti(int,A) = zero_zero(int). [resolve(5721,a,5680,a)]. 86.71/86.66 5722 -linordered_idom(A) | hAPP(A,A,sgn_sgn(A),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_2202_sgn__0__0) # label(axiom). [clausify(4300)]. 86.71/86.66 Derived: hAPP(real,real,sgn_sgn(real),A) = zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(5722,a,5585,a)]. 86.71/86.66 Derived: hAPP(rat,rat,sgn_sgn(rat),A) = zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(5722,a,5672,a)]. 86.71/86.66 Derived: hAPP(int,int,sgn_sgn(int),A) = zero_zero(int) | ti(int,A) != zero_zero(int). [resolve(5722,a,5680,a)]. 86.71/86.66 5723 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom). [clausify(4317)]. 86.71/86.66 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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(5723,a,5585,a)]. 86.71/86.66 Derived: ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),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(5723,a,5672,a)]. 86.71/86.66 Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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(5723,a,5680,a)]. 86.71/86.66 5724 -linordered_idom(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom). [clausify(4317)]. 86.71/86.66 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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(5724,a,5585,a)]. 86.71/86.66 Derived: ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),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(5724,a,5672,a)]. 86.81/86.72 Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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(5724,a,5680,a)]. 86.81/86.72 5725 -linordered_idom(A) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))))) # label(fact_8_sum__power2__gt__zero__iff) # label(axiom). [clausify(4317)]. 86.81/86.72 Derived: ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,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(5725,a,5585,a)]. 86.81/86.72 Derived: ti(rat,A) != zero_zero(rat) | ti(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),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(5725,a,5672,a)]. 86.81/86.72 Derived: ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,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(5725,a,5680,a)]. 86.81/86.72 5726 -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(int,A,number_number_of(A),B) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2113_abs__number__of) # label(axiom). [clausify(4362)]. 86.81/86.72 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hAPP(int,real,number_number_of(real),A) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)). [resolve(5726,b,5585,a)]. 86.81/86.72 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(int,rat,number_number_of(rat),A) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(5726,b,5672,a)]. 86.81/86.72 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,number_number_of(int),A) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)). [resolve(5726,b,5680,a)]. 86.81/86.72 5727 -number_ring(A) | -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),hAPP(int,A,number_number_of(A),B)) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2113_abs__number__of) # label(axiom). [clausify(4362)]. 87.13/87.04 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,uminus_uminus(real),hAPP(int,real,number_number_of(real),A)) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)). [resolve(5727,b,5585,a)]. 87.13/87.04 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,uminus_uminus(rat),hAPP(int,rat,number_number_of(rat),A)) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(5727,b,5672,a)]. 87.13/87.04 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,uminus_uminus(int),hAPP(int,int,number_number_of(int),A)) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),A)). [resolve(5727,b,5680,a)]. 87.13/87.04 5728 -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_1847_dvd__if__abs__eq) # label(axiom). [clausify(4451)]. 87.13/87.04 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(5728,a,5585,a)]. 87.13/87.04 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(5728,a,5672,a)]. 87.13/87.04 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(5728,a,5680,a)]. 87.13/87.04 5729 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),C)),B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) # label(fact_2426_power__even__abs) # label(axiom). [clausify(4649)]. 87.13/87.04 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(5729,a,5585,a)]. 87.13/87.04 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(5729,a,5672,a)]. 87.13/87.04 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(5729,a,5680,a)]. 87.13/87.04 5730 -linordered_idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),C)) | 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))) # label(fact_2436_power__less__zero__eq) # label(axiom). [clausify(4665)]. 87.13/87.04 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | 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))). [resolve(5730,a,5585,a)]. 87.13/87.04 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | 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))). [resolve(5730,a,5672,a)]. 87.13/87.04 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hBOOL(hAPP(nat,bool,even_odd_even(nat),B)) | 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))). [resolve(5730,a,5680,a)]. 87.13/87.04 5731 -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),C)),zero_zero(A))) # label(fact_2436_power__less__zero__eq) # label(axiom). [clausify(4665)]. 87.22/87.15 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),B)),zero_zero(real))). [resolve(5731,a,5585,a)]. 87.22/87.15 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),B)),zero_zero(rat))). [resolve(5731,a,5672,a)]. 87.22/87.15 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),B)),zero_zero(int))). [resolve(5731,a,5680,a)]. 87.22/87.15 5732 -linordered_idom(A) | -hBOOL(hAPP(nat,bool,even_odd_even(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),B)),zero_zero(A))) # label(fact_2436_power__less__zero__eq) # label(axiom). [clausify(4665)]. 87.22/87.15 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A)),zero_zero(real))). [resolve(5732,a,5585,a)]. 87.22/87.15 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A)),zero_zero(rat))). [resolve(5732,a,5672,a)]. 87.22/87.15 Derived: -hBOOL(hAPP(nat,bool,even_odd_even(nat),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A)),zero_zero(int))). [resolve(5732,a,5680,a)]. 87.22/87.15 5733 -linordered_idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,abs_abs(A),B)),C))) # label(fact_1880_zero__le__power__abs) # label(axiom). [clausify(4704)]. 87.22/87.15 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(5733,a,5585,a)]. 87.22/87.15 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(5733,a,5672,a)]. 87.22/87.15 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),hAPP(int,int,abs_abs(int),A)),B))). [resolve(5733,a,5680,a)]. 87.22/87.15 5734 -linordered_idom(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_1855_abs__mult__self) # label(axiom). [clausify(4752)]. 87.22/87.15 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(5734,a,5585,a)]. 87.22/87.15 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(5734,a,5672,a)]. 87.22/87.15 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(5734,a,5680,a)]. 87.22/87.15 5735 -linordered_idom(A) | -number_ring(A) | one_one(A) = hAPP(A,A,abs_abs(A),hAPP(int,A,number_number_of(A),min_1)) # label(fact_1885_abs__minus__one) # label(axiom). [clausify(4759)]. 87.22/87.15 Derived: -number_ring(real) | one_one(real) = hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),min_1)). [resolve(5735,a,5585,a)]. 87.22/87.15 Derived: -number_ring(rat) | one_one(rat) = hAPP(rat,rat,abs_abs(rat),hAPP(int,rat,number_number_of(rat),min_1)). [resolve(5735,a,5672,a)]. 87.22/87.15 Derived: -number_ring(int) | one_one(int) = hAPP(int,int,abs_abs(int),hAPP(int,int,number_number_of(int),min_1)). [resolve(5735,a,5680,a)]. 90.23/90.18 5736 linordered_field(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field) # label(axiom). [assumption]. 90.23/90.18 5737 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1705_frac__le) # label(axiom). [clausify(59)]. 90.23/90.18 5738 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2613_inv__of__nat__fact__gt__zero) # label(axiom). [clausify(100)]. 90.23/90.18 5739 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1717_divide__strict__left__mono__neg) # label(axiom). [clausify(121)]. 90.23/90.18 5740 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))),C)) # label(fact_1731_gt__half__sum) # label(axiom). [clausify(369)]. 90.23/90.18 5741 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2544_inverse__positive__imp__positive) # label(axiom). [clausify(511)]. 90.23/90.18 5742 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2610_one__le__inverse) # label(axiom). [clausify(769)]. 90.23/90.18 5743 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2549_inverse__less__imp__less) # label(axiom). [clausify(785)]. 90.23/90.18 5744 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1716_divide__strict__left__mono) # label(axiom). [clausify(799)]. 90.23/90.18 5745 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2547_less__imp__inverse__less__neg) # label(axiom). [clausify(821)]. 90.23/90.18 5746 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) # label(fact_2550_inverse__less__imp__less__neg) # label(axiom). [clausify(848)]. 90.23/90.18 5747 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2576_one__less__inverse) # label(axiom). [clausify(892)]. 90.23/90.18 5748 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1684_divide__strict__right__mono__neg) # label(axiom). [clausify(954)]. 90.23/90.18 5749 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B))))) # label(fact_2612_inv__of__nat__fact__ge__zero) # label(axiom). [clausify(1011)]. 90.23/90.18 5750 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1739_mult__imp__div__pos__le) # label(axiom). [clausify(1060)]. 90.23/90.18 5751 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1713_mult__imp__less__div__pos) # label(axiom). [clausify(1106)]. 90.23/90.18 5752 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1704_frac__less) # label(axiom). [clausify(1142)]. 90.23/90.18 5753 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1743_divide__left__mono) # label(axiom). [clausify(1564)]. 90.23/90.18 5754 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1682_divide__neg__neg) # label(axiom). [clausify(1567)]. 90.23/90.18 5755 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2548_inverse__negative__imp__negative) # label(axiom). [clausify(1884)]. 90.23/90.18 5756 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2571_le__imp__inverse__le__neg) # label(axiom). [clausify(1897)]. 90.23/90.18 5757 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1740_mult__imp__le__div__pos) # label(axiom). [clausify(1946)]. 90.23/90.18 5758 -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_1711_pos__divide__less__eq) # label(axiom). [clausify(2043)]. 90.23/90.18 5759 -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_1711_pos__divide__less__eq) # label(axiom). [clausify(2043)]. 90.23/90.18 5760 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),C)) # label(fact_1715_neg__divide__less__eq) # label(axiom). [clausify(2110)]. 90.23/90.18 5761 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),C)) # label(fact_1715_neg__divide__less__eq) # label(axiom). [clausify(2110)]. 90.23/90.18 5762 -linordered_field(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D)) # label(fact_3948_abs__setprod) # label(axiom). [clausify(2151)]. 90.23/90.18 5763 -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),times_times(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)),C)) # label(fact_1742_neg__divide__le__eq) # label(axiom). [clausify(2187)]. 90.23/90.18 5764 -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),times_times(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)),C)) # label(fact_1742_neg__divide__le__eq) # label(axiom). [clausify(2187)]. 90.23/90.18 5765 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1681_divide__neg__pos) # label(axiom). [clausify(2206)]. 90.23/90.18 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(5736,a,5737,a)]. 90.23/90.18 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(5736,a,5738,a)]. 90.23/90.18 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(5736,a,5739,a)]. 90.23/90.21 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),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(5736,a,5740,a)]. 90.23/90.21 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5736,a,5741,a)]. 90.23/90.21 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(5736,a,5742,a)]. 90.23/90.21 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(5736,a,5743,a)]. 90.23/90.21 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5736,a,5744,a)]. 90.23/90.21 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5736,a,5745,a)]. 90.23/90.21 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(5736,a,5746,a)]. 90.23/90.21 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(5736,a,5747,a)]. 90.23/90.21 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5736,a,5748,a)]. 90.23/90.21 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(5736,a,5749,a)]. 90.23/90.21 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(5736,a,5750,a)]. 90.33/90.23 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(5736,a,5751,a)]. 90.33/90.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5736,a,5752,a)]. 90.33/90.23 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(5736,a,5753,a)]. 90.33/90.23 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(5736,a,5754,a)]. 90.33/90.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(5736,a,5755,a)]. 90.33/90.23 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(5736,a,5756,a)]. 90.33/90.23 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(5736,a,5757,a)]. 90.33/90.23 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(5736,a,5758,a)]. 90.33/90.23 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(5736,a,5759,a)]. 90.33/90.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),B)). [resolve(5736,a,5760,a)]. 90.33/90.23 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),B)). [resolve(5736,a,5761,a)]. 90.70/90.60 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(5736,a,5762,a)]. 90.70/90.60 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),B),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),B)). [resolve(5736,a,5763,a)]. 90.70/90.60 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),B),A)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),B)). [resolve(5736,a,5764,a)]. 90.70/90.60 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(5736,a,5765,a)]. 90.70/90.60 5766 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1680_divide__pos__neg) # label(axiom). [clausify(2625)]. 90.70/90.60 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(5766,a,5736,a)]. 90.70/90.60 5767 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1702_divide__nonneg__neg) # label(axiom). [clausify(3015)]. 90.70/90.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),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(5767,a,5736,a)]. 90.70/90.60 5768 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1683_divide__strict__right__mono) # label(axiom). [clausify(3058)]. 90.70/90.60 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(5768,a,5736,a)]. 90.70/90.60 5769 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))))) # label(fact_1730_less__half__sum) # label(axiom). [clausify(3116)]. 91.12/91.01 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))))). [resolve(5769,a,5736,a)]. 91.12/91.01 5770 -linordered_field(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2559_nonzero__abs__inverse) # label(axiom). [clausify(3164)]. 91.12/91.01 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,inverse_inverse(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5770,a,5736,a)]. 91.12/91.01 5771 -linordered_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f556(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1540_field__le__epsilon) # label(axiom). [clausify(3231)]. 91.12/91.01 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f556(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5771,a,5736,a)]. 91.12/91.01 5772 -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),f556(A,B,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1540_field__le__epsilon) # label(axiom). [clausify(3231)]. 91.12/91.01 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),f556(real,A,B)))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5772,a,5736,a)]. 91.12/91.01 5773 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1706_divide__nonpos__pos) # label(axiom). [clausify(3409)]. 91.12/91.01 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5773,a,5736,a)]. 91.12/91.01 5774 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2570_le__imp__inverse__le) # label(axiom). [clausify(3417)]. 91.12/91.01 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5774,a,5736,a)]. 91.12/91.01 5775 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) # label(fact_1712_mult__imp__div__pos__less) # label(axiom). [clausify(3443)]. 91.12/91.01 5776 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),C)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2546_less__imp__inverse__less) # label(axiom). [clausify(3530)]. 91.30/91.28 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(5776,a,5736,a)]. 91.30/91.28 5777 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2573_inverse__le__imp__le__neg) # label(axiom). [clausify(3549)]. 91.30/91.28 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(5777,a,5736,a)]. 91.30/91.28 5778 -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),inverse_divide(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1714_neg__less__divide__eq) # label(axiom). [clausify(3564)]. 91.30/91.28 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),inverse_divide(real),C),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(5778,a,5736,a)]. 91.30/91.28 5779 -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),inverse_divide(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_1714_neg__less__divide__eq) # label(axiom). [clausify(3564)]. 91.30/91.28 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),inverse_divide(real),C),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A))). [resolve(5779,a,5736,a)]. 91.30/91.28 5780 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1707_divide__nonpos__neg) # label(axiom). [clausify(3682)]. 91.30/91.28 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(5780,a,5736,a)]. 91.30/91.28 5781 -linordered_field(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),hAPP(A,A,abs_abs(A),B)) # label(fact_1871_nonzero__abs__divide) # label(axiom). [clausify(3764)]. 91.30/91.28 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),B)),hAPP(real,real,abs_abs(real),A)). [resolve(5781,a,5736,a)]. 91.30/91.28 5782 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1703_frac__less2) # label(axiom). [clausify(3888)]. 91.60/91.50 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(5782,a,5736,a)]. 91.60/91.50 5783 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1741_neg__le__divide__eq) # label(axiom). [clausify(3956)]. 91.60/91.50 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(5783,a,5736,a)]. 91.60/91.50 5784 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1741_neg__le__divide__eq) # label(axiom). [clausify(3956)]. 91.60/91.50 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(5784,a,5736,a)]. 91.60/91.50 5785 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1738_pos__divide__le__eq) # label(axiom). [clausify(4129)]. 91.60/91.50 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(5785,a,5736,a)]. 91.60/91.50 5786 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_1738_pos__divide__le__eq) # label(axiom). [clausify(4129)]. 91.60/91.50 5787 linordered_field(rat) # label(arity_Rat_Orat___Fields_Olinordered__field) # label(axiom). [assumption]. 91.60/91.50 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(5787,a,5737,a)]. 91.60/91.51 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(5787,a,5738,a)]. 91.60/91.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5787,a,5739,a)]. 91.60/91.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5787,a,5740,a)]. 91.60/91.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5787,a,5741,a)]. 91.60/91.51 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(5787,a,5742,a)]. 91.60/91.51 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(5787,a,5743,a)]. 91.60/91.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5787,a,5744,a)]. 91.60/91.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5787,a,5745,a)]. 91.60/91.51 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(5787,a,5746,a)]. 91.60/91.51 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(5787,a,5747,a)]. 91.60/91.51 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5787,a,5748,a)]. 91.60/91.51 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(5787,a,5749,a)]. 91.60/91.52 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_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(5787,a,5750,a)]. 91.60/91.52 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),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(5787,a,5751,a)]. 91.60/91.52 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),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(5787,a,5752,a)]. 91.60/91.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_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(5787,a,5753,a)]. 91.60/91.52 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(5787,a,5754,a)]. 91.60/91.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(5787,a,5755,a)]. 91.60/91.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),B)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5787,a,5756,a)]. 91.60/91.52 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_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(5787,a,5757,a)]. 91.60/91.52 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),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(5787,a,5758,a)]. 91.60/91.52 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),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(5787,a,5759,a)]. 91.60/91.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),B)). [resolve(5787,a,5760,a)]. 91.60/91.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),B)). [resolve(5787,a,5761,a)]. 91.60/91.54 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(5787,a,5762,a)]. 91.60/91.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),B)). [resolve(5787,a,5763,a)]. 91.60/91.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),B)). [resolve(5787,a,5764,a)]. 91.60/91.54 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5787,a,5765,a)]. 91.60/91.54 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),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(5787,a,5766,a)]. 91.60/91.54 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(5787,a,5767,a)]. 91.60/91.54 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),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(5787,a,5768,a)]. 91.60/91.54 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(5787,a,5769,a)]. 91.60/91.54 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5787,a,5770,a)]. 91.60/91.54 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f556(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5787,a,5771,a)]. 91.60/91.54 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),f556(rat,A,B)))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5787,a,5772,a)]. 91.60/91.54 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),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(5787,a,5773,a)]. 91.60/91.55 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(5787,a,5774,a)]. 91.60/91.55 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(5787,a,5776,a)]. 91.60/91.55 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(5787,a,5777,a)]. 91.60/91.55 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),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),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(5787,a,5778,a)]. 91.60/91.55 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),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),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A))). [resolve(5787,a,5779,a)]. 91.60/91.55 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(5787,a,5780,a)]. 91.60/91.55 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),B)),hAPP(rat,rat,abs_abs(rat),A)). [resolve(5787,a,5781,a)]. 91.60/91.55 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(5787,a,5782,a)]. 91.60/91.55 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_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(5787,a,5783,a)]. 91.60/91.55 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_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(5787,a,5784,a)]. 91.60/91.55 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(5787,a,5785,a)]. 92.22/92.13 5788 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1701_divide__nonneg__pos) # label(axiom). [clausify(4284)]. 92.22/92.13 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(5788,a,5736,a)]. 92.22/92.13 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(5788,a,5787,a)]. 92.22/92.13 5789 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2572_inverse__le__imp__le) # label(axiom). [clausify(4309)]. 92.22/92.13 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(5789,a,5736,a)]. 92.22/92.13 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(5789,a,5787,a)]. 92.22/92.13 5790 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2545_negative__imp__inverse__negative) # label(axiom). [clausify(4467)]. 92.22/92.13 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(5790,a,5736,a)]. 92.22/92.13 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(5790,a,5787,a)]. 92.22/92.13 5791 -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),inverse_divide(A),D),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)) # label(fact_1737_pos__le__divide__eq) # label(axiom). [clausify(4817)]. 92.22/92.13 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),inverse_divide(real),C),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)). [resolve(5791,a,5736,a)]. 92.22/92.13 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),inverse_divide(rat),C),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)). [resolve(5791,a,5787,a)]. 92.22/92.13 5792 -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),inverse_divide(A),D),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)) # label(fact_1737_pos__le__divide__eq) # label(axiom). [clausify(4817)]. 94.53/94.49 5793 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1679_divide__pos__pos) # label(axiom). [clausify(4840)]. 94.53/94.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5793,a,5736,a)]. 94.53/94.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(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(5793,a,5787,a)]. 94.53/94.49 5794 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) # label(fact_1710_pos__less__divide__eq) # label(axiom). [clausify(4855)]. 94.53/94.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(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(5794,a,5736,a)]. 94.53/94.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(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(5794,a,5787,a)]. 94.53/94.49 5795 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) # label(fact_1710_pos__less__divide__eq) # label(axiom). [clausify(4855)]. 94.53/94.49 5796 -linordered_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2543_positive__imp__inverse__positive) # label(axiom). [clausify(4923)]. 94.53/94.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5796,a,5736,a)]. 94.53/94.49 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5796,a,5787,a)]. 94.53/94.49 5797 linord1117847801e_zero(rat) # label(arity_Rat_Orat___Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption]. 94.53/94.49 5798 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) # label(fact_2574_inverse__le__1__iff) # label(axiom). [clausify(60)]. 94.53/94.49 5799 -linord1117847801e_zero(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),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) # label(fact_2574_inverse__le__1__iff) # label(axiom). [clausify(60)]. 94.62/94.50 5800 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) # label(fact_2574_inverse__le__1__iff) # label(axiom). [clausify(60)]. 94.62/94.50 5801 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom). [clausify(83)]. 94.62/94.50 5802 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_1677_divide__less__0__iff) # label(axiom). [clausify(83)]. 94.62/94.50 5803 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),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),C),zero_zero(A))) # label(fact_1677_divide__less__0__iff) # label(axiom). [clausify(83)]. 94.62/94.50 5804 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),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),zero_zero(A)),B)) # label(fact_1677_divide__less__0__iff) # label(axiom). [clausify(83)]. 94.62/94.50 5805 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1677_divide__less__0__iff) # label(axiom). [clausify(83)]. 94.62/94.50 5806 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),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)),B)) # label(fact_1677_divide__less__0__iff) # label(axiom). [clausify(83)]. 94.62/94.50 5807 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),f18(A,B,C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1523_field__le__mult__one__interval) # label(axiom). [clausify(90)]. 94.62/94.50 5808 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),f18(A,B,C)),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1523_field__le__mult__one__interval) # label(axiom). [clausify(90)]. 94.62/94.50 5809 -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),f18(A,B,C)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1523_field__le__mult__one__interval) # label(axiom). [clausify(90)]. 94.62/94.50 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))). [resolve(5797,a,5798,a)]. 94.62/94.50 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),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))). [resolve(5797,a,5799,a)]. 94.62/94.50 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))). [resolve(5797,a,5800,a)]. 94.62/94.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(5797,a,5801,a)]. 94.62/94.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5797,a,5802,a)]. 94.62/94.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),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),B),zero_zero(rat))). [resolve(5797,a,5803,a)]. 94.62/94.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),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),zero_zero(rat)),A)). [resolve(5797,a,5804,a)]. 94.62/94.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),f18(rat,A,B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5797,a,5807,a)]. 94.62/94.55 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),f18(rat,A,B)),one_one(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5797,a,5808,a)]. 94.62/94.55 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),f18(rat,A,B)),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5797,a,5809,a)]. 94.62/94.55 5810 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom). [clausify(273)]. 94.62/94.55 5811 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) # label(fact_2542_inverse__negative__iff__negative) # label(axiom). [clausify(273)]. 94.62/94.55 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,inverse_inverse(rat),A)),zero_zero(rat))). [resolve(5811,a,5797,a)]. 94.62/94.55 5812 -number_ring(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),one_one(A)),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1768_half) # label(axiom). [clausify(321)]. 94.62/94.55 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5812,b,5797,a)]. 94.62/94.55 5813 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1672_divide__right__mono__neg) # label(axiom). [clausify(336)]. 94.62/94.55 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C))). [resolve(5813,a,5797,a)]. 94.62/94.57 5814 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.62/94.57 5815 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.62/94.57 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5815,b,5797,a)]. 94.62/94.57 5816 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.62/94.57 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),A)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5816,b,5797,a)]. 94.62/94.57 5817 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.62/94.57 5818 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.62/94.57 5819 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.71/94.60 Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),B)),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5819,b,5797,a)]. 94.71/94.60 5820 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),D)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.71/94.60 5821 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),hAPP(int,A,number_number_of(A),D))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.71/94.60 5822 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.71/94.60 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(int,rat,number_number_of(rat),B))). [resolve(5822,b,5797,a)]. 94.71/94.60 5823 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(int,A,number_number_of(A),C))) # label(fact_1747_divide__less__eq__number__of) # label(axiom). [clausify(428)]. 94.71/94.60 5824 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1744_divide__left__mono__neg) # label(axiom). [clausify(501)]. 94.71/94.64 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(5824,a,5797,a)]. 94.71/94.64 5825 -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),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.64 5826 -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),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.64 Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))). [resolve(5826,b,5797,a)]. 94.71/94.64 5827 -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),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.64 5828 -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),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.64 5829 -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),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.64 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5829,b,5797,a)]. 94.71/94.64 5830 -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),C)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),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),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.66 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),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),hAPP(int,rat,number_number_of(rat),C)),B))). [resolve(5830,b,5797,a)]. 94.71/94.66 5831 -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),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.66 5832 -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),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.66 5833 -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),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.66 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5833,b,5797,a)]. 94.71/94.66 5834 -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),C)),hAPP(int,A,number_number_of(A),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(int,A,number_number_of(A),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),hAPP(int,A,number_number_of(A),D)),C))) # label(fact_1754_divide__le__eq__number__of) # label(axiom). [clausify(732)]. 94.71/94.66 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(int,rat,number_number_of(rat),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),C)),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),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),hAPP(int,rat,number_number_of(rat),C)),B))). [resolve(5834,b,5797,a)]. 94.71/94.67 5835 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1675_zero__le__divide__iff) # label(axiom). [clausify(737)]. 94.71/94.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B))). [resolve(5835,a,5797,a)]. 94.71/94.67 5836 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom). [clausify(737)]. 94.71/94.67 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5836,a,5797,a)]. 94.71/94.67 5837 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),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_1675_zero__le__divide__iff) # label(axiom). [clausify(737)]. 94.71/94.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),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(5837,a,5797,a)]. 94.71/94.67 5838 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) # label(fact_1675_zero__le__divide__iff) # label(axiom). [clausify(737)]. 94.71/94.67 5839 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom). [clausify(737)]. 94.71/94.67 5840 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1675_zero__le__divide__iff) # label(axiom). [clausify(737)]. 94.71/94.67 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A))). [resolve(5840,a,5797,a)]. 94.83/94.77 5841 -linord1117847801e_zero(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_1848_abs__divide) # label(axiom). [clausify(759)]. 94.83/94.77 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),A)),hAPP(rat,rat,abs_abs(rat),B)). [resolve(5841,a,5797,a)]. 94.83/94.77 5842 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.77 5843 -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_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.77 Derived: -number(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(5843,a,5797,a)]. 94.83/94.77 5844 -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_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.77 Derived: -number(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(5844,a,5797,a)]. 94.83/94.77 5845 -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_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.77 5846 -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_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.78 5847 -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_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.78 Derived: -number(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(int,rat,number_number_of(rat),C)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5847,a,5797,a)]. 94.83/94.78 5848 -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_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.78 5849 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.78 5850 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.78 Derived: -number(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(int,rat,number_number_of(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),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(5850,a,5797,a)]. 94.83/94.78 5851 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1745_less__divide__eq__number__of1) # label(axiom). [clausify(1067)]. 94.83/94.80 5852 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 94.83/94.80 5853 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),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))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 94.83/94.80 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)),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))). [resolve(5853,a,5797,a)]. 94.83/94.80 5854 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 94.83/94.80 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),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(5854,a,5797,a)]. 94.83/94.80 5855 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 94.83/94.80 5856 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),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),D))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 94.83/94.80 5857 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),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)),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),D))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 94.83/94.80 Derived: -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),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)),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),C))). [resolve(5857,a,5797,a)]. 95.02/94.94 5858 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),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),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),D))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 95.02/94.94 5859 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 95.02/94.94 5860 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 95.02/94.94 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(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5860,a,5797,a)]. 95.02/94.94 5861 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1708_less__divide__eq) # label(axiom). [clausify(1071)]. 95.02/94.94 5862 -linord1117847801e_zero(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(A,A,inverse_inverse(A),B)),one_one(A))) # label(fact_2609_inverse__less__1__iff) # label(axiom). [clausify(1287)]. 95.02/94.94 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(rat,rat,inverse_inverse(rat),A)),one_one(rat))). [resolve(5862,a,5797,a)]. 95.02/94.94 5863 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) # label(fact_2609_inverse__less__1__iff) # label(axiom). [clausify(1287)]. 95.02/94.94 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),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))). [resolve(5863,a,5797,a)]. 95.02/94.94 5864 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),one_one(A))) # label(fact_2609_inverse__less__1__iff) # label(axiom). [clausify(1287)]. 95.02/94.94 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),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,inverse_inverse(rat),A)),one_one(rat))). [resolve(5864,a,5797,a)]. 95.02/94.94 5865 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(1524)]. 95.13/95.04 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5865,a,5797,a)]. 95.13/95.04 5866 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,inverse_inverse(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2539_inverse__nonpositive__iff__nonpositive) # label(axiom). [clausify(1524)]. 95.13/95.04 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,inverse_inverse(rat),A)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))). [resolve(5866,a,5797,a)]. 95.13/95.04 5867 -linord1117847801e_zero(A) | hAPP(A,A,inverse_inverse(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),hAPP(A,A,inverse_inverse(A),B)) # label(fact_2534_abs__inverse) # label(axiom). [clausify(1697)]. 95.13/95.04 Derived: hAPP(rat,rat,inverse_inverse(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,inverse_inverse(rat),A)). [resolve(5867,a,5797,a)]. 95.13/95.04 5868 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.13/95.04 5869 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.13/95.04 5870 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.13/95.04 5871 -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)),C)) | 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),D),C))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.13/95.04 5872 -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),hAPP(int,A,number_number_of(A),B)),C)),D)) | 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),D),C))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.13/95.04 5873 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),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)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.23/95.11 5874 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),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)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.23/95.11 5875 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.23/95.11 5876 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.23/95.11 5877 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1746_less__divide__eq__number__of) # label(axiom). [clausify(1763)]. 95.23/95.11 5878 -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_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.11 5879 -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_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.11 Derived: -number(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(5879,b,5797,a)]. 95.23/95.13 5880 -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_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.13 5881 -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_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.13 5882 -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),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.13 Derived: -number(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),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))). [resolve(5882,b,5797,a)]. 95.23/95.13 5883 -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),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),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.13 Derived: -number(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),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),hAPP(int,rat,number_number_of(rat),B))),A)). [resolve(5883,b,5797,a)]. 95.23/95.13 5884 -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_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.13 5885 -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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.15 5886 -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)),D)) | 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_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.15 Derived: -number(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),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),B)),zero_zero(rat))). [resolve(5886,b,5797,a)]. 95.23/95.15 5887 -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)),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),hAPP(int,A,number_number_of(A),C))),B)) # label(fact_1748_divide__less__eq__number__of1) # label(axiom). [clausify(1924)]. 95.23/95.15 5888 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_1700_divide__le__cancel) # label(axiom). [clausify(1948)]. 95.23/95.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(5888,a,5797,a)]. 95.23/95.15 5889 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_1700_divide__le__cancel) # label(axiom). [clausify(1948)]. 95.23/95.15 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5889,a,5797,a)]. 95.23/95.15 5890 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1700_divide__le__cancel) # label(axiom). [clausify(1948)]. 95.43/95.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(5890,a,5797,a)]. 95.43/95.30 5891 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_1700_divide__le__cancel) # label(axiom). [clausify(1948)]. 95.43/95.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5891,a,5797,a)]. 95.43/95.30 5892 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1700_divide__le__cancel) # label(axiom). [clausify(1948)]. 95.43/95.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))). [resolve(5892,a,5797,a)]. 95.43/95.30 5893 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),B)) # label(fact_1700_divide__le__cancel) # label(axiom). [clausify(1948)]. 95.43/95.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),A)). [resolve(5893,a,5797,a)]. 95.43/95.30 5894 -linord1117847801e_zero(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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2607_inverse__le__iff) # label(axiom). [clausify(2319)]. 95.43/95.30 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_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)). [resolve(5894,a,5797,a)]. 95.43/95.30 5895 -linord1117847801e_zero(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)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2607_inverse__le__iff) # label(axiom). [clausify(2319)]. 95.43/95.30 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)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5895,a,5797,a)]. 95.44/95.34 5896 -linord1117847801e_zero(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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_2607_inverse__le__iff) # label(axiom). [clausify(2319)]. 95.44/95.34 5897 -linord1117847801e_zero(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_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2607_inverse__le__iff) # label(axiom). [clausify(2319)]. 95.44/95.34 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_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5897,a,5797,a)]. 95.44/95.34 5898 -linord1117847801e_zero(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_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_2607_inverse__le__iff) # label(axiom). [clausify(2319)]. 95.44/95.34 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_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B))). [resolve(5898,a,5797,a)]. 95.44/95.34 5899 -linord1117847801e_zero(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_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2607_inverse__le__iff) # label(axiom). [clausify(2319)]. 95.44/95.34 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_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),A)). [resolve(5899,a,5797,a)]. 95.44/95.34 5900 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2575_one__less__inverse__iff) # label(axiom). [clausify(2364)]. 95.44/95.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5900,a,5797,a)]. 95.44/95.34 5901 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2575_one__less__inverse__iff) # label(axiom). [clausify(2364)]. 95.44/95.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))). [resolve(5901,a,5797,a)]. 95.44/95.34 5902 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) # label(fact_2575_one__less__inverse__iff) # label(axiom). [clausify(2364)]. 95.63/95.52 5903 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.63/95.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)). [resolve(5903,a,5797,a)]. 95.63/95.52 5904 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | ti(A,C) != zero_zero(A) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.63/95.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | ti(rat,B) != zero_zero(rat). [resolve(5904,a,5797,a)]. 95.63/95.52 5905 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.63/95.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(5905,a,5797,a)]. 95.63/95.52 5906 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.63/95.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | ti(rat,B) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5906,a,5797,a)]. 95.63/95.52 5907 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.63/95.52 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | ti(rat,B) = zero_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(5907,a,5797,a)]. 95.63/95.52 5908 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) | ti(A,C) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.72/95.68 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),A)) | ti(rat,B) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5908,a,5797,a)]. 95.72/95.68 5909 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),B)) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_1678_divide__less__cancel) # label(axiom). [clausify(2714)]. 95.72/95.68 5910 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(2818)]. 95.72/95.68 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5910,a,5797,a)]. 95.72/95.68 5911 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_2540_inverse__nonnegative__iff__nonnegative) # label(axiom). [clausify(2818)]. 95.72/95.68 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(5911,a,5797,a)]. 95.72/95.68 5912 -number_ring(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1756_half__gt__zero__iff) # label(axiom). [clausify(2835)]. 95.72/95.68 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5912,b,5797,a)]. 95.72/95.68 5913 -number_ring(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1756_half__gt__zero__iff) # label(axiom). [clausify(2835)]. 95.72/95.68 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5913,b,5797,a)]. 95.72/95.68 5914 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.72/95.68 5915 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)). [resolve(5915,a,5797,a)]. 95.82/95.69 5916 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 5917 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 5918 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5918,a,5797,a)]. 95.82/95.69 5919 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),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),C))) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),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),B))). [resolve(5919,a,5797,a)]. 95.82/95.69 5920 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 5921 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.82/95.69 5922 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.84/95.76 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5922,a,5797,a)]. 95.84/95.76 5923 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),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),C))) # label(fact_1736_divide__le__eq) # label(axiom). [clausify(3028)]. 95.84/95.76 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),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),B))). [resolve(5923,a,5797,a)]. 95.84/95.76 5924 -linord1117847801e_zero(A) | -number_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) # label(fact_1757_half__gt__zero) # label(axiom). [clausify(3066)]. 95.84/95.76 5925 linord1117847801e_zero(real) # label(arity_RealDef_Oreal___Fields_Olinordered__field__inverse__zero) # label(axiom). [assumption]. 95.84/95.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))). [resolve(5925,a,5798,a)]. 95.84/95.76 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),hAPP(real,real,inverse_inverse(real),A)),one_one(real))). [resolve(5925,a,5799,a)]. 95.84/95.76 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))). [resolve(5925,a,5800,a)]. 95.84/95.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(5925,a,5801,a)]. 95.84/95.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5925,a,5802,a)]. 95.84/95.76 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),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),B),zero_zero(real))). [resolve(5925,a,5803,a)]. 95.84/95.79 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),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),zero_zero(real)),A)). [resolve(5925,a,5804,a)]. 95.84/95.79 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),f18(real,A,B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5925,a,5807,a)]. 95.84/95.79 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),f18(real,A,B)),one_one(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5925,a,5808,a)]. 95.84/95.79 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),f18(real,A,B)),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5925,a,5809,a)]. 95.84/95.79 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(5925,a,5811,a)]. 95.84/95.79 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),one_one(real)),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5925,a,5812,b)]. 95.84/95.79 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C))). [resolve(5925,a,5813,a)]. 95.84/95.79 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5925,a,5815,b)]. 95.84/95.79 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),A)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5925,a,5816,b)]. 95.84/95.79 Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),B)),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(int,real,number_number_of(real),B))). [resolve(5925,a,5819,b)]. 95.84/95.79 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(int,real,number_number_of(real),B))). [resolve(5925,a,5822,b)]. 95.93/95.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(5925,a,5824,a)]. 95.93/95.82 Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))). [resolve(5925,a,5826,b)]. 95.93/95.82 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5925,a,5829,b)]. 95.93/95.82 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))). [resolve(5925,a,5830,b)]. 95.93/95.82 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5925,a,5833,b)]. 95.93/95.82 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(int,real,number_number_of(real),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),C)),B))). [resolve(5925,a,5834,b)]. 95.93/95.82 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_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B))). [resolve(5925,a,5835,a)]. 95.93/95.82 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))). [resolve(5925,a,5836,a)]. 95.93/95.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),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(5925,a,5837,a)]. 95.93/95.84 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A))). [resolve(5925,a,5840,a)]. 95.93/95.84 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B)). [resolve(5925,a,5841,a)]. 95.93/95.84 Derived: -number(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(5925,a,5843,a)]. 95.93/95.84 Derived: -number(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(5925,a,5844,a)]. 95.93/95.84 Derived: -number(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),hAPP(int,real,number_number_of(real),C)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5925,a,5847,a)]. 95.93/95.84 Derived: -number(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(int,real,number_number_of(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),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(5925,a,5850,a)]. 95.93/95.84 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)),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))). [resolve(5925,a,5853,a)]. 95.93/95.84 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),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(5925,a,5854,a)]. 96.02/95.89 Derived: -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),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)),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),C))). [resolve(5925,a,5857,a)]. 96.02/95.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5925,a,5860,a)]. 96.02/95.89 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(real,real,inverse_inverse(real),A)),one_one(real))). [resolve(5925,a,5862,a)]. 96.02/95.89 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),hAPP(real,real,inverse_inverse(real),A)),one_one(real))). [resolve(5925,a,5863,a)]. 96.02/95.89 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),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),A)),one_one(real))). [resolve(5925,a,5864,a)]. 96.02/95.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5925,a,5865,a)]. 96.02/95.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,inverse_inverse(real),A)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))). [resolve(5925,a,5866,a)]. 96.02/95.89 Derived: hAPP(real,real,inverse_inverse(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),hAPP(real,real,inverse_inverse(real),A)). [resolve(5925,a,5867,a)]. 96.02/95.89 Derived: -number(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(5925,a,5879,b)]. 96.02/95.89 Derived: -number(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),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))). [resolve(5925,a,5882,b)]. 96.02/95.89 Derived: -number(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),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),hAPP(int,real,number_number_of(real),B))),A)). [resolve(5925,a,5883,b)]. 96.02/95.91 Derived: -number(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),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),B)),zero_zero(real))). [resolve(5925,a,5886,b)]. 96.02/95.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(5925,a,5888,a)]. 96.02/95.91 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5925,a,5889,a)]. 96.02/95.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(5925,a,5890,a)]. 96.02/95.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5925,a,5891,a)]. 96.02/95.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))). [resolve(5925,a,5892,a)]. 96.02/95.91 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),A)). [resolve(5925,a,5893,a)]. 96.02/95.91 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_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)). [resolve(5925,a,5894,a)]. 96.02/95.91 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)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5925,a,5895,a)]. 96.02/95.94 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_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5925,a,5897,a)]. 96.02/95.94 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_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B))). [resolve(5925,a,5898,a)]. 96.02/95.94 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_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),A)). [resolve(5925,a,5899,a)]. 96.02/95.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5925,a,5900,a)]. 96.02/95.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))). [resolve(5925,a,5901,a)]. 96.02/95.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)). [resolve(5925,a,5903,a)]. 96.02/95.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | ti(real,B) != zero_zero(real). [resolve(5925,a,5904,a)]. 96.02/95.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(5925,a,5905,a)]. 96.02/95.94 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | ti(real,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5925,a,5906,a)]. 96.02/95.94 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | ti(real,B) = zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(5925,a,5907,a)]. 96.02/95.94 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),A)) | ti(real,B) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5925,a,5908,a)]. 96.02/95.94 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5925,a,5910,a)]. 96.02/95.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(5925,a,5911,a)]. 96.02/95.97 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5925,a,5912,b)]. 96.02/95.97 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))). [resolve(5925,a,5913,b)]. 96.02/95.97 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)). [resolve(5925,a,5915,a)]. 96.02/95.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5925,a,5918,a)]. 96.02/95.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5925,a,5919,a)]. 96.02/95.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5925,a,5922,a)]. 96.02/95.97 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5925,a,5923,a)]. 96.02/95.97 5926 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2541_inverse__positive__iff__positive) # label(axiom). [clausify(3125)]. 96.02/95.97 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,inverse_inverse(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(5926,a,5797,a)]. 96.02/95.97 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,inverse_inverse(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(5926,a,5925,a)]. 96.23/96.13 5927 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,inverse_inverse(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2541_inverse__positive__iff__positive) # label(axiom). [clausify(3125)]. 96.23/96.13 5928 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,abs_abs(A),C)),B) # label(fact_1884_abs__div__pos) # label(axiom). [clausify(3239)]. 96.23/96.13 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),hAPP(rat,rat,abs_abs(rat),B)),A). [resolve(5928,a,5797,a)]. 96.23/96.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,abs_abs(real),B)),A). [resolve(5928,a,5925,a)]. 96.23/96.13 5929 -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_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.23/96.13 5930 -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_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.23/96.13 5931 -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_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.23/96.13 5932 -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_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.23/96.13 5933 -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),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)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.31/96.20 5934 -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),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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.31/96.20 5935 -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),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))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.31/96.20 5936 -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),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))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.31/96.20 5937 -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),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)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.31/96.20 5938 -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),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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1755_divide__le__eq__number__of1) # label(axiom). [clausify(3341)]. 96.31/96.20 5939 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1673_divide__right__mono) # label(axiom). [clausify(3404)]. 96.31/96.20 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5939,a,5797,a)]. 96.31/96.20 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5939,a,5925,a)]. 96.44/96.35 5940 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.35 5941 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),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),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.35 5942 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),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),times_times(A),D),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.35 5943 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.35 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),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(5943,a,5797,a)]. 96.44/96.35 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),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(5943,a,5925,a)]. 96.44/96.35 5944 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.35 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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),B))). [resolve(5944,a,5797,a)]. 96.44/96.35 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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B))). [resolve(5944,a,5925,a)]. 96.44/96.36 5945 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),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)),D)) | 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),D))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),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),zero_zero(rat)),C)) | 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),C))). [resolve(5945,a,5797,a)]. 96.44/96.36 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5945,a,5925,a)]. 96.44/96.36 5946 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),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),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),D))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.36 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),C))). [resolve(5946,a,5797,a)]. 96.44/96.36 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),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),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C))). [resolve(5946,a,5925,a)]. 96.44/96.36 5947 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.44/96.36 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),C),A))). [resolve(5947,a,5797,a)]. 96.44/96.36 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),A))). [resolve(5947,a,5925,a)]. 96.84/96.79 5948 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.84/96.79 5949 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1735_le__divide__eq) # label(axiom). [clausify(3427)]. 96.84/96.79 5950 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2606_inverse__less__iff) # label(axiom). [clausify(3996)]. 96.84/96.79 5951 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | 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))) # label(fact_2606_inverse__less__iff) # label(axiom). [clausify(3996)]. 96.84/96.79 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),A)) | 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))). [resolve(5951,a,5797,a)]. 96.84/96.79 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),A)) | 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))). [resolve(5951,a,5925,a)]. 96.84/96.79 5952 -linord1117847801e_zero(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)),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,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2606_inverse__less__iff) # label(axiom). [clausify(3996)]. 96.84/96.79 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)),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,inverse_inverse(rat),A)),hAPP(rat,rat,inverse_inverse(rat),B))). [resolve(5952,a,5797,a)]. 96.84/96.79 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)),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,inverse_inverse(real),A)),hAPP(real,real,inverse_inverse(real),B))). [resolve(5952,a,5925,a)]. 