%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT253^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:45:18 AM UTC 2026
% Result : Theorem 2.82s 1.67s
% Output : Refutation 2.82s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT253^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n009.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 06:11:40 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.25/0.47 ---- Original DTF file ---
% 0.25/0.47 thf(spec,logic,$$dhol).
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 % File : DAT253^1 : TPTP v9.2.1. Released v7.0.0.
% 0.25/0.47 % Domain : Data Structures
% 0.25/0.47 % Problem : Infinite streams (sequences/lists) 551
% 0.25/0.47 % Version : [Bla16] axioms : Especial.
% 0.25/0.47 % English :
% 0.25/0.47
% 0.25/0.47 % Refs : [BH+14] Blanchette et al. (2014), Truly Modular (Co)datatypes
% 0.25/0.47 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.25/0.47 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.25/0.47 % Source : [Bla16]
% 0.25/0.47 % Names : stream__551.p [Bla16]
% 0.25/0.47
% 0.25/0.47 % Status : Theorem
% 0.25/0.47 % Rating : 0.00 v7.2.0, 0.25 v7.1.0
% 0.25/0.47 % Syntax : Number of formulae : 356 ( 110 unt; 65 typ; 0 def)
% 0.25/0.47 % Number of atoms : 567 ( 313 equ; 0 cnn)
% 0.25/0.47 % Maximal formula atoms : 4 ( 1 avg)
% 0.25/0.47 % Number of connectives : 3264 ( 22 ~; 5 |; 15 &;3028 @)
% 0.25/0.47 % ( 0 <=>; 194 =>; 0 <=; 0 <~>)
% 0.25/0.47 % Maximal formula depth : 14 ( 5 avg)
% 0.25/0.47 % Number of types : 4 ( 3 usr)
% 0.25/0.47 % Number of type conns : 119 ( 119 >; 0 *; 0 +; 0 <<)
% 0.25/0.47 % Number of symbols : 63 ( 62 usr; 5 con; 0-4 aty)
% 0.25/0.47 % Number of variables : 813 ( 38 ^; 714 !; 9 ?; 813 :)
% 0.25/0.47 % ( 52 !>; 0 ?*; 0 @-; 0 @+)
% 0.25/0.47 % SPC : TH1_THM_EQU_NAR
% 0.25/0.47
% 0.25/0.47 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.25/0.47 % 2016-07-13 14:43:07.811
% 0.25/0.47 %------------------------------------------------------------------------------
% 0.25/0.47 %----Could-be-implicit typings (6)
% 0.25/0.47 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream,type,
% 0.25/0.47 stream170649215stream: $tType > $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_t_Set_Oset,type,
% 0.25/0.47 set: $tType > $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_t_Num_Onum,type,
% 0.25/0.47 num: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_t_Nat_Onat,type,
% 0.25/0.47 nat: $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_t_itself,type,
% 0.25/0.47 itself: $tType > $tType ).
% 0.25/0.47
% 0.25/0.47 thf(ty_tf_a,type,
% 0.25/0.47 a: $tType ).
% 0.25/0.47
% 0.25/0.47 %----Explicit typings (59)
% 0.25/0.47 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.25/0.47 bounded_lattice:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_HOL_Otype,type,
% 0.25/0.47 type:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Oone,type,
% 0.25/0.47 one:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Oidom,type,
% 0.25/0.47 idom:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Oring,type,
% 0.25/0.47 ring:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Num_Onumeral,type,
% 0.25/0.47 numeral:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Oring__1,type,
% 0.25/0.47 ring_1:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Ouminus,type,
% 0.25/0.47 uminus:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Orderings_Otop,type,
% 0.25/0.47 top:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Osemiring,type,
% 0.25/0.47 semiring:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Nat_Oring__char__0,type,
% 0.25/0.47 ring_char_0:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Num_Oneg__numeral,type,
% 0.25/0.47 neg_numeral:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Ogroup__add,type,
% 0.25/0.47 group_add:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Lattices_Olattice,type,
% 0.25/0.47 lattice:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Ocomm__ring__1,type,
% 0.25/0.47 comm_ring_1:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.25/0.47 monoid_mult:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Oab__group__add,type,
% 0.25/0.47 ab_group_add:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.25/0.47 semiring_char_0:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Ocomm__semiring,type,
% 0.25/0.47 comm_semiring:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Osemigroup__add,type,
% 0.25/0.47 semigroup_add:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Num_Osemiring__numeral,type,
% 0.25/0.47 semiring_numeral:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.25/0.47 semigroup_mult:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.25/0.47 comm_semiring_1:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Fields_Olinordered__field,type,