96.84/96.79 5953 -linord1117847801e_zero(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,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C))) # label(fact_2606_inverse__less__iff) # label(axiom). [clausify(3996)]. 96.84/96.79 5954 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -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))) # label(fact_2606_inverse__less__iff) # label(axiom). [clausify(3996)]. 97.03/96.90 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)) | -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))). [resolve(5954,a,5797,a)]. 97.03/96.90 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -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))). [resolve(5954,a,5925,a)]. 97.03/96.90 5955 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),B)) | -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))) # label(fact_2606_inverse__less__iff) # label(axiom). [clausify(3996)]. 97.03/96.90 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),B),A)) | -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))). [resolve(5955,a,5797,a)]. 97.03/96.90 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),B),A)) | -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))). [resolve(5955,a,5925,a)]. 97.03/96.90 5956 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.03/96.90 5957 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.03/96.90 5958 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B))),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.03/96.90 5959 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5960 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(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),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),inverse_divide(A),D),hAPP(int,A,number_number_of(A),C)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5961 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),D)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5962 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),D))),C)) | 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)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5963 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5964 -number(A) | -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),B)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5965 -number(A) | -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(int,A,number_number_of(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(int,A,number_number_of(A),B))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),hAPP(int,A,number_number_of(A),B)))) # label(fact_1752_le__divide__eq__number__of1) # label(axiom). [clausify(4115)]. 97.05/97.00 5966 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5967 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5968 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5969 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5970 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5971 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5972 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),C))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.14/97.02 5973 -linord1117847801e_zero(A) | -number(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),C)),B)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.35/97.29 5974 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),C)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),D),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.35/97.29 5975 -linord1117847801e_zero(A) | -number(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),D)),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),D)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B))) # label(fact_1753_le__divide__eq__number__of) # label(axiom). [clausify(4225)]. 97.35/97.29 5976 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.29 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)). [resolve(5976,a,5797,a)]. 97.35/97.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)). [resolve(5976,a,5925,a)]. 97.35/97.29 5977 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.29 5978 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.29 5979 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.29 5980 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.30 5981 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.30 5982 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5982,a,5797,a)]. 97.35/97.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5982,a,5925,a)]. 97.35/97.30 5983 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(5983,a,5797,a)]. 97.35/97.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(5983,a,5925,a)]. 97.35/97.30 5984 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.35/97.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5984,a,5797,a)]. 97.35/97.30 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5984,a,5925,a)]. 97.44/97.33 5985 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_1709_divide__less__eq) # label(axiom). [clausify(4504)]. 97.44/97.33 5986 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_1676_zero__less__divide__iff) # label(axiom). [clausify(4522)]. 97.44/97.33 Derived: -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))) | 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)). [resolve(5986,a,5797,a)]. 97.44/97.33 Derived: -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))) | 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)). [resolve(5986,a,5925,a)]. 97.44/97.33 5987 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) # label(fact_1676_zero__less__divide__iff) # label(axiom). [clausify(4522)]. 97.44/97.33 Derived: -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))) | 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)). [resolve(5987,a,5797,a)]. 97.44/97.33 Derived: -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))) | 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)). [resolve(5987,a,5925,a)]. 97.44/97.33 5988 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),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),zero_zero(A)),B)) # label(fact_1676_zero__less__divide__iff) # label(axiom). [clausify(4522)]. 97.44/97.33 Derived: -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))) | 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)),A)). [resolve(5988,a,5797,a)]. 97.44/97.33 Derived: -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))) | 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)),A)). [resolve(5988,a,5925,a)]. 97.44/97.33 5989 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),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),zero_zero(A)),C)) # label(fact_1676_zero__less__divide__iff) # label(axiom). [clausify(4522)]. 97.65/97.59 Derived: -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))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),B)). [resolve(5989,a,5797,a)]. 97.65/97.59 Derived: -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))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),B)). [resolve(5989,a,5925,a)]. 97.65/97.59 5990 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) # label(fact_1676_zero__less__divide__iff) # label(axiom). [clausify(4522)]. 97.65/97.59 5991 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),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_1676_zero__less__divide__iff) # label(axiom). [clausify(4522)]. 97.65/97.59 5992 -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),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_2608_one__le__inverse__iff) # label(axiom). [clausify(4706)]. 97.65/97.59 5993 -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),one_one(A)),hAPP(A,A,inverse_inverse(A),B))) # label(fact_2608_one__le__inverse__iff) # label(axiom). [clausify(4706)]. 97.65/97.59 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),hAPP(rat,rat,inverse_inverse(rat),A))). [resolve(5993,a,5797,a)]. 97.65/97.59 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),hAPP(real,real,inverse_inverse(real),A))). [resolve(5993,a,5925,a)]. 97.65/97.59 5994 -linord1117847801e_zero(A) | 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_2608_one__le__inverse__iff) # label(axiom). [clausify(4706)]. 97.65/97.59 Derived: 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(5994,a,5797,a)]. 97.65/97.59 Derived: 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(5994,a,5925,a)]. 97.65/97.59 5995 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),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),C),B)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom). [clausify(4789)]. 97.65/97.59 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),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),B),A)),zero_zero(rat))). [resolve(5995,a,5797,a)]. 97.65/97.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),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),B),A)),zero_zero(real))). [resolve(5995,a,5925,a)]. 97.65/97.60 5996 -linord1117847801e_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom). [clausify(4789)]. 97.65/97.60 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),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(5996,a,5797,a)]. 97.65/97.60 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),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(5996,a,5925,a)]. 97.65/97.60 5997 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom). [clausify(4789)]. 97.65/97.60 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),B),A)),zero_zero(rat))). [resolve(5997,a,5797,a)]. 97.65/97.60 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)),zero_zero(real))). [resolve(5997,a,5925,a)]. 97.65/97.60 5998 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),C),B)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom). [clausify(4789)]. 97.65/97.60 5999 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom). [clausify(4789)]. 97.65/97.60 6000 -linord1117847801e_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),B),C)),zero_zero(A))) # label(fact_1674_divide__le__0__iff) # label(axiom). [clausify(4789)]. 97.65/97.60 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),inverse_divide(rat),A),B)),zero_zero(rat))). [resolve(6000,a,5797,a)]. 100.45/100.37 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)),zero_zero(real))). [resolve(6000,a,5925,a)]. 100.45/100.37 6001 -number_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B) # label(fact_139_semiring__mult__2) # label(axiom). [clausify(823)]. 100.45/100.37 6002 number_semiring(complex) # label(arity_Complex_Ocomplex___Int_Onumber__semiring) # label(axiom). [assumption]. 100.45/100.37 6003 number_semiring(real) # label(arity_RealDef_Oreal___Int_Onumber__semiring) # label(axiom). [assumption]. 100.45/100.37 6004 number_semiring(nat) # label(arity_Nat_Onat___Int_Onumber__semiring) # label(axiom). [assumption]. 100.45/100.37 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(6001,a,6002,a)]. 100.45/100.37 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(6001,a,6003,a)]. 100.45/100.37 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(6001,a,6004,a)]. 100.45/100.37 6005 -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(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),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)) # label(fact_41_semiring__mult__number__of) # label(axiom). [clausify(940)]. 100.45/100.37 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,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),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)). [resolve(6005,a,6002,a)]. 100.45/100.37 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,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),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)). [resolve(6005,a,6003,a)]. 100.45/100.37 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,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),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)). [resolve(6005,a,6004,a)]. 100.45/100.37 6006 -number_semiring(A) | 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)))) = 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)) # label(fact_169_power2__sum) # label(axiom). [clausify(1215)]. 100.54/100.48 Derived: 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)))) = 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)). [resolve(6006,a,6002,a)]. 100.54/100.48 Derived: 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)))) = 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)). [resolve(6006,a,6004,a)]. 100.54/100.48 6007 number_semiring(int) # label(arity_Int_Oint___Int_Onumber__semiring) # label(axiom). [assumption]. 100.54/100.48 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(6007,a,6001,a)]. 100.54/100.48 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,number_number_of(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,number_number_of(int),A)),hAPP(int,int,number_number_of(int),B)). [resolve(6007,a,6005,a)]. 100.54/100.48 Derived: 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)))) = 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)). [resolve(6007,a,6006,a)]. 100.54/100.48 6008 -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(int,A,number_number_of(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),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)) # label(fact_86_semiring__add__number__of) # label(axiom). [clausify(1571)]. 100.54/100.48 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,complex,number_number_of(complex),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),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)). [resolve(6008,a,6002,a)]. 101.05/100.93 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(int,real,number_number_of(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),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)). [resolve(6008,a,6003,a)]. 101.05/100.93 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(int,nat,number_number_of(nat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),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)). [resolve(6008,a,6004,a)]. 101.05/100.93 6009 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),hAPP(int,A,number_number_of(A),B)) # label(fact_1534_semiring__1__add__number__of) # label(axiom). [clausify(1619)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,succ,A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),hAPP(int,complex,number_number_of(complex),A)). [resolve(6009,a,6002,a)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),hAPP(int,real,number_number_of(real),A)). [resolve(6009,a,6003,a)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6009,a,6004,a)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),hAPP(int,int,number_number_of(int),A)). [resolve(6009,a,6007,a)]. 101.05/100.93 6010 -number_semiring(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),B)) | hAPP(int,A,number_number_of(A),hAPP(int,int,succ,B)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),B)),one_one(A)) # label(fact_1533_semiring__number__of__add__1) # label(axiom). [clausify(2070)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,succ,A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(int,complex,number_number_of(complex),A)),one_one(complex)). [resolve(6010,a,6002,a)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,real,number_number_of(real),hAPP(int,int,succ,A)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,number_number_of(real),A)),one_one(real)). [resolve(6010,a,6003,a)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,nat,number_number_of(nat),hAPP(int,int,succ,A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(int,nat,number_number_of(nat),A)),one_one(nat)). [resolve(6010,a,6004,a)]. 101.05/100.93 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,int,number_number_of(int),hAPP(int,int,succ,A)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,number_number_of(int),A)),one_one(int)). [resolve(6010,a,6007,a)]. 101.05/100.93 6011 number_semiring(rat) # label(arity_Rat_Orat___Int_Onumber__semiring) # label(axiom). [assumption]. 101.05/100.93 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),A). [resolve(6011,a,6001,a)]. 101.52/101.46 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,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),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)). [resolve(6011,a,6005,a)]. 101.52/101.46 Derived: 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)))) = 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)). [resolve(6011,a,6006,a)]. 101.52/101.46 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,rat,number_number_of(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),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)). [resolve(6011,a,6008,a)]. 101.52/101.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,succ,A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),hAPP(int,rat,number_number_of(rat),A)). [resolve(6011,a,6009,a)]. 101.52/101.46 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),pls),A)) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,succ,A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat)). [resolve(6011,a,6010,a)]. 101.52/101.46 6012 -number_semiring(A) | 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),one_one(A)),one_one(A)) # label(fact_178_semiring__one__add__one__is__two) # label(axiom). [clausify(2800)]. 101.52/101.46 Derived: 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),one_one(complex)),one_one(complex)). [resolve(6012,a,6002,a)]. 101.52/101.46 Derived: 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),one_one(real)),one_one(real)). [resolve(6012,a,6003,a)]. 101.52/101.46 Derived: 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),one_one(nat)),one_one(nat)). [resolve(6012,a,6004,a)]. 101.52/101.46 Derived: 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),one_one(int)),one_one(int)). [resolve(6012,a,6007,a)]. 101.52/101.46 Derived: 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),one_one(rat)),one_one(rat)). [resolve(6012,a,6011,a)]. 101.52/101.46 6013 -number_semiring(A) | hAPP(int,A,number_number_of(A),pls) = zero_zero(A) # label(fact_145_semiring__numeral__0__eq__0) # label(axiom). [clausify(3445)]. 101.52/101.46 Derived: hAPP(int,complex,number_number_of(complex),pls) = zero_zero(complex). [resolve(6013,a,6002,a)]. 101.52/101.46 Derived: hAPP(int,real,number_number_of(real),pls) = zero_zero(real). [resolve(6013,a,6003,a)]. 101.52/101.46 Derived: hAPP(int,nat,number_number_of(nat),pls) = zero_zero(nat). [resolve(6013,a,6004,a)]. 101.52/101.46 Derived: hAPP(int,rat,number_number_of(rat),pls) = zero_zero(rat). [resolve(6013,a,6011,a)]. 105.33/105.24 6014 -number_semiring(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) # label(fact_141_semiring__mult__2__right) # label(axiom). [clausify(3636)]. 105.33/105.24 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6014,a,6002,a)]. 105.33/105.24 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6014,a,6003,a)]. 105.33/105.24 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6014,a,6004,a)]. 105.33/105.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6014,a,6007,a)]. 105.33/105.24 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))). [resolve(6014,a,6011,a)]. 105.33/105.24 6015 -number_semiring(A) | hAPP(int,A,number_number_of(A),hAPP(nat,int,semiring_1_of_nat(int),B)) = hAPP(nat,A,semiring_1_of_nat(A),B) # label(fact_1212_number__of__int) # label(axiom). [clausify(4381)]. 105.33/105.24 Derived: hAPP(int,complex,number_number_of(complex),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,complex,semiring_1_of_nat(complex),A). [resolve(6015,a,6002,a)]. 105.33/105.24 Derived: hAPP(int,real,number_number_of(real),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,real,semiring_1_of_nat(real),A). [resolve(6015,a,6003,a)]. 105.33/105.24 Derived: hAPP(int,nat,number_number_of(nat),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,nat,semiring_1_of_nat(nat),A). [resolve(6015,a,6004,a)]. 105.33/105.24 Derived: hAPP(int,int,number_number_of(int),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,int,semiring_1_of_nat(int),A). [resolve(6015,a,6007,a)]. 105.33/105.24 Derived: hAPP(int,rat,number_number_of(rat),hAPP(nat,int,semiring_1_of_nat(int),A)) = hAPP(nat,rat,semiring_1_of_nat(rat),A). [resolve(6015,a,6011,a)]. 105.33/105.24 6016 -number_semiring(A) | one_one(A) = hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) # label(fact_172_semiring__numeral__1__eq__1) # label(axiom). [clausify(4611)]. 105.33/105.24 Derived: one_one(complex) = hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)). [resolve(6016,a,6002,a)]. 105.33/105.24 Derived: one_one(real) = hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)). [resolve(6016,a,6003,a)]. 105.33/105.24 Derived: one_one(nat) = hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit1,pls)). [resolve(6016,a,6004,a)]. 105.33/105.24 Derived: one_one(int) = hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,pls)). [resolve(6016,a,6007,a)]. 105.33/105.24 Derived: one_one(rat) = hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)). [resolve(6016,a,6011,a)]. 105.33/105.24 6017 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),D)),C) # label(fact_2011_mod__minus__cong) # label(axiom). [clausify(510)]. 105.33/105.24 6018 ring_div(int) # label(arity_Int_Oint___Divides_Oring__div) # label(axiom). [assumption]. 105.33/105.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),C)),B). [resolve(6017,a,6018,a)]. 105.33/105.24 6019 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D) # label(fact_946_mod__diff__right__eq) # label(axiom). [clausify(1132)]. 107.52/107.40 6020 -ring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2086_dvd__div__neg) # label(axiom). [clausify(1220)]. 107.52/107.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),hAPP(int,int,uminus_uminus(int),A)). [resolve(6020,a,6018,a)]. 107.52/107.40 6021 -ring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,uminus_uminus(A),C)),B) # label(fact_2085_dvd__neg__div) # label(axiom). [clausify(2953)]. 107.52/107.40 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,uminus_uminus(int),B)),A). [resolve(6021,a,6018,a)]. 107.52/107.40 6022 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2012_mod__minus__eq) # label(axiom). [clausify(3724)]. 107.52/107.40 Derived: 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),A),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,uminus_uminus(int),A)),B). [resolve(6022,a,6018,a)]. 107.52/107.40 6023 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_944_mod__diff__eq) # label(axiom). [clausify(4294)]. 107.52/107.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B))),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),B). [resolve(6023,a,6018,a)]. 107.52/107.40 6024 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),F)),C) # label(fact_943_mod__diff__cong) # label(axiom). [clausify(4319)]. 107.52/107.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),C),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),D),B) != hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),E),B) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),D)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),E)),B). [resolve(6024,a,6018,a)]. 107.52/107.40 6025 -ring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),C) # label(fact_945_mod__diff__left__eq) # label(axiom). [clausify(4535)]. 107.52/107.40 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),B). [resolve(6025,a,6018,a)]. 110.82/110.72 6026 -metric_space(A) | -real_n2089651433ebra_1(B) | ti(A,C) = ti(A,D) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),combk(A,B),D)),C),hAPP(B,filter(B),at(B),E))) # label(fact_4559_LIM__const__not__eq) # label(axiom). [clausify(114)]. 110.82/110.72 6027 real_n2089651433ebra_1(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption]. 110.82/110.72 Derived: -metric_space(A) | ti(A,B) = ti(A,C) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(A,fun(complex,A),combk(A,complex),C)),B),hAPP(complex,filter(complex),at(complex),D))). [resolve(6026,b,6027,a)]. 110.82/110.72 6028 -real_n2089651433ebra_1(A) | -number_ring(A) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),B)) = hAPP(A,real,norm_norm(A),hAPP(int,A,number_number_of(A),B)) # label(fact_1892_norm__number__of) # label(axiom). [clausify(427)]. 110.82/110.72 Derived: -number_ring(complex) | hAPP(real,real,abs_abs(real),hAPP(int,real,number_number_of(real),A)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,number_number_of(complex),A)). [resolve(6028,a,6027,a)]. 110.82/110.72 6029 -real_n2089651433ebra_1(A) | hAPP(nat,real,semiring_1_of_nat(real),B) = hAPP(A,real,norm_norm(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_1775_norm__of__nat) # label(axiom). [clausify(430)]. 110.82/110.72 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,semiring_1_of_nat(complex),A)). [resolve(6029,a,6027,a)]. 110.82/110.72 6030 -real_n2089651433ebra_1(A) | hAPP(real,A,of_real(A),hAPP(real,real,sgn_sgn(real),B)) = hAPP(A,A,sgn_sgn(A),hAPP(real,A,of_real(A),B)) # label(fact_2801_sgn__of__real) # label(axiom). [clausify(709)]. 110.82/110.72 Derived: hAPP(real,complex,of_real(complex),hAPP(real,real,sgn_sgn(real),A)) = hAPP(complex,complex,sgn_sgn(complex),hAPP(real,complex,of_real(complex),A)). [resolve(6030,a,6027,a)]. 110.82/110.72 6031 -real_n2089651433ebra_1(A) | one_one(A) = hAPP(A,A,sgn_sgn(A),one_one(A)) # label(fact_2206_sgn__one) # label(axiom). [clausify(1417)]. 110.82/110.72 Derived: one_one(complex) = hAPP(complex,complex,sgn_sgn(complex),one_one(complex)). [resolve(6031,a,6027,a)]. 110.82/110.72 6032 -real_n2089651433ebra_1(A) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,norm_norm(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(A,real,norm_norm(A),B)),C))) # label(fact_1794_norm__power__ineq) # label(axiom). [clausify(1800)]. 110.82/110.72 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(complex,real,norm_norm(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(complex,real,norm_norm(complex),A)),B))). [resolve(6032,a,6027,a)]. 110.82/110.72 6033 -real_n2089651433ebra_1(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(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(A,fun(nat,A),power_power(A),B)),zero_zero(A)),sequentially)) # label(fact_4487_LIMSEQ__power__zero) # label(axiom). [clausify(1823)]. 110.82/110.72 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(complex,real,norm_norm(complex),A)),one_one(real))) | hBOOL(hAPP(filter(nat),bool,hAPP(complex,fun(filter(nat),bool),hAPP(fun(nat,complex),fun(complex,fun(filter(nat),bool)),tendsto(nat,complex),hAPP(complex,fun(nat,complex),power_power(complex),A)),zero_zero(complex)),sequentially)). [resolve(6033,a,6027,a)]. 110.82/110.72 6034 -zero(A) | -metric_space(A) | -real_n2089651433ebra_1(B) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),hAPP(A,fun(B,A),combk(A,B),C)),zero_zero(A)),hAPP(B,filter(B),at(B),D))) # label(fact_4562_LIM__not__zero) # label(axiom). [clausify(2264)]. 111.64/111.51 Derived: -zero(A) | -metric_space(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(A,fun(complex,A),combk(A,complex),B)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),C))). [resolve(6034,c,6027,a)]. 111.64/111.51 6035 -topological_space(A) | -real_n2089651433ebra_1(B) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),C),D)) | hBOOL(hAPP(A,bool,hAPP(fun(A,B),fun(A,bool),isCont(A,B),hAPP(fun(A,real),fun(A,B),hAPP(fun(real,B),fun(fun(A,real),fun(A,B)),combb(real,B,A),of_real(B)),C)),D)) # label(fact_4904_isCont__of__real) # label(axiom). [clausify(2335)]. 111.64/111.51 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,complex),fun(A,bool),isCont(A,complex),hAPP(fun(A,real),fun(A,complex),hAPP(fun(real,complex),fun(fun(A,real),fun(A,complex)),combb(real,complex,A),of_real(complex)),B)),C)). [resolve(6035,b,6027,a)]. 111.64/111.51 6036 -real_n2089651433ebra_1(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,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_4748_summable__exp__generic) # label(axiom). [clausify(2525)]. 111.64/111.51 Derived: -banach(complex) | hBOOL(hAPP(fun(nat,complex),bool,summable(complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,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(6036,a,6027,a)]. 111.64/111.51 6037 -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_4025_complete__algebra__summable__geometric) # label(axiom). [clausify(2861)]. 111.64/111.51 6038 -real_n2089651433ebra_1(A) | hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),B)) = hAPP(A,real,norm_norm(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3575_norm__of__int) # label(axiom). [clausify(3001)]. 111.64/111.51 Derived: hAPP(real,real,abs_abs(real),hAPP(int,real,ring_1_of_int(real),A)) = hAPP(complex,real,norm_norm(complex),hAPP(int,complex,ring_1_of_int(complex),A)). [resolve(6038,a,6027,a)]. 111.64/111.51 6039 -real_n2089651433ebra_1(A) | hAPP(real,real,abs_abs(real),B) = hAPP(A,real,norm_norm(A),hAPP(real,A,of_real(A),B)) # label(fact_2797_norm__of__real) # label(axiom). [clausify(3289)]. 111.64/111.51 Derived: hAPP(real,real,abs_abs(real),A) = hAPP(complex,real,norm_norm(complex),hAPP(real,complex,of_real(complex),A)). [resolve(6039,a,6027,a)]. 111.64/111.51 6040 -real_n2089651433ebra_1(A) | one_one(real) = hAPP(A,real,norm_norm(A),one_one(A)) # label(fact_1781_norm__one) # label(axiom). [clausify(3359)]. 111.64/111.51 Derived: one_one(real) = hAPP(complex,real,norm_norm(complex),one_one(complex)). [resolve(6040,a,6027,a)]. 111.64/111.51 6041 real_n2089651433ebra_1(real) # label(arity_RealDef_Oreal___RealVector_Oreal__normed__algebra__1) # label(axiom). [assumption]. 111.64/111.51 Derived: -metric_space(A) | ti(A,B) = ti(A,C) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(A,fun(real,A),combk(A,real),C)),B),hAPP(real,filter(real),at(real),D))). [resolve(6041,a,6026,b)]. 111.73/111.59 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(real,real,norm_norm(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(6041,a,6029,a)]. 111.73/111.59 Derived: hAPP(real,real,of_real(real),hAPP(real,real,sgn_sgn(real),A)) = hAPP(real,real,sgn_sgn(real),hAPP(real,real,of_real(real),A)). [resolve(6041,a,6030,a)]. 111.73/111.59 Derived: one_one(real) = hAPP(real,real,sgn_sgn(real),one_one(real)). [resolve(6041,a,6031,a)]. 111.73/111.59 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,norm_norm(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,norm_norm(real),A)),B))). [resolve(6041,a,6032,a)]. 111.73/111.59 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,norm_norm(real),A)),one_one(real))) | hBOOL(hAPP(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),A)),zero_zero(real)),sequentially)). [resolve(6041,a,6033,a)]. 111.73/111.59 Derived: -zero(A) | -metric_space(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(A,fun(real,A),combk(A,real),B)),zero_zero(A)),hAPP(real,filter(real),at(real),C))). [resolve(6041,a,6034,c)]. 111.73/111.59 Derived: -topological_space(A) | -hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),B),C)) | hBOOL(hAPP(A,bool,hAPP(fun(A,real),fun(A,bool),isCont(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),of_real(real)),B)),C)). [resolve(6041,a,6035,b)]. 111.73/111.59 Derived: -banach(real) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),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(6041,a,6036,a)]. 111.73/111.59 Derived: hAPP(real,real,abs_abs(real),A) = hAPP(real,real,norm_norm(real),hAPP(real,real,of_real(real),A)). [resolve(6041,a,6039,a)]. 111.73/111.59 Derived: one_one(real) = hAPP(real,real,norm_norm(real),one_one(real)). [resolve(6041,a,6040,a)]. 111.73/111.59 6042 -real_n2089651433ebra_1(A) | -metric_space(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),D),hAPP(A,filter(A),at(A),E))) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),C),F),hAPP(A,filter(A),at(A),E))) | ti(B,F) = ti(B,D) # label(fact_4546_LIM__unique) # label(axiom). [clausify(3629)]. 111.73/111.59 Derived: -metric_space(A) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),B),C),hAPP(complex,filter(complex),at(complex),D))) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),B),E),hAPP(complex,filter(complex),at(complex),D))) | ti(A,E) = ti(A,C). [resolve(6042,a,6027,a)]. 111.73/111.59 Derived: -metric_space(A) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),B),C),hAPP(real,filter(real),at(real),D))) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),B),E),hAPP(real,filter(real),at(real),D))) | ti(A,E) = ti(A,C). [resolve(6042,a,6041,a)]. 111.73/111.59 6043 -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_4749_summable__norm__exp) # label(axiom). [clausify(3692)]. 111.94/111.89 Derived: -banach(complex) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,complex),fun(nat,real),hAPP(fun(complex,real),fun(fun(nat,complex),fun(nat,real)),combb(complex,real,nat),norm_norm(complex)),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(6043,b,6027,a)]. 111.94/111.89 Derived: -banach(real) | hBOOL(hAPP(fun(nat,real),bool,summable(real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(real,real),fun(fun(nat,real),fun(nat,real)),combb(real,real,nat),norm_norm(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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(6043,b,6041,a)]. 111.94/111.89 6044 -real_n2089651433ebra_1(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,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),zero_zero(A)))) = hAPP(nat,A,B,zero_zero(nat)) # label(fact_3973_powser__zero) # label(axiom). [clausify(4080)]. 111.94/111.89 Derived: 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)),A)),hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)))) = hAPP(nat,complex,A,zero_zero(nat)). [resolve(6044,a,6027,a)]. 111.94/111.89 Derived: 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)),A)),hAPP(real,fun(nat,real),power_power(real),zero_zero(real)))) = hAPP(nat,real,A,zero_zero(nat)). [resolve(6044,a,6041,a)]. 111.94/111.89 6045 -real_n2089651433ebra_1(A) | -metric_space(B) | -hBOOL(hAPP(filter(A),bool,hAPP(B,fun(filter(A),bool),hAPP(fun(A,B),fun(B,fun(filter(A),bool)),tendsto(A,B),hAPP(B,fun(A,B),combk(B,A),C)),D),hAPP(A,filter(A),at(A),E))) | ti(B,D) = ti(B,C) # label(fact_4557_LIM__const__eq) # label(axiom). [clausify(4109)]. 115.25/115.14 6046 field(real) # label(arity_RealDef_Oreal___Fields_Ofield) # label(axiom). [assumption]. 115.25/115.14 6047 -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_2558_field__divide__inverse) # label(axiom). [clausify(95)]. 115.25/115.14 6048 -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_1733_divide__numeral__1) # label(axiom). [clausify(172)]. 115.25/115.14 6049 -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_4218_setsum__divide__distrib) # label(axiom). [clausify(731)]. 115.25/115.14 6050 -field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | 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_1722_add__frac__eq) # label(axiom). [clausify(751)]. 115.25/115.14 6051 -field(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,inverse_inverse(A),B)),B) # label(fact_2580_field__inverse) # label(axiom). [clausify(1256)]. 115.25/115.14 6052 -field(A) | -number_ring(A) | hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls)) = hAPP(A,A,inverse_inverse(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,pls))) # label(fact_2587_inverse__numeral__1) # label(axiom). [clausify(1283)]. 115.25/115.14 6053 -field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | 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_1727_diff__frac__eq) # label(axiom). [clausify(1321)]. 115.25/115.14 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(6046,a,6048,a)]. 115.25/115.14 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = 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,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(6046,a,6050,a)]. 115.25/115.14 Derived: -number_ring(real) | hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls)) = hAPP(real,real,inverse_inverse(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,pls))). [resolve(6046,a,6052,a)]. 115.25/115.14 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(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,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(6046,a,6053,a)]. 115.64/115.50 6054 -field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,inverse_inverse(A),B)),hAPP(A,A,inverse_inverse(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,inverse_inverse(A),B))),hAPP(A,A,inverse_inverse(A),C)) # label(fact_2578_inverse__add) # label(axiom). [clausify(1751)]. 115.64/115.50 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(real) | 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)) = 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)). [resolve(6054,a,6046,a)]. 115.64/115.50 6055 -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_2561_field__class_Onormalizing__field__rules_I2_J) # label(axiom). [clausify(1806)]. 115.64/115.50 6056 -field(A) | ti(A,B) = zero_zero(A) | 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_1729_diff__divide__eq__iff) # label(axiom). [clausify(2197)]. 115.64/115.50 Derived: ti(real,A) = zero_zero(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,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(6056,a,6046,a)]. 115.64/115.50 6057 -field(A) | ti(A,B) = zero_zero(A) | 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) = 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)) # label(fact_1697_nonzero__power__divide) # label(axiom). [clausify(2258)]. 115.64/115.50 Derived: ti(real,A) = zero_zero(real) | 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) = 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)). [resolve(6057,a,6046,a)]. 115.64/115.50 6058 -field(A) | ti(A,B) = zero_zero(A) | 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_1719_add__divide__eq__iff) # label(axiom). [clausify(2283)]. 115.64/115.50 Derived: ti(real,A) = 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,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(6058,a,6046,a)]. 115.64/115.50 6059 -field(A) | ti(A,B) = zero_zero(A) | 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_1721_divide__add__eq__iff) # label(axiom). [clausify(2430)]. 115.64/115.50 Derived: ti(real,A) = 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),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(6059,a,6046,a)]. 115.94/115.86 6060 -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_4179_geometric__sum) # label(axiom). [clausify(2843)]. 115.94/115.86 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(6060,a,6046,a)]. 115.94/115.86 6061 -field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(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),E),B) | 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) # label(fact_1691_frac__eq__eq) # label(axiom). [clausify(2898)]. 115.94/115.86 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(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),D),A) | 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). [resolve(6061,a,6046,a)]. 115.94/115.86 6062 -field(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(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),E),B) | 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) # label(fact_1691_frac__eq__eq) # label(axiom). [clausify(2898)]. 115.94/115.86 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = zero_zero(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),D),A) | 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). [resolve(6062,a,6046,a)]. 115.94/115.86 6063 -field(A) | ti(A,B) = zero_zero(A) | 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_1728_divide__diff__eq__iff) # label(axiom). [clausify(3076)]. 115.94/115.86 Derived: ti(real,A) = zero_zero(real) | 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(6063,a,6046,a)]. 115.94/115.86 6064 field(complex) # label(arity_Complex_Ocomplex___Fields_Ofield) # label(axiom). [assumption]. 115.94/115.86 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(6064,a,6048,a)]. 115.94/115.86 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | 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(6064,a,6050,a)]. 115.94/115.87 Derived: -number_ring(complex) | hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls)) = hAPP(complex,complex,inverse_inverse(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,pls))). [resolve(6064,a,6052,a)]. 115.94/115.87 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | 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(6064,a,6053,a)]. 115.94/115.87 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | 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)) = 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)). [resolve(6064,a,6054,a)]. 115.94/115.87 Derived: ti(complex,A) = zero_zero(complex) | 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(6064,a,6056,a)]. 115.94/115.87 Derived: ti(complex,A) = zero_zero(complex) | 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) = 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)). [resolve(6064,a,6057,a)]. 115.94/115.87 Derived: ti(complex,A) = zero_zero(complex) | 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(6064,a,6058,a)]. 115.94/115.87 Derived: ti(complex,A) = zero_zero(complex) | 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(6064,a,6059,a)]. 115.94/115.87 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(6064,a,6060,a)]. 116.94/116.86 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | 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) | 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). [resolve(6064,a,6061,a)]. 116.94/116.86 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = zero_zero(complex) | 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) | 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). [resolve(6064,a,6062,a)]. 116.94/116.86 Derived: ti(complex,A) = zero_zero(complex) | 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(6064,a,6063,a)]. 116.94/116.86 6065 -field(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | 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)) = 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)) # label(fact_1751_power__diff) # label(axiom). [clausify(3401)]. 116.94/116.86 Derived: ti(real,A) = zero_zero(real) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | 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)) = 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)). [resolve(6065,a,6046,a)]. 116.94/116.86 Derived: ti(complex,A) = zero_zero(complex) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | 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)) = 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)). [resolve(6065,a,6064,a)]. 116.94/116.86 6066 -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_1734_divide__Numeral1) # label(axiom). [clausify(4276)]. 116.94/116.86 6067 field(rat) # label(arity_Rat_Orat___Fields_Ofield) # label(axiom). [assumption]. 116.94/116.86 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(6067,a,6048,a)]. 116.94/116.86 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(6067,a,6049,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | 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(6067,a,6050,a)]. 116.94/116.87 Derived: -number_ring(rat) | hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls)) = hAPP(rat,rat,inverse_inverse(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,pls))). [resolve(6067,a,6052,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | 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(6067,a,6053,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(rat) | 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)) = 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)). [resolve(6067,a,6054,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | 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(6067,a,6056,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | 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) = 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)). [resolve(6067,a,6057,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | 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(6067,a,6058,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | 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(6067,a,6059,a)]. 116.94/116.87 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(6067,a,6060,a)]. 116.94/116.87 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(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),D),A) | 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). [resolve(6067,a,6061,a)]. 117.33/117.22 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = zero_zero(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),D),A) | 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). [resolve(6067,a,6062,a)]. 117.33/117.22 Derived: ti(rat,A) = zero_zero(rat) | 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(6067,a,6063,a)]. 117.33/117.22 Derived: ti(rat,A) = zero_zero(rat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | 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)) = 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)). [resolve(6067,a,6065,a)]. 117.33/117.22 6068 -field(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),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)))))) = 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)))))) # label(fact_4238_lemma__termdiff2) # label(axiom). [clausify(4832)]. 117.33/117.22 Derived: ti(real,A) = 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(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)))))) = 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)))))). [resolve(6068,a,6046,a)]. 117.33/117.22 Derived: ti(complex,A) = zero_zero(complex) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A)),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)))))) = 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)))))). [resolve(6068,a,6064,a)]. 119.95/119.90 Derived: ti(rat,A) = zero_zero(rat) | 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)))))) = 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)))))). [resolve(6068,a,6067,a)]. 119.95/119.90 6069 ordere142940540dd_abs(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 119.95/119.90 6070 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,abs_abs(A),B))) # label(fact_1843_abs__ge__self) # label(axiom). [clausify(96)]. 119.95/119.90 6071 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_2095_abs__of__nonpos) # label(axiom). [clausify(659)]. 119.95/119.90 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,abs_abs(int),A))). [resolve(6069,a,6070,a)]. 119.95/119.90 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,abs_abs(int),A). [resolve(6069,a,6071,a)]. 119.95/119.90 6072 -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_1868_abs__triangle__ineq3) # label(axiom). [clausify(924)]. 119.95/119.90 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(6072,a,6069,a)]. 119.95/119.90 6073 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)) # label(fact_1858_abs__minus__commute) # label(axiom). [clausify(996)]. 120.34/120.24 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(6073,a,6069,a)]. 120.34/120.24 6074 ordere142940540dd_abs(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 120.34/120.24 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,abs_abs(rat),A))). [resolve(6074,a,6070,a)]. 120.34/120.24 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6074,a,6071,a)]. 120.34/120.24 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(6074,a,6072,a)]. 120.34/120.24 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(6074,a,6073,a)]. 120.34/120.24 6075 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)))) # label(fact_1869_abs__triangle__ineq2) # label(axiom). [clausify(1557)]. 120.34/120.24 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(6075,a,6069,a)]. 120.34/120.24 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(6075,a,6074,a)]. 120.34/120.24 6076 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,abs_abs(A),B))) # label(fact_2079_abs__ge__minus__self) # label(axiom). [clausify(1568)]. 120.34/120.24 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(6076,a,6069,a)]. 120.34/120.24 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(6076,a,6074,a)]. 120.34/120.24 6077 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,uminus_uminus(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_2010_abs__minus__cancel) # label(axiom). [clausify(1709)]. 120.34/120.24 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,uminus_uminus(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(6077,a,6069,a)]. 120.34/120.24 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,uminus_uminus(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6077,a,6074,a)]. 120.34/120.24 6078 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),hAPP(A,A,abs_abs(A),B))),zero_zero(A))) # label(fact_2096_abs__minus__le__zero) # label(axiom). [clausify(2063)]. 120.34/120.24 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(6078,a,6069,a)]. 120.34/120.24 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(6078,a,6074,a)]. 120.34/120.24 6079 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_1842_abs__le__D1) # label(axiom). [clausify(2087)]. 120.34/120.24 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(6079,a,6069,a)]. 120.55/120.42 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(6079,a,6074,a)]. 120.55/120.42 6080 -ordere142940540dd_abs(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D) = hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D)) # label(fact_4212_abs__setsum__abs) # label(axiom). [clausify(2403)]. 120.55/120.42 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),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(6080,a,6069,a)]. 120.55/120.42 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C) = hAPP(rat,rat,abs_abs(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),abs_abs(rat)),B)),C)). [resolve(6080,a,6074,a)]. 120.55/120.42 6081 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_1867_abs__triangle__ineq) # label(axiom). [clausify(2470)]. 120.55/120.42 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(6081,a,6069,a)]. 120.55/120.42 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(6081,a,6074,a)]. 120.55/120.42 6082 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) | ti(A,B) = zero_zero(A) # label(fact_1861_abs__le__zero__iff) # label(axiom). [clausify(2503)]. 120.55/120.42 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))) | ti(int,A) = zero_zero(int). [resolve(6082,a,6069,a)]. 120.55/120.42 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))) | ti(rat,A) = zero_zero(rat). [resolve(6082,a,6074,a)]. 120.55/120.42 6083 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) | ti(A,B) != zero_zero(A) # label(fact_1861_abs__le__zero__iff) # label(axiom). [clausify(2503)]. 120.55/120.42 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))) | ti(int,A) != zero_zero(int). [resolve(6083,a,6069,a)]. 120.55/120.42 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))) | ti(rat,A) != zero_zero(rat). [resolve(6083,a,6074,a)]. 120.55/120.42 6084 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) # label(fact_1862_abs__ge__zero) # label(axiom). [clausify(2515)]. 120.55/120.42 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(6084,a,6069,a)]. 120.55/120.42 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(6084,a,6074,a)]. 120.95/120.83 6085 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = hAPP(A,A,abs_abs(A),B) # label(fact_1860_abs__of__nonneg) # label(axiom). [clausify(2762)]. 120.95/120.83 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(6085,a,6069,a)]. 120.95/120.83 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(6085,a,6074,a)]. 120.95/120.83 6086 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B)))) # label(fact_1870_abs__triangle__ineq2__sym) # label(axiom). [clausify(2801)]. 120.95/120.83 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(6086,a,6069,a)]. 120.95/120.83 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(6086,a,6074,a)]. 120.95/120.83 6087 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),zero_zero(A)) = zero_zero(A) # label(fact_1851_abs__zero) # label(axiom). [clausify(2916)]. 120.95/120.83 Derived: hAPP(int,int,abs_abs(int),zero_zero(int)) = zero_zero(int). [resolve(6087,a,6069,a)]. 120.95/120.83 Derived: hAPP(rat,rat,abs_abs(rat),zero_zero(rat)) = zero_zero(rat). [resolve(6087,a,6074,a)]. 120.95/120.83 6088 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D))) # label(fact_4166_setsum__abs__ge__zero) # label(axiom). [clausify(2931)]. 120.95/120.83 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(6088,a,6069,a)]. 120.95/120.83 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(6088,a,6074,a)]. 120.95/120.83 6089 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,abs_abs(A),B)),zero_zero(A))) # label(fact_1863_abs__not__less__zero) # label(axiom). [clausify(2969)]. 120.95/120.83 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,abs_abs(int),A)),zero_zero(int))). [resolve(6089,a,6069,a)]. 120.95/120.83 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,abs_abs(rat),A)),zero_zero(rat))). [resolve(6089,a,6074,a)]. 120.95/120.83 6090 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | ti(A,B) = hAPP(A,A,abs_abs(A),B) # label(fact_1865_abs__of__pos) # label(axiom). [clausify(3300)]. 120.95/120.83 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(6090,a,6069,a)]. 120.95/120.83 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(6090,a,6074,a)]. 120.95/120.83 6091 -ordere142940540dd_abs(A) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) # label(fact_1864_zero__less__abs__iff) # label(axiom). [clausify(3304)]. 120.95/120.83 Derived: ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))). [resolve(6091,a,6069,a)]. 120.95/120.87 Derived: ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))). [resolve(6091,a,6074,a)]. 120.95/120.87 6092 -ordere142940540dd_abs(A) | ti(A,B) != zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,abs_abs(A),B))) # label(fact_1864_zero__less__abs__iff) # label(axiom). [clausify(3304)]. 120.95/120.87 Derived: ti(int,A) != zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,abs_abs(int),A))). [resolve(6092,a,6069,a)]. 120.95/120.87 Derived: ti(rat,A) != zero_zero(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,abs_abs(rat),A))). [resolve(6092,a,6074,a)]. 120.95/120.87 6093 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),abs_abs(A)),C)),D))) # label(fact_4165_setsum__abs) # label(axiom). [clausify(3311)]. 120.95/120.87 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(6093,a,6069,a)]. 120.95/120.87 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(6093,a,6074,a)]. 120.95/120.87 6094 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)))) # label(fact_1882_abs__triangle__ineq4) # label(axiom). [clausify(3321)]. 120.95/120.87 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(6094,a,6069,a)]. 120.95/120.87 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(6094,a,6074,a)]. 120.95/120.87 6095 ordere142940540dd_abs(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add__abs) # label(axiom). [assumption]. 120.95/120.87 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,abs_abs(real),A))). [resolve(6095,a,6070,a)]. 120.95/120.87 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,abs_abs(real),A). [resolve(6095,a,6071,a)]. 120.95/120.87 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(6095,a,6072,a)]. 120.95/120.87 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(6095,a,6073,a)]. 120.95/120.87 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(6095,a,6075,a)]. 120.95/120.89 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(6095,a,6076,a)]. 120.95/120.89 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,uminus_uminus(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(6095,a,6077,a)]. 120.95/120.89 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(6095,a,6078,a)]. 120.95/120.89 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(6095,a,6079,a)]. 120.95/120.89 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(6095,a,6080,a)]. 120.95/120.89 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(6095,a,6081,a)]. 120.95/120.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))) | ti(real,A) = zero_zero(real). [resolve(6095,a,6082,a)]. 120.95/120.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))) | ti(real,A) != zero_zero(real). [resolve(6095,a,6083,a)]. 120.95/120.89 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(6095,a,6084,a)]. 120.95/120.89 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(6095,a,6085,a)]. 120.95/120.89 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,abs_abs(real),A)),hAPP(real,real,abs_abs(real),B))),hAPP(real,real,abs_abs(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A)))). [resolve(6095,a,6086,a)]. 120.95/120.89 Derived: hAPP(real,real,abs_abs(real),zero_zero(real)) = zero_zero(real). [resolve(6095,a,6087,a)]. 120.95/120.89 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(6095,a,6088,a)]. 120.95/120.89 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,abs_abs(real),A)),zero_zero(real))). [resolve(6095,a,6089,a)]. 120.95/120.89 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(6095,a,6090,a)]. 120.95/120.89 Derived: ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))). [resolve(6095,a,6091,a)]. 120.95/120.89 Derived: ti(real,A) != zero_zero(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,abs_abs(real),A))). [resolve(6095,a,6092,a)]. 120.95/120.89 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(6095,a,6093,a)]. 121.24/121.17 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(6095,a,6094,a)]. 121.24/121.17 6096 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2082_abs__le__D2) # label(axiom). [clausify(3398)]. 121.24/121.17 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(6096,a,6069,a)]. 121.24/121.17 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(6096,a,6074,a)]. 121.24/121.17 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(6096,a,6095,a)]. 121.24/121.17 6097 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_2080_abs__le__iff) # label(axiom). [clausify(3423)]. 121.24/121.17 6098 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2080_abs__le__iff) # label(axiom). [clausify(3423)]. 121.24/121.17 6099 -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)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) # label(fact_2080_abs__le__iff) # label(axiom). [clausify(3423)]. 121.24/121.17 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)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),B)). [resolve(6099,a,6069,a)]. 121.24/121.17 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)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B)). [resolve(6099,a,6074,a)]. 121.24/121.17 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)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)). [resolve(6099,a,6095,a)]. 121.24/121.17 6100 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_1850_abs__eq__0) # label(axiom). [clausify(3592)]. 121.24/121.17 Derived: hAPP(int,int,abs_abs(int),A) != zero_zero(int) | ti(int,A) = zero_zero(int). [resolve(6100,a,6069,a)]. 121.24/121.17 Derived: hAPP(rat,rat,abs_abs(rat),A) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(6100,a,6074,a)]. 121.24/121.17 Derived: hAPP(real,real,abs_abs(real),A) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(6100,a,6095,a)]. 121.24/121.17 6101 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_1850_abs__eq__0) # label(axiom). [clausify(3592)]. 121.24/121.17 Derived: hAPP(int,int,abs_abs(int),A) = zero_zero(int) | ti(int,A) != zero_zero(int). [resolve(6101,a,6069,a)]. 122.23/122.14 Derived: hAPP(rat,rat,abs_abs(rat),A) = zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(6101,a,6074,a)]. 122.23/122.14 Derived: hAPP(real,real,abs_abs(real),A) = zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(6101,a,6095,a)]. 122.23/122.14 6102 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),B)),hAPP(A,A,abs_abs(A),C)) # label(fact_1856_abs__add__abs) # label(axiom). [clausify(3668)]. 122.23/122.14 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(6102,a,6069,a)]. 122.23/122.14 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(6102,a,6074,a)]. 122.23/122.14 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(6102,a,6095,a)]. 122.23/122.14 6103 -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_2081_abs__leI) # label(axiom). [clausify(3752)]. 122.23/122.14 6104 -ordere142940540dd_abs(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_2099_abs__of__neg) # label(axiom). [clausify(3772)]. 122.23/122.14 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,abs_abs(int),A). [resolve(6104,a,6069,a)]. 122.23/122.14 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6104,a,6074,a)]. 122.23/122.14 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,abs_abs(real),A). [resolve(6104,a,6095,a)]. 122.23/122.14 6105 -ordere142940540dd_abs(A) | hAPP(A,A,abs_abs(A),hAPP(A,A,abs_abs(A),B)) = hAPP(A,A,abs_abs(A),B) # label(fact_1852_abs__idempotent) # label(axiom). [clausify(4161)]. 122.23/122.14 Derived: hAPP(int,int,abs_abs(int),hAPP(int,int,abs_abs(int),A)) = hAPP(int,int,abs_abs(int),A). [resolve(6105,a,6069,a)]. 122.23/122.14 Derived: hAPP(rat,rat,abs_abs(rat),hAPP(rat,rat,abs_abs(rat),A)) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6105,a,6074,a)]. 122.23/122.14 Derived: hAPP(real,real,abs_abs(real),hAPP(real,real,abs_abs(real),A)) = hAPP(real,real,abs_abs(real),A). [resolve(6105,a,6095,a)]. 122.23/122.14 6106 -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(4314)]. 122.23/122.14 Derived: abs_abs(int) = ti(fun(int,int),abs_abs(int)). [resolve(6106,a,6069,a)]. 122.23/122.14 Derived: abs_abs(rat) = ti(fun(rat,rat),abs_abs(rat)). [resolve(6106,a,6074,a)]. 122.23/122.14 Derived: abs_abs(real) = ti(fun(real,real),abs_abs(real)). [resolve(6106,a,6095,a)]. 122.23/122.14 6107 -ordere142940540dd_abs(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)))),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D))),hAPP(A,A,abs_abs(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))))) # label(fact_1881_abs__diff__triangle__ineq) # label(axiom). [clausify(4895)]. 122.23/122.14 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(6107,a,6069,a)]. 125.03/124.94 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(6107,a,6074,a)]. 125.03/124.94 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(6107,a,6095,a)]. 125.03/124.94 6108 ordere236663937imp_le(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__ab__semigroup__add__im) # label(axiom). [assumption]. 125.03/124.94 6109 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_780_add__le__imp__le__right) # label(axiom). [clausify(109)]. 125.03/124.94 6110 -ordere236663937imp_le(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)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_791_add__less__cancel__left) # label(axiom). [clausify(224)]. 125.03/124.94 6111 -ordere236663937imp_le(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)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_791_add__less__cancel__left) # label(axiom). [clausify(224)]. 125.03/124.94 6112 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,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_785_add__le__cancel__right) # label(axiom). [clausify(302)]. 125.03/124.94 6113 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,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_785_add__le__cancel__right) # label(axiom). [clausify(302)]. 125.03/124.94 6114 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_784_add__le__cancel__left) # label(axiom). [clausify(673)]. 125.03/124.94 6115 -ordere236663937imp_le(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_784_add__le__cancel__left) # label(axiom). [clausify(673)]. 125.03/124.94 6116 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_4959_max__add__distrib__left) # label(axiom). [clausify(964)]. 125.03/124.96 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),C)). [resolve(6108,a,6109,a)]. 125.03/124.96 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)). [resolve(6108,a,6110,a)]. 125.03/124.96 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)). [resolve(6108,a,6111,a)]. 125.03/124.96 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(6108,a,6112,a)]. 125.03/124.96 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(6108,a,6114,a)]. 125.03/124.96 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)). [resolve(6108,a,6115,a)]. 125.03/124.96 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B)) = 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),ord_max(quickcheck_code_int),A),C)),B). [resolve(6108,a,6116,a)]. 125.23/125.13 6117 ordere236663937imp_le(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 125.23/125.13 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),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),C)). [resolve(6117,a,6109,a)]. 125.23/125.13 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6117,a,6110,a)]. 125.23/125.13 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),B),C)). [resolve(6117,a,6111,a)]. 125.23/125.13 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(6117,a,6112,a)]. 125.23/125.13 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),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6117,a,6114,a)]. 125.23/125.13 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),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),C)). [resolve(6117,a,6115,a)]. 125.23/125.13 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(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),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B). [resolve(6117,a,6116,a)]. 125.23/125.13 6118 -ordere236663937imp_le(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)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) # label(fact_786_add__less__imp__less__left) # label(axiom). [clausify(1439)]. 125.23/125.13 6119 -ordere236663937imp_le(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)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_787_add__less__imp__less__right) # label(axiom). [clausify(1476)]. 125.23/125.13 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(6119,a,6108,a)]. 125.23/125.13 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6119,a,6117,a)]. 125.23/125.13 6120 ordere236663937imp_le(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 126.05/125.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),C)). [resolve(6120,a,6109,a)]. 126.05/125.98 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(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),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_max(nat),A),C)),B). [resolve(6120,a,6116,a)]. 126.05/125.98 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),C)). [resolve(6120,a,6119,a)]. 126.05/125.98 6121 ordere236663937imp_le(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 126.05/125.98 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),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),C)). [resolve(6121,a,6109,a)]. 126.05/125.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(6121,a,6110,a)]. 126.05/125.98 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)). [resolve(6121,a,6111,a)]. 126.05/125.98 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(6121,a,6112,a)]. 126.05/125.98 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),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)). [resolve(6121,a,6114,a)]. 126.05/125.98 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(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),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(6121,a,6116,a)]. 126.05/125.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(6121,a,6119,a)]. 126.05/125.98 6122 ordere236663937imp_le(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__ab__semigroup__add__imp__l) # label(axiom). [assumption]. 126.05/125.98 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),C)). [resolve(6122,a,6109,a)]. 126.05/125.98 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)). [resolve(6122,a,6110,a)]. 126.55/126.43 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)). [resolve(6122,a,6111,a)]. 126.55/126.43 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(6122,a,6112,a)]. 126.55/126.43 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(6122,a,6114,a)]. 126.55/126.43 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)). [resolve(6122,a,6115,a)]. 126.55/126.43 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B)) = 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),ord_max(code_code_numeral),A),C)),B). [resolve(6122,a,6116,a)]. 126.55/126.43 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(6122,a,6119,a)]. 126.55/126.43 6123 ordere236663937imp_le(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add__imp__le) # label(axiom). [assumption]. 126.55/126.43 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),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),C)). [resolve(6123,a,6109,a)]. 126.55/126.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(6123,a,6110,a)]. 126.55/126.49 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),C)). [resolve(6123,a,6111,a)]. 126.55/126.49 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(6123,a,6112,a)]. 126.55/126.49 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),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)). [resolve(6123,a,6114,a)]. 126.55/126.49 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(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),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B). [resolve(6123,a,6116,a)]. 126.55/126.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6123,a,6119,a)]. 126.55/126.49 6124 -ordere236663937imp_le(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)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_792_add__less__cancel__right) # label(axiom). [clausify(3654)]. 