% 0.25/0.47 linordered_field:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 0.25/0.47 ab_semigroup_add:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.25/0.47 comm_monoid_mult:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.25/0.47 ab_semigroup_mult:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.25/0.47 boolean_algebra:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 0.25/0.47 semilattice_sup:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 0.25/0.47 cancel_semigroup_add:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 0.25/0.47 bounded_lattice_top:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 0.25/0.47 ring_11004092258visors:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 0.25/0.47 ordere779506340up_add:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 0.25/0.47 semiri456707255roduct:
% 0.25/0.47 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.25/0.47 one_one:
% 0.25/0.47 !>[A: $tType] : A ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 0.25/0.47 plus_plus:
% 0.25/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.25/0.47 times_times:
% 0.25/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.25/0.47 uminus_uminus:
% 0.25/0.47 !>[A: $tType] : ( A > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.25/0.47 sup_sup:
% 0.25/0.47 !>[A: $tType] : ( A > A > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Nat_OSuc,type,
% 0.25/0.47 suc: nat > nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Num_Oinc,type,
% 0.25/0.47 inc: num > num ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 0.25/0.47 neg_numeral_dbl:
% 0.25/0.47 !>[A: $tType] : ( A > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Num_Onum_OBit0,type,
% 0.25/0.47 bit0: num > num ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Num_Onum_OOne,type,
% 0.25/0.47 one2: num ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.25/0.47 numeral_numeral:
% 0.25/0.47 !>[A: $tType] : ( num > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Orderings_Otop__class_Otop,type,
% 0.25/0.47 top_top:
% 0.25/0.47 !>[A: $tType] : A ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Pure_Otype,type,
% 0.25/0.47 type2:
% 0.25/0.47 !>[A: $tType] : ( itself @ A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Set_OCollect,type,
% 0.25/0.47 collect:
% 0.25/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Set_Oimage,type,
% 0.25/0.47 image:
% 0.25/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osinterleave,type,
% 0.25/0.47 stream865922174rleave:
% 0.25/0.47 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember,type,
% 0.25/0.47 stream1586597341member:
% 0.25/0.47 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmerge,type,
% 0.25/0.47 stream857257621smerge:
% 0.25/0.47 !>[A: $tType] : ( ( stream170649215stream @ ( stream170649215stream @ A ) ) > ( stream170649215stream @ A ) ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osnth,type,
% 0.25/0.47 stream370371455e_snth:
% 0.25/0.47 !>[A: $tType] : ( ( stream170649215stream @ A ) > nat > A ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osset,type,
% 0.25/0.47 stream30925839e_sset:
% 0.25/0.47 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( set @ A ) ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_c_member,type,
% 0.25/0.47 member:
% 0.25/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_n____,type,
% 0.25/0.47 n: nat ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_s1,type,
% 0.25/0.47 s1: stream170649215stream @ a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_s2,type,
% 0.25/0.47 s2: stream170649215stream @ a ).
% 0.25/0.47
% 0.25/0.47 thf(sy_v_x____,type,
% 0.25/0.47 x: a ).
% 0.25/0.47
% 0.25/0.47 %----Relevant facts (251)
% 0.25/0.47 thf(fact_0__092_060open_062x_A_061_As1_A_B_B_An_092_060close_062,axiom,
% 0.25/0.47 ( x
% 0.25/0.47 = ( stream370371455e_snth @ a @ s1 @ n ) ) ).
% 0.25/0.47
% 0.25/0.47 % \<open>x = s1 !! n\<close>
% 0.25/0.47 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Ax_A_061_As1_A_B_B_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.25/0.47 ~ ! [N: nat] :
% 0.25/0.47 ( x
% 0.25/0.47 != ( stream370371455e_snth @ a @ s1 @ N ) ) ).
% 0.25/0.47
% 0.25/0.47 % \<open>\<And>thesis. (\<And>n. x = s1 !! n \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.25/0.47 thf(fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062,axiom,
% 0.25/0.47 ( ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ n ) )
% 0.25/0.47 = x ) ).
% 0.25/0.47
% 0.25/0.47 % \<open>sinterleave s1 s2 !! (2 * n) = x\<close>
% 0.25/0.47 thf(fact_3__092_060open_062x_A_092_060in_062_Asset_As1_092_060close_062,axiom,
% 0.25/0.47 member @ a @ x @ ( stream30925839e_sset @ a @ s1 ) ).