126.55/126.49 6125 -ordere236663937imp_le(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)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_792_add__less__cancel__right) # label(axiom). [clausify(3654)]. 126.55/126.49 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),C)). [resolve(6125,a,6108,a)]. 126.55/126.49 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),C)). [resolve(6125,a,6117,a)]. 126.55/126.49 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),C)). [resolve(6125,a,6121,a)]. 126.55/126.49 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),C)). [resolve(6125,a,6122,a)]. 127.04/126.88 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),C)). [resolve(6125,a,6123,a)]. 127.04/126.88 6126 -ordere236663937imp_le(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_4805_min__add__distrib__left) # label(axiom). [clausify(3662)]. 127.04/126.88 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),plus_plus(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),B)) = 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),ord_min(quickcheck_code_int),A),C)),B). [resolve(6126,a,6108,a)]. 127.04/126.88 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(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),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),C)),B). [resolve(6126,a,6117,a)]. 127.04/126.88 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(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),B)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),ord_min(nat),A),C)),B). [resolve(6126,a,6120,a)]. 127.04/126.88 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_min(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),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),C)),B). [resolve(6126,a,6121,a)]. 127.04/126.88 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),plus_plus(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),B)) = 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),ord_min(code_code_numeral),A),C)),B). [resolve(6126,a,6122,a)]. 127.04/126.88 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_min(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),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),C)),B). [resolve(6126,a,6123,a)]. 127.04/126.88 6127 -ordere236663937imp_le(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) # label(fact_779_add__le__imp__le__left) # label(axiom). [clausify(4125)]. 127.04/126.88 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)). [resolve(6127,a,6120,a)]. 131.25/131.10 6128 ordered_ab_group_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 131.25/131.10 6129 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_gr676655987ssThan(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_3678_image__uminus__greaterThanLessThan) # label(axiom). [clausify(113)]. 131.25/131.10 6130 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2026_le__minus__iff) # label(axiom). [clausify(312)]. 131.25/131.10 6131 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2026_le__minus__iff) # label(axiom). [clausify(312)]. 131.25/131.10 6132 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2059_neg__0__le__iff__le) # label(axiom). [clausify(324)]. 131.25/131.10 6133 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) # label(fact_2059_neg__0__le__iff__le) # label(axiom). [clausify(324)]. 131.25/131.10 6134 -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(365)]. 131.25/131.10 6135 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),D)),C) # label(fact_4803_min__diff__distrib__left) # label(axiom). [clausify(594)]. 131.25/131.10 6136 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_825_le__iff__diff__le__0) # label(axiom). [clausify(758)]. 131.25/131.10 6137 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_825_le__iff__diff__le__0) # label(axiom). [clausify(758)]. 131.25/131.10 6138 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2061_neg__0__less__iff__less) # label(axiom). [clausify(943)]. 131.25/131.10 6139 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2061_neg__0__less__iff__less) # label(axiom). [clausify(943)]. 131.25/131.10 6140 -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),f254(B,A,D,E,F,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),F),C) != E | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,F,D)),E)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom). [clausify(1242)]. 131.25/131.10 6141 -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,f254(B,A,E,F,D,C)))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) != F | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,D,E)),F)) # label(fact_4299_setsum__nonneg__leq__bound) # label(axiom). [clausify(1242)]. 131.25/131.10 6142 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2027_minus__le__iff) # label(axiom). [clausify(1375)]. 131.25/131.10 6143 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2027_minus__le__iff) # label(axiom). [clausify(1375)]. 131.25/131.10 6144 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2014_less__minus__iff) # label(axiom). [clausify(1816)]. 131.25/131.10 6145 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2014_less__minus__iff) # label(axiom). [clausify(1816)]. 131.25/131.10 6146 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2029_le__imp__neg__le) # label(axiom). [clausify(1847)]. 131.25/131.10 6147 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_798_diff__eq__diff__less) # label(axiom). [clausify(1902)]. 131.25/131.10 6148 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_798_diff__eq__diff__less) # label(axiom). [clausify(1902)]. 131.25/131.10 6149 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) # label(fact_2057_neg__le__0__iff__le) # label(axiom). [clausify(2033)]. 131.25/131.10 6150 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) # label(fact_2057_neg__le__0__iff__le) # label(axiom). [clausify(2033)]. 131.25/131.10 6151 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2028_neg__le__iff__le) # label(axiom). [clausify(2205)]. 131.25/131.10 6152 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),B)) # label(fact_2028_neg__le__iff__le) # label(axiom). [clausify(2205)]. 131.25/131.10 6153 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2015_minus__less__iff) # label(axiom). [clausify(2553)]. 131.25/131.10 6154 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2015_minus__less__iff) # label(axiom). [clausify(2553)]. 131.25/131.10 6155 -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),f489(B,A,D,E,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hAPP(B,A,E,D) = zero_zero(A) # label(fact_4300_setsum__nonneg__0) # label(axiom). [clausify(2651)]. 131.25/131.12 6156 -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,f489(B,A,E,D,C)))) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),C) != zero_zero(A) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),E),C)) | hAPP(B,A,D,E) = zero_zero(A) # label(fact_4300_setsum__nonneg__0) # label(axiom). [clausify(2651)]. 131.25/131.12 6157 -ordered_ab_group_add(A) | -hBOOL(hAPP(fun(nat,A),bool,monoseq(A),B)) | hBOOL(hAPP(fun(nat,A),bool,monoseq(A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(A,A),fun(fun(nat,A),fun(nat,A)),combb(A,A,nat),uminus_uminus(A)),B))) # label(fact_3921_monoseq__minus) # label(axiom). [clausify(3118)]. 131.25/131.12 6158 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_797_diff__eq__diff__less__eq) # label(axiom). [clausify(3143)]. 131.25/131.12 6159 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) # label(fact_797_diff__eq__diff__less__eq) # label(axiom). [clausify(3143)]. 131.25/131.12 6160 -ordered_ab_group_add(A) | hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,A),fun(fun(A,bool),fun(A,bool)),image(A,A),uminus_uminus(A)),hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),B),C)) = hAPP(A,fun(A,bool),hAPP(A,fun(A,fun(A,bool)),ord_atLeastAtMost(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_4526_image__uminus__atLeastAtMost) # label(axiom). [clausify(3145)]. 131.25/131.12 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(6128,a,6129,a)]. 131.25/131.12 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(6128,a,6130,a)]. 131.25/131.12 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(6128,a,6132,a)]. 131.25/131.12 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(6128,a,6133,a)]. 131.25/131.12 Derived: ord_gr676655987ssThan(int) = ti(fun(int,fun(int,fun(int,bool))),ord_gr676655987ssThan(int)). [resolve(6128,a,6134,a)]. 131.25/131.12 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(6128,a,6135,a)]. 131.25/131.12 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(6128,a,6136,a)]. 131.25/131.12 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(6128,a,6137,a)]. 131.25/131.15 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(6128,a,6138,a)]. 131.25/131.15 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(6128,a,6139,a)]. 131.25/131.15 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),f254(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(6128,a,6140,a)]. 131.25/131.15 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,f254(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(6128,a,6141,a)]. 131.25/131.15 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(6128,a,6142,a)]. 131.25/131.15 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(6128,a,6144,a)]. 131.25/131.15 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A))). [resolve(6128,a,6146,a)]. 131.25/131.15 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6128,a,6147,a)]. 131.25/131.15 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)). [resolve(6128,a,6148,a)]. 131.25/131.15 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(6128,a,6149,a)]. 131.25/131.15 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(6128,a,6150,a)]. 131.25/131.15 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(6128,a,6151,a)]. 131.25/131.15 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(6128,a,6153,a)]. 131.25/131.15 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),f489(A,int,C,D,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,int,D,C) = zero_zero(int). [resolve(6128,a,6155,a)]. 131.25/131.15 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,f489(A,int,D,C,B)))) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),B) != zero_zero(int) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,int,C,D) = zero_zero(int). [resolve(6128,a,6156,a)]. 132.05/131.95 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(6128,a,6157,a)]. 132.05/131.95 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)). [resolve(6128,a,6158,a)]. 132.05/131.95 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),D)). [resolve(6128,a,6159,a)]. 132.05/131.95 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(6128,a,6160,a)]. 132.05/131.95 6161 -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_2016_neg__less__iff__less) # label(axiom). [clausify(3421)]. 132.05/131.95 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(6161,a,6128,a)]. 132.05/131.95 6162 -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_2016_neg__less__iff__less) # label(axiom). [clausify(3421)]. 132.05/131.95 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(6162,a,6128,a)]. 132.05/131.95 6163 ordered_ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 132.05/131.95 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_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(6163,a,6129,a)]. 132.05/131.95 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(6163,a,6130,a)]. 132.05/131.95 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(6163,a,6132,a)]. 132.05/131.95 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(6163,a,6133,a)]. 132.05/131.95 Derived: ord_gr676655987ssThan(rat) = ti(fun(rat,fun(rat,fun(rat,bool))),ord_gr676655987ssThan(rat)). [resolve(6163,a,6134,a)]. 132.05/131.95 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(6163,a,6135,a)]. 132.05/131.97 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(6163,a,6136,a)]. 132.05/131.97 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(6163,a,6137,a)]. 132.05/131.97 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(6163,a,6138,a)]. 132.05/131.97 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(6163,a,6139,a)]. 132.05/131.97 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),f254(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(6163,a,6140,a)]. 132.05/131.97 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,f254(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(6163,a,6141,a)]. 132.05/131.97 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(6163,a,6142,a)]. 132.05/131.97 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(6163,a,6144,a)]. 132.05/131.97 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(6163,a,6146,a)]. 132.05/131.97 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6163,a,6147,a)]. 132.05/131.97 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),B)). [resolve(6163,a,6148,a)]. 132.05/131.97 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),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))). [resolve(6163,a,6149,a)]. 132.05/131.97 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),hAPP(rat,rat,uminus_uminus(rat),A)),zero_zero(rat))). [resolve(6163,a,6150,a)]. 132.05/131.97 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(6163,a,6151,a)]. 132.05/131.97 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(6163,a,6153,a)]. 132.14/132.04 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f489(A,rat,C,D,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,rat,D,C) = zero_zero(rat). [resolve(6163,a,6155,a)]. 132.14/132.04 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,f489(A,rat,D,C,B)))) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),B) != zero_zero(rat) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,rat,C,D) = zero_zero(rat). [resolve(6163,a,6156,a)]. 132.14/132.04 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(6163,a,6157,a)]. 132.14/132.04 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)). [resolve(6163,a,6158,a)]. 132.14/132.04 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),D)). [resolve(6163,a,6159,a)]. 132.14/132.04 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(6163,a,6160,a)]. 132.14/132.04 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(6163,a,6161,a)]. 132.14/132.04 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(6163,a,6162,a)]. 132.14/132.04 6164 -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,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_826_less__iff__diff__less__0) # label(axiom). [clausify(4331)]. 132.14/132.04 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),minus_minus(int),A),B)),zero_zero(int))). [resolve(6164,a,6128,a)]. 132.14/132.04 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),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(6164,a,6163,a)]. 132.14/132.04 6165 -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,hAPP(A,fun(A,A),minus_minus(A),B),C)),zero_zero(A))) # label(fact_826_less__iff__diff__less__0) # label(axiom). [clausify(4331)]. 132.14/132.04 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),minus_minus(int),A),B)),zero_zero(int))). [resolve(6165,a,6128,a)]. 132.14/132.04 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),minus_minus(rat),A),B)),zero_zero(rat))). [resolve(6165,a,6163,a)]. 132.25/132.10 6166 ordered_ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__group__add) # label(axiom). [assumption]. 132.25/132.10 Derived: hAPP(fun(real,bool),fun(real,bool),hAPP(fun(real,real),fun(fun(real,bool),fun(real,bool)),image(real,real),uminus_uminus(real)),hAPP(real,fun(real,bool),hAPP(real,fun(real,fun(real,bool)),ord_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(6166,a,6129,a)]. 132.25/132.10 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(6166,a,6130,a)]. 132.25/132.10 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(6166,a,6132,a)]. 132.25/132.10 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(6166,a,6133,a)]. 132.25/132.10 Derived: ord_gr676655987ssThan(real) = ti(fun(real,fun(real,fun(real,bool))),ord_gr676655987ssThan(real)). [resolve(6166,a,6134,a)]. 132.25/132.10 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(6166,a,6135,a)]. 132.25/132.10 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),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(6166,a,6136,a)]. 132.25/132.10 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),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(6166,a,6137,a)]. 132.25/132.10 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)),hAPP(real,real,uminus_uminus(real),A))). [resolve(6166,a,6138,a)]. 132.25/132.10 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)),hAPP(real,real,uminus_uminus(real),A))). [resolve(6166,a,6139,a)]. 132.25/132.10 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f254(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(6166,a,6140,a)]. 132.25/132.10 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,f254(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(6166,a,6141,a)]. 132.25/132.10 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),B)),A)). [resolve(6166,a,6142,a)]. 132.26/132.12 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(6166,a,6144,a)]. 132.26/132.12 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(6166,a,6146,a)]. 132.26/132.12 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6166,a,6147,a)]. 132.26/132.12 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)). [resolve(6166,a,6148,a)]. 132.26/132.12 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(6166,a,6149,a)]. 132.26/132.12 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(6166,a,6150,a)]. 132.26/132.12 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(6166,a,6151,a)]. 132.26/132.12 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(6166,a,6153,a)]. 132.26/132.12 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),f489(A,real,C,D,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | hAPP(A,real,D,C) = zero_zero(real). [resolve(6166,a,6155,a)]. 132.26/132.12 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,f489(A,real,D,C,B)))) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),B) != zero_zero(real) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),D),B)) | hAPP(A,real,C,D) = zero_zero(real). [resolve(6166,a,6156,a)]. 132.26/132.12 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(6166,a,6157,a)]. 132.26/132.12 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)). [resolve(6166,a,6158,a)]. 132.26/132.12 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)). [resolve(6166,a,6159,a)]. 132.26/132.12 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(6166,a,6160,a)]. 132.55/132.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))). [resolve(6166,a,6161,a)]. 132.55/132.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A))). [resolve(6166,a,6162,a)]. 132.55/132.47 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(6166,a,6164,a)]. 132.55/132.47 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),zero_zero(real))). [resolve(6166,a,6165,a)]. 132.55/132.47 6167 -ordered_ab_group_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2062_neg__less__0__iff__less) # label(axiom). [clausify(4659)]. 132.55/132.47 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(6167,a,6128,a)]. 132.55/132.47 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(6167,a,6163,a)]. 132.55/132.47 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(6167,a,6166,a)]. 132.55/132.47 6168 -ordered_ab_group_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_2062_neg__less__0__iff__less) # label(axiom). [clausify(4659)]. 132.55/132.47 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(6168,a,6128,a)]. 132.55/132.47 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(6168,a,6163,a)]. 132.55/132.47 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(6168,a,6166,a)]. 132.55/132.47 6169 -ordered_ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),D)),C) # label(fact_4958_max__diff__distrib__left) # label(axiom). [clausify(4830)]. 132.55/132.47 Derived: hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),C)),B). [resolve(6169,a,6128,a)]. 132.55/132.47 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),C)),B). [resolve(6169,a,6163,a)]. 135.36/135.22 Derived: hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),C)),B). [resolve(6169,a,6166,a)]. 135.36/135.22 6170 semiring_div(int) # label(arity_Int_Oint___Divides_Osemiring__div) # label(axiom). [assumption]. 135.36/135.22 6171 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) # label(fact_915_mod__div__equality) # label(axiom). [clausify(123)]. 135.36/135.22 6172 -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(301)]. 135.36/135.22 6173 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),D) # label(fact_1001_dvd__div__mult) # label(axiom). [clausify(308)]. 135.36/135.22 6174 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_930_mod__mult__eq) # label(axiom). [clausify(350)]. 135.36/135.22 6175 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_938_mod__add__eq) # label(axiom). [clausify(400)]. 135.36/135.22 6176 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B)) # label(fact_1005_div__add) # label(axiom). [clausify(421)]. 135.36/135.22 6177 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),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_1043_dvd__div__div__eq__mult) # label(axiom). [clausify(444)]. 135.36/135.22 6178 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),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_1043_dvd__div__div__eq__mult) # label(axiom). [clausify(444)]. 135.36/135.22 6179 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) # label(fact_941_mod__add__self1) # label(axiom). [clausify(460)]. 135.36/135.22 6180 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),zero_zero(A)) = zero_zero(A) # label(fact_964_div__by__0) # label(axiom). [clausify(585)]. 135.36/135.22 6181 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),E),D)) # label(fact_1000_div__mult__div__if__dvd) # label(axiom). [clausify(600)]. 135.36/135.22 6182 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),B) # label(fact_997_div__mult__self2__is__id) # label(axiom). [clausify(631)]. 135.36/135.25 6183 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_937_zmod__simps_I2_J) # label(axiom). [clausify(733)]. 135.36/135.25 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(6170,a,6171,a)]. 135.36/135.25 Derived: div_mod(int) = ti(fun(int,fun(int,int)),div_mod(int)). [resolve(6170,a,6172,a)]. 135.36/135.25 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(6170,a,6173,a)]. 135.36/135.25 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(6170,a,6174,a)]. 135.36/135.25 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(6170,a,6175,a)]. 135.36/135.25 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(6170,a,6176,a)]. 135.36/135.25 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),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(6170,a,6177,a)]. 135.36/135.25 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = zero_zero(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),D)) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),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(6170,a,6178,a)]. 135.36/135.25 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A). [resolve(6170,a,6179,a)]. 135.36/135.25 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(6170,a,6181,a)]. 135.36/135.25 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),A). [resolve(6170,a,6182,a)]. 135.46/135.35 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(6170,a,6183,a)]. 135.46/135.35 6184 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1039_div__mult__self1) # label(axiom). [clausify(880)]. 135.46/135.35 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(6184,a,6170,a)]. 135.46/135.35 6185 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),F)),C) # label(fact_935_mod__add__cong) # label(axiom). [clausify(884)]. 135.46/135.35 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(6185,a,6170,a)]. 135.46/135.35 6186 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | 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) = 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)) # label(fact_1006_div__power) # label(axiom). [clausify(1102)]. 135.46/135.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | 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) = 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)). [resolve(6186,a,6170,a)]. 135.46/135.35 6187 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_967_div__dvd__div) # label(axiom). [clausify(1208)]. 135.46/135.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(6187,a,6170,a)]. 135.46/135.35 6188 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),D),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_967_div__dvd__div) # label(axiom). [clausify(1208)]. 135.46/135.35 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),C),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(6188,a,6170,a)]. 135.76/135.69 6189 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1040_div__mult__self2) # label(axiom). [clausify(1310)]. 135.76/135.69 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)). [resolve(6189,a,6170,a)]. 135.76/135.69 6190 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D) # label(fact_916_div__mod__equality2) # label(axiom). [clausify(1376)]. 135.76/135.69 6191 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_906_mod__mod__trivial) # label(axiom). [clausify(1397)]. 135.76/135.69 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(6191,a,6170,a)]. 135.76/135.69 6192 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),B) # label(fact_1002_dvd__div__mult__self) # label(axiom). [clausify(1716)]. 135.76/135.69 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(6192,a,6170,a)]. 135.76/135.69 6193 -semiring_div(A) | ti(A,B) = zero_zero(A) | one_one(A) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),B) # label(fact_999_div__self) # label(axiom). [clausify(1805)]. 135.76/135.69 6194 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),zero_zero(A)),B) = zero_zero(A) # label(fact_965_div__0) # label(axiom). [clausify(1818)]. 135.76/135.69 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),zero_zero(int)),A) = zero_zero(int). [resolve(6194,a,6170,a)]. 135.76/135.69 6195 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_942_mod__add__self2) # label(axiom). [clausify(1848)]. 135.76/135.69 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(6195,a,6170,a)]. 135.76/135.69 6196 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) # label(fact_949_dvd__mod) # label(axiom). [clausify(1965)]. 135.76/135.69 6197 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) = zero_zero(A) # label(fact_973_mod__mult__self1__is__0) # label(axiom). [clausify(2021)]. 135.76/135.69 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A) = zero_zero(int). [resolve(6197,a,6170,a)]. 135.76/135.69 6198 -semiring_div(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = zero_zero(A) # label(fact_998_div__mult__mult1__if) # label(axiom). [clausify(2265)]. 135.76/135.69 Derived: ti(int,A) != zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = zero_zero(int). [resolve(6198,a,6170,a)]. 135.86/135.79 6199 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_998_div__mult__mult1__if) # label(axiom). [clausify(2265)]. 135.86/135.79 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(6199,a,6170,a)]. 135.86/135.79 6200 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1042_div__add__self2) # label(axiom). [clausify(2279)]. 135.86/135.79 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)). [resolve(6200,a,6170,a)]. 135.86/135.79 6201 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_929_mod__mult__left__eq) # label(axiom). [clausify(2343)]. 135.86/135.79 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(6201,a,6170,a)]. 135.86/135.79 6202 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) # label(fact_928_mod__mult__right__eq) # label(axiom). [clausify(2349)]. 135.86/135.79 6203 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) # label(fact_950_dvd__mod__imp__dvd) # label(axiom). [clausify(2421)]. 135.86/135.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)). [resolve(6203,a,6170,a)]. 135.86/135.79 6204 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) = zero_zero(A) # label(fact_979_dvd__imp__mod__0) # label(axiom). [clausify(2438)]. 135.86/135.79 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A) = zero_zero(int). [resolve(6204,a,6170,a)]. 135.86/135.79 6205 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_995_div__mult__mult2) # label(axiom). [clausify(2460)]. 135.86/135.79 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A)) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),C). [resolve(6205,a,6170,a)]. 135.86/135.79 6206 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) = zero_zero(A) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom). [clausify(2473)]. 135.86/135.79 6207 -semiring_div(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),B) != zero_zero(A) # label(fact_980_dvd__eq__mod__eq__0) # label(axiom). [clausify(2473)]. 135.95/135.81 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),B),A) != zero_zero(int). [resolve(6207,a,6170,a)]. 135.95/135.81 6208 semiring_div(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Divides_Osemiring__div) # label(axiom). [assumption]. 135.95/135.81 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(6208,a,6171,a)]. 135.95/135.81 Derived: div_mod(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_mod(quickcheck_code_int)). [resolve(6208,a,6172,a)]. 135.95/135.81 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(6208,a,6173,a)]. 135.95/135.81 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(6208,a,6174,a)]. 135.95/135.81 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(6208,a,6175,a)]. 135.95/135.81 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | 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(6208,a,6176,a)]. 135.95/135.82 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),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(6208,a,6177,a)]. 135.95/135.82 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),D)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),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(6208,a,6178,a)]. 135.95/135.82 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),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(6208,a,6179,a)]. 135.95/135.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(6208,a,6180,a)]. 135.95/135.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),C),D)) | 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(6208,a,6181,a)]. 135.95/135.82 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),A). [resolve(6208,a,6182,a)]. 135.95/135.82 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),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(6208,a,6183,a)]. 135.95/135.82 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(6208,a,6184,a)]. 135.95/135.82 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),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(6208,a,6185,a)]. 135.95/135.82 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(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) = 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)). [resolve(6208,a,6186,a)]. 135.95/135.83 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(6208,a,6187,a)]. 135.95/135.83 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),C),A))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),B),C)). [resolve(6208,a,6188,a)]. 135.95/135.83 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C))),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)). [resolve(6208,a,6189,a)]. 135.95/135.83 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(6208,a,6190,a)]. 135.95/135.85 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(6208,a,6191,a)]. 135.95/135.85 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(6208,a,6192,a)]. 135.95/135.85 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | one_one(quickcheck_code_int) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),A),A). [resolve(6208,a,6193,a)]. 135.95/135.85 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(6208,a,6194,a)]. 135.95/135.85 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(6208,a,6195,a)]. 135.95/135.85 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(6208,a,6196,a)]. 135.95/135.85 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A) = zero_zero(quickcheck_code_int). [resolve(6208,a,6197,a)]. 135.95/135.85 Derived: ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = zero_zero(quickcheck_code_int). [resolve(6208,a,6198,a)]. 135.95/135.85 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(6208,a,6199,a)]. 135.95/135.86 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),A)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)). [resolve(6208,a,6200,a)]. 135.95/135.86 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(6208,a,6201,a)]. 135.95/135.86 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(6208,a,6202,a)]. 135.95/135.86 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),C))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)). [resolve(6208,a,6203,a)]. 135.95/135.86 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A) = zero_zero(quickcheck_code_int). [resolve(6208,a,6204,a)]. 135.95/135.86 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),C). [resolve(6208,a,6205,a)]. 136.15/136.02 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),B),A) != zero_zero(quickcheck_code_int). [resolve(6208,a,6207,a)]. 136.15/136.02 6209 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_933_zmod__simps_I4_J) # label(axiom). [clausify(2566)]. 136.15/136.02 6210 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C))),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) # label(fact_914_mod__div__equality2) # label(axiom). [clausify(2775)]. 136.15/136.02 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B))),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)). [resolve(6210,a,6170,a)]. 136.15/136.02 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(6210,a,6208,a)]. 136.15/136.02 6211 semiring_div(nat) # label(arity_Nat_Onat___Divides_Osemiring__div) # label(axiom). [assumption]. 136.15/136.02 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(6211,a,6171,a)]. 136.15/136.02 Derived: div_mod(nat) = ti(fun(nat,fun(nat,nat)),div_mod(nat)). [resolve(6211,a,6172,a)]. 136.15/136.02 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(6211,a,6173,a)]. 136.15/136.02 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(6211,a,6174,a)]. 136.15/136.02 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(6211,a,6175,a)]. 136.15/136.02 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(6211,a,6176,a)]. 136.15/136.02 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),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(6211,a,6177,a)]. 136.15/136.04 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = zero_zero(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),D)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),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(6211,a,6178,a)]. 136.15/136.04 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(6211,a,6179,a)]. 136.15/136.04 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(6211,a,6180,a)]. 136.15/136.04 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(6211,a,6181,a)]. 136.15/136.04 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),A). [resolve(6211,a,6182,a)]. 136.15/136.04 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(6211,a,6183,a)]. 136.15/136.04 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(6211,a,6184,a)]. 136.15/136.04 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(6211,a,6185,a)]. 136.15/136.04 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | 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) = 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)). [resolve(6211,a,6186,a)]. 136.15/136.04 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(6211,a,6187,a)]. 136.15/136.04 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),C),A))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),C)). [resolve(6211,a,6188,a)]. 136.15/136.07 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C))),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)). [resolve(6211,a,6189,a)]. 136.15/136.07 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(6211,a,6190,a)]. 136.15/136.07 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(6211,a,6191,a)]. 136.15/136.07 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(6211,a,6192,a)]. 136.15/136.07 Derived: ti(nat,A) = zero_zero(nat) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),A). [resolve(6211,a,6193,a)]. 136.15/136.07 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(6211,a,6194,a)]. 136.15/136.07 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(6211,a,6195,a)]. 136.15/136.07 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(6211,a,6196,a)]. 136.15/136.07 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A) = zero_zero(nat). [resolve(6211,a,6197,a)]. 136.15/136.07 Derived: ti(nat,A) != zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = zero_zero(nat). [resolve(6211,a,6198,a)]. 136.15/136.07 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(6211,a,6199,a)]. 136.15/136.07 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)). [resolve(6211,a,6200,a)]. 136.15/136.07 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(6211,a,6201,a)]. 136.15/136.07 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(6211,a,6202,a)]. 136.15/136.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)). [resolve(6211,a,6203,a)]. 136.15/136.07 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A) = zero_zero(nat). [resolve(6211,a,6204,a)]. 136.15/136.07 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),C). [resolve(6211,a,6205,a)]. 136.25/136.19 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),B)) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),B),A) != zero_zero(nat). [resolve(6211,a,6207,a)]. 136.25/136.19 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(6211,a,6210,a)]. 136.25/136.19 6212 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),B) # label(fact_948_mod__mod__cancel) # label(axiom). [clausify(2892)]. 136.25/136.19 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(6212,a,6170,a)]. 136.25/136.19 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(6212,a,6208,a)]. 136.25/136.19 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(6212,a,6211,a)]. 136.25/136.19 6213 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),E),C) != hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),F),C) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),F)),C) # label(fact_934_mod__mult__cong) # label(axiom). [clausify(3041)]. 136.25/136.19 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(6213,a,6170,a)]. 136.25/136.19 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(6213,a,6208,a)]. 136.36/136.26 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(6213,a,6211,a)]. 136.36/136.26 6214 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) = zero_zero(A) # label(fact_974_mod__mult__self2__is__0) # label(axiom). [clausify(3048)]. 136.36/136.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B) = zero_zero(int). [resolve(6214,a,6170,a)]. 136.36/136.26 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B) = zero_zero(quickcheck_code_int). [resolve(6214,a,6208,a)]. 136.36/136.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B) = zero_zero(nat). [resolve(6214,a,6211,a)]. 136.36/136.26 6215 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D) # label(fact_977_mod__mult__self1) # label(axiom). [clausify(3087)]. 136.36/136.26 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(6215,a,6170,a)]. 136.36/136.26 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(6215,a,6208,a)]. 136.36/136.26 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(6215,a,6211,a)]. 136.36/136.26 6216 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),one_one(A)) = zero_zero(A) # label(fact_975_mod__by__1) # label(axiom). [clausify(3128)]. 136.36/136.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),one_one(int)) = zero_zero(int). [resolve(6216,a,6170,a)]. 136.36/136.26 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),one_one(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(6216,a,6208,a)]. 136.36/136.26 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),one_one(nat)) = zero_zero(nat). [resolve(6216,a,6211,a)]. 136.36/136.26 6217 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_936_zmod__simps_I1_J) # label(axiom). [clausify(3156)]. 136.36/136.26 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),C)),B) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),B). [resolve(6217,a,6170,a)]. 136.65/136.56 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(6217,a,6208,a)]. 136.65/136.56 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(6217,a,6211,a)]. 136.65/136.56 6218 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),D)),C) # label(fact_932_mod__mult__mult2) # label(axiom). [clausify(3301)]. 136.65/136.56 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(6218,a,6170,a)]. 136.65/136.56 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(6218,a,6208,a)]. 136.65/136.56 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),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(6218,a,6211,a)]. 136.65/136.56 6219 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),B) = zero_zero(A) # label(fact_924_mod__self) # label(axiom). [clausify(3305)]. 136.65/136.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),A) = zero_zero(int). [resolve(6219,a,6170,a)]. 136.65/136.56 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),A) = zero_zero(quickcheck_code_int). [resolve(6219,a,6208,a)]. 136.65/136.56 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),A) = zero_zero(nat). [resolve(6219,a,6211,a)]. 136.65/136.56 6220 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C))),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D) # label(fact_917_div__mod__equality) # label(axiom). [clausify(3460)]. 136.65/136.56 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),B)),B)),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B))),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C). [resolve(6220,a,6170,a)]. 136.76/136.65 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(6220,a,6208,a)]. 136.76/136.65 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(6220,a,6211,a)]. 136.76/136.65 6221 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)) # label(fact_913_semiring__div__class_Omod__div__equality_H) # label(axiom). [clausify(3507)]. 136.76/136.65 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(6221,a,6170,a)]. 136.76/136.65 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(6221,a,6208,a)]. 136.76/136.65 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(6221,a,6211,a)]. 136.76/136.65 6222 -semiring_div(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) # label(fact_1044_dvd__div__eq__mult) # label(axiom). [clausify(3575)]. 136.76/136.65 Derived: ti(int,A) = zero_zero(int) | -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),C),A) | ti(int,C) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A). [resolve(6222,a,6170,a)]. 136.76/136.65 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,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) | 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). [resolve(6222,a,6208,a)]. 136.76/136.65 Derived: ti(nat,A) = zero_zero(nat) | -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),C),A) | ti(nat,C) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A). [resolve(6222,a,6211,a)]. 136.76/136.69 6223 -semiring_div(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B) # label(fact_1044_dvd__div__eq__mult) # label(axiom). [clausify(3575)]. 136.76/136.69 Derived: ti(int,A) = zero_zero(int) | -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),C),A) | ti(int,C) != hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A). [resolve(6223,a,6170,a)]. 136.76/136.69 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | ti(quickcheck_code_int,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) | 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). [resolve(6223,a,6208,a)]. 136.76/136.69 Derived: ti(nat,A) = zero_zero(nat) | -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),C),A) | ti(nat,C) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A). [resolve(6223,a,6211,a)]. 136.76/136.69 6224 semiring_div(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Divides_Osemiring__div) # label(axiom). [assumption]. 136.76/136.69 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),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(6224,a,6171,a)]. 136.76/136.69 Derived: div_mod(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_mod(code_code_numeral)). [resolve(6224,a,6172,a)]. 136.76/136.69 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(6224,a,6173,a)]. 136.76/136.69 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(6224,a,6174,a)]. 136.76/136.70 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(6224,a,6175,a)]. 136.76/136.70 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(6224,a,6176,a)]. 136.76/136.70 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),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(6224,a,6177,a)]. 136.76/136.70 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),D)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),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(6224,a,6178,a)]. 136.76/136.70 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(6224,a,6179,a)]. 136.85/136.70 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(6224,a,6180,a)]. 136.85/136.70 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(6224,a,6181,a)]. 136.85/136.70 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),A). [resolve(6224,a,6182,a)]. 136.85/136.70 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(6224,a,6183,a)]. 136.85/136.70 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(6224,a,6184,a)]. 136.85/136.70 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(6224,a,6185,a)]. 136.85/136.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),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),div_div(code_code_numeral),B),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(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)). [resolve(6224,a,6186,a)]. 136.85/136.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(6224,a,6187,a)]. 136.85/136.71 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),C),A))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),B),C)). [resolve(6224,a,6188,a)]. 136.85/136.71 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C))),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)). [resolve(6224,a,6189,a)]. 136.85/136.71 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(6224,a,6190,a)]. 136.85/136.72 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(6224,a,6191,a)]. 136.85/136.72 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(6224,a,6192,a)]. 136.85/136.72 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | one_one(code_code_numeral) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),A),A). [resolve(6224,a,6193,a)]. 136.85/136.72 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(6224,a,6194,a)]. 136.85/136.72 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(6224,a,6195,a)]. 136.85/136.72 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(6224,a,6196,a)]. 136.85/136.72 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A) = zero_zero(code_code_numeral). [resolve(6224,a,6197,a)]. 136.85/136.72 Derived: ti(code_code_numeral,A) != zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = zero_zero(code_code_numeral). [resolve(6224,a,6198,a)]. 136.85/136.72 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(6224,a,6199,a)]. 136.85/136.73 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),A)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)). [resolve(6224,a,6200,a)]. 136.85/136.73 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(6224,a,6201,a)]. 136.85/136.73 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(6224,a,6202,a)]. 136.85/136.73 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),C))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)). [resolve(6224,a,6203,a)]. 136.85/136.73 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A) = zero_zero(code_code_numeral). [resolve(6224,a,6204,a)]. 136.85/136.73 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),C). [resolve(6224,a,6205,a)]. 136.85/136.73 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),B),A) != zero_zero(code_code_numeral). [resolve(6224,a,6207,a)]. 136.85/136.75 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(6224,a,6210,a)]. 136.85/136.75 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(6224,a,6212,a)]. 136.85/136.75 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(6224,a,6213,a)]. 136.85/136.75 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),B) = zero_zero(code_code_numeral). [resolve(6224,a,6214,a)]. 136.85/136.75 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(6224,a,6215,a)]. 136.85/136.75 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),one_one(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(6224,a,6216,a)]. 136.85/136.75 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(6224,a,6217,a)]. 136.95/136.82 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(6224,a,6218,a)]. 136.95/136.82 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),A) = zero_zero(code_code_numeral). [resolve(6224,a,6219,a)]. 136.95/136.82 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(6224,a,6220,a)]. 136.95/136.82 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(6224,a,6221,a)]. 136.95/136.82 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | ti(code_code_numeral,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) | 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). [resolve(6224,a,6222,a)]. 136.95/136.82 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | ti(code_code_numeral,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) | 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). [resolve(6224,a,6223,a)]. 136.95/136.82 6225 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),D) # label(fact_994_div__mult__mult1) # label(axiom). [clausify(3740)]. 137.24/137.11 6226 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C) # label(fact_978_mod__mult__self2) # label(axiom). [clausify(3770)]. 137.24/137.11 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(6226,a,6170,a)]. 137.24/137.11 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(6226,a,6208,a)]. 137.24/137.11 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(6226,a,6211,a)]. 137.24/137.11 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),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(6226,a,6224,a)]. 137.24/137.11 6227 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),one_one(A)) # label(fact_966_div__by__1) # label(axiom). [clausify(3893)]. 137.24/137.11 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),A),one_one(int)). [resolve(6227,a,6170,a)]. 137.24/137.11 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(6227,a,6208,a)]. 137.24/137.11 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),A),one_one(nat)). [resolve(6227,a,6211,a)]. 137.24/137.11 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(6227,a,6224,a)]. 137.24/137.11 6228 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),B),C)),C)),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)) # label(fact_1074_mod__div__decomp) # label(axiom). [clausify(4059)]. 137.24/137.11 6229 -semiring_div(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)),one_one(A)) # label(fact_1041_div__add__self1) # label(axiom). [clausify(4114)]. 137.24/137.11 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),div_div(int),B),A)),one_one(int)). [resolve(6229,a,6170,a)]. 137.24/137.11 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),B),A)),one_one(quickcheck_code_int)). [resolve(6229,a,6208,a)]. 137.36/137.28 Derived: ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),B),A)),one_one(nat)). [resolve(6229,a,6211,a)]. 137.36/137.28 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),B),A)),one_one(code_code_numeral)). [resolve(6229,a,6224,a)]. 137.36/137.28 6230 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),C) = zero_zero(A) # label(fact_909_mod__div__trivial) # label(axiom). [clausify(4151)]. 137.36/137.28 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),B)),B) = zero_zero(int). [resolve(6230,a,6170,a)]. 137.36/137.28 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),A),B)),B) = zero_zero(quickcheck_code_int). [resolve(6230,a,6208,a)]. 137.36/137.28 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),B)),B) = zero_zero(nat). [resolve(6230,a,6211,a)]. 137.36/137.28 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),A),B)),B) = zero_zero(code_code_numeral). [resolve(6230,a,6224,a)]. 137.36/137.28 6231 -semiring_div(A) | ti(A,B) = zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),B) # label(fact_996_div__mult__self1__is__id) # label(axiom). [clausify(4270)]. 137.36/137.28 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),div_div(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),A). [resolve(6231,a,6170,a)]. 137.36/137.28 Derived: ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_div(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),A). [resolve(6231,a,6208,a)]. 137.36/137.28 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_div(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),A). [resolve(6231,a,6211,a)]. 137.36/137.28 Derived: ti(code_code_numeral,A) = zero_zero(code_code_numeral) | ti(code_code_numeral,B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_div(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),A). [resolve(6231,a,6224,a)]. 137.36/137.28 6232 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1004_dvd__mult__div__cancel) # label(axiom). [clausify(4335)]. 137.64/137.49 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(6232,a,6170,a)]. 137.64/137.49 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(6232,a,6208,a)]. 137.64/137.49 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(6232,a,6211,a)]. 137.64/137.49 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(6232,a,6224,a)]. 137.64/137.49 6233 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),C)),D)),C) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_939_mod__add__left__eq) # label(axiom). [clausify(4552)]. 137.64/137.49 6234 -number(A) | -semiring_div(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)) != zero_zero(A) | 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_1009_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(4557)]. 137.64/137.49 6235 -number(A) | -semiring_div(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)) = zero_zero(A) | -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_1009_dvd__eq__mod__eq__0__number__of) # label(axiom). [clausify(4557)]. 137.64/137.49 6236 -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(4561)]. 137.64/137.49 Derived: div_div(int) = ti(fun(int,fun(int,int)),div_div(int)). [resolve(6236,a,6170,a)]. 137.64/137.49 Derived: div_div(quickcheck_code_int) = ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),div_div(quickcheck_code_int)). [resolve(6236,a,6208,a)]. 137.64/137.49 Derived: div_div(nat) = ti(fun(nat,fun(nat,nat)),div_div(nat)). [resolve(6236,a,6211,a)]. 137.64/137.49 Derived: div_div(code_code_numeral) = ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),div_div(code_code_numeral)). [resolve(6236,a,6224,a)]. 137.64/137.49 6237 -semiring_div(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),B),zero_zero(A)) # label(fact_925_mod__by__0) # label(axiom). [clausify(4567)]. 137.64/137.49 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),A),zero_zero(int)). [resolve(6237,a,6170,a)]. 137.64/137.49 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(6237,a,6208,a)]. 137.64/137.49 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),A),zero_zero(nat)). [resolve(6237,a,6211,a)]. 137.64/137.49 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(6237,a,6224,a)]. 137.76/137.67 6238 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) # label(fact_947_dvd__mod__iff) # label(axiom). [clausify(4676)]. 137.76/137.67 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(6238,a,6170,a)]. 137.76/137.67 6239 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),D),C))) # label(fact_947_dvd__mod__iff) # label(axiom). [clausify(4676)]. 137.76/137.67 6240 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),zero_zero(A)),B) = zero_zero(A) # label(fact_926_mod__0) # label(axiom). [clausify(4681)]. 137.76/137.67 Derived: hAPP(int,int,hAPP(int,fun(int,int),div_mod(int),zero_zero(int)),A) = zero_zero(int). [resolve(6240,a,6170,a)]. 137.76/137.67 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),div_mod(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(6240,a,6208,a)]. 137.76/137.67 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),div_mod(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(6240,a,6211,a)]. 137.76/137.67 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),div_mod(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(6240,a,6224,a)]. 137.76/137.67 6241 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D))),D) = hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) # label(fact_940_mod__add__right__eq) # label(axiom). [clausify(4708)]. 137.76/137.67 6242 -semiring_div(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hAPP(A,A,hAPP(A,fun(A,A),div_div(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),div_div(A),C),B)) # label(fact_1003_div__mult__swap) # label(axiom). [clausify(4754)]. 137.76/137.67 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(6242,a,6170,a)]. 137.76/137.67 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(6242,a,6208,a)]. 137.76/137.67 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(6242,a,6211,a)]. 137.76/137.67 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(6242,a,6224,a)]. 140.75/140.66 6243 -semiring_div(A) | hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),div_mod(A),C),D)) # label(fact_931_mod__mult__mult1) # label(axiom). [clausify(4874)]. 140.75/140.66 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(6243,a,6170,a)]. 140.75/140.66 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(6243,a,6208,a)]. 140.75/140.66 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(6243,a,6211,a)]. 140.75/140.66 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(6243,a,6224,a)]. 140.75/140.66 6244 -comm_monoid_add(A) | -t2_space(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),f56(A,C,B))) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),C),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))) # label(fact_4291_series__zero) # label(axiom). [clausify(236)]. 140.75/140.66 6245 t2_space(real) # label(arity_RealDef_Oreal___RealVector_Ot2__space) # label(axiom). [assumption]. 140.75/140.66 Derived: -comm_monoid_add(real) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f56(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(6244,b,6245,a)]. 140.75/140.66 6246 -comm_monoid_add(A) | -t2_space(A) | hAPP(nat,A,B,f56(A,B,C)) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)))) # label(fact_4291_series__zero) # label(axiom). [clausify(236)]. 142.15/142.02 Derived: -comm_monoid_add(real) | hAPP(nat,real,A,f56(real,A,B)) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(6246,b,6245,a)]. 142.15/142.02 6247 -t2_space(A) | -comm_monoid_add(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(filter(nat),bool,hAPP(A,fun(filter(nat),bool),hAPP(fun(nat,A),fun(A,fun(filter(nat),bool)),tendsto(nat,A),hAPP(fun(nat,fun(nat,bool)),fun(nat,A),hAPP(fun(fun(nat,bool),A),fun(fun(nat,fun(nat,bool)),fun(nat,A)),combb(fun(nat,bool),A,nat),hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B)),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)))),hAPP(fun(nat,A),A,suminf(A),B)),sequentially)) # label(fact_4497_summable__sumr__LIMSEQ__suminf) # label(axiom). [clausify(1947)]. 142.15/142.02 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(6247,a,6245,a)]. 142.15/142.02 6248 t2_space(complex) # label(arity_Complex_Ocomplex___RealVector_Ot2__space) # label(axiom). [assumption]. 142.15/142.02 Derived: -comm_monoid_add(complex) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),f56(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(6248,a,6244,b)]. 142.15/142.02 Derived: -comm_monoid_add(complex) | hAPP(nat,complex,A,f56(complex,A,B)) != zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B)))). [resolve(6248,a,6246,b)]. 142.15/142.02 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(6248,a,6247,a)]. 142.15/142.03 6249 -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_4089_sums__unique) # label(axiom). [clausify(2590)]. 142.15/142.03 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(6249,b,6245,a)]. 142.15/142.03 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(6249,b,6248,a)]. 142.15/142.03 6250 -t2_space(A) | hBOOL(hAPP(filter(B),bool,trivial_limit(B),C)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),E),C)) | -hBOOL(hAPP(filter(B),bool,hAPP(A,fun(filter(B),bool),hAPP(fun(B,A),fun(A,fun(filter(B),bool)),tendsto(B,A),D),F),C)) | ti(A,F) = ti(A,E) # label(fact_4767_tendsto__unique) # label(axiom). [clausify(3841)]. 146.25/146.14 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(6250,a,6245,a)]. 146.25/146.14 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(6250,a,6248,a)]. 146.25/146.14 6251 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | ti(A,C) != hAPP(fun(nat,A),A,suminf(A),B) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),C)) # label(fact_4093_sums__iff) # label(axiom). [clausify(4249)]. 146.25/146.14 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(fun(nat,real),bool,summable(real),A)) | ti(real,B) != hAPP(fun(nat,real),real,suminf(real),A) | hBOOL(hAPP(real,bool,hAPP(fun(nat,real),fun(real,bool),sums(real),A),B)). [resolve(6251,b,6245,a)]. 146.25/146.14 Derived: -comm_monoid_add(complex) | -hBOOL(hAPP(fun(nat,complex),bool,summable(complex),A)) | ti(complex,B) != hAPP(fun(nat,complex),complex,suminf(complex),A) | hBOOL(hAPP(complex,bool,hAPP(fun(nat,complex),fun(complex,bool),sums(complex),A),B)). [resolve(6251,b,6248,a)]. 146.25/146.14 6252 -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),C)) # label(fact_4093_sums__iff) # label(axiom). [clausify(4249)]. 146.25/146.14 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),B)). [resolve(6252,b,6245,a)]. 146.25/146.14 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),B)). [resolve(6252,b,6248,a)]. 146.25/146.14 6253 -comm_monoid_add(A) | -t2_space(A) | ti(A,B) = hAPP(fun(nat,A),A,suminf(A),C) | -hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),C),B)) # label(fact_4093_sums__iff) # label(axiom). [clausify(4249)]. 146.25/146.14 6254 -comm_monoid_add(A) | -t2_space(A) | -hBOOL(hAPP(fun(nat,A),bool,summable(A),B)) | hBOOL(hAPP(A,bool,hAPP(fun(nat,A),fun(A,bool),sums(A),B),hAPP(fun(nat,A),A,suminf(A),B))) # label(fact_4092_summable__sums) # label(axiom). [clausify(4435)]. 146.25/146.14 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(6254,b,6245,a)]. 146.25/146.14 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(6254,b,6248,a)]. 146.25/146.14 6255 -comm_monoid_add(A) | -t2_space(A) | hAPP(fun(nat,A),A,suminf(A),hAPP(A,fun(nat,A),combk(A,nat),zero_zero(A))) = zero_zero(A) # label(fact_3968_suminf__zero) # label(axiom). [clausify(4852)]. 146.25/146.14 Derived: -comm_monoid_add(real) | hAPP(fun(nat,real),real,suminf(real),hAPP(real,fun(nat,real),combk(real,nat),zero_zero(real))) = zero_zero(real). [resolve(6255,b,6245,a)]. 146.25/146.14 Derived: -comm_monoid_add(complex) | hAPP(fun(nat,complex),complex,suminf(complex),hAPP(complex,fun(nat,complex),combk(complex,nat),zero_zero(complex))) = zero_zero(complex). [resolve(6255,b,6248,a)]. 146.25/146.14 6256 linordered_semidom(rat) # label(arity_Rat_Orat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 146.25/146.14 6257 -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_1284_of__nat__less__iff) # label(axiom). [clausify(127)]. 146.25/146.14 6258 -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_1284_of__nat__less__iff) # label(axiom). [clausify(127)]. 146.25/146.14 6259 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C != D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_413_power__inject__exp) # label(axiom). [clausify(129)]. 146.25/146.14 6260 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | C = D | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D) # label(fact_413_power__inject__exp) # label(axiom). [clausify(129)]. 146.25/146.14 6261 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) # label(fact_1282_of__nat__less__imp__less) # label(axiom). [clausify(141)]. 146.25/146.14 6262 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),one_one(A))) # label(fact_1404_power__Suc__less__one) # label(axiom). [clausify(179)]. 146.25/146.14 6263 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_412_one__le__power) # label(axiom). [clausify(297)]. 146.25/146.14 6264 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_105_power2__less__imp__less) # label(axiom). [clausify(518)]. 146.25/146.14 6265 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),one_one(A))) # label(fact_400_zero__le__one) # label(axiom). [clausify(542)]. 146.25/146.14 6266 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_404_power__mono) # label(axiom). [clausify(586)]. 146.25/146.14 6267 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_443_power__increasing__iff) # label(axiom). [clausify(645)]. 146.25/146.14 6268 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_443_power__increasing__iff) # label(axiom). [clausify(645)]. 146.25/146.14 6269 -linordered_semidom(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),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4151_setprod__nonneg) # label(axiom). [clausify(750)]. 146.25/146.14 6270 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f138(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4151_setprod__nonneg) # label(axiom). [clausify(750)]. 146.25/146.14 6271 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),zero_zero(A))) # label(fact_403_not__one__less__zero) # label(axiom). [clausify(937)]. 146.25/146.14 6272 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A)))) # label(fact_408_less__add__one) # label(axiom). [clausify(1029)]. 146.25/146.14 6273 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f206(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4149_setprod__pos) # label(axiom). [clausify(1064)]. 146.25/146.14 6274 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(B,A,C,f206(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),D))) # label(fact_4149_setprod__pos) # label(axiom). [clausify(1064)]. 146.25/146.14 6275 -linordered_semidom(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | ti(A,B) = ti(A,C) # label(fact_102_power2__eq__imp__eq) # label(axiom). [clausify(1077)]. 146.25/146.14 6276 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_405_zero__le__power) # label(axiom). [clausify(1087)]. 146.25/146.14 6277 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_458_power__Suc__less) # label(axiom). [clausify(1222)]. 146.25/146.14 6278 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_1278_zero__le__imp__of__nat) # label(axiom). [clausify(1563)]. 146.25/146.14 6279 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),zero_zero(A))) # label(fact_1280_of__nat__less__0__iff) # label(axiom). [clausify(1674)]. 146.25/146.14 6280 -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)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | ti(A,B) = ti(A,D) # label(fact_1373_power__inject__base) # label(axiom). [clausify(1929)]. 146.25/146.14 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))). [resolve(6256,a,6257,a)]. 146.25/146.14 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))). [resolve(6256,a,6258,a)]. 146.32/146.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | B != C | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C). [resolve(6256,a,6259,a)]. 146.32/146.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | B = C | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C). [resolve(6256,a,6260,a)]. 146.32/146.18 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(6256,a,6262,a)]. 146.32/146.18 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(6256,a,6263,a)]. 146.32/146.18 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(6256,a,6264,a)]. 146.32/146.18 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),one_one(rat))). [resolve(6256,a,6265,a)]. 146.32/146.18 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(6256,a,6266,a)]. 146.32/146.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))). [resolve(6256,a,6267,a)]. 146.32/146.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))). [resolve(6256,a,6268,a)]. 146.32/146.18 Derived: 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),zero_zero(rat)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),B),C))). [resolve(6256,a,6269,a)]. 146.32/146.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f138(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(6256,a,6270,a)]. 146.32/146.18 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),zero_zero(rat))). [resolve(6256,a,6271,a)]. 146.32/146.18 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(6256,a,6272,a)]. 146.32/146.18 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f206(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(6256,a,6273,a)]. 146.32/146.26 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(A,rat,B,f206(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(6256,a,6274,a)]. 