% 0.25/0.47
% 0.25/0.47 % \<open>x \<in> sset s1\<close>
% 0.25/0.47 thf(fact_4__092_060open_062x_A_092_060in_062_Asset_As1_A_092_060union_062_Asset_As2_092_060close_062,axiom,
% 0.25/0.47 member @ a @ x @ ( sup_sup @ ( set @ a ) @ ( stream30925839e_sset @ a @ s1 ) @ ( stream30925839e_sset @ a @ s2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % \<open>x \<in> sset s1 \<union> sset s2\<close>
% 0.25/0.47 thf(fact_5_UNIV__I,axiom,
% 0.25/0.47 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % UNIV_I
% 0.25/0.47 thf(fact_6_iso__tuple__UNIV__I,axiom,
% 0.25/0.47 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % iso_tuple_UNIV_I
% 0.25/0.47 thf(fact_7_top__apply,axiom,
% 0.25/0.47 ! [C: $tType,D: $tType] :
% 0.25/0.47 ( ( top @ C @ ( type2 @ C ) )
% 0.25/0.47 => ( ( top_top @ ( D > C ) )
% 0.25/0.47 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % top_apply
% 0.25/0.47 thf(fact_8_image__eqI,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,B2: A,F: B > A,X: B,A2: set @ B] :
% 0.25/0.47 ( ( B2
% 0.25/0.47 = ( F @ X ) )
% 0.25/0.47 => ( ( member @ B @ X @ A2 )
% 0.25/0.47 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % image_eqI
% 0.25/0.47 thf(fact_9_surjD,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.25/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.25/0.47 = ( top_top @ ( set @ A ) ) )
% 0.25/0.47 => ? [X3: B] :
% 0.25/0.47 ( Y
% 0.25/0.47 = ( F @ X3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % surjD
% 0.25/0.47 thf(fact_10_surjE,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 0.25/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.25/0.47 = ( top_top @ ( set @ A ) ) )
% 0.25/0.47 => ~ ! [X3: B] :
% 0.25/0.47 ( Y
% 0.25/0.47 != ( F @ X3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % surjE
% 0.25/0.47 thf(fact_11_surjI,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType,G: B > A,F: A > B] :
% 0.25/0.47 ( ! [X3: A] :
% 0.25/0.47 ( ( G @ ( F @ X3 ) )
% 0.25/0.47 = X3 )
% 0.25/0.47 => ( ( image @ B @ A @ G @ ( top_top @ ( set @ B ) ) )
% 0.25/0.47 = ( top_top @ ( set @ A ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % surjI
% 0.25/0.47 thf(fact_12_rangeI,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,F: B > A,X: B] : ( member @ A @ ( F @ X ) @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % rangeI
% 0.25/0.47 thf(fact_13_surj__def,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType,F: B > A] :
% 0.25/0.47 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 0.25/0.47 = ( top_top @ ( set @ A ) ) )
% 0.25/0.47 = ( ! [Y2: A] :
% 0.25/0.47 ? [X2: B] :
% 0.25/0.47 ( Y2
% 0.25/0.47 = ( F @ X2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % surj_def
% 0.25/0.47 thf(fact_14_range__eqI,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,B2: A,F: B > A,X: B] :
% 0.25/0.47 ( ( B2
% 0.25/0.47 = ( F @ X ) )
% 0.25/0.47 => ( member @ A @ B2 @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % range_eqI
% 0.25/0.47 thf(fact_15_sset__range,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( stream30925839e_sset @ A )
% 0.25/0.47 = ( ^ [S: stream170649215stream @ A] : ( image @ nat @ A @ ( stream370371455e_snth @ A @ S ) @ ( top_top @ ( set @ nat ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sset_range
% 0.25/0.47 thf(fact_16_UnCI,axiom,
% 0.25/0.47 ! [A: $tType,C2: A,B3: set @ A,A2: set @ A] :
% 0.25/0.47 ( ( ~ ( member @ A @ C2 @ B3 )
% 0.25/0.47 => ( member @ A @ C2 @ A2 ) )
% 0.25/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % UnCI
% 0.25/0.47 thf(fact_17_Un__iff,axiom,
% 0.25/0.47 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.25/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 0.25/0.47 = ( ( member @ A @ C2 @ A2 )
% 0.25/0.47 | ( member @ A @ C2 @ B3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_iff
% 0.25/0.47 thf(fact_18_UnE,axiom,
% 0.25/0.47 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.25/0.47 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 0.25/0.47 => ( ~ ( member @ A @ C2 @ A2 )
% 0.25/0.47 => ( member @ A @ C2 @ B3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % UnE
% 0.25/0.47 thf(fact_19_UnI1,axiom,
% 0.25/0.47 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 0.25/0.47 ( ( member @ A @ C2 @ A2 )
% 0.25/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % UnI1
% 0.25/0.47 thf(fact_20_UnI2,axiom,
% 0.25/0.47 ! [A: $tType,C2: A,B3: set @ A,A2: set @ A] :
% 0.25/0.47 ( ( member @ A @ C2 @ B3 )
% 0.25/0.47 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % UnI2
% 0.25/0.47 thf(fact_21_bex__Un,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A,B3: set @ A,P: A > $o] :
% 0.25/0.47 ( ( ? [X2: A] :
% 0.25/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 0.25/0.47 & ( P @ X2 ) ) )
% 0.25/0.47 = ( ? [X2: A] :
% 0.25/0.47 ( ( member @ A @ X2 @ A2 )
% 0.25/0.47 & ( P @ X2 ) )
% 0.25/0.47 | ? [X2: A] :
% 0.25/0.47 ( ( member @ A @ X2 @ B3 )
% 0.25/0.47 & ( P @ X2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % bex_Un
% 0.25/0.47 thf(fact_22_ball__Un,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A,B3: set @ A,P: A > $o] :
% 0.25/0.47 ( ( ! [X2: A] :
% 0.25/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 0.25/0.47 => ( P @ X2 ) ) )
% 0.25/0.47 = ( ! [X2: A] :
% 0.25/0.47 ( ( member @ A @ X2 @ A2 )
% 0.25/0.47 => ( P @ X2 ) )
% 0.25/0.47 & ! [X2: A] :
% 0.25/0.47 ( ( member @ A @ X2 @ B3 )
% 0.25/0.47 => ( P @ X2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ball_Un
% 0.25/0.47 thf(fact_23_Un__assoc,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A,B3: set @ A,C3: set @ A] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) @ C3 )
% 0.25/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B3 @ C3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_assoc
% 0.25/0.47 thf(fact_24_Un__absorb,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.25/0.47 = A2 ) ).
% 0.25/0.47
% 0.25/0.47 % Un_absorb
% 0.25/0.47 thf(fact_25_Un__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.25/0.47 = ( ^ [A3: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_commute
% 0.25/0.47 thf(fact_26_Un__left__absorb,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 0.25/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_left_absorb
% 0.25/0.47 thf(fact_27_Un__left__commute,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A,B3: set @ A,C3: set @ A] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B3 @ C3 ) )
% 0.25/0.47 = ( sup_sup @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_left_commute
% 0.25/0.47 thf(fact_28_image__Un,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,B3: set @ B] :
% 0.25/0.47 ( ( image @ B @ A @ F @ ( sup_sup @ ( set @ B ) @ A2 @ B3 ) )
% 0.25/0.47 = ( sup_sup @ ( set @ A ) @ ( image @ B @ A @ F @ A2 ) @ ( image @ B @ A @ F @ B3 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % image_Un
% 0.25/0.47 thf(fact_29_top__set__def,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( top_top @ ( set @ A ) )
% 0.25/0.47 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % top_set_def
% 0.25/0.47 thf(fact_30_Un__UNIV__right,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 0.25/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_UNIV_right
% 0.25/0.47 thf(fact_31_Un__UNIV__left,axiom,
% 0.25/0.47 ! [A: $tType,B3: set @ A] :
% 0.25/0.47 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B3 )
% 0.25/0.47 = ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Un_UNIV_left
% 0.25/0.47 thf(fact_32_snth__sset,axiom,
% 0.25/0.47 ! [A: $tType,S2: stream170649215stream @ A,N2: nat] : ( member @ A @ ( stream370371455e_snth @ A @ S2 @ N2 ) @ ( stream30925839e_sset @ A @ S2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % snth_sset
% 0.25/0.47 thf(fact_33_rev__image__eqI,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType,X: A,A2: set @ A,B2: B,F: A > B] :
% 0.25/0.47 ( ( member @ A @ X @ A2 )
% 0.25/0.47 => ( ( B2
% 0.25/0.47 = ( F @ X ) )
% 0.25/0.47 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % rev_image_eqI
% 0.25/0.47 thf(fact_34_ball__imageD,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P: A > $o] :