146.32/146.26 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(6256,a,6275,a)]. 146.32/146.26 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(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(6256,a,6277,a)]. 146.32/146.26 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(6256,a,6278,a)]. 146.32/146.26 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(6256,a,6279,a)]. 146.32/146.26 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)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | ti(rat,A) = ti(rat,C). [resolve(6256,a,6280,a)]. 146.32/146.26 6281 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),zero_zero(A))) # label(fact_401_not__one__le__zero) # label(axiom). [clausify(1939)]. 146.32/146.26 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),zero_zero(rat))). [resolve(6281,a,6256,a)]. 146.32/146.26 6282 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_1279_of__nat__0__le__iff) # label(axiom). [clausify(1981)]. 146.32/146.26 6283 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_447_power__strict__increasing) # label(axiom). [clausify(2031)]. 146.32/146.26 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(6283,a,6256,a)]. 146.32/146.26 6284 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_1397_of__nat__0__less__iff) # label(axiom). [clausify(2073)]. 146.32/146.26 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(6284,a,6256,a)]. 146.32/146.26 6285 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),B))) # label(fact_1397_of__nat__0__less__iff) # label(axiom). [clausify(2073)]. 146.32/146.26 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(6285,a,6256,a)]. 146.50/146.36 6286 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_406_less__1__mult) # label(axiom). [clausify(2199)]. 146.50/146.36 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(6286,a,6256,a)]. 146.50/146.36 6287 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)))) # label(fact_1375_power__gt1) # label(axiom). [clausify(2270)]. 146.50/146.36 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(6287,a,6256,a)]. 146.50/146.36 6288 linordered_semidom(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__semidom) # label(axiom). [assumption]. 146.50/146.36 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))). [resolve(6288,a,6257,a)]. 146.50/146.36 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))). [resolve(6288,a,6258,a)]. 146.50/146.36 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | B != C | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C). [resolve(6288,a,6259,a)]. 146.50/146.36 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | B = C | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C). [resolve(6288,a,6260,a)]. 146.50/146.36 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(6288,a,6262,a)]. 146.50/146.36 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(6288,a,6263,a)]. 146.50/146.37 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(6288,a,6264,a)]. 146.50/146.37 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(6288,a,6265,a)]. 146.50/146.37 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(6288,a,6266,a)]. 146.50/146.37 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))). [resolve(6288,a,6267,a)]. 146.50/146.37 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))). [resolve(6288,a,6268,a)]. 146.50/146.37 Derived: 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),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(6288,a,6269,a)]. 146.50/146.37 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,f138(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(6288,a,6270,a)]. 146.50/146.39 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(6288,a,6271,a)]. 146.50/146.39 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(6288,a,6272,a)]. 146.50/146.39 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f206(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(6288,a,6273,a)]. 146.50/146.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(A,quickcheck_code_int,B,f206(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(6288,a,6274,a)]. 146.50/146.39 Derived: hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) != hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,B). [resolve(6288,a,6275,a)]. 146.50/146.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),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(6288,a,6276,a)]. 146.50/146.39 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),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(6288,a,6277,a)]. 146.50/146.39 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A))). [resolve(6288,a,6278,a)]. 146.50/146.42 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)),zero_zero(quickcheck_code_int))). [resolve(6288,a,6279,a)]. 146.50/146.42 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)),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)) | ti(quickcheck_code_int,A) = ti(quickcheck_code_int,C). [resolve(6288,a,6280,a)]. 146.50/146.42 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(6288,a,6281,a)]. 146.50/146.42 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(6288,a,6283,a)]. 146.50/146.42 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(6288,a,6284,a)]. 146.50/146.42 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(6288,a,6285,a)]. 146.50/146.42 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)),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(6288,a,6286,a)]. 146.50/146.42 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(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(6288,a,6287,a)]. 146.50/146.42 6289 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),D)) # label(fact_440_power__less__imp__less__base) # label(axiom). [clausify(2321)]. 146.76/146.63 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(6289,a,6256,a)]. 146.76/146.63 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(6289,a,6288,a)]. 146.76/146.63 6290 -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)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | ti(A,B) = ti(A,D) # label(fact_460_power__eq__imp__eq__base) # label(axiom). [clausify(2561)]. 146.76/146.63 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)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(rat,A) = ti(rat,C). [resolve(6290,a,6256,a)]. 146.76/146.63 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)),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(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(6290,a,6288,a)]. 146.76/146.63 6291 linordered_semidom(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__semidom) # label(axiom). [assumption]. 146.76/146.63 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))). [resolve(6291,a,6257,a)]. 146.76/146.63 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))). [resolve(6291,a,6258,a)]. 146.76/146.63 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | B != C | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C). [resolve(6291,a,6259,a)]. 146.76/146.63 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | B = C | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C). [resolve(6291,a,6260,a)]. 146.80/146.65 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(6291,a,6262,a)]. 146.80/146.65 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(6291,a,6263,a)]. 146.80/146.65 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(6291,a,6264,a)]. 146.80/146.65 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(6291,a,6265,a)]. 146.80/146.65 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_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(6291,a,6266,a)]. 146.80/146.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))). [resolve(6291,a,6267,a)]. 146.80/146.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))). [resolve(6291,a,6268,a)]. 146.80/146.66 Derived: 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),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(6291,a,6269,a)]. 146.80/146.66 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,f138(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(6291,a,6270,a)]. 146.80/146.66 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(6291,a,6271,a)]. 146.80/146.66 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(6291,a,6272,a)]. 146.80/146.66 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f206(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(6291,a,6273,a)]. 146.80/146.66 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,f206(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(6291,a,6274,a)]. 146.80/146.66 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(6291,a,6275,a)]. 146.80/146.66 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(6291,a,6276,a)]. 146.80/146.66 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(6291,a,6277,a)]. 146.80/146.68 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A))). [resolve(6291,a,6278,a)]. 146.80/146.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),zero_zero(code_code_numeral))). [resolve(6291,a,6279,a)]. 146.80/146.68 Derived: hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),hAPP(nat,nat,suc,B)) != hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),C),hAPP(nat,nat,suc,B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),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)) | ti(code_code_numeral,A) = ti(code_code_numeral,C). [resolve(6291,a,6280,a)]. 146.80/146.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),one_one(code_code_numeral)),zero_zero(code_code_numeral))). [resolve(6291,a,6281,a)]. 146.80/146.68 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),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(6291,a,6283,a)]. 146.80/146.68 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(6291,a,6284,a)]. 146.80/146.68 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(6291,a,6285,a)]. 146.80/146.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),B)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B))). [resolve(6291,a,6286,a)]. 146.80/146.68 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),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(6291,a,6287,a)]. 146.80/146.72 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(6291,a,6289,a)]. 146.80/146.72 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)),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(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(6291,a,6290,a)]. 146.80/146.72 6292 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_1285_of__nat__le__iff) # label(axiom). [clausify(2738)]. 146.80/146.72 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6292,a,6256,a)]. 146.80/146.72 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6292,a,6288,a)]. 146.80/146.72 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6292,a,6291,a)]. 146.80/146.72 6293 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) # label(fact_1285_of__nat__le__iff) # label(axiom). [clausify(2738)]. 146.80/146.72 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)),hAPP(nat,rat,semiring_1_of_nat(rat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6293,a,6256,a)]. 146.80/146.72 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A)),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6293,a,6288,a)]. 146.80/146.72 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A)),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6293,a,6291,a)]. 147.09/147.00 6294 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,semiring_1_of_nat(A),B)),hAPP(nat,A,semiring_1_of_nat(A),C))) # label(fact_1283_less__imp__of__nat__less) # label(axiom). [clausify(2788)]. 147.09/147.00 6295 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_276_power__strict__mono) # label(axiom). [clausify(3115)]. 147.09/147.00 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(6295,a,6256,a)]. 147.09/147.00 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(6295,a,6288,a)]. 147.09/147.00 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(6295,a,6291,a)]. 147.09/147.00 6296 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_449_power__strict__increasing__iff) # label(axiom). [clausify(3247)]. 147.09/147.00 6297 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) # label(fact_449_power__strict__increasing__iff) # label(axiom). [clausify(3247)]. 147.09/147.00 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),one_one(rat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B)),hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),C))). [resolve(6297,a,6256,a)]. 147.09/147.00 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),one_one(quickcheck_code_int)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),B)),hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),A),C))). [resolve(6297,a,6288,a)]. 147.25/147.11 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),one_one(code_code_numeral)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),B)),hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),A),C))). [resolve(6297,a,6291,a)]. 147.25/147.11 6298 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_461_one__less__power) # label(axiom). [clausify(3328)]. 147.25/147.11 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(6298,a,6256,a)]. 147.25/147.11 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(6298,a,6288,a)]. 147.25/147.11 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(6298,a,6291,a)]. 147.25/147.11 6299 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),B)) # label(fact_1403_realpow__Suc__le__self) # label(axiom). [clausify(3375)]. 147.25/147.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),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(6299,a,6256,a)]. 147.25/147.11 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(6299,a,6288,a)]. 147.49/147.39 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(6299,a,6291,a)]. 147.49/147.39 6300 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_411_power__increasing) # label(axiom). [clausify(3515)]. 147.49/147.39 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(6300,a,6256,a)]. 147.49/147.39 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(6300,a,6288,a)]. 147.49/147.39 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(6300,a,6291,a)]. 147.49/147.39 6301 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),one_one(A))) # label(fact_402_zero__less__one) # label(axiom). [clausify(3546)]. 147.49/147.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),one_one(rat))). [resolve(6301,a,6256,a)]. 147.49/147.39 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),one_one(quickcheck_code_int))). [resolve(6301,a,6288,a)]. 147.49/147.39 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(6301,a,6291,a)]. 147.49/147.39 6302 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),hAPP(nat,nat,suc,C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),D)) # label(fact_1374_power__le__imp__le__base) # label(axiom). [clausify(3586)]. 147.49/147.39 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(6302,a,6256,a)]. 147.63/147.48 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(6302,a,6288,a)]. 147.63/147.48 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(6302,a,6291,a)]. 147.63/147.48 6303 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_445_power__gt1__lemma) # label(axiom). [clausify(3591)]. 147.63/147.48 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(6303,a,6256,a)]. 147.63/147.48 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(6303,a,6288,a)]. 147.63/147.48 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(6303,a,6291,a)]. 147.63/147.48 6304 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) # label(fact_448_power__less__imp__less__exp) # label(axiom). [clausify(3671)]. 147.63/147.48 6305 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_459_power__strict__decreasing) # label(axiom). [clausify(3702)]. 147.63/147.50 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(6305,a,6256,a)]. 147.63/147.50 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(6305,a,6288,a)]. 147.63/147.50 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(6305,a,6291,a)]. 147.63/147.50 6306 -linordered_semidom(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f646(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E))) # label(fact_4150_setprod__mono) # label(axiom). [clausify(3711)]. 147.63/147.50 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f646(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(6306,a,6256,a)]. 147.63/147.50 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f646(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(6306,a,6288,a)]. 147.63/147.50 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f646(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(6306,a,6291,a)]. 147.63/147.52 6307 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(B,A,C,f646(B,A,D,C,E)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f646(B,A,D,C,E))),hAPP(B,A,D,f646(B,A,D,C,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),E))) # label(fact_4150_setprod__mono) # label(axiom). [clausify(3711)]. 147.63/147.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,B,f646(A,rat,C,B,D)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f646(A,rat,C,B,D))),hAPP(A,rat,C,f646(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(6307,a,6256,a)]. 147.63/147.52 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,f646(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(A,quickcheck_code_int,B,f646(A,quickcheck_code_int,C,B,D))),hAPP(A,quickcheck_code_int,C,f646(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(6307,a,6288,a)]. 147.63/147.52 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,f646(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(A,code_code_numeral,B,f646(A,code_code_numeral,C,B,D))),hAPP(A,code_code_numeral,C,f646(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(6307,a,6291,a)]. 147.63/147.52 6308 -linordered_semidom(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(A,B,C,D,E)),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),C),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),B)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),D))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(3737)]. 147.63/147.52 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(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(6308,a,6256,a)]. 147.63/147.53 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(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(6308,a,6288,a)]. 147.63/147.53 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(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(6308,a,6291,a)]. 147.63/147.53 6309 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,B,f648(A,C,B,D,E))),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),E),C)))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(nat,A,semiring_1_of_nat(A),E)),D))) # label(fact_4273_real__setsum__nat__ivl__bounded2) # label(axiom). [clausify(3737)]. 147.63/147.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(nat,rat,A,f648(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(6309,a,6256,a)]. 147.63/147.53 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,f648(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(6309,a,6288,a)]. 147.80/147.69 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,f648(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(6309,a,6291,a)]. 147.80/147.69 6310 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A)))) # label(fact_439_zero__less__two) # label(axiom). [clausify(3831)]. 147.80/147.69 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(6310,a,6256,a)]. 147.80/147.69 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(6310,a,6288,a)]. 147.80/147.69 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(6310,a,6291,a)]. 147.80/147.69 6311 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_399_pos__add__strict) # label(axiom). [clausify(3926)]. 147.80/147.69 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),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),C))). [resolve(6311,a,6256,a)]. 147.80/147.69 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(6311,a,6288,a)]. 147.80/147.69 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(6311,a,6291,a)]. 147.87/147.76 6312 linordered_semidom(nat) # label(arity_Nat_Onat___Rings_Olinordered__semidom) # label(axiom). [assumption]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(6312,a,6257,a)]. 147.87/147.76 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))). [resolve(6312,a,6258,a)]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B != C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C). [resolve(6312,a,6259,a)]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | B = C | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C). [resolve(6312,a,6260,a)]. 147.87/147.76 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(6312,a,6262,a)]. 147.87/147.76 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(6312,a,6263,a)]. 147.87/147.76 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(6312,a,6264,a)]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(6312,a,6266,a)]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(6312,a,6267,a)]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(6312,a,6268,a)]. 147.87/147.76 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(6312,a,6272,a)]. 147.87/147.76 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f206(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(6312,a,6273,a)]. 147.87/147.76 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),hAPP(A,nat,B,f206(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(6312,a,6274,a)]. 147.94/147.77 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(6312,a,6275,a)]. 147.94/147.77 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(6312,a,6277,a)]. 147.94/147.77 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)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),C)) | ti(nat,A) = ti(nat,C). [resolve(6312,a,6280,a)]. 147.94/147.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),zero_zero(nat))). [resolve(6312,a,6281,a)]. 147.94/147.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),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(6312,a,6283,a)]. 147.94/147.77 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(6312,a,6284,a)]. 147.94/147.77 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(6312,a,6285,a)]. 147.94/147.77 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(6312,a,6286,a)]. 147.94/147.77 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(6312,a,6287,a)]. 147.94/147.77 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(6312,a,6289,a)]. 147.94/147.77 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)),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),zero_zero(nat)),B)) | ti(nat,A) = ti(nat,C). [resolve(6312,a,6290,a)]. 147.94/147.77 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6312,a,6292,a)]. 147.94/147.79 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,semiring_1_of_nat(nat),A)),hAPP(nat,nat,semiring_1_of_nat(nat),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6312,a,6293,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),C))). [resolve(6312,a,6295,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),C))). [resolve(6312,a,6297,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B))). [resolve(6312,a,6298,a)]. 147.94/147.79 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(6312,a,6299,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),one_one(nat)),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B))). [resolve(6312,a,6300,a)]. 147.94/147.79 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),one_one(nat))). [resolve(6312,a,6301,a)]. 147.94/147.79 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(6312,a,6302,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),one_one(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)))). [resolve(6312,a,6303,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),one_one(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),C),A))). [resolve(6312,a,6305,a)]. 147.94/147.79 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f646(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(6312,a,6306,a)]. 147.94/147.79 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,B,f646(A,nat,C,B,D)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f646(A,nat,C,B,D))),hAPP(A,nat,C,f646(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(6312,a,6307,a)]. 148.18/148.03 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(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(6312,a,6308,a)]. 148.18/148.03 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,A,f648(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(6312,a,6309,a)]. 148.18/148.03 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(6312,a,6310,a)]. 148.18/148.03 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(6312,a,6311,a)]. 148.18/148.03 6313 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) # label(fact_103_power2__le__imp__le) # label(axiom). [clausify(4267)]. 148.18/148.03 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(6313,a,6256,a)]. 148.18/148.03 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(6313,a,6288,a)]. 148.18/148.03 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(6313,a,6291,a)]. 148.24/148.11 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(6313,a,6312,a)]. 148.24/148.11 6314 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_2494_of__nat__fact__ge__zero) # label(axiom). [clausify(4333)]. 148.24/148.11 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),hAPP(nat,nat,fact_fact(nat),A)))). [resolve(6314,a,6312,a)]. 148.24/148.11 6315 linordered_semidom(real) # label(arity_RealDef_Oreal___Rings_Olinordered__semidom) # label(axiom). [assumption]. 148.24/148.11 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))). [resolve(6315,a,6257,a)]. 148.24/148.11 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))). [resolve(6315,a,6258,a)]. 148.24/148.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | B != C | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C). [resolve(6315,a,6259,a)]. 148.24/148.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | B = C | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C). [resolve(6315,a,6260,a)]. 148.24/148.11 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(6315,a,6262,a)]. 148.24/148.11 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(6315,a,6263,a)]. 148.24/148.11 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(6315,a,6264,a)]. 148.24/148.11 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),one_one(real))). [resolve(6315,a,6265,a)]. 148.24/148.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_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(6315,a,6266,a)]. 148.24/148.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))). [resolve(6315,a,6267,a)]. 148.24/148.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))). [resolve(6315,a,6268,a)]. 148.24/148.13 Derived: 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),zero_zero(real)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),B),C))). [resolve(6315,a,6269,a)]. 148.24/148.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f138(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(6315,a,6270,a)]. 148.24/148.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),zero_zero(real))). [resolve(6315,a,6271,a)]. 148.24/148.13 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(6315,a,6272,a)]. 148.24/148.13 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f206(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(6315,a,6273,a)]. 148.24/148.13 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(A,real,B,f206(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(6315,a,6274,a)]. 148.24/148.13 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(6315,a,6275,a)]. 148.24/148.13 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(6315,a,6277,a)]. 148.24/148.13 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(6315,a,6278,a)]. 148.24/148.13 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(6315,a,6279,a)]. 148.24/148.13 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)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | ti(real,A) = ti(real,C). [resolve(6315,a,6280,a)]. 148.24/148.15 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),zero_zero(real))). [resolve(6315,a,6281,a)]. 148.24/148.15 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(6315,a,6283,a)]. 148.24/148.15 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(6315,a,6284,a)]. 148.24/148.15 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(6315,a,6285,a)]. 148.24/148.15 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(6315,a,6286,a)]. 148.24/148.15 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(6315,a,6287,a)]. 148.24/148.15 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(6315,a,6289,a)]. 148.24/148.15 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)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(real,A) = ti(real,C). [resolve(6315,a,6290,a)]. 148.24/148.15 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6315,a,6292,a)]. 148.24/148.15 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,semiring_1_of_nat(real),A)),hAPP(nat,real,semiring_1_of_nat(real),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6315,a,6293,a)]. 148.24/148.15 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(6315,a,6295,a)]. 148.24/148.15 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),one_one(real)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),C))). [resolve(6315,a,6297,a)]. 148.24/148.15 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(6315,a,6298,a)]. 148.33/148.16 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(6315,a,6299,a)]. 148.33/148.16 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(6315,a,6300,a)]. 148.33/148.16 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),one_one(real))). [resolve(6315,a,6301,a)]. 148.33/148.16 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(6315,a,6302,a)]. 148.33/148.16 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(6315,a,6303,a)]. 148.33/148.16 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(6315,a,6305,a)]. 148.33/148.16 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f646(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(6315,a,6306,a)]. 148.33/148.16 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,B,f646(A,real,C,B,D)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f646(A,real,C,B,D))),hAPP(A,real,C,f646(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(6315,a,6307,a)]. 148.33/148.16 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(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(6315,a,6308,a)]. 148.33/148.16 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(nat,real,A,f648(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(6315,a,6309,a)]. 148.39/148.23 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(6315,a,6310,a)]. 148.39/148.23 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(6315,a,6311,a)]. 148.39/148.23 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(6315,a,6313,a)]. 148.39/148.23 6316 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)))) # label(fact_444_power__less__power__Suc) # label(axiom). [clausify(4414)]. 148.39/148.23 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(6316,a,6256,a)]. 148.39/148.23 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(6316,a,6288,a)]. 148.39/148.23 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(6316,a,6291,a)]. 148.39/148.23 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(6316,a,6312,a)]. 148.39/148.23 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(6316,a,6315,a)]. 148.40/148.29 6317 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_407_zero__less__power) # label(axiom). [clausify(4418)]. 148.40/148.29 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(6317,a,6256,a)]. 148.40/148.29 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(6317,a,6288,a)]. 148.40/148.29 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(6317,a,6291,a)]. 148.40/148.29 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B))). [resolve(6317,a,6315,a)]. 148.40/148.29 6318 linordered_semidom(int) # label(arity_Int_Oint___Rings_Olinordered__semidom) # label(axiom). [assumption]. 148.40/148.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B != C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C). [resolve(6318,a,6259,a)]. 148.40/148.29 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | B = C | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C). [resolve(6318,a,6260,a)]. 148.40/148.29 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(6318,a,6262,a)]. 148.40/148.29 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(6318,a,6263,a)]. 148.40/148.29 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(6318,a,6264,a)]. 148.40/148.29 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),one_one(int))). [resolve(6318,a,6265,a)]. 148.40/148.29 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(6318,a,6266,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(6318,a,6267,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(6318,a,6268,a)]. 148.48/148.31 Derived: 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),zero_zero(int)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),B),C))). [resolve(6318,a,6269,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f138(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(6318,a,6270,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),zero_zero(int))). [resolve(6318,a,6271,a)]. 148.48/148.31 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(6318,a,6272,a)]. 148.48/148.31 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f206(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(6318,a,6273,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,B,f206(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(6318,a,6274,a)]. 148.48/148.31 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(6318,a,6275,a)]. 148.48/148.31 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(6318,a,6277,a)]. 148.48/148.31 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(6318,a,6278,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,semiring_1_of_nat(int),A)),zero_zero(int))). [resolve(6318,a,6279,a)]. 148.48/148.31 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)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | ti(int,A) = ti(int,C). [resolve(6318,a,6280,a)]. 148.48/148.31 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),zero_zero(int))). [resolve(6318,a,6281,a)]. 148.48/148.31 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(6318,a,6283,a)]. 148.48/148.32 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(6318,a,6284,a)]. 148.48/148.32 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(nat,int,semiring_1_of_nat(int),A))). [resolve(6318,a,6285,a)]. 148.48/148.32 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(6318,a,6286,a)]. 148.48/148.32 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(6318,a,6287,a)]. 148.48/148.32 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(6318,a,6289,a)]. 148.48/148.32 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)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | ti(int,A) = ti(int,C). [resolve(6318,a,6290,a)]. 148.48/148.32 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6318,a,6292,a)]. 148.48/148.32 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,semiring_1_of_nat(int),A)),hAPP(nat,int,semiring_1_of_nat(int),B))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)). [resolve(6318,a,6293,a)]. 148.48/148.32 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),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(6318,a,6295,a)]. 148.48/148.32 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B)),hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),C))). [resolve(6318,a,6297,a)]. 148.48/148.32 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(6318,a,6298,a)]. 148.48/148.32 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(6318,a,6299,a)]. 148.48/148.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),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(6318,a,6300,a)]. 148.48/148.34 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),one_one(int))). [resolve(6318,a,6301,a)]. 148.48/148.34 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(6318,a,6302,a)]. 148.48/148.34 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(6318,a,6303,a)]. 148.48/148.34 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(6318,a,6305,a)]. 148.48/148.34 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f646(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(6318,a,6306,a)]. 148.48/148.34 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,B,f646(A,int,C,B,D)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f646(A,int,C,B,D))),hAPP(A,int,C,f646(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(6318,a,6307,a)]. 148.48/148.34 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),f648(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(6318,a,6308,a)]. 148.48/148.34 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(nat,int,A,f648(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(6318,a,6309,a)]. 148.48/148.34 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(6318,a,6310,a)]. 148.48/148.34 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(6318,a,6311,a)]. 148.84/148.73 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(6318,a,6313,a)]. 148.84/148.73 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(6318,a,6316,a)]. 148.84/148.73 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(6318,a,6317,a)]. 148.84/148.73 6319 -linordered_semidom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)))) # label(fact_2495_of__nat__fact__gt__zero) # label(axiom). [clausify(4701)]. 148.84/148.73 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(6319,a,6256,a)]. 148.84/148.73 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(6319,a,6288,a)]. 148.84/148.73 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(6319,a,6291,a)]. 148.84/148.73 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(6319,a,6312,a)]. 148.84/148.73 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(6319,a,6315,a)]. 148.84/148.73 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(6319,a,6318,a)]. 148.84/148.73 6320 -linordered_semidom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) # label(fact_442_power__le__imp__le__exp) # label(axiom). [clausify(4831)]. 148.84/148.73 6321 -linordered_semidom(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),one_one(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B))) # label(fact_441_power__decreasing) # label(axiom). [clausify(4897)]. 148.84/148.73 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(6321,a,6256,a)]. 152.12/152.01 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(6321,a,6288,a)]. 152.12/152.01 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(6321,a,6291,a)]. 152.12/152.01 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_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(6321,a,6312,a)]. 152.12/152.01 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(6321,a,6315,a)]. 152.12/152.01 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(6321,a,6318,a)]. 152.12/152.01 6322 ring_char_0(rat) # label(arity_Rat_Orat___Int_Oring__char__0) # label(axiom). [assumption]. 152.12/152.01 6323 -ring_char_0(A) | ti(int,B) != zero_zero(int) | hAPP(int,A,ring_1_of_int(A),B) = zero_zero(A) # label(fact_3578_of__int__eq__0__iff) # label(axiom). [clausify(131)]. 152.12/152.01 6324 -ring_char_0(A) | ti(int,B) = zero_zero(int) | hAPP(int,A,ring_1_of_int(A),B) != zero_zero(A) # label(fact_3578_of__int__eq__0__iff) # label(axiom). [clausify(131)]. 152.12/152.01 6325 -ring_char_0(A) | ti(int,B) != zero_zero(int) | hAPP(int,A,ring_1_of_int(A),B) = zero_zero(A) # label(fact_3579_of__int__0__eq__iff) # label(axiom). [clausify(138)]. 152.12/152.01 6326 -ring_char_0(A) | ti(int,B) = zero_zero(int) | hAPP(int,A,ring_1_of_int(A),B) != zero_zero(A) # label(fact_3579_of__int__0__eq__iff) # label(axiom). [clausify(138)]. 152.12/152.01 6327 -ring_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_3886_Ints__double__eq__0__iff) # label(axiom). [clausify(653)]. 152.12/152.01 6328 -ring_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(A))) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_3886_Ints__double__eq__0__iff) # label(axiom). [clausify(653)]. 152.97/152.81 6329 -ring_char_0(A) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),B),ring_1_Ints(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_3907_Ints__odd__nonzero) # label(axiom). [clausify(717)]. 152.97/152.81 Derived: ti(int,A) != zero_zero(int) | hAPP(int,rat,ring_1_of_int(rat),A) = zero_zero(rat). [resolve(6322,a,6323,a)]. 152.97/152.81 Derived: ti(int,A) = zero_zero(int) | hAPP(int,rat,ring_1_of_int(rat),A) != zero_zero(rat). [resolve(6322,a,6324,a)]. 152.97/152.81 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(6322,a,6327,a)]. 152.97/152.81 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(rat))) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(6322,a,6328,a)]. 152.97/152.81 Derived: -hBOOL(hAPP(fun(rat,bool),bool,hAPP(rat,fun(fun(rat,bool),bool),member(rat),A),ring_1_Ints(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(6322,a,6329,a)]. 152.97/152.81 6330 -number_ring(A) | -ring_char_0(A) | ti(int,B) != ti(int,C) | hAPP(int,A,number_number_of(A),B) = hAPP(int,A,number_number_of(A),C) # label(fact_89_eq__number__of) # label(axiom). [clausify(1846)]. 152.97/152.81 Derived: -number_ring(rat) | ti(int,A) != ti(int,B) | hAPP(int,rat,number_number_of(rat),A) = hAPP(int,rat,number_number_of(rat),B). [resolve(6330,b,6322,a)]. 152.97/152.81 6331 -number_ring(A) | -ring_char_0(A) | ti(int,B) = ti(int,C) | hAPP(int,A,number_number_of(A),B) != hAPP(int,A,number_number_of(A),C) # label(fact_89_eq__number__of) # label(axiom). [clausify(1846)]. 152.97/152.81 Derived: -number_ring(rat) | ti(int,A) = ti(int,B) | hAPP(int,rat,number_number_of(rat),A) != hAPP(int,rat,number_number_of(rat),B). [resolve(6331,b,6322,a)]. 152.97/152.81 6332 -number_ring(A) | -ring_char_0(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit1,B)))) # label(fact_2602_iszero__number__of__Bit1) # label(axiom). [clausify(2532)]. 152.97/152.81 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit1,A)))). [resolve(6332,b,6322,a)]. 152.97/152.81 6333 ring_char_0(real) # label(arity_RealDef_Oreal___Int_Oring__char__0) # label(axiom). [assumption]. 152.97/152.81 Derived: ti(int,A) != zero_zero(int) | hAPP(int,real,ring_1_of_int(real),A) = zero_zero(real). [resolve(6333,a,6323,a)]. 152.97/152.81 Derived: ti(int,A) = zero_zero(int) | hAPP(int,real,ring_1_of_int(real),A) != zero_zero(real). [resolve(6333,a,6324,a)]. 152.97/152.81 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(6333,a,6327,a)]. 152.97/152.81 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(real))) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(6333,a,6328,a)]. 152.97/152.81 Derived: -hBOOL(hAPP(fun(real,bool),bool,hAPP(real,fun(fun(real,bool),bool),member(real),A),ring_1_Ints(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(6333,a,6329,a)]. 152.97/152.81 Derived: -number_ring(real) | ti(int,A) != ti(int,B) | hAPP(int,real,number_number_of(real),A) = hAPP(int,real,number_number_of(real),B). [resolve(6333,a,6330,b)]. 152.97/152.81 Derived: -number_ring(real) | ti(int,A) = ti(int,B) | hAPP(int,real,number_number_of(real),A) != hAPP(int,real,number_number_of(real),B). [resolve(6333,a,6331,b)]. 153.71/153.56 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit1,A)))). [resolve(6333,a,6332,b)]. 153.71/153.56 6334 -number_ring(A) | -ring_char_0(A) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)))) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),B))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom). [clausify(3822)]. 153.71/153.56 Derived: -number_ring(rat) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),A))). [resolve(6334,b,6322,a)]. 153.71/153.56 Derived: -number_ring(real) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),A))). [resolve(6334,b,6333,a)]. 153.71/153.56 6335 -number_ring(A) | -ring_char_0(A) | hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,B)))) | -hBOOL(hAPP(A,bool,iszero(A),hAPP(int,A,number_number_of(A),B))) # label(fact_2604_iszero__number__of__Bit0) # label(axiom). [clausify(3822)]. 153.71/153.56 Derived: -number_ring(rat) | hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(rat,bool,iszero(rat),hAPP(int,rat,number_number_of(rat),A))). [resolve(6335,b,6322,a)]. 153.71/153.56 Derived: -number_ring(real) | hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(real,bool,iszero(real),hAPP(int,real,number_number_of(real),A))). [resolve(6335,b,6333,a)]. 153.71/153.56 6336 ring_char_0(complex) # label(arity_Complex_Ocomplex___Int_Oring__char__0) # label(axiom). [assumption]. 153.71/153.56 Derived: ti(int,A) != zero_zero(int) | hAPP(int,complex,ring_1_of_int(complex),A) = zero_zero(complex). [resolve(6336,a,6323,a)]. 153.71/153.56 Derived: ti(int,A) = zero_zero(int) | hAPP(int,complex,ring_1_of_int(complex),A) != zero_zero(complex). [resolve(6336,a,6324,a)]. 153.71/153.56 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) != zero_zero(complex) | ti(complex,A) = zero_zero(complex). [resolve(6336,a,6327,a)]. 153.71/153.56 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = zero_zero(complex) | ti(complex,A) != zero_zero(complex). [resolve(6336,a,6328,a)]. 153.71/153.56 Derived: -hBOOL(hAPP(fun(complex,bool),bool,hAPP(complex,fun(fun(complex,bool),bool),member(complex),A),ring_1_Ints(complex))) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),A)),A) != zero_zero(complex). [resolve(6336,a,6329,a)]. 153.71/153.56 Derived: -number_ring(complex) | ti(int,A) != ti(int,B) | hAPP(int,complex,number_number_of(complex),A) = hAPP(int,complex,number_number_of(complex),B). [resolve(6336,a,6330,b)]. 153.71/153.56 Derived: -number_ring(complex) | ti(int,A) = ti(int,B) | hAPP(int,complex,number_number_of(complex),A) != hAPP(int,complex,number_number_of(complex),B). [resolve(6336,a,6331,b)]. 153.71/153.56 Derived: -number_ring(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit1,A)))). [resolve(6336,a,6332,b)]. 153.71/153.56 Derived: -number_ring(complex) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),A))). [resolve(6336,a,6334,b)]. 153.71/153.56 Derived: -number_ring(complex) | hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(complex,bool,iszero(complex),hAPP(int,complex,number_number_of(complex),A))). [resolve(6336,a,6335,b)]. 153.71/153.56 6337 -ring_char_0(A) | ti(int,B) != ti(int,C) | hAPP(int,A,ring_1_of_int(A),B) = hAPP(int,A,ring_1_of_int(A),C) # label(fact_3574_of__int__eq__iff) # label(axiom). [clausify(4230)]. 157.54/157.37 Derived: ti(int,A) != ti(int,B) | hAPP(int,rat,ring_1_of_int(rat),A) = hAPP(int,rat,ring_1_of_int(rat),B). [resolve(6337,a,6322,a)]. 157.54/157.37 Derived: ti(int,A) != ti(int,B) | hAPP(int,real,ring_1_of_int(real),A) = hAPP(int,real,ring_1_of_int(real),B). [resolve(6337,a,6333,a)]. 157.54/157.37 Derived: ti(int,A) != ti(int,B) | hAPP(int,complex,ring_1_of_int(complex),A) = hAPP(int,complex,ring_1_of_int(complex),B). [resolve(6337,a,6336,a)]. 157.54/157.37 6338 -ring_char_0(A) | ti(int,B) = ti(int,C) | hAPP(int,A,ring_1_of_int(A),B) != hAPP(int,A,ring_1_of_int(A),C) # label(fact_3574_of__int__eq__iff) # label(axiom). [clausify(4230)]. 157.54/157.37 Derived: ti(int,A) = ti(int,B) | hAPP(int,rat,ring_1_of_int(rat),A) != hAPP(int,rat,ring_1_of_int(rat),B). [resolve(6338,a,6322,a)]. 157.54/157.37 Derived: ti(int,A) = ti(int,B) | hAPP(int,real,ring_1_of_int(real),A) != hAPP(int,real,ring_1_of_int(real),B). [resolve(6338,a,6333,a)]. 157.54/157.37 Derived: ti(int,A) = ti(int,B) | hAPP(int,complex,ring_1_of_int(complex),A) != hAPP(int,complex,ring_1_of_int(complex),B). [resolve(6338,a,6336,a)]. 157.54/157.37 6339 ring_char_0(int) # label(arity_Int_Oint___Int_Oring__char__0) # label(axiom). [assumption]. 157.54/157.37 Derived: ti(int,A) != zero_zero(int) | hAPP(int,int,ring_1_of_int(int),A) = zero_zero(int). [resolve(6339,a,6323,a)]. 157.54/157.37 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,ring_1_of_int(int),A) != zero_zero(int). [resolve(6339,a,6324,a)]. 157.54/157.37 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int) | ti(int,A) = zero_zero(int). [resolve(6339,a,6327,a)]. 157.54/157.37 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(int))) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int) | ti(int,A) != zero_zero(int). [resolve(6339,a,6328,a)]. 157.54/157.37 Derived: -hBOOL(hAPP(fun(int,bool),bool,hAPP(int,fun(fun(int,bool),bool),member(int),A),ring_1_Ints(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)),A)),A) != zero_zero(int). [resolve(6339,a,6329,a)]. 157.54/157.37 Derived: -number_ring(int) | ti(int,A) != ti(int,B) | hAPP(int,int,number_number_of(int),A) = hAPP(int,int,number_number_of(int),B). [resolve(6339,a,6330,b)]. 157.54/157.37 Derived: -number_ring(int) | ti(int,A) = ti(int,B) | hAPP(int,int,number_number_of(int),A) != hAPP(int,int,number_number_of(int),B). [resolve(6339,a,6331,b)]. 157.54/157.37 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit1,A)))). [resolve(6339,a,6332,b)]. 157.54/157.37 Derived: -number_ring(int) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)))) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),A))). [resolve(6339,a,6334,b)]. 157.54/157.37 Derived: -number_ring(int) | hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),hAPP(int,int,bit0,A)))) | -hBOOL(hAPP(int,bool,iszero(int),hAPP(int,int,number_number_of(int),A))). [resolve(6339,a,6335,b)]. 157.54/157.37 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,ring_1_of_int(int),A) = hAPP(int,int,ring_1_of_int(int),B). [resolve(6339,a,6337,a)]. 157.54/157.37 Derived: ti(int,A) = ti(int,B) | hAPP(int,int,ring_1_of_int(int),A) != hAPP(int,int,ring_1_of_int(int),B). [resolve(6339,a,6338,a)]. 157.54/157.37 6340 -idom(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),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_410_dvd__mult__cancel__right) # label(axiom). [clausify(1470)]. 157.54/157.37 6341 idom(complex) # label(arity_Complex_Ocomplex___Rings_Oidom) # label(axiom). [assumption]. 157.54/157.37 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,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))). [resolve(6340,a,6341,a)]. 158.45/158.29 6342 -idom(A) | ti(A,B) != zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(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))) # label(fact_410_dvd__mult__cancel__right) # label(axiom). [clausify(1470)]. 158.45/158.29 Derived: ti(complex,A) != zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),A))). [resolve(6342,a,6341,a)]. 158.45/158.29 6343 -idom(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | ti(A,D) = zero_zero(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),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_410_dvd__mult__cancel__right) # label(axiom). [clausify(1470)]. 158.45/158.29 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | ti(complex,C) = zero_zero(complex) | -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),C))). [resolve(6343,a,6341,a)]. 158.45/158.29 6344 idom(real) # label(arity_RealDef_Oreal___Rings_Oidom) # label(axiom). [assumption]. 158.45/158.29 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,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))). [resolve(6344,a,6340,a)]. 158.45/158.29 Derived: ti(real,A) != zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(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),C),A))). [resolve(6344,a,6342,a)]. 158.45/158.29 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),B)) | ti(real,C) = zero_zero(real) | -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),C))). [resolve(6344,a,6343,a)]. 158.45/158.29 6345 -idom(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_2034_square__eq__iff) # label(axiom). [clausify(3490)]. 158.45/158.29 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A). [resolve(6345,a,6341,a)]. 158.45/158.29 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A). [resolve(6345,a,6344,a)]. 158.45/158.29 6346 -idom(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) # label(fact_2034_square__eq__iff) # label(axiom). [clausify(3490)]. 158.45/158.29 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),B). [resolve(6346,a,6341,a)]. 158.45/158.29 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B). [resolve(6346,a,6344,a)]. 158.45/158.29 6347 -idom(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = ti(A,B) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),C) != hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_2034_square__eq__iff) # label(axiom). [clausify(3490)]. 158.45/158.29 Derived: ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,B) = ti(complex,A) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),A). [resolve(6347,a,6341,a)]. 158.61/158.44 Derived: ti(real,A) = hAPP(real,real,uminus_uminus(real),B) | ti(real,B) = ti(real,A) | hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),B) != hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),A). [resolve(6347,a,6344,a)]. 158.61/158.44 6348 -idom(A) | ti(A,B) != ti(A,C) | 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_2100_realpow__two__disj) # label(axiom). [clausify(3624)]. 158.61/158.44 Derived: ti(complex,A) != ti(complex,B) | 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(6348,a,6341,a)]. 158.61/158.44 Derived: ti(real,A) != ti(real,B) | 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(6348,a,6344,a)]. 158.61/158.44 6349 -idom(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) # label(fact_2100_realpow__two__disj) # label(axiom). [clausify(3624)]. 158.61/158.44 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))). [resolve(6349,a,6341,a)]. 158.61/158.44 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))). [resolve(6349,a,6344,a)]. 158.61/158.44 6350 -idom(A) | ti(A,B) = ti(A,C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) | 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_2100_realpow__two__disj) # label(axiom). [clausify(3624)]. 158.61/158.44 Derived: ti(complex,A) = ti(complex,B) | ti(complex,B) = hAPP(complex,complex,uminus_uminus(complex),A) | 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(6350,a,6341,a)]. 158.61/158.44 Derived: ti(real,A) = ti(real,B) | ti(real,B) = hAPP(real,real,uminus_uminus(real),A) | 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(6350,a,6344,a)]. 158.61/158.44 6351 idom(int) # label(arity_Int_Oint___Rings_Oidom) # label(axiom). [assumption]. 158.61/158.44 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,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(6351,a,6340,a)]. 158.61/158.44 Derived: ti(int,A) != 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),B),A)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(6351,a,6342,a)]. 158.61/158.44 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | ti(int,C) = 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),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(6351,a,6343,a)]. 159.16/159.02 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A). [resolve(6351,a,6345,a)]. 159.16/159.02 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B). [resolve(6351,a,6346,a)]. 159.16/159.02 Derived: ti(int,A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,B) = ti(int,A) | hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),B) != hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),A). [resolve(6351,a,6347,a)]. 159.16/159.02 Derived: ti(int,A) != ti(int,B) | 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(6351,a,6348,a)]. 159.16/159.02 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))). [resolve(6351,a,6349,a)]. 159.16/159.02 Derived: ti(int,A) = ti(int,B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A) | 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(6351,a,6350,a)]. 159.16/159.02 6352 -idom(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)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | ti(A,B) = zero_zero(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_409_dvd__mult__cancel__left) # label(axiom). [clausify(4545)]. 159.16/159.02 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)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))) | ti(complex,A) = zero_zero(complex) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)). [resolve(6352,a,6341,a)]. 159.16/159.02 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)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | ti(real,A) = zero_zero(real) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)). [resolve(6352,a,6344,a)]. 159.16/159.02 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)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | ti(int,A) = zero_zero(int) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(6352,a,6351,a)]. 159.16/159.02 6353 -idom(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)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | ti(A,B) != zero_zero(A) # label(fact_409_dvd__mult__cancel__left) # label(axiom). [clausify(4545)]. 159.16/159.02 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)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))) | ti(complex,A) != zero_zero(complex). [resolve(6353,a,6341,a)]. 159.16/159.02 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)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | ti(real,A) != zero_zero(real). [resolve(6353,a,6344,a)]. 159.16/159.02 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)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | ti(int,A) != zero_zero(int). [resolve(6353,a,6351,a)]. 159.16/159.02 6354 -idom(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)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_409_dvd__mult__cancel__left) # label(axiom). [clausify(4545)]. 159.47/159.31 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)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),C)). [resolve(6354,a,6341,a)]. 159.47/159.31 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)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),C)). [resolve(6354,a,6344,a)]. 159.47/159.31 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)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),C)). [resolve(6354,a,6351,a)]. 159.47/159.31 6355 idom(rat) # label(arity_Rat_Orat___Rings_Oidom) # label(axiom). [assumption]. 159.47/159.31 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,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))). [resolve(6355,a,6340,a)]. 159.47/159.31 Derived: ti(rat,A) != zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(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),C),A))). [resolve(6355,a,6342,a)]. 159.47/159.31 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),B)) | ti(rat,C) = zero_zero(rat) | -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),C))). [resolve(6355,a,6343,a)]. 159.47/159.31 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A). [resolve(6355,a,6345,a)]. 159.47/159.31 Derived: ti(rat,A) != ti(rat,B) | 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). [resolve(6355,a,6346,a)]. 159.47/159.31 Derived: ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,B) = ti(rat,A) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),A). [resolve(6355,a,6347,a)]. 159.47/159.31 Derived: ti(rat,A) != ti(rat,B) | 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(6355,a,6348,a)]. 159.47/159.31 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,hAPP(nat,nat,suc,zero_zero(nat)))). [resolve(6355,a,6349,a)]. 159.47/159.31 Derived: ti(rat,A) = ti(rat,B) | ti(rat,B) = hAPP(rat,rat,uminus_uminus(rat),A) | 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(6355,a,6350,a)]. 159.47/159.31 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)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | ti(rat,A) = zero_zero(rat) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)). [resolve(6355,a,6352,a)]. 159.47/159.31 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)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | ti(rat,A) != zero_zero(rat). [resolve(6355,a,6353,a)]. 162.74/162.57 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)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),C)). [resolve(6355,a,6354,a)]. 162.74/162.57 6356 archim1727834104eiling(rat) # label(arity_Rat_Orat___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption]. 162.74/162.57 6357 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3612_floor__correct) # label(axiom). [clausify(142)]. 162.74/162.57 6358 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))))) # label(fact_3612_floor__correct) # label(axiom). [clausify(142)]. 162.74/162.57 6359 -archim1727834104eiling(A) | hAPP(int,int,number_number_of(int),B) = hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,number_number_of(A),B)) # label(fact_2872_floor__number__of) # label(axiom). [clausify(146)]. 162.74/162.57 6360 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2879_floor__less__zero) # label(axiom). [clausify(160)]. 162.74/162.57 6361 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_2879_floor__less__zero) # label(axiom). [clausify(160)]. 162.74/162.57 6362 -archim1727834104eiling(A) | hAPP(nat,int,semiring_1_of_nat(int),B) = hAPP(A,int,archimedean_ceiling(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_3285_ceiling__of__nat) # label(axiom). [clausify(222)]. 162.74/162.57 6363 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_2894_floor__le__number__of) # label(axiom). [clausify(461)]. 162.74/162.57 6364 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_2894_floor__le__number__of) # label(axiom). [clausify(461)]. 162.74/162.57 6365 -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_3357_ceiling__floor) # label(axiom). [clausify(476)]. 162.74/162.57 6366 -archim1727834104eiling(A) | ti(int,B) = hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3564_ceiling__of__int) # label(axiom). [clausify(504)]. 162.74/162.57 6367 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archim2085082626_floor(A),B))),B)) # label(fact_3567_of__int__floor__le) # label(axiom). [clausify(519)]. 162.74/162.57 6368 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2883_floor__less__one) # label(axiom). [clausify(534)]. 162.74/162.57 6369 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2883_floor__less__one) # label(axiom). [clausify(534)]. 162.74/162.57 6370 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) # label(fact_3305_ceiling__add__one) # label(axiom). [clausify(535)]. 162.74/162.59 6371 -archim1727834104eiling(A) | hAPP(nat,int,semiring_1_of_nat(int),B) = hAPP(A,int,archim2085082626_floor(A),hAPP(nat,A,semiring_1_of_nat(A),B)) # label(fact_2875_floor__of__nat) # label(axiom). [clausify(559)]. 162.74/162.59 6372 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2865_floor__mono) # label(axiom). [clausify(576)]. 162.74/162.59 6373 -archim1727834104eiling(A) | ti(int,B) = hAPP(A,int,archim2085082626_floor(A),hAPP(int,A,ring_1_of_int(A),B)) # label(fact_3576_floor__of__int) # label(axiom). [clausify(630)]. 162.74/162.59 6374 -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(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3297_zero__less__ceiling) # label(axiom). [clausify(640)]. 162.74/162.59 6375 -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(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3297_zero__less__ceiling) # label(axiom). [clausify(640)]. 162.74/162.59 6376 -archim1727834104eiling(A) | 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)) = 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))) # label(fact_2888_floor__add__number__of) # label(axiom). [clausify(652)]. 162.74/162.59 6377 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_2885_floor__less__number__of) # label(axiom). [clausify(740)]. 162.74/162.59 6378 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_2885_floor__less__number__of) # label(axiom). [clausify(740)]. 162.74/162.59 6379 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) # label(fact_3595_ceiling__le__iff) # label(axiom). [clausify(760)]. 162.74/162.59 6380 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),C))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) # label(fact_3595_ceiling__le__iff) # label(axiom). [clausify(760)]. 162.74/162.59 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(6356,a,6357,a)]. 162.74/162.59 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(6356,a,6358,a)]. 162.74/162.59 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(6356,a,6359,a)]. 162.74/162.59 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6356,a,6360,a)]. 162.74/162.59 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),zero_zero(int))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))). [resolve(6356,a,6361,a)]. 162.74/162.63 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(6356,a,6362,a)]. 162.74/162.63 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(6356,a,6363,a)]. 162.74/162.63 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(6356,a,6364,a)]. 162.74/162.63 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(6356,a,6365,a)]. 162.74/162.63 Derived: ti(int,A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(6356,a,6366,a)]. 162.74/162.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))). [resolve(6356,a,6368,a)]. 162.74/162.63 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),one_one(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))). [resolve(6356,a,6369,a)]. 162.74/162.63 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))). [resolve(6356,a,6370,a)]. 162.74/162.63 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(nat,rat,semiring_1_of_nat(rat),A)). [resolve(6356,a,6371,a)]. 162.74/162.63 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(6356,a,6372,a)]. 162.74/162.63 Derived: ti(int,A) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(int,rat,ring_1_of_int(rat),A)). [resolve(6356,a,6373,a)]. 162.74/162.63 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(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(6356,a,6374,a)]. 162.74/162.63 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(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))). [resolve(6356,a,6375,a)]. 162.74/162.63 Derived: 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)) = 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))). [resolve(6356,a,6376,a)]. 162.74/162.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(6356,a,6377,a)]. 162.74/162.63 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),B))). [resolve(6356,a,6378,a)]. 162.74/162.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)). [resolve(6356,a,6379,a)]. 162.84/162.68 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)). [resolve(6356,a,6380,a)]. 162.84/162.68 6381 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2882_floor__le__zero) # label(axiom). [clausify(802)]. 162.84/162.68 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(6381,a,6356,a)]. 162.84/162.68 6382 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),one_one(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),zero_zero(int))) # label(fact_2882_floor__le__zero) # label(axiom). [clausify(802)]. 162.84/162.68 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(6382,a,6356,a)]. 162.84/162.68 6383 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2880_zero__le__floor) # label(axiom). [clausify(807)]. 162.84/162.68 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(6383,a,6356,a)]. 162.84/162.68 6384 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2880_zero__le__floor) # label(axiom). [clausify(807)]. 162.84/162.68 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(6384,a,6356,a)]. 162.84/162.68 6385 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3608_less__floor__iff) # label(axiom). [clausify(818)]. 162.84/162.68 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(6385,a,6356,a)]. 162.84/162.68 6386 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) # label(fact_3608_less__floor__iff) # label(axiom). [clausify(818)]. 162.84/162.68 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(rat,int,archim2085082626_floor(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)). [resolve(6386,a,6356,a)]. 162.84/162.68 6387 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3607_ceiling__correct) # label(axiom). [clausify(900)]. 162.84/162.68 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(6387,a,6356,a)]. 162.98/162.82 6388 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B))),one_one(A))),B)) # label(fact_3607_ceiling__correct) # label(axiom). [clausify(900)]. 162.98/162.82 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(6388,a,6356,a)]. 162.98/162.82 6389 -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_3355_floor__ceiling) # label(axiom). [clausify(945)]. 162.98/162.82 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(6389,a,6356,a)]. 162.98/162.82 6390 -archim1727834104eiling(A) | hAPP(int,int,uminus_uminus(int),hAPP(A,int,archimedean_ceiling(A),B)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_3293_floor__minus) # label(axiom). [clausify(957)]. 162.98/162.82 Derived: hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archimedean_ceiling(rat),A)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6390,a,6356,a)]. 162.98/162.82 6391 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archimedean_ceiling(A),one_one(A)) # label(fact_3282_ceiling__one) # label(axiom). [clausify(962)]. 162.98/162.82 Derived: one_one(int) = hAPP(rat,int,archimedean_ceiling(rat),one_one(rat)). [resolve(6391,a,6356,a)]. 162.98/162.82 6392 -archim1727834104eiling(A) | hAPP(A,int,archim2085082626_floor(A),zero_zero(A)) = zero_zero(int) # label(fact_2863_floor__zero) # label(axiom). [clausify(1122)]. 162.98/162.82 Derived: hAPP(rat,int,archim2085082626_floor(rat),zero_zero(rat)) = zero_zero(int). [resolve(6392,a,6356,a)]. 162.98/162.82 6393 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) = 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))) # label(fact_3597_ceiling__add__of__int) # label(axiom). [clausify(1174)]. 