% 0.25/0.47 ( ! [X3: A] :
% 0.25/0.47 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A2 ) )
% 0.25/0.47 => ( P @ X3 ) )
% 0.25/0.47 => ! [X4: B] :
% 0.25/0.47 ( ( member @ B @ X4 @ A2 )
% 0.25/0.47 => ( P @ ( F @ X4 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ball_imageD
% 0.25/0.47 thf(fact_35_image__cong,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType,M: set @ A,N3: set @ A,F: A > B,G: A > B] :
% 0.25/0.47 ( ( M = N3 )
% 0.25/0.47 => ( ! [X3: A] :
% 0.25/0.47 ( ( member @ A @ X3 @ N3 )
% 0.25/0.47 => ( ( F @ X3 )
% 0.25/0.47 = ( G @ X3 ) ) )
% 0.25/0.47 => ( ( image @ A @ B @ F @ M )
% 0.25/0.47 = ( image @ A @ B @ G @ N3 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % image_cong
% 0.25/0.47 thf(fact_36_bex__imageD,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P: A > $o] :
% 0.25/0.47 ( ? [X4: A] :
% 0.25/0.47 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A2 ) )
% 0.25/0.47 & ( P @ X4 ) )
% 0.25/0.47 => ? [X3: B] :
% 0.25/0.47 ( ( member @ B @ X3 @ A2 )
% 0.25/0.47 & ( P @ ( F @ X3 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % bex_imageD
% 0.25/0.47 thf(fact_37_image__iff,axiom,
% 0.25/0.47 ! [A: $tType,B: $tType,Z: A,F: B > A,A2: set @ B] :
% 0.25/0.47 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A2 ) )
% 0.25/0.47 = ( ? [X2: B] :
% 0.25/0.47 ( ( member @ B @ X2 @ A2 )
% 0.25/0.47 & ( Z
% 0.25/0.47 = ( F @ X2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % image_iff
% 0.25/0.47 thf(fact_38_imageI,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType,X: A,A2: set @ A,F: A > B] :
% 0.25/0.47 ( ( member @ A @ X @ A2 )
% 0.25/0.47 => ( member @ B @ ( F @ X ) @ ( image @ A @ B @ F @ A2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % imageI
% 0.25/0.47 thf(fact_39_UNIV__witness,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % UNIV_witness
% 0.25/0.47 thf(fact_40_UNIV__eq__I,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A] :
% 0.25/0.47 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 0.25/0.47 => ( ( top_top @ ( set @ A ) )
% 0.25/0.47 = A2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % UNIV_eq_I
% 0.25/0.47 thf(fact_41_sup__top__right,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 0.25/0.47 = ( top_top @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_top_right
% 0.25/0.47 thf(fact_42_sup__top__left,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 0.25/0.47 = ( top_top @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_top_left
% 0.25/0.47 thf(fact_43_semiring__norm_I169_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [V: num,W: num,Z: A] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( times_times @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.25/0.47 = ( times_times @ A @ ( numeral_numeral @ A @ ( times_times @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(169)
% 0.25/0.47 thf(fact_44_numeral__times__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ M2 ) @ ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_times_numeral
% 0.25/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.25/0.47 ! [A: $tType,A4: A,P: A > $o] :
% 0.25/0.47 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 0.25/0.47 = ( P @ A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % mem_Collect_eq
% 0.25/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.25/0.47 ! [A: $tType,A2: set @ A] :
% 0.25/0.47 ( ( collect @ A
% 0.25/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.25/0.47 = A2 ) ).
% 0.25/0.47
% 0.25/0.47 % Collect_mem_eq
% 0.25/0.47 thf(fact_47_Collect__cong,axiom,
% 0.25/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.25/0.47 ( ! [X3: A] :
% 0.25/0.47 ( ( P @ X3 )
% 0.25/0.47 = ( Q @ X3 ) )
% 0.25/0.47 => ( ( collect @ A @ P )
% 0.25/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Collect_cong
% 0.25/0.47 thf(fact_48_ext,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.25/0.47 ( ! [X3: A] :
% 0.25/0.47 ( ( F @ X3 )
% 0.25/0.47 = ( G @ X3 ) )
% 0.25/0.47 => ( F = G ) ) ).
% 0.25/0.47
% 0.25/0.47 % ext
% 0.25/0.47 thf(fact_49_semiring__norm_I85_J,axiom,
% 0.25/0.47 ! [M2: num] :
% 0.25/0.47 ( ( bit0 @ M2 )
% 0.25/0.47 != one2 ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(85)
% 0.25/0.47 thf(fact_50_semiring__norm_I83_J,axiom,
% 0.25/0.47 ! [N2: num] :
% 0.25/0.47 ( one2
% 0.25/0.47 != ( bit0 @ N2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(83)
% 0.25/0.47 thf(fact_51_mult__numeral__1,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ one2 ) @ A4 )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_numeral_1
% 0.25/0.47 thf(fact_52_mult__numeral__1__right,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( numeral_numeral @ A @ one2 ) )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_numeral_1_right
% 0.25/0.47 thf(fact_53_sup__apply,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.25/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.25/0.47 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_apply
% 0.25/0.47 thf(fact_54_sup_Oidem,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( sup_sup @ A @ A4 @ A4 )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup.idem
% 0.25/0.47 thf(fact_55_semiring__norm_I87_J,axiom,
% 0.25/0.47 ! [M2: num,N2: num] :
% 0.25/0.47 ( ( ( bit0 @ M2 )
% 0.25/0.47 = ( bit0 @ N2 ) )
% 0.25/0.47 = ( M2 = N2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(87)
% 0.25/0.47 thf(fact_56_num_Oinject_I1_J,axiom,
% 0.25/0.47 ! [X22: num,Y22: num] :
% 0.25/0.47 ( ( ( bit0 @ X22 )
% 0.25/0.47 = ( bit0 @ Y22 ) )
% 0.25/0.47 = ( X22 = Y22 ) ) ).
% 0.25/0.47
% 0.25/0.47 % num.inject(1)
% 0.25/0.47 thf(fact_57_numeral__eq__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( ( numeral_numeral @ A @ M2 )
% 0.25/0.47 = ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( M2 = N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_eq_iff
% 0.25/0.47 thf(fact_58_sup_Oright__idem,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B2 ) @ B2 )
% 0.25/0.47 = ( sup_sup @ A @ A4 @ B2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup.right_idem
% 0.25/0.47 thf(fact_59_sup__left__idem,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.25/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_left_idem
% 0.25/0.47 thf(fact_60_sup_Oleft__idem,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B2 ) )
% 0.25/0.47 = ( sup_sup @ A @ A4 @ B2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup.left_idem
% 0.25/0.47 thf(fact_61_sup__idem,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ X )
% 0.25/0.47 = X ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_idem
% 0.25/0.47 thf(fact_62_top1I,axiom,
% 0.25/0.47 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 0.25/0.47
% 0.25/0.47 % top1I
% 0.25/0.47 thf(fact_63_semiring__norm_I13_J,axiom,
% 0.25/0.47 ! [M2: num,N2: num] :
% 0.25/0.47 ( ( times_times @ num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.25/0.47 = ( bit0 @ ( bit0 @ ( times_times @ num @ M2 @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(13)
% 0.25/0.47 thf(fact_64_semiring__norm_I11_J,axiom,
% 0.25/0.47 ! [M2: num] :
% 0.25/0.47 ( ( times_times @ num @ M2 @ one2 )
% 0.25/0.47 = M2 ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(11)
% 0.25/0.47 thf(fact_65_semiring__norm_I12_J,axiom,
% 0.25/0.47 ! [N2: num] :
% 0.25/0.47 ( ( times_times @ num @ one2 @ N2 )
% 0.25/0.47 = N2 ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(12)
% 0.25/0.47 thf(fact_66_sup__left__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A,Z: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.25/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_left_commute
% 0.25/0.47 thf(fact_67_sup_Oleft__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup.left_commute
% 0.25/0.47 thf(fact_68_sup__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( sup_sup @ A )
% 0.25/0.47 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_commute
% 0.25/0.47 thf(fact_69_sup_Ocommute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( sup_sup @ A )
% 0.25/0.47 = ( ^ [A5: A,B5: A] : ( sup_sup @ A @ B5 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup.commute
% 0.25/0.47 thf(fact_70_sup__assoc,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A,Z: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.25/0.47 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_assoc
% 0.25/0.47 thf(fact_71_sup_Oassoc,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup.assoc
% 0.25/0.47 thf(fact_72_sup__fun__def,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType] :
% 0.25/0.47 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 0.25/0.47 => ( ( sup_sup @ ( A > B ) )
% 0.25/0.47 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_fun_def
% 0.25/0.47 thf(fact_73_inf__sup__aci_I5_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( sup_sup @ A )
% 0.25/0.47 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % inf_sup_aci(5)
% 0.25/0.47 thf(fact_74_inf__sup__aci_I6_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A,Z: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 0.25/0.47 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % inf_sup_aci(6)
% 0.25/0.47 thf(fact_75_inf__sup__aci_I7_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A,Z: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 0.25/0.47 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % inf_sup_aci(7)
% 0.25/0.47 thf(fact_76_inf__sup__aci_I8_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( lattice @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 0.25/0.47 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % inf_sup_aci(8)
% 0.25/0.47 thf(fact_77_num_Odistinct_I1_J,axiom,
% 0.25/0.47 ! [X22: num] :
% 0.25/0.47 ( one2
% 0.25/0.47 != ( bit0 @ X22 ) ) ).