162.98/162.82 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B) = 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))). [resolve(6393,a,6356,a)]. 162.98/162.82 6394 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3300_one__le__ceiling) # label(axiom). [clausify(1457)]. 162.98/162.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6394,a,6356,a)]. 162.98/162.82 6395 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) # label(fact_3300_one__le__ceiling) # label(axiom). [clausify(1457)]. 162.98/162.82 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)). [resolve(6395,a,6356,a)]. 162.98/162.82 6396 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3592_floor__less__iff) # label(axiom). [clausify(1467)]. 162.98/162.82 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(6396,a,6356,a)]. 163.22/163.04 6397 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),C))) # label(fact_3592_floor__less__iff) # label(axiom). [clausify(1467)]. 163.22/163.04 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),B))). [resolve(6397,a,6356,a)]. 163.22/163.04 6398 -archim1727834104eiling(A) | 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)) = 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))) # label(fact_3306_ceiling__add__number__of) # label(axiom). [clausify(1473)]. 163.22/163.04 Derived: 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)) = 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))). [resolve(6398,a,6356,a)]. 163.22/163.04 6399 -archim1727834104eiling(A) | hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),B)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_3294_ceiling__minus) # label(axiom). [clausify(1670)]. 163.22/163.04 Derived: hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),A)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6399,a,6356,a)]. 163.22/163.04 6400 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_2889_floor__diff__one) # label(axiom). [clausify(1876)]. 163.22/163.04 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))). [resolve(6400,a,6356,a)]. 163.22/163.04 6401 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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),hAPP(int,A,number_number_of(A),min_1))) # label(fact_3309_ceiling__less__zero) # label(axiom). [clausify(1908)]. 163.22/163.04 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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),hAPP(int,rat,number_number_of(rat),min_1))). [resolve(6401,a,6356,a)]. 163.22/163.04 6402 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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),hAPP(int,A,number_number_of(A),min_1))) # label(fact_3309_ceiling__less__zero) # label(axiom). [clausify(1908)]. 163.22/163.04 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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),hAPP(int,rat,number_number_of(rat),min_1))). [resolve(6402,a,6356,a)]. 163.22/163.04 6403 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) = 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))) # label(fact_3596_floor__add__of__int) # label(axiom). [clausify(2050)]. 163.22/163.04 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B) = 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))). [resolve(6403,a,6356,a)]. 163.22/163.04 6404 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3299_ceiling__less__one) # label(axiom). [clausify(2147)]. 163.44/163.29 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))). [resolve(6404,a,6356,a)]. 163.44/163.29 6405 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int))) # label(fact_3299_ceiling__less__one) # label(axiom). [clausify(2147)]. 163.44/163.29 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int))). [resolve(6405,a,6356,a)]. 163.44/163.29 6406 -archim1727834104eiling(A) | hAPP(int,int,number_number_of(int),B) = hAPP(A,int,archimedean_ceiling(A),hAPP(int,A,number_number_of(A),B)) # label(fact_3283_ceiling__number__of) # label(axiom). [clausify(2257)]. 163.44/163.29 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(int,rat,number_number_of(rat),A)). [resolve(6406,a,6356,a)]. 163.44/163.29 6407 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3281_ceiling__mono) # label(axiom). [clausify(2626)]. 163.44/163.29 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(6407,a,6356,a)]. 163.44/163.29 6408 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archim2085082626_floor(A),B)),C) = 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))) # label(fact_3598_floor__diff__of__int) # label(axiom). [clausify(2687)]. 163.44/163.29 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),B) = 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))). [resolve(6408,a,6356,a)]. 163.44/163.29 6409 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2886_number__of__le__floor) # label(axiom). [clausify(2698)]. 163.44/163.29 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(6409,a,6356,a)]. 163.44/163.29 6410 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,number_number_of(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archim2085082626_floor(A),C))) # label(fact_2886_number__of__le__floor) # label(axiom). [clausify(2698)]. 163.44/163.29 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,number_number_of(rat),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archim2085082626_floor(rat),B))). [resolve(6410,a,6356,a)]. 163.44/163.29 6411 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archim2085082626_floor(A),B)),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_2864_floor__less__cancel) # label(axiom). [clausify(2722)]. 163.44/163.29 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(6411,a,6356,a)]. 163.61/163.44 6412 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) # label(fact_3280_ceiling__less__cancel) # label(axiom). [clausify(2752)]. 163.61/163.44 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(6412,a,6356,a)]. 163.61/163.44 6413 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3611_le__ceiling__iff) # label(axiom). [clausify(2984)]. 163.61/163.44 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(6413,a,6356,a)]. 163.61/163.44 6414 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3611_le__ceiling__iff) # label(axiom). [clausify(2984)]. 163.61/163.44 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),A)),one_one(rat))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(rat,int,archimedean_ceiling(rat),B))). [resolve(6414,a,6356,a)]. 163.61/163.44 6415 -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_3302_ceiling__le__one) # label(axiom). [clausify(3071)]. 163.61/163.44 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(6415,a,6356,a)]. 163.61/163.44 6416 -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_3302_ceiling__le__one) # label(axiom). [clausify(3071)]. 163.61/163.44 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(6416,a,6356,a)]. 163.61/163.44 6417 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3609_floor__le__iff) # label(axiom). [clausify(3072)]. 163.61/163.44 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(6417,a,6356,a)]. 163.61/163.44 6418 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),C)) # label(fact_3609_floor__le__iff) # label(axiom). [clausify(3072)]. 163.61/163.44 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(6418,a,6356,a)]. 163.67/163.52 6419 -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_2884_one__le__floor) # label(axiom). [clausify(3082)]. 163.67/163.52 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(6419,a,6356,a)]. 163.67/163.52 6420 -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_2884_one__le__floor) # label(axiom). [clausify(3082)]. 163.67/163.52 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(6420,a,6356,a)]. 163.67/163.52 6421 -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_3298_ceiling__le__zero) # label(axiom). [clausify(3117)]. 163.67/163.52 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(6421,a,6356,a)]. 163.67/163.52 6422 -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_3298_ceiling__le__zero) # label(axiom). [clausify(3117)]. 163.67/163.52 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(6422,a,6356,a)]. 163.67/163.52 6423 archim1727834104eiling(real) # label(arity_RealDef_Oreal___Archimedean__Field_Ofloor__ceiling) # label(axiom). [assumption]. 163.67/163.52 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(6423,a,6357,a)]. 163.67/163.52 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(6423,a,6358,a)]. 163.67/163.52 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,number_number_of(real),A)). [resolve(6423,a,6359,a)]. 163.67/163.52 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6423,a,6360,a)]. 163.67/163.52 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),zero_zero(int))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))). [resolve(6423,a,6361,a)]. 163.67/163.52 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(6423,a,6362,a)]. 163.67/163.52 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(6423,a,6363,a)]. 163.67/163.55 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(6423,a,6364,a)]. 163.67/163.55 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(6423,a,6365,a)]. 163.67/163.55 Derived: ti(int,A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(6423,a,6366,a)]. 163.67/163.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))). [resolve(6423,a,6368,a)]. 163.67/163.55 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),one_one(real))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))). [resolve(6423,a,6369,a)]. 163.67/163.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))). [resolve(6423,a,6370,a)]. 163.67/163.55 Derived: hAPP(nat,int,semiring_1_of_nat(int),A) = hAPP(real,int,archim2085082626_floor(real),hAPP(nat,real,semiring_1_of_nat(real),A)). [resolve(6423,a,6371,a)]. 163.67/163.55 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(6423,a,6372,a)]. 163.67/163.55 Derived: ti(int,A) = hAPP(real,int,archim2085082626_floor(real),hAPP(int,real,ring_1_of_int(real),A)). [resolve(6423,a,6373,a)]. 163.67/163.55 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(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(6423,a,6374,a)]. 163.67/163.55 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(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))). [resolve(6423,a,6375,a)]. 163.67/163.55 Derived: 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)) = 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))). [resolve(6423,a,6376,a)]. 163.67/163.55 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(6423,a,6377,a)]. 163.67/163.55 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),B))). [resolve(6423,a,6378,a)]. 163.67/163.55 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)). [resolve(6423,a,6379,a)]. 163.67/163.55 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),B))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archimedean_ceiling(real),A)),B)). [resolve(6423,a,6380,a)]. 163.67/163.55 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(6423,a,6381,a)]. 163.74/163.58 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(6423,a,6382,a)]. 163.74/163.58 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(6423,a,6383,a)]. 163.74/163.58 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(6423,a,6384,a)]. 163.74/163.58 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(6423,a,6385,a)]. 163.74/163.58 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),hAPP(real,int,archim2085082626_floor(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)). [resolve(6423,a,6386,a)]. 163.74/163.58 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(6423,a,6387,a)]. 163.74/163.58 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(6423,a,6388,a)]. 163.74/163.58 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(6423,a,6389,a)]. 163.74/163.58 Derived: hAPP(int,int,uminus_uminus(int),hAPP(real,int,archimedean_ceiling(real),A)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(6423,a,6390,a)]. 163.74/163.58 Derived: one_one(int) = hAPP(real,int,archimedean_ceiling(real),one_one(real)). [resolve(6423,a,6391,a)]. 163.74/163.58 Derived: hAPP(real,int,archim2085082626_floor(real),zero_zero(real)) = zero_zero(int). [resolve(6423,a,6392,a)]. 163.74/163.58 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archimedean_ceiling(real),A)),B) = 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))). [resolve(6423,a,6393,a)]. 163.74/163.58 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6423,a,6394,a)]. 163.74/163.58 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),one_one(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)). [resolve(6423,a,6395,a)]. 163.74/163.58 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(6423,a,6396,a)]. 163.74/163.58 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archim2085082626_floor(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),B))). [resolve(6423,a,6397,a)]. 163.74/163.58 Derived: 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)) = 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))). [resolve(6423,a,6398,a)]. 163.78/163.61 Derived: hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),A)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(6423,a,6399,a)]. 163.78/163.61 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(6423,a,6400,a)]. 163.78/163.61 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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),hAPP(int,real,number_number_of(real),min_1))). [resolve(6423,a,6401,a)]. 163.78/163.61 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(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),hAPP(int,real,number_number_of(real),min_1))). [resolve(6423,a,6402,a)]. 163.78/163.61 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),B) = 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))). [resolve(6423,a,6403,a)]. 163.78/163.61 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(6423,a,6404,a)]. 163.78/163.61 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(6423,a,6405,a)]. 163.78/163.61 Derived: hAPP(int,int,number_number_of(int),A) = hAPP(real,int,archimedean_ceiling(real),hAPP(int,real,number_number_of(real),A)). [resolve(6423,a,6406,a)]. 163.78/163.61 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(6423,a,6407,a)]. 163.78/163.61 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archim2085082626_floor(real),A)),B) = 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))). [resolve(6423,a,6408,a)]. 163.78/163.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(6423,a,6409,a)]. 163.78/163.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,number_number_of(real),A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archim2085082626_floor(real),B))). [resolve(6423,a,6410,a)]. 163.78/163.61 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(6423,a,6411,a)]. 163.78/163.61 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(6423,a,6412,a)]. 163.78/163.61 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(6423,a,6413,a)]. 163.78/163.61 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),A)),one_one(real))),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(real,int,archimedean_ceiling(real),B))). [resolve(6423,a,6414,a)]. 163.81/163.69 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(6423,a,6415,a)]. 163.81/163.69 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(6423,a,6416,a)]. 163.81/163.69 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(6423,a,6417,a)]. 163.81/163.69 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(6423,a,6418,a)]. 163.81/163.69 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(6423,a,6419,a)]. 163.81/163.69 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(6423,a,6420,a)]. 163.81/163.69 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(6423,a,6421,a)]. 163.81/163.69 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(6423,a,6422,a)]. 163.81/163.69 6424 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),hAPP(A,int,archimedean_ceiling(A),B)))) # label(fact_3586_le__of__int__ceiling) # label(axiom). [clausify(3223)]. 163.81/163.69 6425 -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(3254)]. 163.81/163.69 Derived: archim2085082626_floor(rat) = ti(fun(rat,int),archim2085082626_floor(rat)). [resolve(6425,a,6356,a)]. 163.81/163.69 Derived: archim2085082626_floor(real) = ti(fun(real,int),archim2085082626_floor(real)). [resolve(6425,a,6423,a)]. 163.81/163.69 6426 -archim1727834104eiling(A) | 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)) = 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))) # label(fact_2890_floor__diff__number__of) # label(axiom). [clausify(3260)]. 163.81/163.69 Derived: 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)) = 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))). [resolve(6426,a,6356,a)]. 163.81/163.69 Derived: 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)) = 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))). [resolve(6426,a,6423,a)]. 163.81/163.69 6427 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_3310_zero__le__ceiling) # label(axiom). [clausify(3290)]. 163.81/163.73 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)). [resolve(6427,a,6356,a)]. 163.81/163.73 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),A)). [resolve(6427,a,6423,a)]. 163.81/163.73 6428 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,archimedean_ceiling(A),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),min_1)),B)) # label(fact_3310_zero__le__ceiling) # label(axiom). [clausify(3290)]. 163.81/163.73 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(rat,int,archimedean_ceiling(rat),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,number_number_of(rat),min_1)),A)). [resolve(6428,a,6356,a)]. 163.81/163.73 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(real,int,archimedean_ceiling(real),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,number_number_of(real),min_1)),A)). [resolve(6428,a,6423,a)]. 163.81/163.73 6429 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_3212_number__of__le__ceiling) # label(axiom). [clausify(3292)]. 163.81/163.73 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(6429,a,6356,a)]. 163.81/163.73 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(6429,a,6423,a)]. 163.81/163.73 6430 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),B)),one_one(A))),C)) # label(fact_3212_number__of__le__ceiling) # label(axiom). [clausify(3292)]. 163.81/163.73 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(rat,int,archimedean_ceiling(rat),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),A)),one_one(rat))),B)). [resolve(6430,a,6356,a)]. 163.81/163.73 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,number_number_of(int),A)),hAPP(real,int,archimedean_ceiling(real),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),A)),one_one(real))),B)). [resolve(6430,a,6423,a)]. 163.81/163.73 6431 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3301_one__less__ceiling) # label(axiom). [clausify(3342)]. 163.81/163.73 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(6431,a,6356,a)]. 164.10/163.94 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(6431,a,6423,a)]. 164.10/163.94 6432 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),one_one(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archimedean_ceiling(A),B))) # label(fact_3301_one__less__ceiling) # label(axiom). [clausify(3342)]. 164.10/163.94 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(6432,a,6356,a)]. 164.10/163.94 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(6432,a,6423,a)]. 164.10/163.94 6433 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3610_ceiling__less__iff) # label(axiom). [clausify(3471)]. 164.10/163.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(6433,a,6356,a)]. 164.10/163.94 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(6433,a,6423,a)]. 164.10/163.94 6434 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),C)),one_one(A)))) # label(fact_3610_ceiling__less__iff) # label(axiom). [clausify(3471)]. 164.10/163.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,ring_1_of_int(rat),B)),one_one(rat)))). [resolve(6434,a,6356,a)]. 164.10/163.94 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,ring_1_of_int(real),B)),one_one(real)))). [resolve(6434,a,6423,a)]. 164.10/163.94 6435 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A))),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(int,A,ring_1_of_int(A),B))) | ti(int,B) = hAPP(A,int,archimedean_ceiling(A),C) # label(fact_3606_ceiling__unique) # label(axiom). [clausify(3493)]. 164.10/163.94 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(6435,a,6356,a)]. 164.10/163.94 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(6435,a,6423,a)]. 164.27/164.15 6436 -archim1727834104eiling(A) | archimedean_ceiling(A) = ti(fun(A,int),archimedean_ceiling(A)) # label(tsy_c_Archimedean__Field_Oceiling_res) # label(axiom). [clausify(3560)]. 164.27/164.15 Derived: archimedean_ceiling(rat) = ti(fun(rat,int),archimedean_ceiling(rat)). [resolve(6436,a,6356,a)]. 164.27/164.15 Derived: archimedean_ceiling(real) = ti(fun(real,int),archimedean_ceiling(real)). [resolve(6436,a,6423,a)]. 164.27/164.15 6437 -archim1727834104eiling(A) | hAPP(int,int,uminus_uminus(int),hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,uminus_uminus(A),B))) = hAPP(A,int,archimedean_ceiling(A),B) # label(fact_3295_ceiling__def) # label(axiom). [clausify(3619)]. 164.27/164.15 Derived: hAPP(int,int,uminus_uminus(int),hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,uminus_uminus(rat),A))) = hAPP(rat,int,archimedean_ceiling(rat),A). [resolve(6437,a,6356,a)]. 164.27/164.15 Derived: hAPP(int,int,uminus_uminus(int),hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,uminus_uminus(real),A))) = hAPP(real,int,archimedean_ceiling(real),A). [resolve(6437,a,6423,a)]. 164.27/164.15 6438 -archim1727834104eiling(A) | -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))) | 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)) # label(fact_2893_number__of__less__floor) # label(axiom). [clausify(3779)]. 164.27/164.15 Derived: -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))) | 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)). [resolve(6438,a,6356,a)]. 164.27/164.15 Derived: -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))) | 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)). [resolve(6438,a,6423,a)]. 164.27/164.15 6439 -archim1727834104eiling(A) | 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))) | -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)) # label(fact_2893_number__of__less__floor) # label(axiom). [clausify(3779)]. 164.27/164.15 Derived: 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))) | -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)). [resolve(6439,a,6356,a)]. 164.27/164.15 Derived: 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))) | -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)). [resolve(6439,a,6423,a)]. 164.27/164.15 6440 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3594_less__ceiling__iff) # label(axiom). [clausify(3843)]. 164.27/164.15 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(6440,a,6356,a)]. 164.27/164.15 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(6440,a,6423,a)]. 164.58/164.45 6441 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3594_less__ceiling__iff) # label(axiom). [clausify(3843)]. 164.58/164.45 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(6441,a,6356,a)]. 164.58/164.45 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(6441,a,6423,a)]. 164.58/164.45 6442 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_3311_ceiling__less__number__of) # label(axiom). [clausify(4027)]. 164.58/164.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(6442,a,6356,a)]. 164.58/164.45 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(6442,a,6423,a)]. 164.58/164.45 6443 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(int,A,number_number_of(A),C)),one_one(A)))) # label(fact_3311_ceiling__less__number__of) # label(axiom). [clausify(4027)]. 164.58/164.45 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(rat,int,archimedean_ceiling(rat),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(int,rat,number_number_of(rat),B)),one_one(rat)))). [resolve(6443,a,6356,a)]. 164.58/164.45 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(real,int,archimedean_ceiling(real),A)),hAPP(int,int,number_number_of(int),B))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(int,real,number_number_of(real),B)),one_one(real)))). [resolve(6443,a,6423,a)]. 164.58/164.45 6444 -archim1727834104eiling(A) | hAPP(A,int,archimedean_ceiling(A),zero_zero(A)) = zero_zero(int) # label(fact_3279_ceiling__zero) # label(axiom). [clausify(4050)]. 164.58/164.45 Derived: hAPP(rat,int,archimedean_ceiling(rat),zero_zero(rat)) = zero_zero(int). [resolve(6444,a,6356,a)]. 164.58/164.45 Derived: hAPP(real,int,archimedean_ceiling(real),zero_zero(real)) = zero_zero(int). [resolve(6444,a,6423,a)]. 164.58/164.45 6445 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_3304_ceiling__le__number__of) # label(axiom). [clausify(4275)]. 164.58/164.45 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(6445,a,6356,a)]. 164.58/164.45 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(6445,a,6423,a)]. 164.66/164.55 6446 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archimedean_ceiling(A),B)),hAPP(int,int,number_number_of(int),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,number_number_of(A),C))) # label(fact_3304_ceiling__le__number__of) # label(axiom). [clausify(4275)]. 164.66/164.55 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(6446,a,6356,a)]. 164.66/164.55 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(6446,a,6423,a)]. 164.66/164.55 6447 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),C) = 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))) # label(fact_3599_ceiling__diff__of__int) # label(axiom). [clausify(4283)]. 164.66/164.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),B) = 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))). [resolve(6447,a,6356,a)]. 164.66/164.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),B) = 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))). [resolve(6447,a,6423,a)]. 164.66/164.55 6448 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3303_number__of__less__ceiling) # label(axiom). [clausify(4322)]. 164.66/164.55 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(6448,a,6356,a)]. 164.66/164.55 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(6448,a,6423,a)]. 164.66/164.55 6449 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,number_number_of(A),B)),C)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,number_number_of(int),B)),hAPP(A,int,archimedean_ceiling(A),C))) # label(fact_3303_number__of__less__ceiling) # label(axiom). [clausify(4322)]. 164.66/164.55 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(6449,a,6356,a)]. 164.66/164.55 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(6449,a,6423,a)]. 164.66/164.55 6450 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int)) = hAPP(A,int,archim2085082626_floor(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))) # label(fact_2887_floor__add__one) # label(axiom). [clausify(4417)]. 164.95/164.78 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int)) = hAPP(rat,int,archim2085082626_floor(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))). [resolve(6450,a,6356,a)]. 164.95/164.78 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int)) = hAPP(real,int,archim2085082626_floor(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))). [resolve(6450,a,6423,a)]. 164.95/164.78 6451 -archim1727834104eiling(A) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(A,int,archimedean_ceiling(A),B)),one_one(int)) = hAPP(A,int,archimedean_ceiling(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),one_one(A))) # label(fact_3307_ceiling__diff__one) # label(axiom). [clausify(4511)]. 164.95/164.78 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(rat,int,archimedean_ceiling(rat),A)),one_one(int)) = hAPP(rat,int,archimedean_ceiling(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),one_one(rat))). [resolve(6451,a,6356,a)]. 164.95/164.78 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(real,int,archimedean_ceiling(real),A)),one_one(int)) = hAPP(real,int,archimedean_ceiling(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),one_one(real))). [resolve(6451,a,6423,a)]. 164.95/164.78 6452 -archim1727834104eiling(A) | one_one(int) = hAPP(A,int,archim2085082626_floor(A),one_one(A)) # label(fact_2870_floor__one) # label(axiom). [clausify(4521)]. 164.95/164.78 Derived: one_one(int) = hAPP(rat,int,archim2085082626_floor(rat),one_one(rat)). [resolve(6452,a,6356,a)]. 164.95/164.78 Derived: one_one(int) = hAPP(real,int,archim2085082626_floor(real),one_one(real)). [resolve(6452,a,6423,a)]. 164.95/164.78 6453 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2847_floor__le__one) # label(axiom). [clausify(4647)]. 164.95/164.78 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))). [resolve(6453,a,6356,a)]. 164.95/164.78 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))). [resolve(6453,a,6423,a)]. 164.95/164.78 6454 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,number_number_of(A),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,archim2085082626_floor(A),B)),one_one(int))) # label(fact_2847_floor__le__one) # label(axiom). [clausify(4647)]. 164.95/164.78 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,number_number_of(rat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(rat,int,archim2085082626_floor(rat),A)),one_one(int))). [resolve(6454,a,6356,a)]. 164.95/164.78 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,number_number_of(real),hAPP(int,int,bit0,hAPP(int,int,bit1,pls))))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(real,int,archim2085082626_floor(real),A)),one_one(int))). [resolve(6454,a,6423,a)]. 164.95/164.78 6455 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(int,A,ring_1_of_int(A),B)),one_one(A)))) | ti(int,B) = hAPP(A,int,archim2085082626_floor(A),C) # label(fact_3605_floor__unique) # label(axiom). [clausify(4698)]. 165.05/164.87 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(6455,a,6356,a)]. 165.05/164.87 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(6455,a,6423,a)]. 165.05/164.87 6456 -archim1727834104eiling(A) | -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)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2895_one__less__floor) # label(axiom). [clausify(4736)]. 165.05/164.87 Derived: -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)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(6456,a,6356,a)]. 165.05/164.87 Derived: -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)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(6456,a,6423,a)]. 165.05/164.87 6457 -archim1727834104eiling(A) | 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)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2895_one__less__floor) # label(axiom). [clausify(4736)]. 165.05/164.87 Derived: 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)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(6457,a,6356,a)]. 165.05/164.87 Derived: 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)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),one_one(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(6457,a,6423,a)]. 165.05/164.87 6458 -archim1727834104eiling(A) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3593_le__floor__iff) # label(axiom). [clausify(4820)]. 165.05/164.87 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(6458,a,6356,a)]. 165.05/164.87 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(6458,a,6423,a)]. 165.05/164.87 6459 -archim1727834104eiling(A) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(A,int,archim2085082626_floor(A),C))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),B)),C)) # label(fact_3593_le__floor__iff) # label(axiom). [clausify(4820)]. 165.05/164.87 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(6459,a,6356,a)]. 165.05/164.87 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(6459,a,6423,a)]. 168.66/168.53 6460 -archim1727834104eiling(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2881_zero__less__floor) # label(axiom). [clausify(4836)]. 168.66/168.53 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(6460,a,6356,a)]. 168.66/168.53 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(6460,a,6423,a)]. 168.66/168.53 6461 -archim1727834104eiling(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),one_one(A)),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(A,int,archim2085082626_floor(A),B))) # label(fact_2881_zero__less__floor) # label(axiom). [clausify(4836)]. 168.66/168.53 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),one_one(rat)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(rat,int,archim2085082626_floor(rat),A))). [resolve(6461,a,6356,a)]. 168.66/168.53 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),one_one(real)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(real,int,archim2085082626_floor(real),A))). [resolve(6461,a,6423,a)]. 168.66/168.53 6462 -archim1727834104eiling(A) | 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)) = 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))) # label(fact_3308_ceiling__diff__number__of) # label(axiom). [clausify(4867)]. 168.66/168.53 Derived: 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)) = 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))). [resolve(6462,a,6356,a)]. 168.66/168.53 Derived: 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)) = 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))). [resolve(6462,a,6423,a)]. 168.66/168.53 6463 -ordere779506340up_add(A) | -semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f253(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_4296_setsum__bounded) # label(axiom). [clausify(1241)]. 168.66/168.53 6464 ordere779506340up_add(int) # label(arity_Int_Oint___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 168.66/168.53 6465 ordere779506340up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 168.66/168.53 6466 ordere779506340up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 168.66/168.53 Derived: -semiring_1(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f253(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(6463,a,6464,a)]. 168.66/168.53 Derived: -semiring_1(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f253(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(6463,a,6465,a)]. 169.08/168.92 Derived: -semiring_1(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f253(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(6463,a,6466,a)]. 169.08/168.92 6467 -ordere779506340up_add(A) | -semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f253(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_4296_setsum__bounded) # label(axiom). [clausify(1241)]. 169.08/168.92 Derived: -semiring_1(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f253(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(6467,a,6464,a)]. 169.08/168.92 Derived: -semiring_1(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f253(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(6467,a,6465,a)]. 169.08/168.92 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,f253(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(6467,a,6466,a)]. 169.08/168.92 6468 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f432(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4309_setsum__nonneg) # label(axiom). [clausify(2307)]. 169.08/168.92 Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f432(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(6468,b,6464,a)]. 169.08/168.92 Derived: -comm_monoid_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f432(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(6468,b,6465,a)]. 169.13/168.95 Derived: -comm_monoid_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f432(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(6468,b,6466,a)]. 169.13/168.95 6469 -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,f432(B,A,C,D)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D))) # label(fact_4309_setsum__nonneg) # label(axiom). [clausify(2307)]. 169.13/168.95 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,f432(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(6469,b,6464,a)]. 169.13/168.95 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,f432(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(6469,b,6465,a)]. 169.13/168.95 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,f432(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(6469,b,6466,a)]. 169.13/168.95 6470 -comm_monoid_add(A) | -ordere779506340up_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),f441(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4292_setsum__mono3) # label(axiom). [clausify(2337)]. 169.13/168.95 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),f441(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(6470,b,6464,a)]. 169.13/168.95 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),f441(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(6470,b,6465,a)]. 169.43/169.24 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),f441(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(6470,b,6466,a)]. 169.43/169.24 6471 -comm_monoid_add(A) | -ordere779506340up_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,f441(B,A,E,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4292_setsum__mono3) # label(axiom). [clausify(2337)]. 169.43/169.24 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,f441(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(6471,b,6464,a)]. 169.43/169.24 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,f441(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(6471,b,6465,a)]. 169.43/169.24 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,f441(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(6471,b,6466,a)]. 169.43/169.24 6472 -ordere779506340up_add(A) | -comm_monoid_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f526(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4343_setsum__mono) # label(axiom). [clausify(2901)]. 169.50/169.33 Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f526(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(6472,a,6464,a)]. 169.50/169.33 Derived: -comm_monoid_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f526(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(6472,a,6465,a)]. 169.50/169.33 Derived: -comm_monoid_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f526(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(6472,a,6466,a)]. 169.50/169.33 6473 -ordere779506340up_add(A) | -comm_monoid_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f526(B,A,C,D,E))),hAPP(B,A,D,f526(B,A,C,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4343_setsum__mono) # label(axiom). [clausify(2901)]. 169.50/169.33 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f526(A,int,B,C,D))),hAPP(A,int,C,f526(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(6473,a,6464,a)]. 169.50/169.33 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f526(A,real,B,C,D))),hAPP(A,real,C,f526(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(6473,a,6465,a)]. 169.50/169.33 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,f526(A,code_code_numeral,B,C,D))),hAPP(A,code_code_numeral,C,f526(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(6473,a,6466,a)]. 169.50/169.33 6474 -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_781_add__mono) # label(axiom). [clausify(3050)]. 169.50/169.33 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(6474,a,6464,a)]. 170.09/169.93 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),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(6474,a,6465,a)]. 170.09/169.93 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(6474,a,6466,a)]. 170.09/169.93 6475 -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_783_add__right__mono) # label(axiom). [clausify(3184)]. 170.09/169.93 6476 ordere779506340up_add(rat) # label(arity_Rat_Orat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 170.09/169.93 Derived: -semiring_1(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f253(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(6476,a,6463,a)]. 170.09/169.93 Derived: -semiring_1(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f253(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(6476,a,6467,a)]. 170.09/169.93 Derived: -comm_monoid_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f432(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(6476,a,6468,b)]. 170.09/169.93 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,f432(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(6476,a,6469,b)]. 170.09/169.93 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),f441(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(6476,a,6470,b)]. 170.09/169.93 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,f441(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(6476,a,6471,b)]. 170.16/170.00 Derived: -comm_monoid_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f526(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(6476,a,6472,a)]. 170.16/170.00 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f526(A,rat,B,C,D))),hAPP(A,rat,C,f526(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(6476,a,6473,a)]. 170.16/170.00 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),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(6476,a,6474,a)]. 170.16/170.00 6477 -comm_monoid_add(A) | -ordere779506340up_add(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f668(B,A,C,D)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)),zero_zero(A))) # label(fact_4308_setsum__nonpos) # label(axiom). [clausify(3854)]. 170.16/170.00 Derived: -comm_monoid_add(int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f668(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(6477,b,6464,a)]. 170.16/170.00 Derived: -comm_monoid_add(real) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f668(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(6477,b,6465,a)]. 170.16/170.00 Derived: -comm_monoid_add(code_code_numeral) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f668(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(6477,b,6466,a)]. 170.16/170.00 Derived: -comm_monoid_add(rat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f668(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(6477,b,6476,a)]. 170.16/170.00 6478 -comm_monoid_add(A) | -ordere779506340up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(B,A,C,f668(B,A,C,D))),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)),zero_zero(A))) # label(fact_4308_setsum__nonpos) # label(axiom). [clausify(3854)]. 170.16/170.00 Derived: -comm_monoid_add(int) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(A,int,B,f668(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(6478,b,6464,a)]. 170.16/170.05 Derived: -comm_monoid_add(real) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(A,real,B,f668(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(6478,b,6465,a)]. 170.16/170.05 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,f668(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(6478,b,6466,a)]. 170.16/170.05 Derived: -comm_monoid_add(rat) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(A,rat,B,f668(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(6478,b,6476,a)]. 170.16/170.05 6479 ordere779506340up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 170.16/170.05 Derived: -semiring_1(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f253(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(6479,a,6463,a)]. 170.16/170.05 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,f253(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(6479,a,6467,a)]. 170.16/170.05 Derived: -comm_monoid_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f432(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(6479,a,6468,b)]. 170.16/170.05 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,f432(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(6479,a,6469,b)]. 170.25/170.06 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),f441(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(6479,a,6470,b)]. 170.25/170.06 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,f441(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(6479,a,6471,b)]. 170.25/170.06 Derived: -comm_monoid_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f526(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(6479,a,6472,a)]. 170.25/170.06 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,f526(A,quickcheck_code_int,B,C,D))),hAPP(A,quickcheck_code_int,C,f526(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(6479,a,6473,a)]. 170.25/170.06 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(6479,a,6474,a)]. 170.25/170.06 Derived: -comm_monoid_add(quickcheck_code_int) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f668(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(6479,a,6477,b)]. 170.79/170.60 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,f668(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(6479,a,6478,b)]. 170.79/170.60 6480 -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_782_add__left__mono) # label(axiom). [clausify(3982)]. 170.79/170.60 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(6480,a,6464,a)]. 170.79/170.60 6481 ordere779506340up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__ab__semigroup__add) # label(axiom). [assumption]. 170.79/170.60 Derived: -semiring_1(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f253(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(6481,a,6463,a)]. 170.79/170.60 Derived: -semiring_1(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f253(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(6481,a,6467,a)]. 170.79/170.60 Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f432(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(6481,a,6468,b)]. 170.79/170.60 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,f432(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(6481,a,6469,b)]. 170.79/170.60 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),f441(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(6481,a,6470,b)]. 170.79/170.60 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,f441(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(6481,a,6471,b)]. 174.49/174.34 Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f526(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(6481,a,6472,a)]. 174.49/174.34 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f526(A,nat,B,C,D))),hAPP(A,nat,C,f526(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(6481,a,6473,a)]. 174.49/174.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(6481,a,6474,a)]. 174.49/174.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(6481,a,6475,a)]. 174.49/174.34 Derived: -comm_monoid_add(nat) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f668(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(6481,a,6477,b)]. 174.49/174.34 Derived: -comm_monoid_add(nat) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(A,nat,B,f668(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(6481,a,6478,b)]. 174.49/174.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),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(6481,a,6480,a)]. 174.49/174.34 6482 comm_semiring_1(nat) # label(arity_Nat_Onat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 174.49/174.34 6483 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,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_1310_comm__semiring__1__class_Onormalizing__semiring__rules_I27_J) # label(axiom). [clausify(153)]. 174.49/174.34 6484 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))) # label(fact_215_comm__semiring__1__class_Onormalizing__semiring__rules_I14_J) # label(axiom). [clausify(194)]. 174.49/174.34 6485 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_332_dvd__triv__left) # label(axiom). [clausify(327)]. 174.49/174.34 6486 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),D))) # label(fact_343_dvd__power__same) # label(axiom). [clausify(340)]. 174.62/174.48 6487 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),one_one(A)),B)) # label(fact_342_one__dvd) # label(axiom). [clausify(348)]. 174.62/174.48 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),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B)). [resolve(6482,a,6483,a)]. 174.62/174.48 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(6482,a,6485,a)]. 174.62/174.48 6488 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),B)) # label(fact_311_dvd__refl) # label(axiom). [clausify(417)]. 174.62/174.48 6489 -comm_semiring_1(A) | ti(A,B) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),one_one(nat)) # label(fact_227_comm__semiring__1__class_Onormalizing__semiring__rules_I33_J) # label(axiom). [clausify(566)]. 174.62/174.48 6490 -comm_semiring_1(A) | 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))) = 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))) # label(fact_4617_gauss__sum) # label(axiom). [clausify(572)]. 174.62/174.48 Derived: 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))) = 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))). [resolve(6490,a,6482,a)]. 174.62/174.48 6491 -comm_semiring_1(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(A,A,hAPP(A,fun(A,A),times_times(A),B),B) # label(fact_193_comm__semiring__1__class_Onormalizing__semiring__rules_I29_J) # label(axiom). [clausify(756)]. 174.62/174.48 6492 -comm_semiring_1(A) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),zero_zero(nat)) # label(fact_249_comm__semiring__1__class_Onormalizing__semiring__rules_I32_J) # label(axiom). [clausify(850)]. 174.62/174.48 Derived: one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),zero_zero(nat)). [resolve(6492,a,6482,a)]. 174.62/174.48 6493 -comm_semiring_1(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))) = 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))) # label(fact_1457_comm__semiring__1__class_Onormalizing__semiring__rules_I37_J) # label(axiom). [clausify(1146)]. 174.62/174.48 Derived: 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))) = 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))). [resolve(6493,a,6482,a)]. 174.62/174.48 6494 -comm_semiring_1(A) | 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),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),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),B),one_one(nat)))),D)))) = 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),C)),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))),D))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),B))) # label(fact_4324_arith__series__general) # label(axiom). [clausify(1187)]. 174.73/174.59 Derived: 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),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),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),A),one_one(nat)))),C)))) = 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),B)),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),hAPP(fun(nat,nat),fun(nat,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(nat,nat),fun(nat,fun(nat,nat))),combb(nat,fun(nat,nat),nat),times_times(nat)),semiring_1_of_nat(nat))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6494,a,6482,a)]. 174.73/174.59 6495 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B))) # label(fact_333_dvd__triv__right) # label(axiom). [clausify(1232)]. 174.73/174.59 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(6495,a,6482,a)]. 174.73/174.59 6496 -comm_semiring_1(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),D),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(B,A,E,D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),C))) # label(fact_3953_dvd__setprod) # label(axiom). [clausify(1399)]. 174.73/174.59 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(6496,a,6482,a)]. 174.73/174.59 6497 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_312_dvd__trans) # label(axiom). [clausify(1403)]. 174.73/174.59 6498 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_243_comm__semiring__1__class_Onormalizing__semiring__rules_I1_J) # label(axiom). [clausify(1534)]. 174.73/174.59 6499 comm_semiring_1(real) # label(arity_RealDef_Oreal___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 174.73/174.59 Derived: hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),hAPP(nat,nat,suc,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(6499,a,6483,a)]. 174.73/174.59 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(6499,a,6485,a)]. 174.73/174.59 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(6499,a,6486,a)]. 174.96/174.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),one_one(real)),A)). [resolve(6499,a,6487,a)]. 174.96/174.77 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),A)). [resolve(6499,a,6488,a)]. 174.96/174.77 Derived: 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))) = 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))). [resolve(6499,a,6490,a)]. 174.96/174.77 Derived: one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),zero_zero(nat)). [resolve(6499,a,6492,a)]. 174.96/174.77 Derived: 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))) = 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))). [resolve(6499,a,6493,a)]. 174.96/174.77 Derived: 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),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),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),A),one_one(nat)))),C)))) = 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),B)),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))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6499,a,6494,a)]. 174.96/174.77 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(6499,a,6495,a)]. 174.96/174.77 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(6499,a,6496,a)]. 174.96/174.77 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(6499,a,6497,a)]. 174.96/174.77 6500 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),one_one(A)) # label(fact_246_comm__semiring__1__class_Onormalizing__semiring__rules_I12_J) # label(axiom). [clausify(1960)]. 174.96/174.77 6501 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),E)) # label(fact_214_comm__semiring__1__class_Onormalizing__semiring__rules_I15_J) # label(axiom). [clausify(2083)]. 175.02/174.89 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(6501,a,6482,a)]. 175.02/174.89 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(6501,a,6499,a)]. 175.02/174.89 6502 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),E),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),E)),D)) # label(fact_344_power__le__dvd) # label(axiom). [clausify(2107)]. 175.02/174.89 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(6502,a,6482,a)]. 175.02/174.89 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(6502,a,6499,a)]. 175.02/174.89 6503 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),zero_zero(A)),B) = zero_zero(A) # label(fact_235_comm__semiring__1__class_Onormalizing__semiring__rules_I9_J) # label(axiom). [clausify(2148)]. 175.02/174.89 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(6503,a,6482,a)]. 175.02/174.89 6504 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C)),D) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) # label(fact_200_comm__semiring__1__class_Onormalizing__semiring__rules_I31_J) # label(axiom). [clausify(2198)]. 175.02/174.89 6505 -comm_semiring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),B)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),D),C))) # label(fact_346_le__imp__power__dvd) # label(axiom). [clausify(2261)]. 175.02/174.89 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(6505,a,6482,a)]. 175.02/174.89 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(6505,a,6499,a)]. 175.02/174.89 6506 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_242_comm__semiring__1__class_Onormalizing__semiring__rules_I8_J) # label(axiom). [clausify(2273)]. 175.02/174.89 6507 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),zero_zero(A)),B)) | ti(A,B) = zero_zero(A) # label(fact_329_dvd__0__left) # label(axiom). [clausify(2385)]. 175.16/175.00 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),zero_zero(nat)),A)) | ti(nat,A) = zero_zero(nat). [resolve(6507,a,6482,a)]. 175.16/175.00 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),zero_zero(real)),A)) | ti(real,A) = zero_zero(real). [resolve(6507,a,6499,a)]. 175.16/175.00 6508 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),one_one(A)),one_one(A))),B) # label(fact_253_comm__semiring__1__class_Onormalizing__semiring__rules_I4_J) # label(axiom). [clausify(2486)]. 175.16/175.00 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),one_one(nat)),one_one(nat))),A). [resolve(6508,a,6482,a)]. 175.16/175.00 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),one_one(real)),one_one(real))),A). [resolve(6508,a,6499,a)]. 175.16/175.00 6509 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),zero_zero(A)),B) # label(fact_237_comm__semiring__1__class_Onormalizing__semiring__rules_I5_J) # label(axiom). [clausify(2506)]. 175.16/175.00 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),zero_zero(nat)),A). [resolve(6509,a,6482,a)]. 175.16/175.00 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),zero_zero(real)),A). [resolve(6509,a,6499,a)]. 175.16/175.00 6510 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) # label(fact_219_comm__semiring__1__class_Onormalizing__semiring__rules_I19_J) # label(axiom). [clausify(2529)]. 175.16/175.00 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(6510,a,6482,a)]. 175.16/175.00 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(6510,a,6499,a)]. 175.16/175.00 6511 -comm_semiring_1(A) | one_one(A) != ti(A,B) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C))) # label(fact_462_dvd__power) # label(axiom). [clausify(2549)]. 175.16/175.00 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(6511,a,6482,a)]. 175.16/175.00 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(6511,a,6499,a)]. 175.16/175.00 6512 -comm_semiring_1(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B))) # label(fact_462_dvd__power) # label(axiom). [clausify(2549)]. 175.16/175.00 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),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),A))). [resolve(6512,a,6482,a)]. 175.16/175.00 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(6512,a,6499,a)]. 175.16/175.00 6513 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),D)),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),E))) # label(fact_345_dvd__power__le) # label(axiom). [clausify(2608)]. 175.26/175.07 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(6513,a,6482,a)]. 175.26/175.07 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(6513,a,6499,a)]. 175.26/175.07 6514 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),zero_zero(A)) = zero_zero(A) # label(fact_236_comm__semiring__1__class_Onormalizing__semiring__rules_I10_J) # label(axiom). [clausify(2649)]. 175.26/175.07 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),zero_zero(nat)) = zero_zero(nat). [resolve(6514,a,6482,a)]. 175.26/175.07 6515 comm_semiring_1(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 175.26/175.07 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(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(6515,a,6483,a)]. 175.26/175.07 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),C),D))). [resolve(6515,a,6484,a)]. 175.26/175.07 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(6515,a,6485,a)]. 175.26/175.07 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(6515,a,6486,a)]. 175.26/175.07 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(6515,a,6487,a)]. 175.26/175.07 Derived: hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),A)). [resolve(6515,a,6488,a)]. 175.26/175.07 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,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))) = 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))). [resolve(6515,a,6490,a)]. 175.26/175.08 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(6515,a,6492,a)]. 175.26/175.08 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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(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))). [resolve(6515,a,6493,a)]. 175.26/175.08 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(nat,code_code_numeral,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),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),hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(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(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),B)),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))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6515,a,6494,a)]. 175.26/175.08 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(6515,a,6495,a)]. 175.28/175.10 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(6515,a,6496,a)]. 175.28/175.10 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(6515,a,6497,a)]. 175.28/175.10 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(6515,a,6501,a)]. 175.28/175.10 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(6515,a,6502,a)]. 175.28/175.10 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(6515,a,6503,a)]. 175.28/175.10 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(6515,a,6505,a)]. 175.28/175.10 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),zero_zero(code_code_numeral)),A)) | ti(code_code_numeral,A) = zero_zero(code_code_numeral). [resolve(6515,a,6507,a)]. 175.28/175.10 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),one_one(code_code_numeral)),one_one(code_code_numeral))),A). [resolve(6515,a,6508,a)]. 175.28/175.10 Derived: ti(code_code_numeral,A) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(6515,a,6509,a)]. 175.28/175.10 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(6515,a,6510,a)]. 175.40/175.24 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(6515,a,6511,a)]. 175.40/175.24 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(6515,a,6512,a)]. 175.40/175.24 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(code_code_numeral),A),B)) | -hBOOL(hAPP(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(6515,a,6513,a)]. 175.40/175.24 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(6515,a,6514,a)]. 175.40/175.24 6516 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) # label(fact_338_dvd__mult__left) # label(axiom). [clausify(2779)]. 175.40/175.24 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(6516,a,6482,a)]. 175.40/175.24 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(6516,a,6499,a)]. 175.40/175.24 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(6516,a,6515,a)]. 175.40/175.24 6517 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),zero_zero(A)) # label(fact_238_comm__semiring__1__class_Onormalizing__semiring__rules_I6_J) # label(axiom). [clausify(2920)]. 175.40/175.24 Derived: ti(nat,A) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),zero_zero(nat)). [resolve(6517,a,6482,a)]. 175.40/175.24 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),zero_zero(real)). [resolve(6517,a,6499,a)]. 175.40/175.24 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(6517,a,6515,a)]. 175.40/175.24 6518 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_335_dvd__mult) # label(axiom). [clausify(3010)]. 175.40/175.26 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(6518,a,6482,a)]. 175.40/175.26 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(6518,a,6499,a)]. 175.40/175.26 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(6518,a,6515,a)]. 175.40/175.26 6519 -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),f548(B,A,E,F,D,C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom). [clausify(3029)]. 175.40/175.26 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),f548(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(6519,a,6482,a)]. 175.40/175.26 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),f548(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(6519,a,6499,a)]. 175.40/175.26 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),f548(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(6519,a,6515,a)]. 175.40/175.26 6520 -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,f548(B,A,E,F,D,C))),hAPP(B,A,F,f548(B,A,E,F,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),F),C))) # label(fact_3965_setprod__dvd__setprod__subset2) # label(axiom). [clausify(3029)]. 175.40/175.26 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,f548(A,nat,D,E,C,B))),hAPP(A,nat,E,f548(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(6520,a,6482,a)]. 175.46/175.31 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(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),hAPP(A,real,D,f548(A,real,D,E,C,B))),hAPP(A,real,E,f548(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(6520,a,6499,a)]. 175.46/175.31 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,f548(A,code_code_numeral,D,E,C,B))),hAPP(A,code_code_numeral,E,f548(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(6520,a,6515,a)]. 175.46/175.31 6521 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) # label(fact_334_dvd__mult2) # label(axiom). [clausify(3035)]. 175.46/175.31 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(6521,a,6482,a)]. 175.46/175.31 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(6521,a,6499,a)]. 175.46/175.31 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),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(6521,a,6515,a)]. 175.46/175.31 6522 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C) # label(fact_225_comm__semiring__1__class_Onormalizing__semiring__rules_I23_J) # label(axiom). [clausify(3122)]. 175.46/175.31 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(6522,a,6482,a)]. 175.46/175.31 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(6522,a,6499,a)]. 175.46/175.31 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(6522,a,6515,a)]. 175.63/175.46 6523 -comm_semiring_1(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),zero_zero(A))) # label(fact_282_dvd__0__right) # label(axiom). [clausify(3160)]. 175.63/175.46 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),zero_zero(nat))). [resolve(6523,a,6482,a)]. 175.63/175.46 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),zero_zero(real))). [resolve(6523,a,6499,a)]. 175.63/175.46 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(6523,a,6515,a)]. 175.63/175.46 6524 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B) # label(fact_220_comm__semiring__1__class_Onormalizing__semiring__rules_I7_J) # label(axiom). [clausify(3186)]. 175.63/175.46 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(6524,a,6482,a)]. 175.63/175.46 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(6524,a,6499,a)]. 175.63/175.46 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(6524,a,6515,a)]. 175.63/175.46 6525 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),one_one(A))),B) # label(fact_254_comm__semiring__1__class_Onormalizing__semiring__rules_I3_J) # label(axiom). [clausify(3259)]. 175.63/175.46 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat))),A). [resolve(6525,a,6482,a)]. 175.63/175.46 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),A)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),one_one(real))),A). [resolve(6525,a,6499,a)]. 175.63/175.46 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),A)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),one_one(code_code_numeral))),A). [resolve(6525,a,6515,a)]. 175.63/175.46 6526 -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)) | 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) = zero_zero(A) # label(fact_3950_setprod__zero) # label(axiom). [clausify(3370)]. 175.63/175.46 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(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) = zero_zero(nat). [resolve(6526,a,6482,a)]. 175.63/175.46 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(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) = zero_zero(real). [resolve(6526,a,6499,a)]. 175.63/175.49 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(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) = zero_zero(code_code_numeral). [resolve(6526,a,6515,a)]. 175.63/175.49 6527 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,C)) = 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) # label(fact_1309_comm__semiring__1__class_Onormalizing__semiring__rules_I28_J) # label(axiom). [clausify(3373)]. 175.63/175.49 6528 comm_semiring_1(rat) # label(arity_Rat_Orat___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 175.63/175.49 Derived: hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),hAPP(nat,nat,suc,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(6528,a,6483,a)]. 175.63/175.49 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D))). [resolve(6528,a,6484,a)]. 175.63/175.49 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(6528,a,6485,a)]. 175.63/175.49 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(6528,a,6486,a)]. 175.63/175.49 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),one_one(rat)),A)). [resolve(6528,a,6487,a)]. 175.63/175.49 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),A)). [resolve(6528,a,6488,a)]. 175.63/175.49 Derived: 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))) = 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))). [resolve(6528,a,6490,a)]. 175.63/175.49 Derived: one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),zero_zero(nat)). [resolve(6528,a,6492,a)]. 175.63/175.49 Derived: 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))) = 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))). [resolve(6528,a,6493,a)]. 175.63/175.49 Derived: 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),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),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),A),one_one(nat)))),C)))) = 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),B)),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))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6528,a,6494,a)]. 175.70/175.52 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(6528,a,6495,a)]. 175.70/175.52 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),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(6528,a,6496,a)]. 175.70/175.52 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(6528,a,6497,a)]. 175.70/175.52 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(6528,a,6501,a)]. 175.70/175.52 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(6528,a,6502,a)]. 175.70/175.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(6528,a,6503,a)]. 175.70/175.52 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(6528,a,6505,a)]. 175.70/175.52 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),zero_zero(rat)),A)) | ti(rat,A) = zero_zero(rat). [resolve(6528,a,6507,a)]. 175.70/175.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),one_one(rat)),one_one(rat))),A). [resolve(6528,a,6508,a)]. 175.70/175.52 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),zero_zero(rat)),A). [resolve(6528,a,6509,a)]. 175.70/175.52 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(6528,a,6510,a)]. 175.70/175.52 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(6528,a,6511,a)]. 175.70/175.52 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(6528,a,6512,a)]. 175.70/175.52 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(6528,a,6513,a)]. 175.70/175.52 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),zero_zero(rat)) = zero_zero(rat). [resolve(6528,a,6514,a)]. 175.70/175.52 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(6528,a,6516,a)]. 175.88/175.71 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),zero_zero(rat)). [resolve(6528,a,6517,a)]. 175.88/175.71 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(6528,a,6518,a)]. 175.88/175.71 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f548(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(6528,a,6519,a)]. 175.88/175.71 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),hAPP(A,rat,D,f548(A,rat,D,E,C,B))),hAPP(A,rat,E,f548(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(6528,a,6520,a)]. 175.88/175.71 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(6528,a,6521,a)]. 175.88/175.71 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(6528,a,6522,a)]. 175.88/175.71 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),zero_zero(rat))). [resolve(6528,a,6523,a)]. 175.88/175.71 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(6528,a,6524,a)]. 175.88/175.71 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),A)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),one_one(rat))),A). [resolve(6528,a,6525,a)]. 175.88/175.71 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(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) = zero_zero(rat). [resolve(6528,a,6526,a)]. 175.88/175.71 6529 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_221_comm__semiring__1__class_Onormalizing__semiring__rules_I24_J) # label(axiom). [clausify(3386)]. 175.88/175.71 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(6529,a,6482,a)]. 175.88/175.71 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(6529,a,6499,a)]. 175.88/175.71 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(6529,a,6515,a)]. 175.88/175.71 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(6529,a,6528,a)]. 175.88/175.71 6530 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E)) # label(fact_226_comm__semiring__1__class_Onormalizing__semiring__rules_I20_J) # label(axiom). [clausify(3491)]. 175.93/175.75 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(6530,a,6482,a)]. 175.93/175.75 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(6530,a,6499,a)]. 175.93/175.75 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(6530,a,6515,a)]. 175.93/175.75 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(6530,a,6528,a)]. 175.93/175.75 6531 comm_semiring_1(int) # label(arity_Int_Oint___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 175.93/175.75 Derived: hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),hAPP(nat,nat,suc,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(6531,a,6483,a)]. 175.93/175.75 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D))). [resolve(6531,a,6484,a)]. 175.93/175.75 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(6531,a,6485,a)]. 175.93/175.75 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(6531,a,6486,a)]. 175.93/175.75 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),one_one(int)),A)). [resolve(6531,a,6487,a)]. 175.93/175.75 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),A)). [resolve(6531,a,6488,a)]. 175.93/175.75 Derived: 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))) = 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))). [resolve(6531,a,6490,a)]. 175.93/175.75 Derived: one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),zero_zero(nat)). [resolve(6531,a,6492,a)]. 175.93/175.78 Derived: 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))) = 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))). [resolve(6531,a,6493,a)]. 175.93/175.78 Derived: 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),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),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),A),one_one(nat)))),C)))) = 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),B)),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))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6531,a,6494,a)]. 175.93/175.78 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(6531,a,6495,a)]. 175.93/175.78 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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(6531,a,6496,a)]. 175.93/175.78 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(6531,a,6497,a)]. 175.93/175.78 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(6531,a,6501,a)]. 175.93/175.78 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(6531,a,6502,a)]. 175.93/175.78 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),zero_zero(int)),A) = zero_zero(int). [resolve(6531,a,6503,a)]. 175.93/175.78 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),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(6531,a,6505,a)]. 175.93/175.78 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),zero_zero(int)),A)) | ti(int,A) = zero_zero(int). [resolve(6531,a,6507,a)]. 175.93/175.78 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),one_one(int)),one_one(int))),A). [resolve(6531,a,6508,a)]. 175.93/175.78 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),zero_zero(int)),A). [resolve(6531,a,6509,a)]. 175.93/175.78 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(6531,a,6510,a)]. 175.93/175.80 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(6531,a,6511,a)]. 175.93/175.80 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(6531,a,6512,a)]. 175.93/175.80 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(6531,a,6513,a)]. 175.93/175.80 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),zero_zero(int)) = zero_zero(int). [resolve(6531,a,6514,a)]. 175.93/175.80 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(6531,a,6516,a)]. 175.93/175.80 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),zero_zero(int)). [resolve(6531,a,6517,a)]. 175.93/175.80 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B))). [resolve(6531,a,6518,a)]. 175.93/175.80 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),f548(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(6531,a,6519,a)]. 175.93/175.80 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,f548(A,int,D,E,C,B))),hAPP(A,int,E,f548(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(6531,a,6520,a)]. 175.93/175.80 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),B)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))). [resolve(6531,a,6521,a)]. 175.93/175.80 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(6531,a,6522,a)]. 175.93/175.80 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),zero_zero(int))). [resolve(6531,a,6523,a)]. 175.93/175.80 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),A)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))),A). [resolve(6531,a,6525,a)]. 175.93/175.80 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(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) = zero_zero(int). [resolve(6531,a,6526,a)]. 175.93/175.80 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(6531,a,6530,a)]. 176.06/175.91 6532 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_218_comm__semiring__1__class_Onormalizing__semiring__rules_I18_J) # label(axiom). [clausify(3556)]. 176.06/175.91 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(6532,a,6482,a)]. 176.06/175.91 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(6532,a,6499,a)]. 176.06/175.91 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(6532,a,6515,a)]. 176.06/175.91 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(6532,a,6528,a)]. 176.06/175.91 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(6532,a,6531,a)]. 176.06/175.91 6533 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) # label(fact_213_comm__semiring__1__class_Onormalizing__semiring__rules_I13_J) # label(axiom). [clausify(3718)]. 176.06/175.91 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(6533,a,6482,a)]. 176.06/175.91 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(6533,a,6499,a)]. 176.06/175.91 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(6533,a,6515,a)]. 176.14/175.97 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(6533,a,6528,a)]. 176.14/175.97 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(6533,a,6531,a)]. 176.14/175.97 6534 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_240_comm__semiring__1__class_Onormalizing__semiring__rules_I34_J) # label(axiom). [clausify(3735)]. 176.14/175.97 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),C)). [resolve(6534,a,6482,a)]. 176.14/175.97 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),B)),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),C)) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),A),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),B),C)). [resolve(6534,a,6515,a)]. 176.14/175.97 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),C)). [resolve(6534,a,6528,a)]. 176.14/175.97 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),C)). [resolve(6534,a,6531,a)]. 176.14/175.97 6535 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(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(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_247_comm__semiring__1__class_Onormalizing__semiring__rules_I30_J) # label(axiom). [clausify(3776)]. 176.14/175.97 6536 -comm_semiring_1(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)) = 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)) # label(fact_192_comm__semiring__1__class_Onormalizing__semiring__rules_I36_J) # label(axiom). [clausify(3809)]. 176.14/175.97 Derived: 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)) = 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)). [resolve(6536,a,6482,a)]. 176.30/176.14 Derived: 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)) = 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)). [resolve(6536,a,6499,a)]. 176.30/176.14 Derived: 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)) = 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)). [resolve(6536,a,6515,a)]. 176.30/176.14 Derived: 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)) = 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)). [resolve(6536,a,6528,a)]. 176.30/176.14 Derived: 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)) = 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)). [resolve(6536,a,6531,a)]. 176.30/176.14 6537 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_224_comm__semiring__1__class_Onormalizing__semiring__rules_I21_J) # label(axiom). [clausify(3920)]. 176.30/176.14 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(6537,a,6499,a)]. 176.30/176.14 Derived: hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),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(6537,a,6515,a)]. 176.30/176.14 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(6537,a,6528,a)]. 176.30/176.14 6538 -comm_semiring_1(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),one_one(A)),B) # label(fact_245_comm__semiring__1__class_Onormalizing__semiring__rules_I11_J) # label(axiom). [clausify(3948)]. 176.30/176.14 6539 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),one_one(A))),C) # label(fact_255_comm__semiring__1__class_Onormalizing__semiring__rules_I2_J) # label(axiom). [clausify(4035)]. 176.30/176.14 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),one_one(nat))),B). [resolve(6539,a,6482,a)]. 176.48/176.31 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),one_one(real))),B). [resolve(6539,a,6499,a)]. 176.48/176.31 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),times_times(code_code_numeral),A),B)),B) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),one_one(code_code_numeral))),B). [resolve(6539,a,6515,a)]. 176.48/176.31 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),one_one(rat))),B). [resolve(6539,a,6528,a)]. 176.48/176.31 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))),B). [resolve(6539,a,6531,a)]. 176.48/176.31 6540 -comm_semiring_1(A) | 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)) = 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)) # label(fact_248_comm__semiring__1__class_Onormalizing__semiring__rules_I26_J) # label(axiom). [clausify(4121)]. 176.48/176.31 6541 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) # label(fact_223_comm__semiring__1__class_Onormalizing__semiring__rules_I25_J) # label(axiom). [clausify(4260)]. 176.48/176.31 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(6541,a,6482,a)]. 176.48/176.31 6542 -comm_semiring_1(A) | hBOOL(hAPP(fun(B,bool),bool,hAPP(B,fun(fun(B,bool),bool),member(B),f743(B,A,C,D,E)),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E))) # label(fact_4773_dvd__setsum) # label(axiom). [clausify(4286)]. 176.48/176.31 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6542,a,6482,a)]. 176.48/176.31 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6542,a,6499,a)]. 176.48/176.31 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6542,a,6515,a)]. 176.48/176.31 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6542,a,6528,a)]. 176.53/176.34 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6542,a,6531,a)]. 176.53/176.34 6543 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(C,A,D,f743(C,A,B,D,E)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),D),E))) # label(fact_4773_dvd__setsum) # label(axiom). [clausify(4286)]. 176.53/176.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),A),hAPP(B,nat,C,f743(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(6543,a,6482,a)]. 176.53/176.34 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),A),hAPP(B,real,C,f743(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(6543,a,6499,a)]. 176.53/176.34 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,f743(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(6543,a,6515,a)]. 176.53/176.34 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),A),hAPP(B,rat,C,f743(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(6543,a,6528,a)]. 176.53/176.34 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),A),hAPP(B,int,C,f743(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(6543,a,6531,a)]. 176.53/176.34 6544 -comm_semiring_1(A) | -no_zero_divisors(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(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) = zero_zero(A) # label(fact_3949_setprod__zero__iff) # label(axiom). [clausify(4293)]. 176.53/176.34 6545 -comm_semiring_1(A) | -no_zero_divisors(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),f744(B,A,D,C)),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co302546470etprod(B,A),D),C) != zero_zero(A) # label(fact_3949_setprod__zero__iff) # label(axiom). [clausify(4293)]. 176.53/176.34 Derived: -no_zero_divisors(nat) | -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),f744(A,nat,C,B)),B)) | hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co302546470etprod(A,nat),C),B) != zero_zero(nat). [resolve(6545,a,6482,a)]. 176.53/176.34 Derived: -no_zero_divisors(real) | -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),f744(A,real,C,B)),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co302546470etprod(A,real),C),B) != zero_zero(real). [resolve(6545,a,6499,a)]. 176.53/176.34 Derived: -no_zero_divisors(code_code_numeral) | -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),f744(A,code_code_numeral,C,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),C),B) != zero_zero(code_code_numeral). [resolve(6545,a,6515,a)]. 176.59/176.42 Derived: -no_zero_divisors(rat) | -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),f744(A,rat,C,B)),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co302546470etprod(A,rat),C),B) != zero_zero(rat). [resolve(6545,a,6528,a)]. 176.59/176.42 Derived: -no_zero_divisors(int) | -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),f744(A,int,C,B)),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co302546470etprod(A,int),C),B) != zero_zero(int). [resolve(6545,a,6531,a)]. 176.59/176.42 6546 -comm_semiring_1(A) | -no_zero_divisors(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | hAPP(B,A,D,f744(B,A,D,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) # label(fact_3949_setprod__zero__iff) # label(axiom). [clausify(4293)]. 176.59/176.42 Derived: -no_zero_divisors(nat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,nat,C,f744(A,nat,C,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). [resolve(6546,a,6482,a)]. 176.59/176.42 Derived: -no_zero_divisors(real) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,real,C,f744(A,real,C,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). [resolve(6546,a,6499,a)]. 176.59/176.42 Derived: -no_zero_divisors(code_code_numeral) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,code_code_numeral,C,f744(A,code_code_numeral,C,B)) = zero_zero(code_code_numeral) | hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co302546470etprod(A,code_code_numeral),C),B) != zero_zero(code_code_numeral). [resolve(6546,a,6515,a)]. 176.59/176.42 Derived: -no_zero_divisors(rat) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,rat,C,f744(A,rat,C,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). [resolve(6546,a,6528,a)]. 176.59/176.42 Derived: -no_zero_divisors(int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,int,C,f744(A,int,C,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). [resolve(6546,a,6531,a)]. 176.59/176.42 6547 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_217_comm__semiring__1__class_Onormalizing__semiring__rules_I17_J) # label(axiom). [clausify(4369)]. 176.59/176.42 6548 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),D)) # label(fact_339_dvd__mult__right) # label(axiom). [clausify(4391)]. 176.59/176.42 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(6548,a,6482,a)]. 176.59/176.42 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(6548,a,6499,a)]. 176.59/176.42 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(6548,a,6515,a)]. 176.59/176.42 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(6548,a,6528,a)]. 176.65/176.49 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(6548,a,6531,a)]. 176.65/176.49 6549 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_336_mult__dvd__mono) # label(axiom). [clausify(4445)]. 176.65/176.49 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(6549,a,6482,a)]. 176.65/176.49 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(6549,a,6499,a)]. 176.65/176.49 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(6549,a,6515,a)]. 176.65/176.49 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(6549,a,6528,a)]. 176.65/176.49 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(6549,a,6531,a)]. 176.65/176.49 6550 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),D) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),C) # label(fact_216_comm__semiring__1__class_Onormalizing__semiring__rules_I16_J) # label(axiom). [clausify(4468)]. 176.65/176.49 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(6550,a,6482,a)]. 176.65/176.49 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(6550,a,6499,a)]. 176.65/176.49 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(6550,a,6515,a)]. 176.83/176.69 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(6550,a,6528,a)]. 176.83/176.69 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(6550,a,6531,a)]. 176.83/176.69 6551 -comm_semiring_1(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),hAPP(nat,nat,suc,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_1311_comm__semiring__1__class_Onormalizing__semiring__rules_I35_J) # label(axiom). [clausify(4587)]. 176.83/176.69 6552 comm_semiring_1(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 176.83/176.69 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(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(6552,a,6483,a)]. 176.83/176.69 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),D))). [resolve(6552,a,6484,a)]. 176.83/176.69 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(6552,a,6485,a)]. 176.83/176.69 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),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(6552,a,6486,a)]. 176.83/176.69 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(6552,a,6487,a)]. 176.83/176.69 Derived: hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),A)). [resolve(6552,a,6488,a)]. 176.83/176.69 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,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))) = 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))). [resolve(6552,a,6490,a)]. 176.83/176.69 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(6552,a,6492,a)]. 176.83/176.69 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,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(int,nat,number_number_of(nat),hAPP(int,int,bit0,hAPP(int,int,bit1,pls)))),B))) = hAPP(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))). [resolve(6552,a,6493,a)]. 176.83/176.69 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,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),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),hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,hAPP(nat,fun(nat,nat),minus_minus(nat),A),one_one(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(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),B)),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))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6552,a,6494,a)]. 176.83/176.70 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(6552,a,6495,a)]. 176.83/176.70 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(6552,a,6496,a)]. 176.83/176.70 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(6552,a,6497,a)]. 176.89/176.70 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(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(6552,a,6501,a)]. 176.89/176.70 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(6552,a,6502,a)]. 176.89/176.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(6552,a,6503,a)]. 176.89/176.70 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(6552,a,6505,a)]. 176.89/176.70 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int). [resolve(6552,a,6507,a)]. 176.89/176.70 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),one_one(quickcheck_code_int)),one_one(quickcheck_code_int))),A). [resolve(6552,a,6508,a)]. 176.89/176.71 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),zero_zero(quickcheck_code_int)),A). [resolve(6552,a,6509,a)]. 176.89/176.71 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),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(6552,a,6510,a)]. 176.89/176.71 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(6552,a,6511,a)]. 176.89/176.71 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(6552,a,6512,a)]. 176.89/176.71 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | -hBOOL(hAPP(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(6552,a,6513,a)]. 176.89/176.71 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),zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(6552,a,6514,a)]. 176.89/176.71 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(6552,a,6516,a)]. 176.89/176.71 Derived: ti(quickcheck_code_int,A) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),zero_zero(quickcheck_code_int)). [resolve(6552,a,6517,a)]. 176.89/176.71 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),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(6552,a,6518,a)]. 176.89/176.71 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f548(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(6552,a,6519,a)]. 176.89/176.72 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)) | -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,f548(A,quickcheck_code_int,D,E,C,B))),hAPP(A,quickcheck_code_int,E,f548(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(6552,a,6520,a)]. 176.89/176.72 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(quickcheck_code_int),A),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(6552,a,6521,a)]. 176.89/176.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),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(6552,a,6522,a)]. 176.89/176.72 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(6552,a,6523,a)]. 176.89/176.72 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(6552,a,6524,a)]. 176.89/176.72 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),one_one(quickcheck_code_int))),A). [resolve(6552,a,6525,a)]. 176.89/176.72 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),C),B)) | 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) = zero_zero(quickcheck_code_int). [resolve(6552,a,6526,a)]. 176.89/176.73 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(6552,a,6529,a)]. 176.89/176.73 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(6552,a,6530,a)]. 176.89/176.73 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(6552,a,6532,a)]. 176.89/176.73 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(6552,a,6533,a)]. 176.89/176.73 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),B),C)). [resolve(6552,a,6534,a)]. 176.89/176.73 Derived: 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)) = 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)). [resolve(6552,a,6536,a)]. 176.89/176.74 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(6552,a,6537,a)]. 176.89/176.74 Derived: hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),B) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),one_one(quickcheck_code_int))),B). [resolve(6552,a,6539,a)]. 176.89/176.74 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6552,a,6542,a)]. 176.89/176.74 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,f743(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(6552,a,6543,a)]. 176.89/176.74 Derived: -no_zero_divisors(quickcheck_code_int) | -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),f744(A,quickcheck_code_int,C,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),C),B) != zero_zero(quickcheck_code_int). [resolve(6552,a,6545,a)]. 176.89/176.74 Derived: -no_zero_divisors(quickcheck_code_int) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,quickcheck_code_int,C,f744(A,quickcheck_code_int,C,B)) = zero_zero(quickcheck_code_int) | hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co302546470etprod(A,quickcheck_code_int),C),B) != zero_zero(quickcheck_code_int). [resolve(6552,a,6546,a)]. 176.89/176.74 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(6552,a,6548,a)]. 176.89/176.74 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(6552,a,6549,a)]. 176.96/176.78 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(6552,a,6550,a)]. 176.96/176.78 6553 -comm_semiring_1(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)) # label(fact_222_comm__semiring__1__class_Onormalizing__semiring__rules_I22_J) # label(axiom). [clausify(4748)]. 176.96/176.78 Derived: 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)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)). [resolve(6553,a,6482,a)]. 176.96/176.78 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(6553,a,6499,a)]. 176.96/176.78 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(6553,a,6515,a)]. 176.96/176.78 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(6553,a,6528,a)]. 176.96/176.78 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(6553,a,6531,a)]. 176.96/176.78 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(6553,a,6552,a)]. 176.96/176.78 6554 comm_semiring_1(complex) # label(arity_Complex_Ocomplex___Rings_Ocomm__semiring__1) # label(axiom). [assumption]. 176.96/176.78 Derived: hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),hAPP(nat,nat,suc,B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B)). [resolve(6554,a,6483,a)]. 176.96/176.80 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D))). [resolve(6554,a,6484,a)]. 176.96/176.80 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(6554,a,6485,a)]. 176.96/176.80 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(6554,a,6486,a)]. 176.96/176.80 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),one_one(complex)),A)). [resolve(6554,a,6487,a)]. 176.96/176.80 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),A)). [resolve(6554,a,6488,a)]. 176.96/176.80 Derived: 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))) = 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))). [resolve(6554,a,6490,a)]. 176.96/176.80 Derived: one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),zero_zero(nat)). [resolve(6554,a,6492,a)]. 176.96/176.80 Derived: 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))) = 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))). [resolve(6554,a,6493,a)]. 176.96/176.80 Derived: 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),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),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),A),one_one(nat)))),C)))) = 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),B)),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))),C))),hAPP(nat,fun(nat,bool),ord_lessThan(nat),A))). [resolve(6554,a,6494,a)]. 176.96/176.81 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(6554,a,6495,a)]. 176.96/176.81 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)) | 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(6554,a,6496,a)]. 176.96/176.81 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(6554,a,6497,a)]. 176.96/176.81 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(6554,a,6501,a)]. 176.96/176.81 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(6554,a,6502,a)]. 176.96/176.81 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(6554,a,6505,a)]. 176.96/176.81 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),zero_zero(complex)),A)) | ti(complex,A) = zero_zero(complex). [resolve(6554,a,6507,a)]. 176.96/176.81 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),one_one(complex)),one_one(complex))),A). [resolve(6554,a,6508,a)]. 176.96/176.81 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),zero_zero(complex)),A). [resolve(6554,a,6509,a)]. 176.96/176.81 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(6554,a,6510,a)]. 176.96/176.81 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(6554,a,6511,a)]. 176.96/176.81 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(6554,a,6512,a)]. 176.96/176.81 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(6554,a,6513,a)]. 176.96/176.83 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(6554,a,6516,a)]. 176.96/176.83 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),zero_zero(complex)). [resolve(6554,a,6517,a)]. 176.96/176.83 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(6554,a,6518,a)]. 176.96/176.83 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),f548(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(6554,a,6519,a)]. 176.96/176.83 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,f548(A,complex,D,E,C,B))),hAPP(A,complex,E,f548(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(6554,a,6520,a)]. 176.96/176.83 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(6554,a,6521,a)]. 176.96/176.83 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(6554,a,6522,a)]. 176.96/176.83 Derived: hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),zero_zero(complex))). [resolve(6554,a,6523,a)]. 176.96/176.83 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(6554,a,6524,a)]. 176.96/176.83 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),one_one(complex))),A). [resolve(6554,a,6525,a)]. 176.96/176.83 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(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) = zero_zero(complex). [resolve(6554,a,6526,a)]. 176.96/176.83 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(6554,a,6529,a)]. 176.96/176.83 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(6554,a,6530,a)]. 176.96/176.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),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(6554,a,6532,a)]. 176.96/176.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),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(6554,a,6533,a)]. 176.96/176.85 Derived: 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)) = 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)). [resolve(6554,a,6536,a)]. 176.96/176.85 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(6554,a,6537,a)]. 176.96/176.85 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),one_one(complex))),B). [resolve(6554,a,6539,a)]. 176.96/176.85 Derived: hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f743(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(6554,a,6542,a)]. 176.96/176.85 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),hAPP(B,complex,C,f743(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(6554,a,6543,a)]. 176.96/176.85 Derived: -no_zero_divisors(complex) | -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),f744(A,complex,C,B)),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co302546470etprod(A,complex),C),B) != zero_zero(complex). [resolve(6554,a,6545,a)]. 176.96/176.85 Derived: -no_zero_divisors(complex) | -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | hAPP(A,complex,C,f744(A,complex,C,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). [resolve(6554,a,6546,a)]. 176.96/176.85 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(6554,a,6548,a)]. 176.96/176.85 Derived: -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),A),B)) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),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(6554,a,6549,a)]. 181.89/181.76 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(6554,a,6550,a)]. 181.89/181.76 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(6554,a,6553,a)]. 181.89/181.76 6555 -comm_semiring_1(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),B),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_340_dvd__add) # label(axiom). [clausify(4847)]. 181.89/181.76 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(6555,a,6482,a)]. 181.89/181.76 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),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(6555,a,6499,a)]. 181.89/181.76 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),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(6555,a,6515,a)]. 181.89/181.76 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),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(6555,a,6528,a)]. 181.89/181.76 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(6555,a,6531,a)]. 181.89/181.76 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),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(6555,a,6552,a)]. 181.89/181.76 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(6555,a,6554,a)]. 181.89/181.76 6556 -linord893533164strict(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_384_comm__mult__strict__left__mono) # label(axiom). [clausify(3661)]. 186.55/186.42 6557 linord893533164strict(int) # label(arity_Int_Oint___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 186.55/186.42 6558 linord893533164strict(nat) # label(arity_Nat_Onat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 186.55/186.42 6559 linord893533164strict(rat) # label(arity_Rat_Orat___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 186.55/186.42 6560 linord893533164strict(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 186.55/186.42 6561 linord893533164strict(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Olinordered__comm__semiring__stri) # label(axiom). [assumption]. 186.55/186.42 6562 linord893533164strict(real) # label(arity_RealDef_Oreal___Rings_Olinordered__comm__semiring__strict) # label(axiom). [assumption]. 186.55/186.42 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(6562,a,6556,a)]. 186.55/186.42 6563 ordere453448008miring(rat) # label(arity_Rat_Orat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 186.55/186.42 6564 -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),C),B)),zero_zero(A))) # label(fact_365_split__mult__neg__le) # label(axiom). [clausify(188)]. 186.55/186.42 6565 -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_365_split__mult__neg__le) # label(axiom). [clausify(188)]. 186.55/186.42 6566 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_375_mult__nonpos__nonneg) # label(axiom). [clausify(819)]. 186.55/186.42 6567 ordere453448008miring(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 186.55/186.42 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),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),times_times(code_code_numeral),B),A)),zero_zero(code_code_numeral))). [resolve(6567,a,6564,a)]. 186.55/186.42 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),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),times_times(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6567,a,6565,a)]. 187.63/187.51 6568 ordere453448008miring(int) # label(arity_Int_Oint___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 187.63/187.51 6569 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_378_mult__nonneg__nonneg) # label(axiom). [clausify(1743)]. 187.63/187.51 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(6569,a,6567,a)]. 187.63/187.51 6570 ordere453448008miring(real) # label(arity_RealDef_Oreal___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 187.63/187.51 6571 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),B)),zero_zero(A))) # label(fact_376_mult__nonneg__nonpos2) # label(axiom). [clausify(2550)]. 187.63/187.51 6572 -ordere453448008miring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),zero_zero(A))) # label(fact_377_mult__nonneg__nonpos) # label(axiom). [clausify(3326)]. 187.63/187.51 6573 ordere453448008miring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 187.63/187.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),A)),zero_zero(quickcheck_code_int))). [resolve(6573,a,6564,a)]. 187.63/187.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6573,a,6565,a)]. 187.63/187.51 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),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(6573,a,6569,a)]. 192.46/192.34 6574 ordere453448008miring(nat) # label(arity_Nat_Onat___Rings_Oordered__cancel__semiring) # label(axiom). [assumption]. 192.46/192.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),A)),zero_zero(nat))). [resolve(6574,a,6564,a)]. 192.46/192.34 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),zero_zero(nat))). [resolve(6574,a,6565,a)]. 192.46/192.34 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(6574,a,6569,a)]. 192.46/192.34 6575 ab_group_add(complex) # label(arity_Complex_Ocomplex___Groups_Oab__group__add) # label(axiom). [assumption]. 192.46/192.34 6576 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,C) != ti(A,B) | ti(A,E) = ti(A,D) # label(fact_773_diff__eq__diff__eq) # label(axiom). [clausify(198)]. 192.46/192.34 6577 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),D),E) | ti(A,C) = ti(A,B) | ti(A,E) != ti(A,D) # label(fact_773_diff__eq__diff__eq) # label(axiom). [clausify(198)]. 192.46/192.34 6578 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2052_minus__diff__minus) # label(axiom). [clausify(765)]. 192.46/192.34 6579 -ab_group_add(A) | -hBOOL(hAPP(fun(B,bool),bool,finite_finite_1(B),C)) | -hBOOL(hAPP(fun(B,bool),bool,hAPP(fun(B,bool),fun(fun(B,bool),bool),ord_less_eq(fun(B,bool)),D),C)) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)) # label(fact_4233_setsum__diff) # label(axiom). [clausify(1028)]. 192.46/192.34 6580 -ab_group_add(A) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),B),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),C))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),C)))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),B),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C))) # label(fact_4180_sumr__offset) # label(axiom). [clausify(1091)]. 192.46/192.34 6581 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),uminus_uminus(A)),C)),D) = hAPP(A,A,uminus_uminus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),D)) # label(fact_4213_setsum__negf) # label(axiom). [clausify(1401)]. 192.55/192.36 6582 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2075_ab__diff__minus) # label(axiom). [clausify(1660)]. 192.55/192.36 6583 -ab_group_add(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) = zero_zero(A) # label(fact_794_eq__iff__diff__eq__0) # label(axiom). [clausify(1688)]. 192.55/192.36 6584 -ab_group_add(A) | ti(A,B) = ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) != zero_zero(A) # label(fact_794_eq__iff__diff__eq__0) # label(axiom). [clausify(1688)]. 192.55/192.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,B) != ti(complex,A) | ti(complex,D) = ti(complex,C). [resolve(6575,a,6576,a)]. 192.55/192.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),C),D) | ti(complex,B) = ti(complex,A) | ti(complex,D) != ti(complex,C). [resolve(6575,a,6577,a)]. 192.55/192.36 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(6575,a,6578,a)]. 192.55/192.36 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),B)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),D),C)). [resolve(6575,a,6579,a)]. 192.55/192.36 Derived: hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(6575,a,6580,a)]. 192.55/192.36 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(complex,complex),fun(fun(A,complex),fun(A,complex)),combb(complex,complex,A),uminus_uminus(complex)),B)),C) = hAPP(complex,complex,uminus_uminus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),C)). [resolve(6575,a,6581,a)]. 192.55/192.36 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(6575,a,6582,a)]. 192.55/192.36 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A) = zero_zero(complex). [resolve(6575,a,6583,a)]. 192.71/192.52 Derived: ti(complex,A) = ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A) != zero_zero(complex). [resolve(6575,a,6584,a)]. 192.71/192.52 6585 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E)) # label(fact_722_add__diff__add) # label(axiom). [clausify(2098)]. 192.71/192.52 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D)). [resolve(6585,a,6575,a)]. 192.71/192.52 6586 -ab_group_add(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(B,fun(A,A)),fun(fun(B,A),fun(B,A)),combs(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),minus_minus(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4221_setsum__subtractf) # label(axiom). [clausify(2288)]. 192.71/192.52 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(A,complex),fun(A,complex),hAPP(fun(A,fun(complex,complex)),fun(fun(A,complex),fun(A,complex)),combs(A,complex,complex),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),minus_minus(complex)),B)),C)),D) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),B),D)),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),D)). [resolve(6586,a,6575,a)]. 192.71/192.52 6587 -ab_group_add(A) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = zero_zero(A) # label(fact_4618_setsum__natinterval__difff) # label(axiom). [clausify(2356)]. 192.71/192.52 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(complex). [resolve(6587,a,6575,a)]. 192.77/192.62 6588 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),hAPP(fun(nat,A),fun(nat,A),hAPP(fun(nat,fun(A,A)),fun(fun(nat,A),fun(nat,A)),combs(nat,A,A),hAPP(fun(nat,A),fun(nat,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(nat,A),fun(nat,fun(A,A))),combb(A,fun(A,A),nat),minus_minus(A)),D)),hAPP(fun(nat,nat),fun(nat,A),hAPP(fun(nat,A),fun(fun(nat,nat),fun(nat,A)),combb(nat,A,nat),D),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(nat,A,D,B)),hAPP(nat,A,D,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),one_one(nat)))) # label(fact_4618_setsum__natinterval__difff) # label(axiom). [clausify(2356)]. 192.77/192.62 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),hAPP(fun(nat,complex),fun(nat,complex),hAPP(fun(nat,fun(complex,complex)),fun(fun(nat,complex),fun(nat,complex)),combs(nat,complex,complex),hAPP(fun(nat,complex),fun(nat,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(nat,complex),fun(nat,fun(complex,complex))),combb(complex,fun(complex,complex),nat),minus_minus(complex)),C)),hAPP(fun(nat,nat),fun(nat,complex),hAPP(fun(nat,complex),fun(fun(nat,nat),fun(nat,complex)),combb(nat,complex,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(nat,complex,C,A)),hAPP(nat,complex,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(6588,a,6575,a)]. 192.77/192.62 6589 ab_group_add(int) # label(arity_Int_Oint___Groups_Oab__group__add) # label(axiom). [assumption]. 192.77/192.62 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,B) != ti(int,A) | ti(int,D) = ti(int,C). [resolve(6589,a,6576,a)]. 192.77/192.62 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B) != hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),C),D) | ti(int,B) = ti(int,A) | ti(int,D) != ti(int,C). [resolve(6589,a,6577,a)]. 192.77/192.62 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(6589,a,6578,a)]. 192.77/192.62 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),B)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),D),C)). [resolve(6589,a,6579,a)]. 192.77/192.62 Derived: hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(6589,a,6580,a)]. 193.19/193.03 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),uminus_uminus(int)),B)),C) = hAPP(int,int,uminus_uminus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),C)). [resolve(6589,a,6581,a)]. 193.19/193.03 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A) = zero_zero(int). [resolve(6589,a,6583,a)]. 193.19/193.03 Derived: ti(int,A) = ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A) != zero_zero(int). [resolve(6589,a,6584,a)]. 193.19/193.03 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D)). [resolve(6589,a,6585,a)]. 193.19/193.03 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(A,fun(int,int)),fun(fun(A,int),fun(A,int)),combs(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),minus_minus(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(6589,a,6586,a)]. 193.19/193.03 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(int). [resolve(6589,a,6587,a)]. 193.19/193.03 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),hAPP(fun(nat,int),fun(nat,int),hAPP(fun(nat,fun(int,int)),fun(fun(nat,int),fun(nat,int)),combs(nat,int,int),hAPP(fun(nat,int),fun(nat,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(nat,int),fun(nat,fun(int,int))),combb(int,fun(int,int),nat),minus_minus(int)),C)),hAPP(fun(nat,nat),fun(nat,int),hAPP(fun(nat,int),fun(fun(nat,nat),fun(nat,int)),combb(nat,int,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(nat,int,C,A)),hAPP(nat,int,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(6589,a,6588,a)]. 193.19/193.03 6590 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2051_minus__add__distrib) # label(axiom). [clausify(3400)]. 193.19/193.03 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(6590,a,6575,a)]. 193.46/193.27 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(6590,a,6589,a)]. 193.46/193.27 6591 ab_group_add(real) # label(arity_RealDef_Oreal___Groups_Oab__group__add) # label(axiom). [assumption]. 193.46/193.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,B) != ti(real,A) | ti(real,D) = ti(real,C). [resolve(6591,a,6576,a)]. 193.46/193.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B) != hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),C),D) | ti(real,B) = ti(real,A) | ti(real,D) != ti(real,C). [resolve(6591,a,6577,a)]. 193.46/193.27 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(6591,a,6578,a)]. 193.46/193.27 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),B)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),D),C)). [resolve(6591,a,6579,a)]. 193.46/193.27 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(real,real),fun(fun(A,real),fun(A,real)),combb(real,real,A),uminus_uminus(real)),B)),C) = hAPP(real,real,uminus_uminus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),C)). [resolve(6591,a,6581,a)]. 193.46/193.27 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(6591,a,6582,a)]. 193.46/193.27 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A) = zero_zero(real). [resolve(6591,a,6583,a)]. 193.46/193.27 Derived: ti(real,A) = ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A) != zero_zero(real). [resolve(6591,a,6584,a)]. 193.46/193.27 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D)). [resolve(6591,a,6585,a)]. 193.46/193.27 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(A,real),fun(A,real),hAPP(fun(A,fun(real,real)),fun(fun(A,real),fun(A,real)),combs(A,real,real),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),minus_minus(real)),B)),C)),D) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),B),D)),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),D)). [resolve(6591,a,6586,a)]. 193.46/193.27 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(real). [resolve(6591,a,6587,a)]. 193.54/193.36 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),minus_minus(real)),C)),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(nat,real,C,A)),hAPP(nat,real,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(6591,a,6588,a)]. 193.54/193.36 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(6591,a,6590,a)]. 193.54/193.36 6592 -ab_group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) = zero_zero(A) # label(fact_2068_ab__left__minus) # label(axiom). [clausify(3669)]. 193.54/193.36 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),A)),A) = zero_zero(complex). [resolve(6592,a,6575,a)]. 193.54/193.36 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),A)),A) = zero_zero(int). [resolve(6592,a,6589,a)]. 193.54/193.36 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),A)),A) = zero_zero(real). [resolve(6592,a,6591,a)]. 193.54/193.36 6593 -ab_group_add(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),C),D)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),D))),hAPP(fun(nat,bool),A,hAPP(fun(nat,A),fun(fun(nat,bool),A),big_co1399186613setsum(nat,A),E),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C))) # label(fact_4200_setsum__diff__nat__ivl) # label(axiom). [clausify(3719)]. 193.54/193.36 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),complex,hAPP(fun(nat,complex),fun(fun(nat,bool),complex),big_co1399186613setsum(nat,complex),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(6593,a,6575,a)]. 194.40/194.21 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),B),C)) | hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),int,hAPP(fun(nat,int),fun(fun(nat,bool),int),big_co1399186613setsum(nat,int),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(6593,a,6589,a)]. 194.40/194.21 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),B),C)) | hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(6593,a,6591,a)]. 194.40/194.21 6594 -ab_group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),B) # label(fact_2053_minus__diff__eq) # label(axiom). [clausify(4844)]. 194.40/194.21 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),A). [resolve(6594,a,6575,a)]. 194.40/194.21 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),A). [resolve(6594,a,6589,a)]. 194.40/194.21 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),A). [resolve(6594,a,6591,a)]. 194.40/194.21 6595 ab_group_add(rat) # label(arity_Rat_Orat___Groups_Oab__group__add) # label(axiom). [assumption]. 194.40/194.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,B) != ti(rat,A) | ti(rat,D) = ti(rat,C). [resolve(6595,a,6576,a)]. 194.40/194.21 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),C),D) | ti(rat,B) = ti(rat,A) | ti(rat,D) != ti(rat,C). [resolve(6595,a,6577,a)]. 194.40/194.21 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6595,a,6578,a)]. 194.40/194.21 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),hAPP(fun(A,bool),fun(A,bool),hAPP(fun(A,bool),fun(fun(A,bool),fun(A,bool)),minus_minus(fun(A,bool)),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),B)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),D),C)). [resolve(6595,a,6579,a)]. 194.40/194.21 Derived: hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),A),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),B))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),B)))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),A),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))). [resolve(6595,a,6580,a)]. 194.40/194.22 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),uminus_uminus(rat)),B)),C) = hAPP(rat,rat,uminus_uminus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),C)). [resolve(6595,a,6581,a)]. 194.40/194.22 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(6595,a,6582,a)]. 194.40/194.22 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A) = zero_zero(rat). [resolve(6595,a,6583,a)]. 194.40/194.22 Derived: ti(rat,A) = ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A) != zero_zero(rat). [resolve(6595,a,6584,a)]. 194.40/194.22 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),D)). [resolve(6595,a,6585,a)]. 194.40/194.22 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(fun(A,rat),fun(A,rat)),combs(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),minus_minus(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(6595,a,6586,a)]. 194.40/194.22 Derived: hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = zero_zero(rat). [resolve(6595,a,6587,a)]. 194.40/194.22 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),hAPP(fun(nat,rat),fun(nat,rat),hAPP(fun(nat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,rat)),combs(nat,rat,rat),hAPP(fun(nat,rat),fun(nat,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(nat,rat),fun(nat,fun(rat,rat))),combb(rat,fun(rat,rat),nat),minus_minus(rat)),C)),hAPP(fun(nat,nat),fun(nat,rat),hAPP(fun(nat,rat),fun(fun(nat,nat),fun(nat,rat)),combb(nat,rat,nat),C),hAPP(nat,fun(nat,nat),hAPP(fun(nat,fun(nat,nat)),fun(nat,fun(nat,nat)),combc(nat,nat,nat),plus_plus(nat)),one_one(nat))))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastAtMost(nat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(nat,rat,C,A)),hAPP(nat,rat,C,hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),one_one(nat)))). [resolve(6595,a,6588,a)]. 198.30/198.15 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6595,a,6590,a)]. 198.30/198.15 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A) = zero_zero(rat). [resolve(6595,a,6592,a)]. 198.30/198.15 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),B),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),C))),hAPP(fun(nat,bool),rat,hAPP(fun(nat,rat),fun(fun(nat,bool),rat),big_co1399186613setsum(nat,rat),D),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),A),B))). [resolve(6595,a,6593,a)]. 198.30/198.16 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),A). [resolve(6595,a,6594,a)]. 198.30/198.16 6596 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | ti(A,B) != zero_zero(A) | zero_zero(nat) = C | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) = zero_zero(A) # label(fact_414_power__eq__0__iff) # label(axiom). [clausify(1027)]. 198.30/198.16 6597 zero_neq_one(nat) # label(arity_Nat_Onat___Rings_Ozero__neq__one) # label(axiom). [assumption]. 198.30/198.16 6598 zero_neq_one(rat) # label(arity_Rat_Orat___Rings_Ozero__neq__one) # label(axiom). [assumption]. 198.30/198.16 Derived: -no_zero_divisors(nat) | -mult_zero(nat) | -power(nat) | ti(nat,A) != zero_zero(nat) | zero_zero(nat) = B | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) = zero_zero(nat). [resolve(6596,a,6597,a)]. 198.30/198.16 Derived: -no_zero_divisors(rat) | -mult_zero(rat) | -power(rat) | ti(rat,A) != zero_zero(rat) | zero_zero(nat) = B | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) = zero_zero(rat). [resolve(6596,a,6598,a)]. 198.30/198.16 6599 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | ti(A,B) = zero_zero(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),B),C) != zero_zero(A) # label(fact_414_power__eq__0__iff) # label(axiom). [clausify(1027)]. 198.30/198.16 Derived: -no_zero_divisors(nat) | -mult_zero(nat) | -power(nat) | ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),A),B) != zero_zero(nat). [resolve(6599,a,6597,a)]. 198.30/198.16 Derived: -no_zero_divisors(rat) | -mult_zero(rat) | -power(rat) | ti(rat,A) = zero_zero(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),A),B) != zero_zero(rat). [resolve(6599,a,6598,a)]. 198.30/198.16 6600 -zero_neq_one(A) | -no_zero_divisors(A) | -mult_zero(A) | -power(A) | zero_zero(nat) != B | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),C),B) != zero_zero(A) # label(fact_414_power__eq__0__iff) # label(axiom). [clausify(1027)]. 198.30/198.16 Derived: -no_zero_divisors(rat) | -mult_zero(rat) | -power(rat) | zero_zero(nat) != A | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),A) != zero_zero(rat). [resolve(6600,a,6598,a)]. 198.30/198.16 6601 zero_neq_one(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Ozero__neq__one) # label(axiom). [assumption]. 198.30/198.16 Derived: -no_zero_divisors(quickcheck_code_int) | -mult_zero(quickcheck_code_int) | -power(quickcheck_code_int) | ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | zero_zero(nat) = B | 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). [resolve(6601,a,6596,a)]. 198.54/198.37 Derived: -no_zero_divisors(quickcheck_code_int) | -mult_zero(quickcheck_code_int) | -power(quickcheck_code_int) | ti(quickcheck_code_int,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),A),B) != zero_zero(quickcheck_code_int). [resolve(6601,a,6599,a)]. 198.54/198.37 Derived: -no_zero_divisors(quickcheck_code_int) | -mult_zero(quickcheck_code_int) | -power(quickcheck_code_int) | zero_zero(nat) != A | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),A) != zero_zero(quickcheck_code_int). [resolve(6601,a,6600,a)]. 198.54/198.37 6602 zero_neq_one(int) # label(arity_Int_Oint___Rings_Ozero__neq__one) # label(axiom). [assumption]. 198.54/198.37 Derived: -no_zero_divisors(int) | -mult_zero(int) | -power(int) | ti(int,A) != zero_zero(int) | zero_zero(nat) = B | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) = zero_zero(int). [resolve(6602,a,6596,a)]. 198.54/198.37 Derived: -no_zero_divisors(int) | -mult_zero(int) | -power(int) | ti(int,A) = zero_zero(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),A),B) != zero_zero(int). [resolve(6602,a,6599,a)]. 198.54/198.37 Derived: -no_zero_divisors(int) | -mult_zero(int) | -power(int) | zero_zero(nat) != A | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),A) != zero_zero(int). [resolve(6602,a,6600,a)]. 198.54/198.37 6603 zero_neq_one(complex) # label(arity_Complex_Ocomplex___Rings_Ozero__neq__one) # label(axiom). [assumption]. 198.54/198.37 Derived: -no_zero_divisors(complex) | -mult_zero(complex) | -power(complex) | ti(complex,A) != zero_zero(complex) | zero_zero(nat) = B | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) = zero_zero(complex). [resolve(6603,a,6596,a)]. 198.54/198.37 Derived: -no_zero_divisors(complex) | -mult_zero(complex) | -power(complex) | ti(complex,A) = zero_zero(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),A),B) != zero_zero(complex). [resolve(6603,a,6599,a)]. 198.54/198.37 Derived: -no_zero_divisors(complex) | -mult_zero(complex) | -power(complex) | zero_zero(nat) != A | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),A) != zero_zero(complex). [resolve(6603,a,6600,a)]. 198.54/198.37 6604 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | ti(A,C) != zero_zero(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_256_power__eq__0__iff__number__of) # label(axiom). [clausify(1830)]. 198.54/198.37 Derived: -power(nat) | -mult_zero(nat) | -no_zero_divisors(nat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(nat,B) != zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(nat). [resolve(6604,d,6597,a)]. 198.54/198.37 Derived: -power(rat) | -mult_zero(rat) | -no_zero_divisors(rat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(rat,B) != zero_zero(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(rat). [resolve(6604,d,6598,a)]. 198.54/198.37 Derived: -power(quickcheck_code_int) | -mult_zero(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(quickcheck_code_int,B) != zero_zero(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(quickcheck_code_int). [resolve(6604,d,6601,a)]. 198.54/198.37 Derived: -power(int) | -mult_zero(int) | -no_zero_divisors(int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(int,B) != zero_zero(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(6604,d,6602,a)]. 198.54/198.37 Derived: -power(complex) | -mult_zero(complex) | -no_zero_divisors(complex) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(complex,B) != zero_zero(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(complex). [resolve(6604,d,6603,a)]. 198.98/198.83 6605 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | 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_256_power__eq__0__iff__number__of) # label(axiom). [clausify(1830)]. 198.98/198.83 Derived: -power(nat) | -mult_zero(nat) | -no_zero_divisors(nat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(nat). [resolve(6605,d,6597,a)]. 198.98/198.83 Derived: -power(rat) | -mult_zero(rat) | -no_zero_divisors(rat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(rat). [resolve(6605,d,6598,a)]. 198.98/198.83 Derived: -power(quickcheck_code_int) | -mult_zero(quickcheck_code_int) | -no_zero_divisors(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(quickcheck_code_int). [resolve(6605,d,6601,a)]. 198.98/198.83 Derived: -power(int) | -mult_zero(int) | -no_zero_divisors(int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(int). [resolve(6605,d,6602,a)]. 198.98/198.83 Derived: -power(complex) | -mult_zero(complex) | -no_zero_divisors(complex) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(complex). [resolve(6605,d,6603,a)]. 198.98/198.83 6606 -power(A) | -mult_zero(A) | -no_zero_divisors(A) | -zero_neq_one(A) | ti(A,B) = 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) # label(fact_256_power__eq__0__iff__number__of) # label(axiom). [clausify(1830)]. 198.98/198.83 6607 -zero_neq_one(A) | one_one(A) != zero_zero(A) # label(fact_324_zero__neq__one) # label(axiom). [clausify(1916)]. 198.98/198.83 Derived: one_one(nat) != zero_zero(nat). [resolve(6607,a,6597,a)]. 198.98/198.83 Derived: one_one(rat) != zero_zero(rat). [resolve(6607,a,6598,a)]. 198.98/198.83 Derived: one_one(quickcheck_code_int) != zero_zero(quickcheck_code_int). [resolve(6607,a,6601,a)]. 198.98/198.83 Derived: one_one(complex) != zero_zero(complex). [resolve(6607,a,6603,a)]. 198.98/198.83 6608 -zero_neq_one(A) | one_one(A) != zero_zero(A) # label(fact_325_one__neq__zero) # label(axiom). [clausify(2701)]. 198.98/198.83 Derived: one_one(int) != zero_zero(int). [resolve(6608,a,6602,a)]. 198.98/198.83 6609 zero_neq_one(real) # label(arity_RealDef_Oreal___Rings_Ozero__neq__one) # label(axiom). [assumption]. 198.98/198.83 Derived: -no_zero_divisors(real) | -mult_zero(real) | -power(real) | ti(real,A) != zero_zero(real) | zero_zero(nat) = B | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) = zero_zero(real). [resolve(6609,a,6596,a)]. 198.98/198.83 Derived: -no_zero_divisors(real) | -mult_zero(real) | -power(real) | ti(real,A) = zero_zero(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),A),B) != zero_zero(real). [resolve(6609,a,6599,a)]. 198.98/198.83 Derived: -no_zero_divisors(real) | -mult_zero(real) | -power(real) | zero_zero(nat) != A | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),A) != zero_zero(real). [resolve(6609,a,6600,a)]. 198.98/198.83 Derived: -power(real) | -mult_zero(real) | -no_zero_divisors(real) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(real,B) != zero_zero(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(6609,a,6604,d)]. 198.98/198.83 Derived: -power(real) | -mult_zero(real) | -no_zero_divisors(real) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(real). [resolve(6609,a,6605,d)]. 204.05/203.90 Derived: one_one(real) != zero_zero(real). [resolve(6609,a,6607,a)]. 204.05/203.90 6610 zero_neq_one(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Ozero__neq__one) # label(axiom). [assumption]. 204.05/203.90 Derived: -no_zero_divisors(code_code_numeral) | -mult_zero(code_code_numeral) | -power(code_code_numeral) | ti(code_code_numeral,A) != zero_zero(code_code_numeral) | zero_zero(nat) = B | 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). [resolve(6610,a,6596,a)]. 204.05/203.90 Derived: -no_zero_divisors(code_code_numeral) | -mult_zero(code_code_numeral) | -power(code_code_numeral) | ti(code_code_numeral,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),A),B) != zero_zero(code_code_numeral). [resolve(6610,a,6599,a)]. 204.05/203.90 Derived: -no_zero_divisors(code_code_numeral) | -mult_zero(code_code_numeral) | -power(code_code_numeral) | zero_zero(nat) != A | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),A) != zero_zero(code_code_numeral). [resolve(6610,a,6600,a)]. 204.05/203.90 Derived: -power(code_code_numeral) | -mult_zero(code_code_numeral) | -no_zero_divisors(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | ti(code_code_numeral,B) != zero_zero(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(code_code_numeral). [resolve(6610,a,6604,d)]. 204.05/203.90 Derived: -power(code_code_numeral) | -mult_zero(code_code_numeral) | -no_zero_divisors(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),B),hAPP(int,nat,number_number_of(nat),A)) != zero_zero(code_code_numeral). [resolve(6610,a,6605,d)]. 204.05/203.90 Derived: one_one(code_code_numeral) != zero_zero(code_code_numeral). [resolve(6610,a,6607,a)]. 204.05/203.90 6611 linord219039673up_add(int) # label(arity_Int_Oint___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 204.05/203.90 6612 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(223)]. 204.05/203.90 6613 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) # label(fact_821_double__add__less__zero__iff__single__add__less__zero) # label(axiom). [clausify(223)]. 204.05/203.90 6614 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2063_neg__less__nonneg) # label(axiom). [clausify(354)]. 204.05/203.90 6615 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2063_neg__less__nonneg) # label(axiom). [clausify(354)]. 204.05/203.90 6616 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(922)]. 204.05/203.90 6617 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B)),zero_zero(A))) # label(fact_817_double__add__le__zero__iff__single__add__le__zero) # label(axiom). [clausify(922)]. 204.34/204.21 6618 -linord219039673up_add(A) | ti(A,B) != zero_zero(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2021_neg__equal__zero) # label(axiom). [clausify(1001)]. 204.34/204.21 6619 -linord219039673up_add(A) | ti(A,B) = zero_zero(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2021_neg__equal__zero) # label(axiom). [clausify(1001)]. 204.34/204.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6611,a,6614,a)]. 204.34/204.21 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6611,a,6615,a)]. 204.34/204.21 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(6611,a,6616,a)]. 204.34/204.21 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A)),zero_zero(int))). [resolve(6611,a,6617,a)]. 204.34/204.21 Derived: ti(int,A) != zero_zero(int) | ti(int,A) = hAPP(int,int,uminus_uminus(int),A). [resolve(6611,a,6618,a)]. 204.34/204.21 Derived: ti(int,A) = zero_zero(int) | ti(int,A) != hAPP(int,int,uminus_uminus(int),A). [resolve(6611,a,6619,a)]. 204.34/204.21 6620 linord219039673up_add(rat) # label(arity_Rat_Orat___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 204.34/204.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6620,a,6614,a)]. 204.34/204.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6620,a,6615,a)]. 204.34/204.21 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(6620,a,6616,a)]. 204.34/204.21 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A)),zero_zero(rat))). [resolve(6620,a,6617,a)]. 204.34/204.21 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6620,a,6618,a)]. 204.34/204.21 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6620,a,6619,a)]. 204.34/204.21 6621 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4943_minus__max__eq__min) # label(axiom). [clausify(1580)]. 204.34/204.21 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(6621,a,6611,a)]. 204.34/204.21 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6621,a,6620,a)]. 204.34/204.21 6622 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(2118)]. 