% 0.25/0.47
% 0.25/0.47 % num.distinct(1)
% 0.25/0.47 thf(fact_78_top__empty__eq,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( top_top @ ( A > $o ) )
% 0.25/0.47 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % top_empty_eq
% 0.25/0.47 thf(fact_79_snth__sset__smerge,axiom,
% 0.25/0.47 ! [A: $tType,Ss: stream170649215stream @ ( stream170649215stream @ A ),N2: nat,M2: nat] : ( member @ A @ ( stream370371455e_snth @ A @ ( stream370371455e_snth @ ( stream170649215stream @ A ) @ Ss @ N2 ) @ M2 ) @ ( stream30925839e_sset @ A @ ( stream857257621smerge @ A @ Ss ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % snth_sset_smerge
% 0.25/0.47 thf(fact_80_dbl__simps_I5_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [K: num] :
% 0.25/0.47 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( bit0 @ K ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % dbl_simps(5)
% 0.25/0.47 thf(fact_81_top__conj_I2_J,axiom,
% 0.25/0.47 ! [A: $tType,P: $o,X: A] :
% 0.25/0.47 ( ( P
% 0.25/0.47 & ( top_top @ ( A > $o ) @ X ) )
% 0.25/0.47 = P ) ).
% 0.25/0.47
% 0.25/0.47 % top_conj(2)
% 0.25/0.47 thf(fact_82_top__conj_I1_J,axiom,
% 0.25/0.47 ! [A: $tType,X: A,P: $o] :
% 0.25/0.47 ( ( ( top_top @ ( A > $o ) @ X )
% 0.25/0.47 & P )
% 0.25/0.47 = P ) ).
% 0.25/0.47
% 0.25/0.47 % top_conj(1)
% 0.25/0.47 thf(fact_83_Stream__Mirabelle__hbrgyiwlrc_Osmember__def,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( stream1586597341member @ A )
% 0.25/0.47 = ( ^ [X2: A,S: stream170649215stream @ A] : ( member @ A @ X2 @ ( stream30925839e_sset @ A @ S ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Stream_Mirabelle_hbrgyiwlrc.smember_def
% 0.25/0.47 thf(fact_84_mult__2__right,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Z: A] :
% 0.25/0.47 ( ( times_times @ A @ Z @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) )
% 0.25/0.47 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_2_right
% 0.25/0.47 thf(fact_85_mult__2,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Z: A] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) @ Z )
% 0.25/0.47 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_2
% 0.25/0.47 thf(fact_86_semiring__norm_I6_J,axiom,
% 0.25/0.47 ! [M2: num,N2: num] :
% 0.25/0.47 ( ( plus_plus @ num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 0.25/0.47 = ( bit0 @ ( plus_plus @ num @ M2 @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(6)
% 0.25/0.47 thf(fact_87_semiring__norm_I2_J,axiom,
% 0.25/0.47 ( ( plus_plus @ num @ one2 @ one2 )
% 0.25/0.47 = ( bit0 @ one2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(2)
% 0.25/0.47 thf(fact_88_add__numeral__left,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [V: num,W: num,Z: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.25/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_numeral_left
% 0.25/0.47 thf(fact_89_numeral__plus__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M2 ) @ ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ M2 @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_plus_numeral
% 0.25/0.47 thf(fact_90_dbl__def,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( neg_numeral_dbl @ A )
% 0.25/0.47 = ( ^ [X2: A] : ( plus_plus @ A @ X2 @ X2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % dbl_def
% 0.25/0.47 thf(fact_91_is__num__normalize_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % is_num_normalize(1)
% 0.25/0.47 thf(fact_92_add__One__commute,axiom,
% 0.25/0.47 ! [N2: num] :
% 0.25/0.47 ( ( plus_plus @ num @ one2 @ N2 )
% 0.25/0.47 = ( plus_plus @ num @ N2 @ one2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_One_commute
% 0.25/0.47 thf(fact_93_left__add__mult__distrib,axiom,
% 0.25/0.47 ! [I: nat,U: nat,J: nat,K: nat] :
% 0.25/0.47 ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ K ) )
% 0.25/0.47 = ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ I @ J ) @ U ) @ K ) ) ).