204.34/204.21 6623 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B))) # label(fact_822_zero__less__double__add__iff__zero__less__single__add) # label(axiom). [clausify(2118)]. 204.81/204.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),zero_zero(int)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A))). [resolve(6623,a,6611,a)]. 204.81/204.66 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A))). [resolve(6623,a,6620,a)]. 204.81/204.66 6624 -linord219039673up_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),B) | ti(A,B) = zero_zero(A) # label(fact_2023_equal__neg__zero) # label(axiom). [clausify(2365)]. 204.81/204.66 6625 -linord219039673up_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),B) | ti(A,B) != zero_zero(A) # label(fact_2023_equal__neg__zero) # label(axiom). [clausify(2365)]. 204.81/204.66 6626 -linord219039673up_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),ord_min(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),ord_max(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) # label(fact_4944_minus__min__eq__max) # label(axiom). [clausify(2476)]. 204.81/204.66 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),ord_min(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),ord_max(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)). [resolve(6626,a,6611,a)]. 204.81/204.66 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_min(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),ord_max(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6626,a,6620,a)]. 204.81/204.66 6627 -linord219039673up_add(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) # label(fact_776_double__zero__sym) # label(axiom). [clausify(3132)]. 204.81/204.66 Derived: ti(int,A) != zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) = zero_zero(int). [resolve(6627,a,6611,a)]. 204.81/204.66 Derived: ti(rat,A) != zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) = zero_zero(rat). [resolve(6627,a,6620,a)]. 204.81/204.66 6628 -linord219039673up_add(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) # label(fact_776_double__zero__sym) # label(axiom). [clausify(3132)]. 204.81/204.66 Derived: ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),A) != zero_zero(int). [resolve(6628,a,6611,a)]. 204.81/204.66 Derived: ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),A) != zero_zero(rat). [resolve(6628,a,6620,a)]. 204.81/204.66 6629 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2056_minus__le__self__iff) # label(axiom). [clausify(3214)]. 204.81/204.66 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6629,a,6611,a)]. 204.81/204.66 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6629,a,6620,a)]. 204.81/204.66 6630 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,uminus_uminus(A),B)),B)) # label(fact_2056_minus__le__self__iff) # label(axiom). [clausify(3214)]. 204.81/204.66 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,uminus_uminus(int),A)),A)). [resolve(6630,a,6611,a)]. 204.81/204.66 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,uminus_uminus(rat),A)),A)). [resolve(6630,a,6620,a)]. 205.81/205.63 6631 -linord219039673up_add(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),B),B))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(3355)]. 205.81/205.63 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),A),A))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6631,a,6611,a)]. 205.81/205.63 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),A),A))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6631,a,6620,a)]. 205.81/205.63 6632 -linord219039673up_add(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),B),B))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) # label(fact_818_zero__le__double__add__iff__zero__le__single__add) # label(axiom). [clausify(3355)]. 205.81/205.63 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),A),A))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)). [resolve(6632,a,6611,a)]. 205.81/205.63 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),A),A))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)). [resolve(6632,a,6620,a)]. 205.81/205.63 6633 -linord219039673up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2058_le__minus__self__iff) # label(axiom). [clausify(3709)]. 205.81/205.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),A))). [resolve(6633,a,6611,a)]. 205.81/205.63 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(6633,a,6620,a)]. 205.81/205.63 6634 -linord219039673up_add(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(A,A,uminus_uminus(A),B))) # label(fact_2058_le__minus__self__iff) # label(axiom). [clausify(3709)]. 205.81/205.63 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),hAPP(int,int,uminus_uminus(int),A))). [resolve(6634,a,6611,a)]. 205.81/205.63 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(rat,rat,uminus_uminus(rat),A))). [resolve(6634,a,6620,a)]. 205.81/205.63 6635 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_115_double__eq__0__iff) # label(axiom). [clausify(3789)]. 205.81/205.63 6636 -linord219039673up_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_115_double__eq__0__iff) # label(axiom). [clausify(3789)]. 205.81/205.63 6637 linord219039673up_add(real) # label(arity_RealDef_Oreal___Groups_Olinordered__ab__group__add) # label(axiom). [assumption]. 205.81/205.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6637,a,6614,a)]. 205.81/205.63 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6637,a,6615,a)]. 205.81/205.63 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))). [resolve(6637,a,6616,a)]. 210.38/210.19 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A)),zero_zero(real))). [resolve(6637,a,6617,a)]. 210.38/210.19 Derived: ti(real,A) != zero_zero(real) | ti(real,A) = hAPP(real,real,uminus_uminus(real),A). [resolve(6637,a,6618,a)]. 210.38/210.19 Derived: ti(real,A) = zero_zero(real) | ti(real,A) != hAPP(real,real,uminus_uminus(real),A). [resolve(6637,a,6619,a)]. 210.38/210.19 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(6637,a,6621,a)]. 210.38/210.19 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A))). [resolve(6637,a,6623,a)]. 210.38/210.19 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),ord_min(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),ord_max(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)). [resolve(6637,a,6626,a)]. 210.38/210.19 Derived: ti(real,A) != zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) = zero_zero(real). [resolve(6637,a,6627,a)]. 210.38/210.19 Derived: ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),A) != zero_zero(real). [resolve(6637,a,6628,a)]. 210.38/210.19 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6637,a,6629,a)]. 210.38/210.19 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,uminus_uminus(real),A)),A)). [resolve(6637,a,6630,a)]. 210.38/210.19 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),A),A))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6637,a,6631,a)]. 210.38/210.19 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),A),A))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)). [resolve(6637,a,6632,a)]. 210.38/210.19 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),A))). [resolve(6637,a,6633,a)]. 210.38/210.19 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(real,real,uminus_uminus(real),A))). [resolve(6637,a,6634,a)]. 210.38/210.19 6638 -ab_semigroup_mult(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),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_765_ab__semigroup__mult__class_Omult__ac_I1_J) # label(axiom). [clausify(1952)]. 210.38/210.19 6639 ab_semigroup_mult(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 210.38/210.19 6640 ab_semigroup_mult(int) # label(arity_Int_Oint___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 210.38/210.19 6641 ab_semigroup_mult(complex) # label(arity_Complex_Ocomplex___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 210.38/210.19 6642 ab_semigroup_mult(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 217.44/217.28 6643 -ab_semigroup_mult(A) | ti(fun(A,fun(A,A)),times_times(A)) = times_times(A) # label(tsy_c_Groups_Otimes__class_Otimes_0_res) # label(axiom). [clausify(2569)]. 217.44/217.28 Derived: ti(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),times_times(quickcheck_code_int)) = times_times(quickcheck_code_int). [resolve(6643,a,6639,a)]. 217.44/217.28 Derived: ti(fun(int,fun(int,int)),times_times(int)) = times_times(int). [resolve(6643,a,6640,a)]. 217.44/217.28 Derived: ti(fun(complex,fun(complex,complex)),times_times(complex)) = times_times(complex). [resolve(6643,a,6641,a)]. 217.44/217.28 Derived: ti(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),times_times(code_code_numeral)) = times_times(code_code_numeral). [resolve(6643,a,6642,a)]. 217.44/217.28 6644 ab_semigroup_mult(real) # label(arity_RealDef_Oreal___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(fun(real,fun(real,real)),times_times(real)) = times_times(real). [resolve(6644,a,6643,a)]. 217.44/217.28 6645 ab_semigroup_mult(rat) # label(arity_Rat_Orat___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(fun(rat,fun(rat,rat)),times_times(rat)) = times_times(rat). [resolve(6645,a,6643,a)]. 217.44/217.28 6646 ab_semigroup_mult(nat) # label(arity_Nat_Onat___Groups_Oab__semigroup__mult) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(fun(nat,fun(nat,nat)),times_times(nat)) = times_times(nat). [resolve(6646,a,6643,a)]. 217.44/217.28 6647 -zero(A) | ti(A,zero_zero(A)) = zero_zero(A) # label(tsy_c_Groups_Ozero__class_Ozero_res) # label(axiom). [clausify(2453)]. 217.44/217.28 6648 zero(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 6649 zero(complex) # label(arity_Complex_Ocomplex___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 6650 zero(int) # label(arity_Int_Oint___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 6651 zero(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(code_code_numeral,zero_zero(code_code_numeral)) = zero_zero(code_code_numeral). [resolve(6647,a,6648,a)]. 217.44/217.28 Derived: ti(complex,zero_zero(complex)) = zero_zero(complex). [resolve(6647,a,6649,a)]. 217.44/217.28 Derived: ti(int,zero_zero(int)) = zero_zero(int). [resolve(6647,a,6650,a)]. 217.44/217.28 Derived: ti(quickcheck_code_int,zero_zero(quickcheck_code_int)) = zero_zero(quickcheck_code_int). [resolve(6647,a,6651,a)]. 217.44/217.28 6652 zero(rat) # label(arity_Rat_Orat___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(rat,zero_zero(rat)) = zero_zero(rat). [resolve(6652,a,6647,a)]. 217.44/217.28 6653 zero(nat) # label(arity_Nat_Onat___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(nat,zero_zero(nat)) = zero_zero(nat). [resolve(6653,a,6647,a)]. 217.44/217.28 6654 zero(real) # label(arity_RealDef_Oreal___Groups_Ozero) # label(axiom). [assumption]. 217.44/217.28 Derived: ti(real,zero_zero(real)) = zero_zero(real). [resolve(6654,a,6647,a)]. 217.44/217.28 6655 -zero(A) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),B)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(A,fun(nat,real),hAPP(fun(nat,fun(A,real)),fun(A,fun(nat,real)),combc(nat,A,real),C),zero_zero(A)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),B))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(A,real,hAPP(nat,fun(A,real),C,B),zero_zero(A))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),B))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))) = hAPP(A,real,hAPP(nat,fun(A,real),C,zero_zero(nat)),zero_zero(A)) # label(fact_4236_Maclaurin__bi__le__lemma) # label(axiom). [clausify(4569)]. 217.44/217.28 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(code_code_numeral,fun(nat,real),hAPP(fun(nat,fun(code_code_numeral,real)),fun(code_code_numeral,fun(nat,real)),combc(nat,code_code_numeral,real),B),zero_zero(code_code_numeral)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(code_code_numeral,real,hAPP(nat,fun(code_code_numeral,real),B,A),zero_zero(code_code_numeral))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(code_code_numeral,real,hAPP(nat,fun(code_code_numeral,real),B,zero_zero(nat)),zero_zero(code_code_numeral)). [resolve(6655,a,6648,a)]. 217.44/217.28 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(complex,fun(nat,real),hAPP(fun(nat,fun(complex,real)),fun(complex,fun(nat,real)),combc(nat,complex,real),B),zero_zero(complex)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(complex,real,hAPP(nat,fun(complex,real),B,A),zero_zero(complex))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(complex,real,hAPP(nat,fun(complex,real),B,zero_zero(nat)),zero_zero(complex)). [resolve(6655,a,6649,a)]. 217.44/217.28 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(int,fun(nat,real),hAPP(fun(nat,fun(int,real)),fun(int,fun(nat,real)),combc(nat,int,real),B),zero_zero(int)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(int,real,hAPP(nat,fun(int,real),B,A),zero_zero(int))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(int,real,hAPP(nat,fun(int,real),B,zero_zero(nat)),zero_zero(int)). [resolve(6655,a,6650,a)]. 217.44/217.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(quickcheck_code_int,fun(nat,real),hAPP(fun(nat,fun(quickcheck_code_int,real)),fun(quickcheck_code_int,fun(nat,real)),combc(nat,quickcheck_code_int,real),B),zero_zero(quickcheck_code_int)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(quickcheck_code_int,real,hAPP(nat,fun(quickcheck_code_int,real),B,A),zero_zero(quickcheck_code_int))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(quickcheck_code_int,real,hAPP(nat,fun(quickcheck_code_int,real),B,zero_zero(nat)),zero_zero(quickcheck_code_int)). [resolve(6655,a,6651,a)]. 217.44/217.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(rat,fun(nat,real),hAPP(fun(nat,fun(rat,real)),fun(rat,fun(nat,real)),combc(nat,rat,real),B),zero_zero(rat)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(rat,real,hAPP(nat,fun(rat,real),B,A),zero_zero(rat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(rat,real,hAPP(nat,fun(rat,real),B,zero_zero(nat)),zero_zero(rat)). [resolve(6655,a,6652,a)]. 217.44/217.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(nat,fun(nat,real),hAPP(fun(nat,fun(nat,real)),fun(nat,fun(nat,real)),combc(nat,nat,real),B),zero_zero(nat)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,hAPP(nat,fun(nat,real),B,A),zero_zero(nat))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(nat,real,hAPP(nat,fun(nat,real),B,zero_zero(nat)),zero_zero(nat)). [resolve(6655,a,6653,a)]. 217.44/217.29 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),A)) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(fun(nat,bool),real,hAPP(fun(nat,real),fun(fun(nat,bool),real),big_co1399186613setsum(nat,real),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),inverse_divide(real)),hAPP(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(nat,real),fun(nat,fun(real,real))),combb(real,fun(real,real),nat),times_times(real)),hAPP(real,fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(real,fun(nat,real)),combc(nat,real,real),B),zero_zero(real)))),hAPP(real,fun(nat,real),power_power(real),zero_zero(real))))),hAPP(fun(nat,nat),fun(nat,real),hAPP(fun(nat,real),fun(fun(nat,nat),fun(nat,real)),combb(nat,real,nat),real_1(nat)),fact_fact(nat)))),hAPP(nat,fun(nat,bool),hAPP(nat,fun(nat,fun(nat,bool)),ord_atLeastLessThan(nat),zero_zero(nat)),A))),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(nat,fun(real,real),B,A),zero_zero(real))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A))),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),A)))) = hAPP(real,real,hAPP(nat,fun(real,real),B,zero_zero(nat)),zero_zero(real)). [resolve(6655,a,6654,a)]. 219.54/219.38 6656 -zero(A) | -metric_space(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(filter(complex),bool,hAPP(A,fun(filter(complex),bool),hAPP(fun(complex,A),fun(A,fun(filter(complex),bool)),tendsto(complex,A),hAPP(A,fun(complex,A),combk(A,complex),B)),zero_zero(A)),hAPP(complex,filter(complex),at(complex),C))). [resolve(6034,c,6027,a)]. 219.54/219.38 Derived: -metric_space(code_code_numeral) | ti(code_code_numeral,A) = zero_zero(code_code_numeral) | -hBOOL(hAPP(filter(complex),bool,hAPP(code_code_numeral,fun(filter(complex),bool),hAPP(fun(complex,code_code_numeral),fun(code_code_numeral,fun(filter(complex),bool)),tendsto(complex,code_code_numeral),hAPP(code_code_numeral,fun(complex,code_code_numeral),combk(code_code_numeral,complex),A)),zero_zero(code_code_numeral)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6648,a)]. 219.54/219.38 Derived: -metric_space(complex) | ti(complex,A) = zero_zero(complex) | -hBOOL(hAPP(filter(complex),bool,hAPP(complex,fun(filter(complex),bool),hAPP(fun(complex,complex),fun(complex,fun(filter(complex),bool)),tendsto(complex,complex),hAPP(complex,fun(complex,complex),combk(complex,complex),A)),zero_zero(complex)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6649,a)]. 219.54/219.38 Derived: -metric_space(int) | ti(int,A) = zero_zero(int) | -hBOOL(hAPP(filter(complex),bool,hAPP(int,fun(filter(complex),bool),hAPP(fun(complex,int),fun(int,fun(filter(complex),bool)),tendsto(complex,int),hAPP(int,fun(complex,int),combk(int,complex),A)),zero_zero(int)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6650,a)]. 219.54/219.38 Derived: -metric_space(quickcheck_code_int) | ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(filter(complex),bool,hAPP(quickcheck_code_int,fun(filter(complex),bool),hAPP(fun(complex,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(complex),bool)),tendsto(complex,quickcheck_code_int),hAPP(quickcheck_code_int,fun(complex,quickcheck_code_int),combk(quickcheck_code_int,complex),A)),zero_zero(quickcheck_code_int)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6651,a)]. 219.54/219.38 Derived: -metric_space(rat) | ti(rat,A) = zero_zero(rat) | -hBOOL(hAPP(filter(complex),bool,hAPP(rat,fun(filter(complex),bool),hAPP(fun(complex,rat),fun(rat,fun(filter(complex),bool)),tendsto(complex,rat),hAPP(rat,fun(complex,rat),combk(rat,complex),A)),zero_zero(rat)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6652,a)]. 219.54/219.38 Derived: -metric_space(nat) | ti(nat,A) = zero_zero(nat) | -hBOOL(hAPP(filter(complex),bool,hAPP(nat,fun(filter(complex),bool),hAPP(fun(complex,nat),fun(nat,fun(filter(complex),bool)),tendsto(complex,nat),hAPP(nat,fun(complex,nat),combk(nat,complex),A)),zero_zero(nat)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6653,a)]. 219.54/219.38 Derived: -metric_space(real) | ti(real,A) = zero_zero(real) | -hBOOL(hAPP(filter(complex),bool,hAPP(real,fun(filter(complex),bool),hAPP(fun(complex,real),fun(real,fun(filter(complex),bool)),tendsto(complex,real),hAPP(real,fun(complex,real),combk(real,complex),A)),zero_zero(real)),hAPP(complex,filter(complex),at(complex),B))). [resolve(6656,a,6654,a)]. 219.54/219.38 6657 -zero(A) | -metric_space(A) | ti(A,B) = zero_zero(A) | -hBOOL(hAPP(filter(real),bool,hAPP(A,fun(filter(real),bool),hAPP(fun(real,A),fun(A,fun(filter(real),bool)),tendsto(real,A),hAPP(A,fun(real,A),combk(A,real),B)),zero_zero(A)),hAPP(real,filter(real),at(real),C))). [resolve(6041,a,6034,c)]. 219.54/219.38 Derived: -metric_space(code_code_numeral) | ti(code_code_numeral,A) = zero_zero(code_code_numeral) | -hBOOL(hAPP(filter(real),bool,hAPP(code_code_numeral,fun(filter(real),bool),hAPP(fun(real,code_code_numeral),fun(code_code_numeral,fun(filter(real),bool)),tendsto(real,code_code_numeral),hAPP(code_code_numeral,fun(real,code_code_numeral),combk(code_code_numeral,real),A)),zero_zero(code_code_numeral)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6648,a)]. 219.54/219.38 Derived: -metric_space(complex) | ti(complex,A) = zero_zero(complex) | -hBOOL(hAPP(filter(real),bool,hAPP(complex,fun(filter(real),bool),hAPP(fun(real,complex),fun(complex,fun(filter(real),bool)),tendsto(real,complex),hAPP(complex,fun(real,complex),combk(complex,real),A)),zero_zero(complex)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6649,a)]. 222.33/222.15 Derived: -metric_space(int) | ti(int,A) = zero_zero(int) | -hBOOL(hAPP(filter(real),bool,hAPP(int,fun(filter(real),bool),hAPP(fun(real,int),fun(int,fun(filter(real),bool)),tendsto(real,int),hAPP(int,fun(real,int),combk(int,real),A)),zero_zero(int)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6650,a)]. 222.33/222.15 Derived: -metric_space(quickcheck_code_int) | ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | -hBOOL(hAPP(filter(real),bool,hAPP(quickcheck_code_int,fun(filter(real),bool),hAPP(fun(real,quickcheck_code_int),fun(quickcheck_code_int,fun(filter(real),bool)),tendsto(real,quickcheck_code_int),hAPP(quickcheck_code_int,fun(real,quickcheck_code_int),combk(quickcheck_code_int,real),A)),zero_zero(quickcheck_code_int)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6651,a)]. 222.33/222.15 Derived: -metric_space(rat) | ti(rat,A) = zero_zero(rat) | -hBOOL(hAPP(filter(real),bool,hAPP(rat,fun(filter(real),bool),hAPP(fun(real,rat),fun(rat,fun(filter(real),bool)),tendsto(real,rat),hAPP(rat,fun(real,rat),combk(rat,real),A)),zero_zero(rat)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6652,a)]. 222.33/222.15 Derived: -metric_space(nat) | ti(nat,A) = zero_zero(nat) | -hBOOL(hAPP(filter(real),bool,hAPP(nat,fun(filter(real),bool),hAPP(fun(real,nat),fun(nat,fun(filter(real),bool)),tendsto(real,nat),hAPP(nat,fun(real,nat),combk(nat,real),A)),zero_zero(nat)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6653,a)]. 222.33/222.15 Derived: -metric_space(real) | ti(real,A) = zero_zero(real) | -hBOOL(hAPP(filter(real),bool,hAPP(real,fun(filter(real),bool),hAPP(fun(real,real),fun(real,fun(filter(real),bool)),tendsto(real,real),hAPP(real,fun(real,real),combk(real,real),A)),zero_zero(real)),hAPP(real,filter(real),at(real),B))). [resolve(6657,a,6654,a)]. 222.33/222.15 6658 archim1804426504_field(rat) # label(arity_Rat_Orat___Archimedean__Field_Oarchimedean__field) # label(axiom). [assumption]. 222.33/222.15 6659 -archim1804426504_field(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),f57(A,B))) # label(fact_2719_ex__inverse__of__nat__less) # label(axiom). [clausify(243)]. 222.33/222.15 6660 -archim1804426504_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,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),f57(A,B)))),B)) # label(fact_2719_ex__inverse__of__nat__less) # label(axiom). [clausify(243)]. 222.33/222.15 6661 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),f96(A,B))),B)) # label(fact_3617_floor__exists1) # label(axiom). [clausify(465)]. 222.33/222.15 6662 -archim1804426504_field(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(int,A,ring_1_of_int(A),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),one_one(int))))) | ti(int,B) = ti(int,f96(A,C)) # label(fact_3617_floor__exists1) # label(axiom). [clausify(465)]. 222.33/222.15 6663 -archim1804426504_field(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),f96(A,B)),one_one(int))))) # label(fact_3617_floor__exists1) # label(axiom). [clausify(465)]. 222.33/222.15 6664 -archim1804426504_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,inverse_inverse(A),hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,suc,f131(A,B))))),B)) # label(fact_2723_ex__inverse__of__nat__Suc__less) # label(axiom). [clausify(727)]. 222.33/222.15 6665 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(int,A,ring_1_of_int(A),f260(A,B)))) # label(fact_3626_ex__le__of__int) # label(axiom). [clausify(1275)]. 222.33/222.15 6666 -archim1804426504_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),hAPP(nat,A,semiring_1_of_nat(A),f501(A,C,B))),B))) # label(fact_2724_ex__less__of__nat__mult) # label(axiom). [clausify(2725)]. 222.78/222.58 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),zero_zero(nat)),f57(rat,A))). [resolve(6658,a,6659,a)]. 222.78/222.58 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,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),f57(rat,A)))),A)). [resolve(6658,a,6660,a)]. 222.78/222.58 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),f96(rat,A))),A)). [resolve(6658,a,6661,a)]. 222.78/222.58 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(int,rat,ring_1_of_int(rat),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))))) | ti(int,A) = ti(int,f96(rat,B)). [resolve(6658,a,6662,a)]. 222.78/222.58 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),f96(rat,A)),one_one(int))))). [resolve(6658,a,6663,a)]. 222.78/222.58 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,inverse_inverse(rat),hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,suc,f131(rat,A))))),A)). [resolve(6658,a,6664,a)]. 222.78/222.58 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(int,rat,ring_1_of_int(rat),f260(rat,A)))). [resolve(6658,a,6665,a)]. 222.78/222.58 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),hAPP(nat,rat,semiring_1_of_nat(rat),f501(rat,B,A))),A))). [resolve(6658,a,6666,a)]. 222.78/222.58 6667 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(int,A,ring_1_of_int(A),f564(A,B))),B)) # label(fact_3616_floor__exists) # label(axiom). [clausify(3255)]. 222.78/222.58 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(int,rat,ring_1_of_int(rat),f564(rat,A))),A)). [resolve(6667,a,6658,a)]. 222.78/222.58 6668 -archim1804426504_field(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),f564(A,B)),one_one(int))))) # label(fact_3616_floor__exists) # label(axiom). [clausify(3255)]. 222.78/222.58 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),f564(rat,A)),one_one(int))))). [resolve(6668,a,6658,a)]. 222.78/222.58 6669 archim1804426504_field(real) # label(arity_RealDef_Oreal___Archimedean__Field_Oarchimedean__field) # label(axiom). [assumption]. 222.78/222.58 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(nat),zero_zero(nat)),f57(real,A))). [resolve(6669,a,6659,a)]. 222.78/222.58 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,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),f57(real,A)))),A)). [resolve(6669,a,6660,a)]. 222.78/222.58 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),f96(real,A))),A)). [resolve(6669,a,6661,a)]. 222.78/222.58 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(int,real,ring_1_of_int(real),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),one_one(int))))) | ti(int,A) = ti(int,f96(real,B)). [resolve(6669,a,6662,a)]. 222.78/222.58 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),f96(real,A)),one_one(int))))). [resolve(6669,a,6663,a)]. 227.57/227.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,suc,f131(real,A))))),A)). [resolve(6669,a,6664,a)]. 227.57/227.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(int,real,ring_1_of_int(real),f260(real,A)))). [resolve(6669,a,6665,a)]. 227.57/227.39 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),zero_zero(real)),A)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(nat,real,semiring_1_of_nat(real),f501(real,B,A))),A))). [resolve(6669,a,6666,a)]. 227.57/227.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(int,real,ring_1_of_int(real),f564(real,A))),A)). [resolve(6669,a,6667,a)]. 227.57/227.39 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),f564(real,A)),one_one(int))))). [resolve(6669,a,6668,a)]. 227.57/227.39 6670 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(nat,A,semiring_1_of_nat(A),f708(A,B)))) # label(fact_2736_ex__less__of__nat) # label(axiom). [clausify(4043)]. 227.57/227.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(nat,rat,semiring_1_of_nat(rat),f708(rat,A)))). [resolve(6670,a,6658,a)]. 227.57/227.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(nat,real,semiring_1_of_nat(real),f708(real,A)))). [resolve(6670,a,6669,a)]. 227.57/227.39 6671 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(int,A,ring_1_of_int(A),f712(A,B))),B)) # label(fact_3624_ex__of__int__less) # label(axiom). [clausify(4078)]. 227.57/227.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(int,rat,ring_1_of_int(rat),f712(rat,A))),A)). [resolve(6671,a,6658,a)]. 227.57/227.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(int,real,ring_1_of_int(real),f712(real,A))),A)). [resolve(6671,a,6669,a)]. 227.57/227.39 6672 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),hAPP(int,A,ring_1_of_int(A),f791(A,B)))) # label(fact_3625_ex__less__of__int) # label(axiom). [clausify(4651)]. 227.57/227.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),hAPP(int,rat,ring_1_of_int(rat),f791(rat,A)))). [resolve(6672,a,6658,a)]. 227.57/227.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),hAPP(int,real,ring_1_of_int(real),f791(real,A)))). [resolve(6672,a,6669,a)]. 227.57/227.39 6673 -archim1804426504_field(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),hAPP(nat,A,semiring_1_of_nat(A),f802(A,B)))) # label(fact_2737_ex__le__of__nat) # label(axiom). [clausify(4713)]. 227.57/227.39 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),hAPP(nat,rat,semiring_1_of_nat(rat),f802(rat,A)))). [resolve(6673,a,6658,a)]. 227.57/227.39 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),hAPP(nat,real,semiring_1_of_nat(real),f802(real,A)))). [resolve(6673,a,6669,a)]. 227.57/227.39 6674 group_add(int) # label(arity_Int_Oint___Groups_Ogroup__add) # label(axiom). [assumption]. 227.57/227.39 6675 -group_add(A) | hAPP(A,A,uminus_uminus(A),zero_zero(A)) = zero_zero(A) # label(fact_2025_minus__zero) # label(axiom). [clausify(271)]. 227.57/227.39 6676 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2042_equation__minus__iff) # label(axiom). [clausify(383)]. 227.57/227.39 6677 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2042_equation__minus__iff) # label(axiom). [clausify(383)]. 227.57/227.39 6678 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) != zero_zero(A) | ti(A,C) = ti(A,B) # label(fact_793_right__minus__eq) # label(axiom). [clausify(391)]. 228.04/227.92 6679 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = zero_zero(A) | ti(A,C) != ti(A,B) # label(fact_793_right__minus__eq) # label(axiom). [clausify(391)]. 228.04/227.92 6680 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),B)) = zero_zero(A) # label(fact_2065_right__minus) # label(axiom). [clausify(588)]. 228.04/227.92 6681 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),zero_zero(A)),B) # label(fact_2070_diff__0) # label(axiom). [clausify(1561)]. 228.04/227.92 6682 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2041_minus__minus) # label(axiom). [clausify(1653)]. 228.04/227.92 Derived: ti(int,A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A). [resolve(6674,a,6676,a)]. 228.04/227.92 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),hAPP(int,int,uminus_uminus(int),A)) = zero_zero(int). [resolve(6674,a,6680,a)]. 228.04/227.92 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),zero_zero(int)),A). [resolve(6674,a,6681,a)]. 228.04/227.92 6683 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),zero_zero(A)) # label(fact_796_diff__0__right) # label(axiom). [clausify(1682)]. 228.04/227.92 Derived: ti(int,A) = hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),zero_zero(int)). [resolve(6683,a,6674,a)]. 228.04/227.92 6684 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2076_Groups_Odiff__def) # label(axiom). [clausify(2379)]. 228.04/227.92 6685 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2064_add__eq__0__iff) # label(axiom). [clausify(2536)]. 228.04/227.92 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | ti(int,B) = hAPP(int,int,uminus_uminus(int),A). [resolve(6685,a,6674,a)]. 228.04/227.92 6686 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2064_add__eq__0__iff) # label(axiom). [clausify(2536)]. 228.04/227.92 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int) | ti(int,B) != hAPP(int,int,uminus_uminus(int),A). [resolve(6686,a,6674,a)]. 228.04/227.92 6687 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,B) = ti(A,C) # label(fact_2044_neg__equal__iff__equal) # label(axiom). [clausify(2733)]. 228.04/227.92 Derived: hAPP(int,int,uminus_uminus(int),A) != hAPP(int,int,uminus_uminus(int),B) | ti(int,A) = ti(int,B). [resolve(6687,a,6674,a)]. 228.04/227.92 6688 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,B) != ti(A,C) # label(fact_2044_neg__equal__iff__equal) # label(axiom). [clausify(2733)]. 228.04/227.92 Derived: hAPP(int,int,uminus_uminus(int),A) = hAPP(int,int,uminus_uminus(int),B) | ti(int,A) != ti(int,B). [resolve(6688,a,6674,a)]. 228.04/227.92 6689 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),B)),B) = zero_zero(A) # label(fact_2067_left__minus) # label(axiom). [clausify(2878)]. 228.04/227.92 6690 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),B) = zero_zero(A) # label(fact_795_diff__self) # label(axiom). [clausify(2914)]. 228.04/227.92 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),A) = zero_zero(int). [resolve(6690,a,6674,a)]. 228.04/227.92 6691 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) # label(fact_2074_diff__minus__eq__add) # label(axiom). [clausify(2930)]. 228.04/227.92 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(6691,a,6674,a)]. 228.04/227.92 6692 group_add(real) # label(arity_RealDef_Oreal___Groups_Ogroup__add) # label(axiom). [assumption]. 228.04/227.92 Derived: hAPP(real,real,uminus_uminus(real),zero_zero(real)) = zero_zero(real). [resolve(6692,a,6675,a)]. 228.04/227.92 Derived: ti(real,A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,B) = hAPP(real,real,uminus_uminus(real),A). [resolve(6692,a,6676,a)]. 228.74/228.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),hAPP(real,real,uminus_uminus(real),A)) = zero_zero(real). [resolve(6692,a,6680,a)]. 228.74/228.57 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),zero_zero(real)),A). [resolve(6692,a,6681,a)]. 228.74/228.57 Derived: ti(real,A) = hAPP(real,real,uminus_uminus(real),hAPP(real,real,uminus_uminus(real),A)). [resolve(6692,a,6682,a)]. 228.74/228.57 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),zero_zero(real)). [resolve(6692,a,6683,a)]. 228.74/228.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | ti(real,B) = hAPP(real,real,uminus_uminus(real),A). [resolve(6692,a,6685,a)]. 228.74/228.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real) | ti(real,B) != hAPP(real,real,uminus_uminus(real),A). [resolve(6692,a,6686,a)]. 228.74/228.57 Derived: hAPP(real,real,uminus_uminus(real),A) != hAPP(real,real,uminus_uminus(real),B) | ti(real,A) = ti(real,B). [resolve(6692,a,6687,a)]. 228.74/228.57 Derived: hAPP(real,real,uminus_uminus(real),A) = hAPP(real,real,uminus_uminus(real),B) | ti(real,A) != ti(real,B). [resolve(6692,a,6688,a)]. 228.74/228.57 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),A) = zero_zero(real). [resolve(6692,a,6690,a)]. 228.74/228.57 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(6692,a,6691,a)]. 228.74/228.57 6693 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) != zero_zero(A) | ti(A,B) = zero_zero(A) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom). [clausify(3204)]. 228.74/228.57 Derived: hAPP(int,int,uminus_uminus(int),A) != zero_zero(int) | ti(int,A) = zero_zero(int). [resolve(6693,a,6674,a)]. 228.74/228.57 Derived: hAPP(real,real,uminus_uminus(real),A) != zero_zero(real) | ti(real,A) = zero_zero(real). [resolve(6693,a,6692,a)]. 228.74/228.57 6694 -group_add(A) | hAPP(A,A,uminus_uminus(A),B) = zero_zero(A) | ti(A,B) != zero_zero(A) # label(fact_2024_neg__0__equal__iff__equal) # label(axiom). [clausify(3204)]. 228.74/228.57 Derived: hAPP(int,int,uminus_uminus(int),A) = zero_zero(int) | ti(int,A) != zero_zero(int). [resolve(6694,a,6674,a)]. 228.74/228.57 Derived: hAPP(real,real,uminus_uminus(real),A) = zero_zero(real) | ti(real,A) != zero_zero(real). [resolve(6694,a,6692,a)]. 228.74/228.57 6695 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),B)) # label(fact_2049_add__minus__cancel) # label(axiom). [clausify(3269)]. 228.74/228.57 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(6695,a,6674,a)]. 228.74/228.57 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(6695,a,6692,a)]. 228.74/228.57 6696 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2069_minus__unique) # label(axiom). [clausify(3520)]. 228.74/228.57 6697 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),C) # label(fact_808_add__diff__cancel) # label(axiom). [clausify(3540)]. 228.74/228.57 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(6697,a,6674,a)]. 228.74/228.57 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(6697,a,6692,a)]. 228.74/228.57 6698 -group_add(A) | ti(A,B) != zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) = zero_zero(A) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom). [clausify(3959)]. 228.74/228.57 6699 -group_add(A) | ti(A,B) = zero_zero(A) | hAPP(A,A,uminus_uminus(A),B) != zero_zero(A) # label(fact_2022_neg__equal__0__iff__equal) # label(axiom). [clausify(3959)]. 228.74/228.57 6700 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),C) # label(fact_809_diff__add__cancel) # label(axiom). [clausify(4009)]. 229.18/229.06 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(6700,a,6674,a)]. 229.18/229.06 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(6700,a,6692,a)]. 229.18/229.06 6701 group_add(rat) # label(arity_Rat_Orat___Groups_Ogroup__add) # label(axiom). [assumption]. 229.18/229.06 Derived: hAPP(rat,rat,uminus_uminus(rat),zero_zero(rat)) = zero_zero(rat). [resolve(6701,a,6675,a)]. 229.18/229.06 Derived: ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,B) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6701,a,6676,a)]. 229.18/229.06 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),hAPP(rat,rat,uminus_uminus(rat),A)) = zero_zero(rat). [resolve(6701,a,6680,a)]. 229.18/229.06 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),zero_zero(rat)),A). [resolve(6701,a,6681,a)]. 229.18/229.06 Derived: ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6701,a,6682,a)]. 229.18/229.06 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),zero_zero(rat)). [resolve(6701,a,6683,a)]. 229.18/229.06 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat) | ti(rat,B) = hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6701,a,6685,a)]. 229.18/229.06 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,uminus_uminus(rat),A). [resolve(6701,a,6686,a)]. 229.18/229.06 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) = ti(rat,B). [resolve(6701,a,6687,a)]. 229.18/229.06 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = hAPP(rat,rat,uminus_uminus(rat),B) | ti(rat,A) != ti(rat,B). [resolve(6701,a,6688,a)]. 229.18/229.06 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),A) = zero_zero(rat). [resolve(6701,a,6690,a)]. 229.18/229.06 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(6701,a,6691,a)]. 229.18/229.06 Derived: hAPP(rat,rat,uminus_uminus(rat),A) != zero_zero(rat) | ti(rat,A) = zero_zero(rat). [resolve(6701,a,6693,a)]. 229.18/229.06 Derived: hAPP(rat,rat,uminus_uminus(rat),A) = zero_zero(rat) | ti(rat,A) != zero_zero(rat). [resolve(6701,a,6694,a)]. 229.18/229.06 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(6701,a,6695,a)]. 229.18/229.06 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(6701,a,6697,a)]. 229.18/229.06 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(6701,a,6700,a)]. 229.18/229.06 6702 group_add(complex) # label(arity_Complex_Ocomplex___Groups_Ogroup__add) # label(axiom). [assumption]. 229.18/229.06 Derived: hAPP(complex,complex,uminus_uminus(complex),zero_zero(complex)) = zero_zero(complex). [resolve(6702,a,6675,a)]. 229.18/229.06 Derived: ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,B) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(6702,a,6676,a)]. 229.18/229.06 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),hAPP(complex,complex,uminus_uminus(complex),A)) = zero_zero(complex). [resolve(6702,a,6680,a)]. 229.18/229.06 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),zero_zero(complex)),A). [resolve(6702,a,6681,a)]. 229.18/229.06 Derived: ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(6702,a,6682,a)]. 229.18/229.06 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),zero_zero(complex)). [resolve(6702,a,6683,a)]. 229.18/229.06 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != zero_zero(complex) | ti(complex,B) = hAPP(complex,complex,uminus_uminus(complex),A). [resolve(6702,a,6685,a)]. 229.42/229.24 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,uminus_uminus(complex),A). [resolve(6702,a,6686,a)]. 229.42/229.24 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) = ti(complex,B). [resolve(6702,a,6687,a)]. 229.42/229.24 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = hAPP(complex,complex,uminus_uminus(complex),B) | ti(complex,A) != ti(complex,B). [resolve(6702,a,6688,a)]. 229.42/229.24 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),A) = zero_zero(complex). [resolve(6702,a,6690,a)]. 229.42/229.24 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(6702,a,6691,a)]. 229.42/229.24 Derived: hAPP(complex,complex,uminus_uminus(complex),A) != zero_zero(complex) | ti(complex,A) = zero_zero(complex). [resolve(6702,a,6693,a)]. 229.42/229.24 Derived: hAPP(complex,complex,uminus_uminus(complex),A) = zero_zero(complex) | ti(complex,A) != zero_zero(complex). [resolve(6702,a,6694,a)]. 229.42/229.24 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(6702,a,6695,a)]. 229.42/229.24 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(6702,a,6697,a)]. 229.42/229.24 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(6702,a,6700,a)]. 229.42/229.24 6703 -group_add(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) | ti(A,C) = hAPP(A,A,uminus_uminus(A),B) # label(fact_2043_minus__equation__iff) # label(axiom). [clausify(4720)]. 229.42/229.24 6704 -group_add(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) | ti(A,C) != hAPP(A,A,uminus_uminus(A),B) # label(fact_2043_minus__equation__iff) # label(axiom). [clausify(4720)]. 229.42/229.24 6705 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) | ti(A,B) = hAPP(A,A,uminus_uminus(A),C) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom). [clausify(4826)]. 229.42/229.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int) | ti(int,A) = hAPP(int,int,uminus_uminus(int),B). [resolve(6705,a,6674,a)]. 229.42/229.24 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real) | ti(real,A) = hAPP(real,real,uminus_uminus(real),B). [resolve(6705,a,6692,a)]. 229.42/229.24 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat) | ti(rat,A) = hAPP(rat,rat,uminus_uminus(rat),B). [resolve(6705,a,6701,a)]. 229.42/229.24 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) != zero_zero(complex) | ti(complex,A) = hAPP(complex,complex,uminus_uminus(complex),B). [resolve(6705,a,6702,a)]. 229.42/229.24 6706 -group_add(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) | ti(A,B) != hAPP(A,A,uminus_uminus(A),C) # label(fact_2066_eq__neg__iff__add__eq__0) # label(axiom). [clausify(4826)]. 229.42/229.24 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int) | ti(int,A) != hAPP(int,int,uminus_uminus(int),B). [resolve(6706,a,6674,a)]. 229.42/229.24 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real) | ti(real,A) != hAPP(real,real,uminus_uminus(real),B). [resolve(6706,a,6692,a)]. 229.42/229.24 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = zero_zero(rat) | ti(rat,A) != hAPP(rat,rat,uminus_uminus(rat),B). [resolve(6706,a,6701,a)]. 229.42/229.24 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B) = zero_zero(complex) | ti(complex,A) != hAPP(complex,complex,uminus_uminus(complex),B). [resolve(6706,a,6702,a)]. 233.55/233.36 6707 -group_add(A) | ti(A,B) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B)) # label(fact_2048_minus__add__cancel) # label(axiom). [clausify(4892)]. 233.55/233.36 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(6707,a,6674,a)]. 233.55/233.36 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(6707,a,6692,a)]. 233.55/233.36 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(6707,a,6701,a)]. 233.55/233.36 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(6707,a,6702,a)]. 233.55/233.36 6708 -group_add(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,uminus_uminus(A),C)),hAPP(A,A,uminus_uminus(A),B)) # label(fact_2050_minus__add) # label(axiom). [clausify(4894)]. 233.55/233.36 Derived: hAPP(int,int,uminus_uminus(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,uminus_uminus(int),B)),hAPP(int,int,uminus_uminus(int),A)). [resolve(6708,a,6674,a)]. 233.55/233.36 Derived: hAPP(real,real,uminus_uminus(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,uminus_uminus(real),B)),hAPP(real,real,uminus_uminus(real),A)). [resolve(6708,a,6692,a)]. 233.55/233.36 Derived: hAPP(rat,rat,uminus_uminus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,uminus_uminus(rat),B)),hAPP(rat,rat,uminus_uminus(rat),A)). [resolve(6708,a,6701,a)]. 233.55/233.36 Derived: hAPP(complex,complex,uminus_uminus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,uminus_uminus(complex),B)),hAPP(complex,complex,uminus_uminus(complex),A)). [resolve(6708,a,6702,a)]. 233.55/233.36 6709 real_field(real) # label(arity_RealDef_Oreal___RealVector_Oreal__field) # label(axiom). [assumption]. 233.55/233.36 6710 -real_field(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,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(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)),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),C)))))),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_atLeastAtMost(nat),zero_zero(nat)),C)) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),C)))),hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),C)) # label(fact_4664_exp__series__add) # label(axiom). [clausify(322)]. 233.76/233.57 6711 -real_field(A) | zero_zero(real) = B | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),C),B)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(real,A,of_real(A),C)),hAPP(real,A,of_real(A),B)) # label(fact_2805_nonzero__of__real__divide) # label(axiom). [clausify(858)]. 233.76/233.57 Derived: 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),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(fun(nat,real),fun(nat,real),hAPP(fun(nat,fun(real,real)),fun(fun(nat,real),fun(nat,real)),combs(nat,real,real),hAPP(fun(nat,real),fun(nat,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)),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),B)))))),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_atLeastAtMost(nat),zero_zero(nat)),B)) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))),hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),C)),B)). [resolve(6709,a,6710,a)]. 233.76/233.57 Derived: zero_zero(real) = A | hAPP(real,real,of_real(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,of_real(real),B)),hAPP(real,real,of_real(real),A)). [resolve(6709,a,6711,a)]. 233.76/233.57 6712 -real_field(A) | 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)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E))),F) = 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),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E)),F))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),F)),E)) # label(fact_1801_DERIV__mult__lemma) # label(axiom). [clausify(1961)]. 233.76/233.57 Derived: 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)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D))),E) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(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),D)),E))),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),A),C)),E)),D)). [resolve(6712,a,6709,a)]. 233.96/233.83 6713 real_field(complex) # label(arity_Complex_Ocomplex___RealVector_Oreal__field) # label(axiom). [assumption]. 233.96/233.83 Derived: 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,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(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)),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),B)))))),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_atLeastAtMost(nat),zero_zero(nat)),B)) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(nat,real,real_1(nat),hAPP(nat,nat,fact_fact(nat),B)))),hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),A),C)),B)). [resolve(6713,a,6710,a)]. 233.96/233.83 Derived: zero_zero(real) = A | hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),A)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,of_real(complex),B)),hAPP(real,complex,of_real(complex),A)). [resolve(6713,a,6711,a)]. 233.96/233.83 Derived: 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)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D))),E) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(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),D)),E))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),E)),D)). [resolve(6713,a,6712,a)]. 240.56/240.38 6714 -real_field(A) | -field_inverse_zero(A) | hAPP(real,A,of_real(A),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),inverse_divide(A),hAPP(real,A,of_real(A),B)),hAPP(real,A,of_real(A),C)) # label(fact_2792_of__real__divide) # label(axiom). [clausify(3638)]. 240.56/240.38 Derived: -field_inverse_zero(real) | hAPP(real,real,of_real(real),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),hAPP(real,real,of_real(real),A)),hAPP(real,real,of_real(real),B)). [resolve(6714,a,6709,a)]. 240.56/240.38 Derived: -field_inverse_zero(complex) | hAPP(real,complex,of_real(complex),hAPP(real,real,hAPP(real,fun(real,real),inverse_divide(real),A),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),inverse_divide(complex),hAPP(real,complex,of_real(complex),A)),hAPP(real,complex,of_real(complex),B)). [resolve(6714,a,6713,a)]. 240.56/240.38 6715 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) != hAPP(nat,A,semiring_1_of_nat(A),C) | B = C # label(fact_1214_of__nat__eq__iff) # label(axiom). [clausify(951)]. 240.56/240.38 6716 semiring_char_0(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Nat_Osemiring__char__0) # label(axiom). [assumption]. 240.56/240.38 6717 semiring_char_0(int) # label(arity_Int_Oint___Nat_Osemiring__char__0) # label(axiom). [assumption]. 240.56/240.38 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) != hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B) | A = B. [resolve(6715,a,6716,a)]. 240.56/240.38 6718 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),B) = hAPP(nat,A,semiring_1_of_nat(A),C) | B != C # label(fact_1214_of__nat__eq__iff) # label(axiom). [clausify(951)]. 240.56/240.38 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),A) = hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),B) | A != B. [resolve(6718,a,6716,a)]. 240.56/240.38 6719 semiring_char_0(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Nat_Osemiring__char__0) # label(axiom). [assumption]. 240.56/240.38 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) != hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B) | A = B. [resolve(6719,a,6715,a)]. 240.56/240.38 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),A) = hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),B) | A != B. [resolve(6719,a,6718,a)]. 240.56/240.38 6720 semiring_char_0(nat) # label(arity_Nat_Onat___Nat_Osemiring__char__0) # label(axiom). [assumption]. 240.56/240.38 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) != hAPP(nat,nat,semiring_1_of_nat(nat),B) | A = B. [resolve(6720,a,6715,a)]. 240.56/240.38 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),A) = hAPP(nat,nat,semiring_1_of_nat(nat),B) | A != B. [resolve(6720,a,6718,a)]. 240.56/240.38 6721 -semiring_char_0(A) | hAPP(nat,A,semiring_1_of_nat(A),hAPP(nat,nat,fact_fact(nat),B)) != zero_zero(A) # label(fact_2486_of__nat__fact__not__zero) # label(axiom). [clausify(3109)]. 240.56/240.38 Derived: hAPP(nat,quickcheck_code_int,semiring_1_of_nat(quickcheck_code_int),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(quickcheck_code_int). [resolve(6721,a,6716,a)]. 240.56/240.38 Derived: hAPP(nat,int,semiring_1_of_nat(int),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(int). [resolve(6721,a,6717,a)]. 240.56/240.38 Derived: hAPP(nat,code_code_numeral,semiring_1_of_nat(code_code_numeral),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(code_code_numeral). [resolve(6721,a,6719,a)]. 240.56/240.38 Derived: hAPP(nat,nat,semiring_1_of_nat(nat),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(nat). [resolve(6721,a,6720,a)]. 240.56/240.38 6722 semiring_char_0(complex) # label(arity_Complex_Ocomplex___Nat_Osemiring__char__0) # label(axiom). [assumption]. 245.48/245.29 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) != hAPP(nat,complex,semiring_1_of_nat(complex),B) | A = B. [resolve(6722,a,6715,a)]. 245.48/245.29 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),A) = hAPP(nat,complex,semiring_1_of_nat(complex),B) | A != B. [resolve(6722,a,6718,a)]. 245.48/245.29 Derived: hAPP(nat,complex,semiring_1_of_nat(complex),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(complex). [resolve(6722,a,6721,a)]. 245.48/245.29 6723 semiring_char_0(rat) # label(arity_Rat_Orat___Nat_Osemiring__char__0) # label(axiom). [assumption]. 245.48/245.29 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) != hAPP(nat,rat,semiring_1_of_nat(rat),B) | A = B. [resolve(6723,a,6715,a)]. 245.48/245.29 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),A) = hAPP(nat,rat,semiring_1_of_nat(rat),B) | A != B. [resolve(6723,a,6718,a)]. 245.48/245.29 Derived: hAPP(nat,rat,semiring_1_of_nat(rat),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(rat). [resolve(6723,a,6721,a)]. 245.48/245.29 6724 semiring_char_0(real) # label(arity_RealDef_Oreal___Nat_Osemiring__char__0) # label(axiom). [assumption]. 245.48/245.29 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) != hAPP(nat,real,semiring_1_of_nat(real),B) | A = B. [resolve(6724,a,6715,a)]. 245.48/245.29 Derived: hAPP(nat,real,semiring_1_of_nat(real),A) = hAPP(nat,real,semiring_1_of_nat(real),B) | A != B. [resolve(6724,a,6718,a)]. 245.48/245.29 Derived: hAPP(nat,real,semiring_1_of_nat(real),hAPP(nat,nat,fact_fact(nat),A)) != zero_zero(real). [resolve(6724,a,6721,a)]. 245.48/245.29 6725 ordere223160158up_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__cancel__ab__semigroup_) # label(axiom). [assumption]. 245.48/245.29 6726 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_823_add__le__less__mono) # label(axiom). [clausify(328)]. 245.48/245.29 6727 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_788_add__strict__mono) # label(axiom). [clausify(459)]. 245.48/245.29 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(6725,a,6726,a)]. 245.48/245.29 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(6725,a,6727,a)]. 245.48/245.29 6728 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),E))) # label(fact_824_add__less__le__mono) # label(axiom). [clausify(1891)]. 246.24/246.10 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(6728,a,6725,a)]. 246.24/246.10 6729 ordere223160158up_add(nat) # label(arity_Nat_Onat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 246.24/246.10 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6729,a,6726,a)]. 246.24/246.10 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),C),D)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),D))). [resolve(6729,a,6728,a)]. 246.24/246.10 6730 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),D))) # label(fact_790_add__strict__right__mono) # label(axiom). [clausify(2578)]. 246.24/246.10 6731 ordere223160158up_add(int) # label(arity_Int_Oint___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 246.24/246.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),D)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),D))). [resolve(6731,a,6726,a)]. 246.24/246.10 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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(6731,a,6727,a)]. 246.24/246.10 6732 -ordere223160158up_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),C))) # label(fact_789_add__strict__left__mono) # label(axiom). [clausify(3437)]. 246.24/246.10 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),A),B)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),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(6732,a,6729,a)]. 246.24/246.10 6733 ordere223160158up_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 246.24/246.10 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),B)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),C),D)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),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(6733,a,6726,a)]. 252.31/252.17 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),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(6733,a,6727,a)]. 252.31/252.17 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_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(6733,a,6728,a)]. 252.31/252.17 6734 ordere223160158up_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 252.31/252.17 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(6734,a,6726,a)]. 252.31/252.17 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),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(6734,a,6727,a)]. 252.31/252.17 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_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(6734,a,6728,a)]. 252.31/252.17 6735 ordere223160158up_add(rat) # label(arity_Rat_Orat___Groups_Oordered__cancel__ab__semigroup__add) # label(axiom). [assumption]. 252.31/252.17 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(6735,a,6726,a)]. 252.31/252.17 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(6735,a,6727,a)]. 252.31/252.17 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(6735,a,6728,a)]. 252.31/252.17 6736 ordered_ring(real) # label(arity_RealDef_Oreal___Rings_Oordered__ring) # label(axiom). [assumption]. 252.31/252.17 6737 -ordered_ring(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),C),B))) # label(fact_366_split__mult__pos__le) # label(axiom). [clausify(332)]. 252.37/252.17 6738 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_366_split__mult__pos__le) # label(axiom). [clausify(332)]. 252.37/252.17 6739 -ordered_ring(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),times_times(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),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_503_less__add__iff2) # label(axiom). [clausify(1141)]. 252.37/252.17 6740 -ordered_ring(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),times_times(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),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_503_less__add__iff2) # label(axiom). [clausify(1141)]. 252.37/252.17 6741 -ordered_ring(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),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_504_less__add__iff1) # label(axiom). [clausify(1708)]. 252.37/252.17 6742 -ordered_ring(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),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_504_less__add__iff1) # label(axiom). [clausify(1708)]. 252.37/252.17 6743 -ordered_ring(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),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_502_le__add__iff2) # label(axiom). [clausify(1822)]. 252.37/252.17 6744 -ordered_ring(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),C)),D)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F))) # label(fact_502_le__add__iff2) # label(axiom). [clausify(1822)]. 252.37/252.17 6745 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D))) # label(fact_370_mult__right__mono__neg) # label(axiom). [clausify(3525)]. 252.37/252.17 6746 -ordered_ring(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),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | 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),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_501_le__add__iff1) # label(axiom). [clausify(3825)]. 252.37/252.18 6747 -ordered_ring(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),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)),D)),E)),F)) | -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),D)),E)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)),F))) # label(fact_501_le__add__iff1) # label(axiom). [clausify(3825)]. 252.37/252.18 6748 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B))) # label(fact_369_mult__left__mono__neg) # label(axiom). [clausify(3894)]. 252.37/252.18 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(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6736,a,6739,a)]. 252.37/252.18 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(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6736,a,6740,a)]. 252.37/252.18 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(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C)),D)),E)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),D)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),E))). [resolve(6736,a,6741,a)]. 252.37/252.18 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(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C)),D)),E)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),D)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),E))). [resolve(6736,a,6742,a)]. 252.37/252.18 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),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6736,a,6743,a)]. 252.49/252.30 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),B)),C)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E))). [resolve(6736,a,6744,a)]. 252.49/252.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C))). [resolve(6736,a,6745,a)]. 252.49/252.30 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),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C)),D)),E)) | 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),C)),D)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),E))). [resolve(6736,a,6746,a)]. 252.49/252.30 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),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)),C)),D)),E)) | -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),C)),D)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)),E))). [resolve(6736,a,6747,a)]. 252.49/252.30 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A))). [resolve(6736,a,6748,a)]. 252.49/252.30 6749 ordered_ring(rat) # label(arity_Rat_Orat___Rings_Oordered__ring) # label(axiom). [assumption]. 252.49/252.30 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(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),D),B)),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6749,a,6739,a)]. 252.49/252.30 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(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),D),B)),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6749,a,6740,a)]. 252.49/252.31 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(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),C)),D)),E)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),E))). [resolve(6749,a,6741,a)]. 252.49/252.31 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(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),C)),D)),E)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),E))). [resolve(6749,a,6742,a)]. 252.49/252.31 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),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6749,a,6743,a)]. 252.49/252.31 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),B)),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E))). [resolve(6749,a,6744,a)]. 252.49/252.31 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C))). [resolve(6749,a,6745,a)]. 252.49/252.31 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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),C)),D)),E)) | 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),C)),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),E))). [resolve(6749,a,6746,a)]. 252.49/252.31 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),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),B)),C)),D)),E)) | -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),C)),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)),E))). [resolve(6749,a,6747,a)]. 252.49/252.31 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),C),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A))). [resolve(6749,a,6748,a)]. 252.84/252.69 6750 -ordered_ring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C))) # label(fact_374_mult__nonpos__nonpos) # label(axiom). [clausify(4655)]. 252.84/252.69 6751 ordered_ring(int) # label(arity_Int_Oint___Rings_Oordered__ring) # label(axiom). [assumption]. 252.84/252.69 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(int,int,hAPP(int,fun(int,int),times_times(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),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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),D),A)),B)),E))). [resolve(6751,a,6739,a)]. 252.84/252.69 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(int,int,hAPP(int,fun(int,int),times_times(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),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),C),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),D),A)),B)),E))). [resolve(6751,a,6740,a)]. 252.84/252.69 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(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))). [resolve(6751,a,6741,a)]. 252.84/252.69 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(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))). [resolve(6751,a,6742,a)]. 252.84/252.69 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),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),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),D),A)),B)),E))). [resolve(6751,a,6743,a)]. 252.84/252.69 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),B)),C)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),C),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),D),A)),B)),E))). [resolve(6751,a,6744,a)]. 252.84/252.69 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),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C))). [resolve(6751,a,6745,a)]. 256.96/256.78 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),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | 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),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))). [resolve(6751,a,6746,a)]. 256.96/256.78 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),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),B)),C)),D)),E)) | -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),C)),D)),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)),E))). [resolve(6751,a,6747,a)]. 256.96/256.78 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),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),C),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),A))). [resolve(6751,a,6748,a)]. 256.96/256.78 6752 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(C,bool),fun(B,A),hAPP(fun(B,fun(fun(C,bool),A)),fun(fun(C,bool),fun(B,A)),combc(B,fun(C,bool),A),hAPP(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A)),hAPP(fun(fun(C,A),fun(fun(C,bool),A)),fun(fun(B,fun(C,A)),fun(B,fun(fun(C,bool),A))),combb(fun(C,A),fun(fun(C,bool),A),B),big_co1399186613setsum(C,A)),hAPP(fun(C,A),fun(B,fun(C,A)),hAPP(fun(B,fun(fun(C,A),fun(C,A))),fun(fun(C,A),fun(B,fun(C,A))),combc(B,fun(C,A),fun(C,A)),hAPP(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A))),hAPP(fun(fun(A,A),fun(fun(C,A),fun(C,A))),fun(fun(B,fun(A,A)),fun(B,fun(fun(C,A),fun(C,A)))),combb(fun(A,A),fun(fun(C,A),fun(C,A)),B),combb(A,A,C)),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),D))),E))),F)),V6) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),V6)),hAPP(fun(C,bool),A,hAPP(fun(C,A),fun(fun(C,bool),A),big_co1399186613setsum(C,A),E),F)) # label(fact_4209_setsum__product) # label(axiom). [clausify(723)]. 256.96/256.78 6753 semiring_0(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Osemiring__0) # label(axiom). [assumption]. 256.96/256.78 6754 semiring_0(nat) # label(arity_Nat_Onat___Rings_Osemiring__0) # label(axiom). [assumption]. 256.96/256.78 6755 semiring_0(int) # label(arity_Int_Oint___Rings_Osemiring__0) # label(axiom). [assumption]. 256.96/256.78 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(B,bool),fun(A,quickcheck_code_int),hAPP(fun(A,fun(fun(B,bool),quickcheck_code_int)),fun(fun(B,bool),fun(A,quickcheck_code_int)),combc(A,fun(B,bool),quickcheck_code_int),hAPP(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int)),hAPP(fun(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int)),fun(fun(A,fun(B,quickcheck_code_int)),fun(A,fun(fun(B,bool),quickcheck_code_int))),combb(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),A),big_co1399186613setsum(B,quickcheck_code_int)),hAPP(fun(B,quickcheck_code_int),fun(A,fun(B,quickcheck_code_int)),hAPP(fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),fun(fun(B,quickcheck_code_int),fun(A,fun(B,quickcheck_code_int))),combc(A,fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),hAPP(fun(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int))),fun(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(A,fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)))),combb(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(B,quickcheck_code_int),fun(B,quickcheck_code_int)),A),combb(quickcheck_code_int,quickcheck_code_int,B)),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),C))),D))),E)),F) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),F)),hAPP(fun(B,bool),quickcheck_code_int,hAPP(fun(B,quickcheck_code_int),fun(fun(B,bool),quickcheck_code_int),big_co1399186613setsum(B,quickcheck_code_int),D),E)). [resolve(6752,a,6753,a)]. 257.00/256.82 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(B,bool),fun(A,nat),hAPP(fun(A,fun(fun(B,bool),nat)),fun(fun(B,bool),fun(A,nat)),combc(A,fun(B,bool),nat),hAPP(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat)),hAPP(fun(fun(B,nat),fun(fun(B,bool),nat)),fun(fun(A,fun(B,nat)),fun(A,fun(fun(B,bool),nat))),combb(fun(B,nat),fun(fun(B,bool),nat),A),big_co1399186613setsum(B,nat)),hAPP(fun(B,nat),fun(A,fun(B,nat)),hAPP(fun(A,fun(fun(B,nat),fun(B,nat))),fun(fun(B,nat),fun(A,fun(B,nat))),combc(A,fun(B,nat),fun(B,nat)),hAPP(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat))),hAPP(fun(fun(nat,nat),fun(fun(B,nat),fun(B,nat))),fun(fun(A,fun(nat,nat)),fun(A,fun(fun(B,nat),fun(B,nat)))),combb(fun(nat,nat),fun(fun(B,nat),fun(B,nat)),A),combb(nat,nat,B)),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),C))),D))),E)),F) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),F)),hAPP(fun(B,bool),nat,hAPP(fun(B,nat),fun(fun(B,bool),nat),big_co1399186613setsum(B,nat),D),E)). [resolve(6752,a,6754,a)]. 257.00/256.82 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(B,bool),fun(A,int),hAPP(fun(A,fun(fun(B,bool),int)),fun(fun(B,bool),fun(A,int)),combc(A,fun(B,bool),int),hAPP(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int)),hAPP(fun(fun(B,int),fun(fun(B,bool),int)),fun(fun(A,fun(B,int)),fun(A,fun(fun(B,bool),int))),combb(fun(B,int),fun(fun(B,bool),int),A),big_co1399186613setsum(B,int)),hAPP(fun(B,int),fun(A,fun(B,int)),hAPP(fun(A,fun(fun(B,int),fun(B,int))),fun(fun(B,int),fun(A,fun(B,int))),combc(A,fun(B,int),fun(B,int)),hAPP(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int))),hAPP(fun(fun(int,int),fun(fun(B,int),fun(B,int))),fun(fun(A,fun(int,int)),fun(A,fun(fun(B,int),fun(B,int)))),combb(fun(int,int),fun(fun(B,int),fun(B,int)),A),combb(int,int,B)),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),C))),D))),E)),F) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),F)),hAPP(fun(B,bool),int,hAPP(fun(B,int),fun(fun(B,bool),int),big_co1399186613setsum(B,int),D),E)). [resolve(6752,a,6755,a)]. 257.00/256.82 6756 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(fun(B,A),fun(B,A),hAPP(fun(A,A),fun(fun(B,A),fun(B,A)),combb(A,A,B),hAPP(A,fun(A,A),times_times(A),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),D),E)) # label(fact_4211_setsum__right__distrib) # label(axiom). [clausify(909)]. 257.06/256.85 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int),hAPP(fun(quickcheck_code_int,quickcheck_code_int),fun(fun(A,quickcheck_code_int),fun(A,quickcheck_code_int)),combb(quickcheck_code_int,quickcheck_code_int,A),hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),C),D)). [resolve(6756,a,6753,a)]. 257.06/256.85 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(fun(A,nat),fun(A,nat),hAPP(fun(nat,nat),fun(fun(A,nat),fun(A,nat)),combb(nat,nat,A),hAPP(nat,fun(nat,nat),times_times(nat),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),C),D)). [resolve(6756,a,6754,a)]. 257.06/256.85 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(fun(A,int),fun(A,int),hAPP(fun(int,int),fun(fun(A,int),fun(A,int)),combb(int,int,A),hAPP(int,fun(int,int),times_times(int),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),C),D)). [resolve(6756,a,6755,a)]. 257.06/256.85 6757 -semiring_0(A) | -dvd(A) | -hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),f183(A,B,C)),zero_zero(A)))) # label(fact_602_unity__coeff__ex) # label(axiom). [clausify(927)]. 257.06/256.85 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),dvd_dvd(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),f183(quickcheck_code_int,A,B)),zero_zero(quickcheck_code_int)))). [resolve(6757,a,6753,a)]. 257.06/256.85 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),f183(nat,A,B)),zero_zero(nat)))). [resolve(6757,a,6754,a)]. 257.06/256.85 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),f183(int,A,B)),zero_zero(int)))). [resolve(6757,a,6755,a)]. 257.06/256.85 6758 -semiring_0(A) | -dvd(A) | -hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D))) | hBOOL(hAPP(A,bool,B,f183(A,B,C))) # label(fact_602_unity__coeff__ex) # label(axiom). [clausify(927)]. 257.06/256.85 Derived: -dvd(quickcheck_code_int) | -hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),C))) | hBOOL(hAPP(quickcheck_code_int,bool,A,f183(quickcheck_code_int,A,B))). [resolve(6758,a,6753,a)]. 257.06/256.85 Derived: -dvd(nat) | -hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C))) | hBOOL(hAPP(nat,bool,A,f183(nat,A,B))). [resolve(6758,a,6754,a)]. 257.06/256.85 Derived: -dvd(int) | -hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C))) | hBOOL(hAPP(int,bool,A,f183(int,A,B))). [resolve(6758,a,6755,a)]. 257.06/256.85 6759 -semiring_0(A) | -dvd(A) | hBOOL(hAPP(A,bool,B,hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),f184(A,B,C)))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),dvd_dvd(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),zero_zero(A)))) | -hBOOL(hAPP(A,bool,B,D)) # label(fact_602_unity__coeff__ex) # label(axiom). [clausify(927)]. 257.26/257.07 Derived: -dvd(quickcheck_code_int) | hBOOL(hAPP(quickcheck_code_int,bool,A,hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),f184(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),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),zero_zero(quickcheck_code_int)))) | -hBOOL(hAPP(quickcheck_code_int,bool,A,C)). [resolve(6759,a,6753,a)]. 257.26/257.07 Derived: -dvd(nat) | hBOOL(hAPP(nat,bool,A,hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),f184(nat,A,B)))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),dvd_dvd(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),zero_zero(nat)))) | -hBOOL(hAPP(nat,bool,A,C)). [resolve(6759,a,6754,a)]. 257.26/257.07 Derived: -dvd(int) | hBOOL(hAPP(int,bool,A,hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),f184(int,A,B)))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),dvd_dvd(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),zero_zero(int)))) | -hBOOL(hAPP(int,bool,A,C)). [resolve(6759,a,6755,a)]. 257.26/257.07 6760 -power(A) | -semiring_0(A) | hAPP(int,nat,number_number_of(nat),B) = zero_zero(nat) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),B)) = zero_zero(A) # label(fact_262_power__0__left__number__of) # label(axiom). [clausify(1405)]. 257.26/257.07 Derived: -power(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(quickcheck_code_int). [resolve(6760,b,6753,a)]. 257.26/257.07 Derived: -power(nat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(nat). [resolve(6760,b,6754,a)]. 257.26/257.07 Derived: -power(int) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(int). [resolve(6760,b,6755,a)]. 257.26/257.07 6761 -power(A) | -semiring_0(A) | hAPP(int,nat,number_number_of(nat),B) != zero_zero(nat) | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(int,nat,number_number_of(nat),B)) # label(fact_262_power__0__left__number__of) # label(axiom). [clausify(1405)]. 257.26/257.07 Derived: -power(quickcheck_code_int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(quickcheck_code_int) = hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6761,b,6753,a)]. 257.26/257.07 Derived: -power(nat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(nat) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6761,b,6754,a)]. 257.26/257.07 Derived: -power(int) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(int) = hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6761,b,6755,a)]. 257.26/257.07 6762 -semiring_0(A) | -power(A) | zero_zero(nat) != B | one_one(A) = hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) # label(fact_446_power__0__left) # label(axiom). [clausify(1814)]. 257.26/257.07 6763 -semiring_0(A) | -power(A) | zero_zero(nat) = B | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),B) = zero_zero(A) # label(fact_446_power__0__left) # label(axiom). [clausify(1814)]. 257.36/257.16 Derived: -power(quickcheck_code_int) | zero_zero(nat) = A | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),A) = zero_zero(quickcheck_code_int). [resolve(6763,a,6753,a)]. 257.36/257.16 Derived: -power(nat) | zero_zero(nat) = A | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),A) = zero_zero(nat). [resolve(6763,a,6754,a)]. 257.36/257.16 Derived: -power(int) | zero_zero(nat) = A | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),A) = zero_zero(int). [resolve(6763,a,6755,a)]. 257.36/257.16 6764 semiring_0(real) # label(arity_RealDef_Oreal___Rings_Osemiring__0) # label(axiom). [assumption]. 257.36/257.16 Derived: hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),hAPP(fun(B,bool),fun(A,real),hAPP(fun(A,fun(fun(B,bool),real)),fun(fun(B,bool),fun(A,real)),combc(A,fun(B,bool),real),hAPP(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real)),hAPP(fun(fun(B,real),fun(fun(B,bool),real)),fun(fun(A,fun(B,real)),fun(A,fun(fun(B,bool),real))),combb(fun(B,real),fun(fun(B,bool),real),A),big_co1399186613setsum(B,real)),hAPP(fun(B,real),fun(A,fun(B,real)),hAPP(fun(A,fun(fun(B,real),fun(B,real))),fun(fun(B,real),fun(A,fun(B,real))),combc(A,fun(B,real),fun(B,real)),hAPP(fun(A,fun(real,real)),fun(A,fun(fun(B,real),fun(B,real))),hAPP(fun(fun(real,real),fun(fun(B,real),fun(B,real))),fun(fun(A,fun(real,real)),fun(A,fun(fun(B,real),fun(B,real)))),combb(fun(real,real),fun(fun(B,real),fun(B,real)),A),combb(real,real,B)),hAPP(fun(A,real),fun(A,fun(real,real)),hAPP(fun(real,fun(real,real)),fun(fun(A,real),fun(A,fun(real,real))),combb(real,fun(real,real),A),times_times(real)),C))),D))),E)),F) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(fun(A,bool),real,hAPP(fun(A,real),fun(fun(A,bool),real),big_co1399186613setsum(A,real),C),F)),hAPP(fun(B,bool),real,hAPP(fun(B,real),fun(fun(B,bool),real),big_co1399186613setsum(B,real),D),E)). [resolve(6764,a,6752,a)]. 257.36/257.16 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),f183(real,A,B)),zero_zero(real)))). [resolve(6764,a,6757,a)]. 257.36/257.16 Derived: -dvd(real) | -hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C))) | hBOOL(hAPP(real,bool,A,f183(real,A,B))). [resolve(6764,a,6758,a)]. 257.36/257.16 Derived: -dvd(real) | hBOOL(hAPP(real,bool,A,hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),f184(real,A,B)))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),dvd_dvd(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),zero_zero(real)))) | -hBOOL(hAPP(real,bool,A,C)). [resolve(6764,a,6759,a)]. 257.36/257.16 Derived: -power(real) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(real). [resolve(6764,a,6760,b)]. 257.36/257.16 Derived: -power(real) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(real) = hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6764,a,6761,b)]. 257.36/257.16 Derived: -power(real) | zero_zero(nat) = A | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),A) = zero_zero(real). [resolve(6764,a,6763,a)]. 257.36/257.16 6765 semiring_0(rat) # label(arity_Rat_Orat___Rings_Osemiring__0) # label(axiom). [assumption]. 257.36/257.16 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(B,bool),fun(A,rat),hAPP(fun(A,fun(fun(B,bool),rat)),fun(fun(B,bool),fun(A,rat)),combc(A,fun(B,bool),rat),hAPP(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat)),hAPP(fun(fun(B,rat),fun(fun(B,bool),rat)),fun(fun(A,fun(B,rat)),fun(A,fun(fun(B,bool),rat))),combb(fun(B,rat),fun(fun(B,bool),rat),A),big_co1399186613setsum(B,rat)),hAPP(fun(B,rat),fun(A,fun(B,rat)),hAPP(fun(A,fun(fun(B,rat),fun(B,rat))),fun(fun(B,rat),fun(A,fun(B,rat))),combc(A,fun(B,rat),fun(B,rat)),hAPP(fun(A,fun(rat,rat)),fun(A,fun(fun(B,rat),fun(B,rat))),hAPP(fun(fun(rat,rat),fun(fun(B,rat),fun(B,rat))),fun(fun(A,fun(rat,rat)),fun(A,fun(fun(B,rat),fun(B,rat)))),combb(fun(rat,rat),fun(fun(B,rat),fun(B,rat)),A),combb(rat,rat,B)),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),C))),D))),E)),F) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),F)),hAPP(fun(B,bool),rat,hAPP(fun(B,rat),fun(fun(B,bool),rat),big_co1399186613setsum(B,rat),D),E)). [resolve(6765,a,6752,a)]. 257.42/257.24 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(fun(A,rat),fun(A,rat),hAPP(fun(rat,rat),fun(fun(A,rat),fun(A,rat)),combb(rat,rat,A),hAPP(rat,fun(rat,rat),times_times(rat),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),C),D)). [resolve(6765,a,6756,a)]. 257.42/257.24 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),f183(rat,A,B)),zero_zero(rat)))). [resolve(6765,a,6757,a)]. 257.42/257.24 Derived: -dvd(rat) | -hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C))) | hBOOL(hAPP(rat,bool,A,f183(rat,A,B))). [resolve(6765,a,6758,a)]. 257.42/257.24 Derived: -dvd(rat) | hBOOL(hAPP(rat,bool,A,hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),f184(rat,A,B)))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),dvd_dvd(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),zero_zero(rat)))) | -hBOOL(hAPP(rat,bool,A,C)). [resolve(6765,a,6759,a)]. 257.42/257.24 Derived: -power(rat) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(rat). [resolve(6765,a,6760,b)]. 257.42/257.24 Derived: -power(rat) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(rat) = hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6765,a,6761,b)]. 257.42/257.24 Derived: -power(rat) | zero_zero(nat) = A | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),A) = zero_zero(rat). [resolve(6765,a,6763,a)]. 257.42/257.24 6766 -semiring_0(A) | hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),hAPP(A,fun(B,A),hAPP(fun(B,fun(A,A)),fun(A,fun(B,A)),combc(B,A,A),hAPP(fun(B,A),fun(B,fun(A,A)),hAPP(fun(A,fun(A,A)),fun(fun(B,A),fun(B,fun(A,A))),combb(A,fun(A,A),B),times_times(A)),C)),D)),E) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),C),E)),D) # label(fact_4210_setsum__left__distrib) # label(axiom). [clausify(2221)]. 257.42/257.24 Derived: hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),hAPP(quickcheck_code_int,fun(A,quickcheck_code_int),hAPP(fun(A,fun(quickcheck_code_int,quickcheck_code_int)),fun(quickcheck_code_int,fun(A,quickcheck_code_int)),combc(A,quickcheck_code_int,quickcheck_code_int),hAPP(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int)),hAPP(fun(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int)),fun(fun(A,quickcheck_code_int),fun(A,fun(quickcheck_code_int,quickcheck_code_int))),combb(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),A),times_times(quickcheck_code_int)),B)),C)),D) = hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),hAPP(fun(A,bool),quickcheck_code_int,hAPP(fun(A,quickcheck_code_int),fun(fun(A,bool),quickcheck_code_int),big_co1399186613setsum(A,quickcheck_code_int),B),D)),C). [resolve(6766,a,6753,a)]. 257.42/257.24 Derived: hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),hAPP(nat,fun(A,nat),hAPP(fun(A,fun(nat,nat)),fun(nat,fun(A,nat)),combc(A,nat,nat),hAPP(fun(A,nat),fun(A,fun(nat,nat)),hAPP(fun(nat,fun(nat,nat)),fun(fun(A,nat),fun(A,fun(nat,nat))),combb(nat,fun(nat,nat),A),times_times(nat)),B)),C)),D) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),hAPP(fun(A,bool),nat,hAPP(fun(A,nat),fun(fun(A,bool),nat),big_co1399186613setsum(A,nat),B),D)),C). [resolve(6766,a,6754,a)]. 258.08/257.88 Derived: hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),hAPP(int,fun(A,int),hAPP(fun(A,fun(int,int)),fun(int,fun(A,int)),combc(A,int,int),hAPP(fun(A,int),fun(A,fun(int,int)),hAPP(fun(int,fun(int,int)),fun(fun(A,int),fun(A,fun(int,int))),combb(int,fun(int,int),A),times_times(int)),B)),C)),D) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(fun(A,bool),int,hAPP(fun(A,int),fun(fun(A,bool),int),big_co1399186613setsum(A,int),B),D)),C). [resolve(6766,a,6755,a)]. 258.08/257.88 Derived: hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),hAPP(rat,fun(A,rat),hAPP(fun(A,fun(rat,rat)),fun(rat,fun(A,rat)),combc(A,rat,rat),hAPP(fun(A,rat),fun(A,fun(rat,rat)),hAPP(fun(rat,fun(rat,rat)),fun(fun(A,rat),fun(A,fun(rat,rat))),combb(rat,fun(rat,rat),A),times_times(rat)),B)),C)),D) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(fun(A,bool),rat,hAPP(fun(A,rat),fun(fun(A,bool),rat),big_co1399186613setsum(A,rat),B),D)),C). [resolve(6766,a,6765,a)]. 258.08/257.88 6767 -power(A) | -semiring_0(A) | hAPP(nat,A,hAPP(A,fun(nat,A),power_power(A),zero_zero(A)),hAPP(nat,nat,suc,B)) = zero_zero(A) # label(fact_1300_power__0__Suc) # label(axiom). [clausify(3249)]. 258.08/257.88 Derived: -power(quickcheck_code_int) | hAPP(nat,quickcheck_code_int,hAPP(quickcheck_code_int,fun(nat,quickcheck_code_int),power_power(quickcheck_code_int),zero_zero(quickcheck_code_int)),hAPP(nat,nat,suc,A)) = zero_zero(quickcheck_code_int). [resolve(6767,b,6753,a)]. 258.08/257.88 Derived: -power(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),power_power(nat),zero_zero(nat)),hAPP(nat,nat,suc,A)) = zero_zero(nat). [resolve(6767,b,6754,a)]. 258.08/257.88 Derived: -power(int) | hAPP(nat,int,hAPP(int,fun(nat,int),power_power(int),zero_zero(int)),hAPP(nat,nat,suc,A)) = zero_zero(int). [resolve(6767,b,6755,a)]. 258.08/257.88 Derived: -power(real) | hAPP(nat,real,hAPP(real,fun(nat,real),power_power(real),zero_zero(real)),hAPP(nat,nat,suc,A)) = zero_zero(real). [resolve(6767,b,6764,a)]. 258.08/257.88 Derived: -power(rat) | hAPP(nat,rat,hAPP(rat,fun(nat,rat),power_power(rat),zero_zero(rat)),hAPP(nat,nat,suc,A)) = zero_zero(rat). [resolve(6767,b,6765,a)]. 258.08/257.88 6768 semiring_0(complex) # label(arity_Complex_Ocomplex___Rings_Osemiring__0) # label(axiom). [assumption]. 258.08/257.88 Derived: hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),hAPP(fun(B,bool),fun(A,complex),hAPP(fun(A,fun(fun(B,bool),complex)),fun(fun(B,bool),fun(A,complex)),combc(A,fun(B,bool),complex),hAPP(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex)),hAPP(fun(fun(B,complex),fun(fun(B,bool),complex)),fun(fun(A,fun(B,complex)),fun(A,fun(fun(B,bool),complex))),combb(fun(B,complex),fun(fun(B,bool),complex),A),big_co1399186613setsum(B,complex)),hAPP(fun(B,complex),fun(A,fun(B,complex)),hAPP(fun(A,fun(fun(B,complex),fun(B,complex))),fun(fun(B,complex),fun(A,fun(B,complex))),combc(A,fun(B,complex),fun(B,complex)),hAPP(fun(A,fun(complex,complex)),fun(A,fun(fun(B,complex),fun(B,complex))),hAPP(fun(fun(complex,complex),fun(fun(B,complex),fun(B,complex))),fun(fun(A,fun(complex,complex)),fun(A,fun(fun(B,complex),fun(B,complex)))),combb(fun(complex,complex),fun(fun(B,complex),fun(B,complex)),A),combb(complex,complex,B)),hAPP(fun(A,complex),fun(A,fun(complex,complex)),hAPP(fun(complex,fun(complex,complex)),fun(fun(A,complex),fun(A,fun(complex,complex))),combb(complex,fun(complex,complex),A),times_times(complex)),C))),D))),E)),F) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(fun(A,bool),complex,hAPP(fun(A,complex),fun(fun(A,bool),complex),big_co1399186613setsum(A,complex),C),F)),hAPP(fun(B,bool),complex,hAPP(fun(B,complex),fun(fun(B,bool),complex),big_co1399186613setsum(B,complex),D),E)). [resolve(6768,a,6752,a)]. 258.55/258.39 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))) | hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),f183(complex,A,B)),zero_zero(complex)))). [resolve(6768,a,6757,a)]. 258.55/258.39 Derived: -dvd(complex) | -hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C))) | hBOOL(hAPP(complex,bool,A,f183(complex,A,B))). [resolve(6768,a,6758,a)]. 258.55/258.39 Derived: -dvd(complex) | hBOOL(hAPP(complex,bool,A,hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),f184(complex,A,B)))) | -hBOOL(hAPP(complex,bool,hAPP(complex,fun(complex,bool),dvd_dvd(complex),B),hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),C),zero_zero(complex)))) | -hBOOL(hAPP(complex,bool,A,C)). [resolve(6768,a,6759,a)]. 258.55/258.39 Derived: -power(complex) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(complex). [resolve(6768,a,6760,b)]. 258.55/258.39 Derived: -power(complex) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(complex) = hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6768,a,6761,b)]. 258.55/258.39 Derived: -power(complex) | zero_zero(nat) = A | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),A) = zero_zero(complex). [resolve(6768,a,6763,a)]. 258.55/258.39 Derived: -power(complex) | hAPP(nat,complex,hAPP(complex,fun(nat,complex),power_power(complex),zero_zero(complex)),hAPP(nat,nat,suc,A)) = zero_zero(complex). [resolve(6768,a,6767,b)]. 258.55/258.39 6769 semiring_0(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Rings_Osemiring__0) # label(axiom). [assumption]. 258.55/258.39 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(B,bool),fun(A,code_code_numeral),hAPP(fun(A,fun(fun(B,bool),code_code_numeral)),fun(fun(B,bool),fun(A,code_code_numeral)),combc(A,fun(B,bool),code_code_numeral),hAPP(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral)),hAPP(fun(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral)),fun(fun(A,fun(B,code_code_numeral)),fun(A,fun(fun(B,bool),code_code_numeral))),combb(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),A),big_co1399186613setsum(B,code_code_numeral)),hAPP(fun(B,code_code_numeral),fun(A,fun(B,code_code_numeral)),hAPP(fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),fun(fun(B,code_code_numeral),fun(A,fun(B,code_code_numeral))),combc(A,fun(B,code_code_numeral),fun(B,code_code_numeral)),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),hAPP(fun(fun(code_code_numeral,code_code_numeral),fun(fun(B,code_code_numeral),fun(B,code_code_numeral))),fun(fun(A,fun(code_code_numeral,code_code_numeral)),fun(A,fun(fun(B,code_code_numeral),fun(B,code_code_numeral)))),combb(fun(code_code_numeral,code_code_numeral),fun(fun(B,code_code_numeral),fun(B,code_code_numeral)),A),combb(code_code_numeral,code_code_numeral,B)),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),C))),D))),E)),F) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),F)),hAPP(fun(B,bool),code_code_numeral,hAPP(fun(B,code_code_numeral),fun(fun(B,bool),code_code_numeral),big_co1399186613setsum(B,code_code_numeral),D),E)). [resolve(6769,a,6752,a)]. 258.55/258.40 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,code_code_numeral),hAPP(fun(code_code_numeral,code_code_numeral),fun(fun(A,code_code_numeral),fun(A,code_code_numeral)),combb(code_code_numeral,code_code_numeral,A),hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),C),D)). [resolve(6769,a,6756,a)]. 258.55/258.40 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),dvd_dvd(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),f183(code_code_numeral,A,B)),zero_zero(code_code_numeral)))). [resolve(6769,a,6757,a)]. 258.55/258.40 Derived: -dvd(code_code_numeral) | -hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),C))) | hBOOL(hAPP(code_code_numeral,bool,A,f183(code_code_numeral,A,B))). [resolve(6769,a,6758,a)]. 258.55/258.40 Derived: -dvd(code_code_numeral) | hBOOL(hAPP(code_code_numeral,bool,A,hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),B),f184(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),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),zero_zero(code_code_numeral)))) | -hBOOL(hAPP(code_code_numeral,bool,A,C)). [resolve(6769,a,6759,a)]. 258.55/258.40 Derived: -power(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) = zero_zero(nat) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),A)) = zero_zero(code_code_numeral). [resolve(6769,a,6760,b)]. 258.55/258.40 Derived: -power(code_code_numeral) | hAPP(int,nat,number_number_of(nat),A) != zero_zero(nat) | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(int,nat,number_number_of(nat),A)). [resolve(6769,a,6761,b)]. 258.55/258.40 Derived: -power(code_code_numeral) | zero_zero(nat) != A | one_one(code_code_numeral) = hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),A). [resolve(6769,a,6762,a)]. 258.55/258.40 Derived: -power(code_code_numeral) | zero_zero(nat) = A | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),A) = zero_zero(code_code_numeral). [resolve(6769,a,6763,a)]. 258.55/258.40 Derived: hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),hAPP(code_code_numeral,fun(A,code_code_numeral),hAPP(fun(A,fun(code_code_numeral,code_code_numeral)),fun(code_code_numeral,fun(A,code_code_numeral)),combc(A,code_code_numeral,code_code_numeral),hAPP(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral)),hAPP(fun(code_code_numeral,fun(code_code_numeral,code_code_numeral)),fun(fun(A,code_code_numeral),fun(A,fun(code_code_numeral,code_code_numeral))),combb(code_code_numeral,fun(code_code_numeral,code_code_numeral),A),times_times(code_code_numeral)),B)),C)),D) = hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),times_times(code_code_numeral),hAPP(fun(A,bool),code_code_numeral,hAPP(fun(A,code_code_numeral),fun(fun(A,bool),code_code_numeral),big_co1399186613setsum(A,code_code_numeral),B),D)),C). [resolve(6769,a,6766,a)]. 275.29/275.09 Derived: -power(code_code_numeral) | hAPP(nat,code_code_numeral,hAPP(code_code_numeral,fun(nat,code_code_numeral),power_power(code_code_numeral),zero_zero(code_code_numeral)),hAPP(nat,nat,suc,A)) = zero_zero(code_code_numeral). [resolve(6769,a,6767,b)]. 275.29/275.09 6770 -abs_if(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | hAPP(A,A,uminus_uminus(A),B) = hAPP(A,A,abs_abs(A),B) # label(fact_2098_abs__if) # label(axiom). [clausify(1324)]. 275.29/275.09 6771 abs_if(int) # label(arity_Int_Oint___Groups_Oabs__if) # label(axiom). [assumption]. 275.29/275.09 6772 abs_if(rat) # label(arity_Rat_Orat___Groups_Oabs__if) # label(axiom). [assumption]. 275.29/275.09 6773 -abs_if(A) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | ti(A,B) = hAPP(A,A,abs_abs(A),B) # label(fact_2098_abs__if) # label(axiom). [clausify(1324)]. 275.29/275.09 Derived: hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | ti(int,A) = hAPP(int,int,abs_abs(int),A). [resolve(6773,a,6771,a)]. 275.29/275.09 Derived: hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | ti(rat,A) = hAPP(rat,rat,abs_abs(rat),A). [resolve(6773,a,6772,a)]. 275.29/275.09 6774 -abs_if(A) | abs_abs(A) = ti(fun(A,A),abs_abs(A)) # label(tsy_c_Groups_Oabs__class_Oabs_0_res) # label(axiom). [clausify(3203)]. 275.29/275.09 6775 abs_if(real) # label(arity_RealDef_Oreal___Groups_Oabs__if) # label(axiom). [assumption]. 275.29/275.09 Derived: hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | ti(real,A) = hAPP(real,real,abs_abs(real),A). [resolve(6775,a,6773,a)]. 275.29/275.09 6776 sgn_div_norm(real) # label(arity_RealDef_Oreal___RealVector_Osgn__div__norm) # label(axiom). [assumption]. 275.29/275.09 6777 -sgn_div_norm(A) | norm_norm(A) = ti(fun(A,real),norm_norm(A)) # label(tsy_c_RealVector_Onorm__class_Onorm_0_res) # label(axiom). [clausify(381)]. 275.29/275.09 Derived: norm_norm(real) = ti(fun(real,real),norm_norm(real)). [resolve(6776,a,6777,a)]. 275.29/275.09 6778 sgn_div_norm(complex) # label(arity_Complex_Ocomplex___RealVector_Osgn__div__norm) # label(axiom). [assumption]. 275.29/275.09 Derived: norm_norm(complex) = ti(fun(complex,real),norm_norm(complex)). [resolve(6778,a,6777,a)]. 275.29/275.09 6779 -sgn_div_norm(A) | hAPP(A,A,sgn_sgn(A),B) = hAPP(A,A,hAPP(real,fun(A,A),scaleR_scaleR(A),hAPP(real,real,inverse_inverse(real),hAPP(A,real,norm_norm(A),B))),B) # label(fact_4725_sgn__div__norm) # label(axiom). [clausify(3483)]. 275.29/275.09 Derived: hAPP(real,real,sgn_sgn(real),A) = hAPP(real,real,hAPP(real,fun(real,real),scaleR_scaleR(real),hAPP(real,real,inverse_inverse(real),hAPP(real,real,norm_norm(real),A))),A). [resolve(6779,a,6776,a)]. 275.29/275.09 Derived: hAPP(complex,complex,sgn_sgn(complex),A) = hAPP(complex,complex,hAPP(real,fun(complex,complex),scaleR_scaleR(complex),hAPP(real,real,inverse_inverse(real),hAPP(complex,real,norm_norm(complex),A))),A). [resolve(6779,a,6778,a)]. 275.29/275.09 6780 -sgn_div_norm(A) | sgn_sgn(A) = ti(fun(A,A),sgn_sgn(A)) # label(tsy_c_Groups_Osgn__class_Osgn_0_res) # label(axiom). [clausify(3708)]. 275.29/275.09 Derived: sgn_sgn(real) = ti(fun(real,real),sgn_sgn(real)). [resolve(6780,a,6776,a)]. 275.29/275.09 Derived: sgn_sgn(complex) = ti(fun(complex,complex),sgn_sgn(complex)). [resolve(6780,a,6778,a)]. 275.29/275.09 6781 -sgn_div_norm(A) | ti(fun(real,fun(A,A)),scaleR_scaleR(A)) = scaleR_scaleR(A) # label(tsy_c_RealVector_OscaleR__class_OscaleR_0_res) # label(axiom). [clausify(4603)]. 275.29/275.09 6782 dist_norm(real) # label(arity_RealDef_Oreal___RealVector_Odist__norm) # label(axiom). [assumption]. 275.29/275.09 6783 -dist_norm(A) | norm_norm(A) = ti(fun(A,real),norm_norm(A)) # label(tsy_c_RealVector_Onorm__class_Onorm_1_res) # label(axiom). [clausify(456)]. 280.82/280.65 6784 -dist_norm(A) | hAPP(A,real,norm_norm(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),C)) = hAPP(A,real,hAPP(A,fun(A,real),dist_dist(A),B),C) # label(fact_3503_dist__norm) # label(axiom). [clausify(2875)]. 280.82/280.65 Derived: hAPP(real,real,norm_norm(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),B)) = hAPP(real,real,hAPP(real,fun(real,real),dist_dist(real),A),B). [resolve(6784,a,6782,a)]. 280.82/280.65 6785 -dist_norm(A) | dist_dist(A) = ti(fun(A,fun(A,real)),dist_dist(A)) # label(tsy_c_RealVector_Odist__class_Odist_0_res) # label(axiom). [clausify(4378)]. 280.82/280.65 Derived: dist_dist(real) = ti(fun(real,fun(real,real)),dist_dist(real)). [resolve(6785,a,6782,a)]. 280.82/280.65 6786 dist_norm(complex) # label(arity_Complex_Ocomplex___RealVector_Odist__norm) # label(axiom). [assumption]. 280.82/280.65 Derived: hAPP(complex,real,norm_norm(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),B)) = hAPP(complex,real,hAPP(complex,fun(complex,real),dist_dist(complex),A),B). [resolve(6786,a,6784,a)]. 280.82/280.65 Derived: dist_dist(complex) = ti(fun(complex,fun(complex,real)),dist_dist(complex)). [resolve(6786,a,6785,a)]. 280.82/280.65 6787 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_816_add__nonneg__nonneg) # label(axiom). [clausify(522)]. 280.82/280.65 6788 ordere216010020id_add(code_code_numeral) # label(arity_Code__Numeral_Ocode__numeral___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 280.82/280.65 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),plus_plus(code_code_numeral),A),B))). [resolve(6787,a,6788,a)]. 280.82/280.65 6789 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_814_add__increasing) # label(axiom). [clausify(1105)]. 280.82/280.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6789,a,6788,a)]. 280.82/280.65 6790 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_759_add__strict__increasing) # label(axiom). [clausify(1422)]. 280.82/280.65 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6790,a,6788,a)]. 280.88/280.72 6791 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_757_add__pos__nonneg) # label(axiom). [clausify(1450)]. 280.88/280.72 6792 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_762_add__nonpos__neg) # label(axiom). [clausify(1488)]. 280.88/280.72 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6792,a,6788,a)]. 280.88/280.72 6793 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_820_add__pos__pos) # label(axiom). [clausify(1528)]. 280.88/280.72 6794 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | ti(A,B) != zero_zero(A) | ti(A,C) != zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) = zero_zero(A) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom). [clausify(1649)]. 280.88/280.72 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)) | ti(code_code_numeral,A) != zero_zero(code_code_numeral) | ti(code_code_numeral,B) != zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) = zero_zero(code_code_numeral). [resolve(6794,a,6788,a)]. 280.88/280.72 6795 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | ti(A,B) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom). [clausify(1649)]. 280.88/280.72 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)) | ti(code_code_numeral,A) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != zero_zero(code_code_numeral). [resolve(6795,a,6788,a)]. 280.88/280.72 6796 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | ti(A,C) = zero_zero(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C) != zero_zero(A) # label(fact_815_add__nonneg__eq__0__iff) # label(axiom). [clausify(1649)]. 280.88/280.72 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)) | ti(code_code_numeral,B) = zero_zero(code_code_numeral) | hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B) != zero_zero(code_code_numeral). [resolve(6796,a,6788,a)]. 281.12/280.92 6797 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),D),B))) # label(fact_813_add__increasing2) # label(axiom). [clausify(2188)]. 281.12/280.92 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),C),A))). [resolve(6797,a,6788,a)]. 281.12/280.92 6798 ordere216010020id_add(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 281.12/280.92 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),plus_plus(quickcheck_code_int),A),B))). [resolve(6798,a,6787,a)]. 281.12/280.92 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6798,a,6789,a)]. 281.12/280.92 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6798,a,6790,a)]. 281.12/280.92 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6798,a,6792,a)]. 281.12/280.92 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)) | ti(quickcheck_code_int,A) != zero_zero(quickcheck_code_int) | ti(quickcheck_code_int,B) != zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) = zero_zero(quickcheck_code_int). [resolve(6798,a,6794,a)]. 281.12/280.95 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)) | ti(quickcheck_code_int,A) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int). [resolve(6798,a,6795,a)]. 281.12/280.95 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)) | ti(quickcheck_code_int,B) = zero_zero(quickcheck_code_int) | hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B) != zero_zero(quickcheck_code_int). [resolve(6798,a,6796,a)]. 281.12/280.95 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),C),A))). [resolve(6798,a,6797,a)]. 281.12/280.95 6799 ordere216010020id_add(real) # label(arity_RealDef_Oreal___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 281.12/280.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B))). [resolve(6799,a,6787,a)]. 281.12/280.95 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(6799,a,6789,a)]. 281.12/280.95 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(6799,a,6790,a)]. 281.12/280.95 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(6799,a,6792,a)]. 281.12/280.95 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | ti(real,A) != zero_zero(real) | ti(real,B) != zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) = zero_zero(real). [resolve(6799,a,6794,a)]. 281.29/281.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | ti(real,A) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real). [resolve(6799,a,6795,a)]. 281.29/281.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | ti(real,B) = zero_zero(real) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B) != zero_zero(real). [resolve(6799,a,6796,a)]. 281.29/281.11 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),A)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),C),A))). [resolve(6799,a,6797,a)]. 281.29/281.11 6800 ordere216010020id_add(rat) # label(arity_Rat_Orat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 281.29/281.11 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),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),plus_plus(rat),A),B))). [resolve(6800,a,6787,a)]. 281.29/281.11 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),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(6800,a,6789,a)]. 281.29/281.11 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),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(6800,a,6790,a)]. 281.29/281.11 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(6800,a,6792,a)]. 281.29/281.11 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),zero_zero(rat)),B)) | ti(rat,A) != zero_zero(rat) | ti(rat,B) != zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) = zero_zero(rat). [resolve(6800,a,6794,a)]. 281.29/281.11 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),zero_zero(rat)),B)) | ti(rat,A) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat). [resolve(6800,a,6795,a)]. 281.29/281.11 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),zero_zero(rat)),B)) | ti(rat,B) = zero_zero(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B) != zero_zero(rat). [resolve(6800,a,6796,a)]. 281.29/281.11 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),B),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),C),A))). [resolve(6800,a,6797,a)]. 281.29/281.11 6801 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),D))) # label(fact_760_add__strict__increasing2) # label(axiom). [clausify(2647)]. 281.48/281.29 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),zero_zero(code_code_numeral)),A)) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),C)) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),C))). [resolve(6801,a,6788,a)]. 281.48/281.29 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),A)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),C))). [resolve(6801,a,6798,a)]. 281.48/281.29 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(6801,a,6799,a)]. 281.48/281.29 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(6801,a,6800,a)]. 281.48/281.29 6802 -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),f550(B,A,E,D,C)),hAPP(fun(B,bool),fun(B,bool),hAPP(fun(B,bool),fun(fun(B,bool),fun(B,bool)),minus_minus(fun(B,bool)),C),D))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4293_setsum__mono2) # label(axiom). [clausify(3089)]. 281.48/281.29 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),f550(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(6802,a,6788,a)]. 281.48/281.29 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),f550(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(6802,a,6798,a)]. 281.48/281.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f550(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(6802,a,6799,a)]. 281.48/281.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f550(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(6802,a,6800,a)]. 281.48/281.30 6803 -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,f550(B,A,E,D,C)))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),D)),hAPP(fun(B,bool),A,hAPP(fun(B,A),fun(fun(B,bool),A),big_co1399186613setsum(B,A),E),C))) # label(fact_4293_setsum__mono2) # label(axiom). [clausify(3089)]. 281.48/281.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(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,f550(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(6803,a,6788,a)]. 281.48/281.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(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,f550(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(6803,a,6798,a)]. 281.48/281.30 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),hAPP(A,real,D,f550(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(6803,a,6799,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),hAPP(A,rat,D,f550(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(6803,a,6800,a)]. 281.79/281.63 6804 ordere216010020id_add(int) # label(arity_Int_Oint___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 281.79/281.63 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),plus_plus(int),A),B))). [resolve(6804,a,6787,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(6804,a,6789,a)]. 281.79/281.63 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_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(6804,a,6790,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(6804,a,6792,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | ti(int,A) != zero_zero(int) | ti(int,B) != zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) = zero_zero(int). [resolve(6804,a,6794,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | ti(int,A) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int). [resolve(6804,a,6795,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),B)) | ti(int,B) = zero_zero(int) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B) != zero_zero(int). [resolve(6804,a,6796,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),C),A))). [resolve(6804,a,6797,a)]. 281.79/281.63 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),A)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),C)) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),C))). [resolve(6804,a,6801,a)]. 281.79/281.63 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),f550(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(6804,a,6802,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),zero_zero(int)),hAPP(A,int,D,f550(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(6804,a,6803,a)]. 282.09/281.90 6805 ordere216010020id_add(nat) # label(arity_Nat_Onat___Groups_Oordered__comm__monoid__add) # label(axiom). [assumption]. 282.09/281.90 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(6805,a,6790,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | ti(nat,A) != zero_zero(nat) | ti(nat,B) != zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) = zero_zero(nat). [resolve(6805,a,6794,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | ti(nat,A) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat). [resolve(6805,a,6795,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),B)) | ti(nat,B) = zero_zero(nat) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B) != zero_zero(nat). [resolve(6805,a,6796,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),C),A))). [resolve(6805,a,6797,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),A)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),C)) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less(nat),B),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),C))). [resolve(6805,a,6801,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | hBOOL(hAPP(fun(A,bool),bool,hAPP(A,fun(fun(A,bool),bool),member(A),f550(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(6805,a,6802,a)]. 282.09/281.90 Derived: -hBOOL(hAPP(fun(A,bool),bool,finite_finite_1(A),B)) | -hBOOL(hAPP(fun(A,bool),bool,hAPP(fun(A,bool),fun(fun(A,bool),bool),ord_less_eq(fun(A,bool)),C),B)) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),zero_zero(nat)),hAPP(A,nat,D,f550(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(6805,a,6803,a)]. 282.09/281.90 6806 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_761_add__neg__nonpos) # label(axiom). [clausify(3988)]. 282.20/281.98 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6806,a,6788,a)]. 282.20/281.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6806,a,6798,a)]. 282.20/281.98 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(6806,a,6799,a)]. 282.20/281.98 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_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(6806,a,6800,a)]. 282.20/281.98 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(6806,a,6804,a)]. 282.20/281.98 6807 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_812_add__nonpos__nonpos) # label(axiom). [clausify(4092)]. 282.20/281.98 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less_eq(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6807,a,6788,a)]. 282.20/281.98 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6807,a,6798,a)]. 282.40/282.20 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6807,a,6799,a)]. 282.40/282.20 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),zero_zero(rat))) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),B),zero_zero(rat))) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),A),B)),zero_zero(rat))). [resolve(6807,a,6800,a)]. 282.40/282.20 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less_eq(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(6807,a,6804,a)]. 282.40/282.20 Derived: -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),A),zero_zero(nat))) | -hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),B),zero_zero(nat))) | hBOOL(hAPP(nat,bool,hAPP(nat,fun(nat,bool),ord_less_eq(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),A),B)),zero_zero(nat))). [resolve(6807,a,6805,a)]. 282.40/282.20 6808 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),C)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),zero_zero(A)),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C))) # label(fact_758_add__nonneg__pos) # label(axiom). [clausify(4250)]. 282.40/282.20 6809 -ordere216010020id_add(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),B),zero_zero(A))) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),C),zero_zero(A))) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less(A),hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),B),C)),zero_zero(A))) # label(fact_819_add__neg__neg) # label(axiom). [clausify(4425)]. 282.40/282.20 Derived: -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),A),zero_zero(code_code_numeral))) | -hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),B),zero_zero(code_code_numeral))) | hBOOL(hAPP(code_code_numeral,bool,hAPP(code_code_numeral,fun(code_code_numeral,bool),ord_less(code_code_numeral),hAPP(code_code_numeral,code_code_numeral,hAPP(code_code_numeral,fun(code_code_numeral,code_code_numeral),plus_plus(code_code_numeral),A),B)),zero_zero(code_code_numeral))). [resolve(6809,a,6788,a)]. 282.40/282.20 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),A),zero_zero(quickcheck_code_int))) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),B),zero_zero(quickcheck_code_int))) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),plus_plus(quickcheck_code_int),A),B)),zero_zero(quickcheck_code_int))). [resolve(6809,a,6798,a)]. 282.40/282.20 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),A),zero_zero(real))) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),B),zero_zero(real))) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less(real),hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),A),B)),zero_zero(real))). [resolve(6809,a,6799,a)]. 282.40/282.20 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(6809,a,6800,a)]. 287.07/286.91 Derived: -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),A),zero_zero(int))) | -hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),B),zero_zero(int))) | hBOOL(hAPP(int,bool,hAPP(int,fun(int,bool),ord_less(int),hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),A),B)),zero_zero(int))). [resolve(6809,a,6804,a)]. 287.07/286.91 6810 -ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2030_minus__mult__right) # label(axiom). [clausify(1205)]. 287.07/286.91 6811 ring(real) # label(arity_RealDef_Oreal___Rings_Oring) # label(axiom). [assumption]. 287.07/286.91 6812 -ring(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),minus_minus(A),C),D)),E)),F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),F) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)),B) # label(fact_489_eq__add__iff2) # label(axiom). [clausify(1361)]. 287.07/286.91 Derived: ti(real,A) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),E) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)),A). [resolve(6812,a,6811,a)]. 287.07/286.91 6813 -ring(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),minus_minus(A),C),D)),E)),F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)),F) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)),B) # label(fact_489_eq__add__iff2) # label(axiom). [clausify(1361)]. 287.07/286.91 Derived: ti(real,A) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),C)),D)),E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)),E) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)),A). [resolve(6813,a,6811,a)]. 287.07/286.91 6814 ring(rat) # label(arity_Rat_Orat___Rings_Oring) # label(axiom). [assumption]. 287.07/286.91 Derived: hAPP(rat,rat,uminus_uminus(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),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6814,a,6810,a)]. 287.07/286.91 Derived: ti(rat,A) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),D)),E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)),E) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)),A). [resolve(6814,a,6812,a)]. 287.07/286.91 Derived: ti(rat,A) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)),D)),E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)),E) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)),A). [resolve(6814,a,6813,a)]. 287.07/286.91 6815 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(int,A,number_number_of(A),C))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),hAPP(int,A,number_number_of(A),C))) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),hAPP(int,A,number_number_of(A),C)) # label(fact_492_left__diff__distrib__number__of) # label(axiom). [clausify(1987)]. 287.66/287.48 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(int,rat,number_number_of(rat),B))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),hAPP(int,rat,number_number_of(rat),B))) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),hAPP(int,rat,number_number_of(rat),B)). [resolve(6815,b,6814,a)]. 287.66/287.48 6816 -ring(A) | hAPP(A,A,uminus_uminus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) # label(fact_2031_minus__mult__left) # label(axiom). [clausify(2164)]. 287.66/287.48 Derived: hAPP(rat,rat,uminus_uminus(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,uminus_uminus(rat),A)),B). [resolve(6816,a,6814,a)]. 287.66/287.48 6817 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),C) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,uminus_uminus(A),C)) # label(fact_2032_minus__mult__commute) # label(axiom). [clausify(2672)]. 287.66/287.48 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),B) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,uminus_uminus(real),B)). [resolve(6817,a,6811,a)]. 287.66/287.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),A)),B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,uminus_uminus(rat),B)). [resolve(6817,a,6814,a)]. 287.66/287.48 6818 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,uminus_uminus(A),B)),hAPP(A,A,uminus_uminus(A),C)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C) # label(fact_2033_minus__mult__minus) # label(axiom). [clausify(3154)]. 287.66/287.48 Derived: hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,uminus_uminus(real),A)),hAPP(real,real,uminus_uminus(real),B)) = hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B). [resolve(6818,a,6811,a)]. 287.66/287.48 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,uminus_uminus(rat),A)),hAPP(rat,rat,uminus_uminus(rat),B)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B). [resolve(6818,a,6814,a)]. 287.66/287.48 6819 ring(complex) # label(arity_Complex_Ocomplex___Rings_Oring) # label(axiom). [assumption]. 287.66/287.48 Derived: ti(complex,A) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)),D)),E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)),E) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)),A). [resolve(6819,a,6812,a)]. 287.66/287.48 Derived: ti(complex,A) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),C)),D)),E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)),E) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)),A). [resolve(6819,a,6813,a)]. 287.66/287.48 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,uminus_uminus(complex),B)). [resolve(6819,a,6817,a)]. 287.66/287.48 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,uminus_uminus(complex),A)),hAPP(complex,complex,uminus_uminus(complex),B)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B). [resolve(6819,a,6818,a)]. 288.64/288.43 6820 -number(A) | -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),D)) = hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(int,A,number_number_of(A),B)),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),D)) # label(fact_491_right__diff__distrib__number__of) # label(axiom). [clausify(3666)]. 288.64/288.43 Derived: -number(rat) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),C)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(int,rat,number_number_of(rat),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),C)). [resolve(6820,b,6814,a)]. 288.64/288.43 6821 ring(int) # label(arity_Int_Oint___Rings_Oring) # label(axiom). [assumption]. 288.64/288.43 Derived: hAPP(int,int,uminus_uminus(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),hAPP(int,int,uminus_uminus(int),B)). [resolve(6821,a,6810,a)]. 288.64/288.43 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),minus_minus(int),B),C)),D)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),E) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)),A). [resolve(6821,a,6812,a)]. 288.64/288.43 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),minus_minus(int),B),C)),D)),E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)),E) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)),A). [resolve(6821,a,6813,a)]. 288.64/288.43 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,number_number_of(int),B))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),hAPP(int,int,number_number_of(int),B))) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),hAPP(int,int,number_number_of(int),B)). [resolve(6821,a,6815,b)]. 288.64/288.43 Derived: hAPP(int,int,uminus_uminus(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,uminus_uminus(int),A)),B). [resolve(6821,a,6816,a)]. 288.64/288.43 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),B) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,uminus_uminus(int),B)). [resolve(6821,a,6817,a)]. 288.64/288.43 Derived: hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,uminus_uminus(int),A)),hAPP(int,int,uminus_uminus(int),B)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B). [resolve(6821,a,6818,a)]. 288.64/288.43 Derived: -number(int) | hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),C)) = hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,number_number_of(int),A)),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),C)). [resolve(6821,a,6820,b)]. 288.64/288.43 6822 -ring(A) | hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),C),E))),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),B),D)),E)) # label(fact_729_mult__diff__mult) # label(axiom). [clausify(4636)]. 288.71/288.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),B),D))),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),A),C)),D)). [resolve(6822,a,6811,a)]. 288.71/288.55 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(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),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),B),D))),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),A),C)),D)). [resolve(6822,a,6814,a)]. 288.71/288.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),B),D))),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),A),C)),D)). [resolve(6822,a,6819,a)]. 288.71/288.55 Derived: hAPP(int,int,hAPP(int,fun(int,int),minus_minus(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),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),B),D))),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),hAPP(int,int,hAPP(int,fun(int,int),minus_minus(int),A),C)),D)). [resolve(6822,a,6821,a)]. 288.71/288.55 6823 -ring(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) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,D) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) # label(fact_490_eq__add__iff1) # label(axiom). [clausify(4794)]. 288.71/288.55 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | ti(real,C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E). [resolve(6823,a,6811,a)]. 288.71/288.55 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E) | ti(rat,C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E). [resolve(6823,a,6814,a)]. 288.71/288.55 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)),E) | ti(complex,C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),A)),B)),E). [resolve(6823,a,6819,a)]. 293.07/292.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,C) = 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),D),A)),B)),E). [resolve(6823,a,6821,a)]. 293.07/292.90 6824 -ring(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) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)),F) | ti(A,D) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),hAPP(A,A,hAPP(A,fun(A,A),minus_minus(A),E),B)),C)),F) # label(fact_490_eq__add__iff1) # label(axiom). [clausify(4794)]. 293.07/292.90 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),C) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),D),B)),E) | ti(real,C) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),hAPP(real,real,hAPP(real,fun(real,real),minus_minus(real),D),A)),B)),E). [resolve(6824,a,6811,a)]. 293.07/292.90 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),C) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),D),B)),E) | ti(rat,C) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),minus_minus(rat),D),A)),B)),E). [resolve(6824,a,6814,a)]. 293.07/292.90 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),C) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),D),B)),E) | ti(complex,C) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),minus_minus(complex),D),A)),B)),E). [resolve(6824,a,6819,a)]. 293.07/292.90 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),C) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),D),B)),E) | ti(int,C) != 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),D),A)),B)),E). [resolve(6824,a,6821,a)]. 293.07/292.90 6825 semiri456707255roduct(complex) # label(arity_Complex_Ocomplex___Semiring__Normalization_Ocomm__semiring__1__cancel__cro) # label(axiom). [assumption]. 293.07/292.90 6826 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) != ti(A,E) # label(fact_241_crossproduct__noteq) # label(axiom). [clausify(608)]. 293.07/292.90 6827 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,D) != ti(A,B) # label(fact_241_crossproduct__noteq) # label(axiom). [clausify(608)]. 293.07/292.90 6828 -semiri456707255roduct(A) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)) | ti(A,C) = ti(A,E) | ti(A,D) = ti(A,B) # label(fact_241_crossproduct__noteq) # label(axiom). [clausify(608)]. 293.15/292.92 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) | ti(complex,B) != ti(complex,D). [resolve(6825,a,6826,a)]. 293.15/292.92 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) | ti(complex,C) != ti(complex,A). [resolve(6825,a,6827,a)]. 293.15/292.92 Derived: hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),D)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),C),B)) | ti(complex,B) = ti(complex,D) | ti(complex,C) = ti(complex,A). [resolve(6825,a,6828,a)]. 293.15/292.92 6829 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_244_crossproduct__eq) # label(axiom). [clausify(1068)]. 293.15/292.92 Derived: ti(complex,A) != ti(complex,B) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(6829,a,6825,a)]. 293.15/292.92 6830 -semiri456707255roduct(A) | ti(A,B) != ti(A,C) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),C)) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),E),B)) # label(fact_244_crossproduct__eq) # label(axiom). [clausify(1068)]. 293.15/292.92 6831 -semiri456707255roduct(A) | ti(A,B) = ti(A,C) | ti(A,D) = ti(A,E) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),E)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),D)) # label(fact_244_crossproduct__eq) # label(axiom). [clausify(1068)]. 293.15/292.92 Derived: ti(complex,A) = ti(complex,B) | ti(complex,C) = ti(complex,D) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),D)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),D)),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),B),C)). [resolve(6831,a,6825,a)]. 293.28/293.06 6832 semiri456707255roduct(int) # label(arity_Int_Oint___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 293.28/293.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,B) != ti(int,D). [resolve(6832,a,6826,a)]. 293.28/293.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,C) != ti(int,A). [resolve(6832,a,6827,a)]. 293.28/293.06 Derived: hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),C),B)) | ti(int,B) = ti(int,D) | ti(int,C) = ti(int,A). [resolve(6832,a,6828,a)]. 293.28/293.06 Derived: ti(int,A) != ti(int,B) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(6832,a,6829,a)]. 293.28/293.06 Derived: ti(int,A) = ti(int,B) | ti(int,C) = ti(int,D) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),D)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),D)),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),B),C)). [resolve(6832,a,6831,a)]. 293.28/293.06 6833 semiri456707255roduct(nat) # label(arity_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 293.28/293.06 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,B) != ti(nat,D). [resolve(6833,a,6826,a)]. 293.28/293.06 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,C) != ti(nat,A). [resolve(6833,a,6827,a)]. 293.28/293.06 Derived: hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),C),B)) | ti(nat,B) = ti(nat,D) | ti(nat,C) = ti(nat,A). [resolve(6833,a,6828,a)]. 293.28/293.06 Derived: ti(nat,A) != ti(nat,B) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6833,a,6829,a)]. 293.57/293.36 Derived: ti(nat,A) = ti(nat,B) | ti(nat,C) = ti(nat,D) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),D)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),D)),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),B),C)). [resolve(6833,a,6831,a)]. 293.57/293.36 6834 semiri456707255roduct(rat) # label(arity_Rat_Orat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduc) # label(axiom). [assumption]. 293.57/293.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) | ti(rat,B) != ti(rat,D). [resolve(6834,a,6826,a)]. 293.57/293.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) | ti(rat,C) != ti(rat,A). [resolve(6834,a,6827,a)]. 293.57/293.36 Derived: hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),D)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B)) | ti(rat,B) = ti(rat,D) | ti(rat,C) = ti(rat,A). [resolve(6834,a,6828,a)]. 293.57/293.36 Derived: ti(rat,A) != ti(rat,B) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(6834,a,6829,a)]. 293.57/293.36 Derived: ti(rat,A) = ti(rat,B) | ti(rat,C) = ti(rat,D) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),D)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),C)). [resolve(6834,a,6831,a)]. 293.57/293.36 6835 -semiri456707255roduct(A) | ti(A,B) != zero_zero(A) | ti(A,C) = hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_239_add__0__iff) # label(axiom). [clausify(2520)]. 293.57/293.36 Derived: ti(complex,A) != zero_zero(complex) | ti(complex,B) = hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(6835,a,6825,a)]. 293.57/293.36 Derived: ti(int,A) != zero_zero(int) | ti(int,B) = hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(6835,a,6832,a)]. 293.57/293.36 Derived: ti(nat,A) != zero_zero(nat) | ti(nat,B) = hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(6835,a,6833,a)]. 293.57/293.36 Derived: ti(rat,A) != zero_zero(rat) | ti(rat,B) = hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(6835,a,6834,a)]. 293.57/293.36 6836 -semiri456707255roduct(A) | ti(A,B) = zero_zero(A) | ti(A,C) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),C),B) # label(fact_239_add__0__iff) # label(axiom). [clausify(2520)]. 293.57/293.36 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),B),A). [resolve(6836,a,6825,a)]. 293.57/293.36 Derived: ti(int,A) = zero_zero(int) | ti(int,B) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),B),A). [resolve(6836,a,6832,a)]. 293.57/293.36 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),B),A). [resolve(6836,a,6833,a)]. 294.71/294.50 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),B),A). [resolve(6836,a,6834,a)]. 294.71/294.50 6837 -semiri456707255roduct(A) | ti(A,B) = zero_zero(A) | ti(A,C) = ti(A,D) | ti(A,E) != ti(A,F) | hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),E),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)) != hAPP(A,A,hAPP(A,fun(A,A),plus_plus(A),F),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),C)) # label(fact_252_add__scale__eq__noteq) # label(axiom). [clausify(4219)]. 294.71/294.50 Derived: ti(complex,A) = zero_zero(complex) | ti(complex,B) = ti(complex,C) | ti(complex,D) != ti(complex,E) | hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),D),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),C)) != hAPP(complex,complex,hAPP(complex,fun(complex,complex),plus_plus(complex),E),hAPP(complex,complex,hAPP(complex,fun(complex,complex),times_times(complex),A),B)). [resolve(6837,a,6825,a)]. 294.71/294.50 Derived: ti(int,A) = zero_zero(int) | ti(int,B) = ti(int,C) | ti(int,D) != ti(int,E) | hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),D),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),C)) != hAPP(int,int,hAPP(int,fun(int,int),plus_plus(int),E),hAPP(int,int,hAPP(int,fun(int,int),times_times(int),A),B)). [resolve(6837,a,6832,a)]. 294.71/294.50 Derived: ti(nat,A) = zero_zero(nat) | ti(nat,B) = ti(nat,C) | ti(nat,D) != ti(nat,E) | hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),D),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),C)) != hAPP(nat,nat,hAPP(nat,fun(nat,nat),plus_plus(nat),E),hAPP(nat,nat,hAPP(nat,fun(nat,nat),times_times(nat),A),B)). [resolve(6837,a,6833,a)]. 294.71/294.50 Derived: ti(rat,A) = zero_zero(rat) | ti(rat,B) = ti(rat,C) | ti(rat,D) != ti(rat,E) | hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),D),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)) != hAPP(rat,rat,hAPP(rat,fun(rat,rat),plus_plus(rat),E),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),B)). [resolve(6837,a,6834,a)]. 294.71/294.50 6838 semiri456707255roduct(real) # label(arity_RealDef_Oreal___Semiring__Normalization_Ocomm__semiring__1__cancel__crossp) # label(axiom). [assumption]. 294.71/294.50 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,B) != ti(real,D). [resolve(6838,a,6826,a)]. 294.71/294.50 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,C) != ti(real,A). [resolve(6838,a,6827,a)]. 294.71/294.50 Derived: hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B)) | ti(real,B) = ti(real,D) | ti(real,C) = ti(real,A). [resolve(6838,a,6828,a)]. 294.71/294.50 Derived: ti(real,A) != ti(real,B) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(6838,a,6829,a)]. 294.71/294.50 Derived: ti(real,A) = ti(real,B) | ti(real,C) = ti(real,D) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),D)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),C)). [resolve(6838,a,6831,a)]. 299.68/299.46 Derived: ti(real,A) != zero_zero(real) | ti(real,B) = hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(6838,a,6835,a)]. 299.68/299.46 Derived: ti(real,A) = zero_zero(real) | ti(real,B) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),B),A). [resolve(6838,a,6836,a)]. 299.68/299.46 Derived: ti(real,A) = zero_zero(real) | ti(real,B) = ti(real,C) | ti(real,D) != ti(real,E) | hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),D),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)) != hAPP(real,real,hAPP(real,fun(real,real),plus_plus(real),E),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),B)). [resolve(6838,a,6837,a)]. 299.68/299.46 6839 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),B)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),D),C))) # label(fact_372_mult__left__mono) # label(axiom). [clausify(1733)]. 299.68/299.46 6840 ordered_semiring(nat) # label(arity_Nat_Onat___Rings_Oordered__semiring) # label(axiom). [assumption]. 299.68/299.46 6841 ordered_semiring(rat) # label(arity_Rat_Orat___Rings_Oordered__semiring) # label(axiom). [assumption]. 299.68/299.46 Derived: -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),A),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),A)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),C),B))). [resolve(6841,a,6839,a)]. 299.68/299.46 6842 ordered_semiring(quickcheck_code_int) # label(arity_Quickcheck__Narrowing_Ocode__int___Rings_Oordered__semiring) # label(axiom). [assumption]. 299.68/299.46 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),A)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),C),B))). [resolve(6842,a,6839,a)]. 299.68/299.46 6843 ordered_semiring(real) # label(arity_RealDef_Oreal___Rings_Oordered__semiring) # label(axiom). [assumption]. 299.68/299.46 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),A)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),C),B))). [resolve(6843,a,6839,a)]. 299.68/299.46 6844 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_367_mult__mono) # label(axiom). [clausify(3124)]. 299.68/299.46 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),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_eq(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(6844,a,6840,a)]. 299.68/299.49 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),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),B)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6844,a,6841,a)]. 299.68/299.49 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),A),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),C),D)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),B)) | -hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),zero_zero(quickcheck_code_int)),C)) | hBOOL(hAPP(quickcheck_code_int,bool,hAPP(quickcheck_code_int,fun(quickcheck_code_int,bool),ord_less_eq(quickcheck_code_int),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),A),C)),hAPP(quickcheck_code_int,quickcheck_code_int,hAPP(quickcheck_code_int,fun(quickcheck_code_int,quickcheck_code_int),times_times(quickcheck_code_int),B),D))). [resolve(6844,a,6842,a)]. 299.68/299.49 Derived: -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),A),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),C),D)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),B)) | -hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),zero_zero(real)),C)) | hBOOL(hAPP(real,bool,hAPP(real,fun(real,bool),ord_less_eq(real),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),A),C)),hAPP(real,real,hAPP(real,fun(real,real),times_times(real),B),D))). [resolve(6844,a,6843,a)]. 299.68/299.49 6845 -ordered_semiring(A) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),B),C)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),D),E)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),B)) | -hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),zero_zero(A)),D)) | hBOOL(hAPP(A,bool,hAPP(A,fun(A,bool),ord_less_eq(A),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),B),D)),hAPP(A,A,hAPP(A,fun(A,A),times_times(A),C),E))) # label(fact_368_mult__mono_H) # label(axiom). [clausify(3167)]. 299.68/299.49 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),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_eq(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(6845,a,6840,a)]. 299.68/299.49 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),C),D)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),A)) | -hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),zero_zero(rat)),C)) | hBOOL(hAPP(rat,bool,hAPP(rat,fun(rat,bool),ord_less_eq(rat),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),A),C)),hAPP(rat,rat,hAPP(rat,fun(rat,rat),times_times(rat),B),D))). [resolve(6845,a,6841,a)]. 299.68/299.49 Derived: -hBOOL(hAPP(quickcheck_code_int,bool,hCputime limit exceeded (core dumped) 300.05/299.83 EOF