% 0.25/0.47
% 0.25/0.47 % left_add_mult_distrib
% 0.25/0.47 thf(fact_94_numeral__Bit0,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( numeral_numeral @ A @ ( bit0 @ N2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ N2 ) @ ( numeral_numeral @ A @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_Bit0
% 0.25/0.47 thf(fact_95_distrib__left__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 & ( semiring @ A @ ( type2 @ A ) ) )
% 0.25/0.47 => ! [V: num,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ B2 ) @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % distrib_left_numeral
% 0.25/0.47 thf(fact_96_distrib__right__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 & ( semiring @ A @ ( type2 @ A ) ) )
% 0.25/0.47 => ! [A4: A,B2: A,V: num] :
% 0.25/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ ( numeral_numeral @ A @ V ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ ( numeral_numeral @ A @ V ) ) @ ( times_times @ A @ B2 @ ( numeral_numeral @ A @ V ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % distrib_right_numeral
% 0.25/0.47 thf(fact_97_add__left__cancel,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ A4 @ B2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( B2 = C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_left_cancel
% 0.25/0.47 thf(fact_98_add__right__cancel,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ B2 @ A4 )
% 0.25/0.47 = ( plus_plus @ A @ C2 @ A4 ) )
% 0.25/0.47 = ( B2 = C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_right_cancel
% 0.25/0.47 thf(fact_99_crossproduct__noteq,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A,D2: A] :
% 0.25/0.47 ( ( ( A4 != B2 )
% 0.25/0.47 & ( C2 != D2 ) )
% 0.25/0.47 = ( ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ D2 ) )
% 0.25/0.47 != ( plus_plus @ A @ ( times_times @ A @ A4 @ D2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % crossproduct_noteq
% 0.25/0.47 thf(fact_100_crossproduct__eq,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [W: A,Y: A,X: A,Z: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ ( times_times @ A @ W @ Y ) @ ( times_times @ A @ X @ Z ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ W @ Z ) @ ( times_times @ A @ X @ Y ) ) )
% 0.25/0.47 = ( ( W = X )
% 0.25/0.47 | ( Y = Z ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % crossproduct_eq
% 0.25/0.47 thf(fact_101_add__right__imp__eq,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ B2 @ A4 )
% 0.25/0.47 = ( plus_plus @ A @ C2 @ A4 ) )
% 0.25/0.47 => ( B2 = C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_right_imp_eq
% 0.25/0.47 thf(fact_102_add__left__imp__eq,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ A4 @ B2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ C2 ) )
% 0.25/0.47 => ( B2 = C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_left_imp_eq
% 0.25/0.47 thf(fact_103_add_Oleft__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.left_commute
% 0.25/0.47 thf(fact_104_add_Ocommute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( plus_plus @ A )
% 0.25/0.47 = ( ^ [A5: A,B5: A] : ( plus_plus @ A @ B5 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.commute
% 0.25/0.47 thf(fact_105_add_Oright__cancel,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ B2 @ A4 )
% 0.25/0.47 = ( plus_plus @ A @ C2 @ A4 ) )
% 0.25/0.47 = ( B2 = C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.right_cancel
% 0.25/0.47 thf(fact_106_add_Oleft__cancel,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( ( plus_plus @ A @ A4 @ B2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( B2 = C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.left_cancel
% 0.25/0.47 thf(fact_107_add_Oassoc,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.assoc
% 0.25/0.47 thf(fact_108_semiring__normalization__rules_I20_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A,D2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ ( plus_plus @ A @ C2 @ D2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A4 @ C2 ) @ ( plus_plus @ A @ B2 @ D2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(20)
% 0.25/0.47 thf(fact_109_semiring__normalization__rules_I21_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(21)
% 0.25/0.47 thf(fact_110_semiring__normalization__rules_I22_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,C2: A,D2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ A4 @ ( plus_plus @ A @ C2 @ D2 ) )
% 0.25/0.47 = ( plus_plus @ A @ C2 @ ( plus_plus @ A @ A4 @ D2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(22)
% 0.25/0.47 thf(fact_111_semiring__normalization__rules_I23_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A4 @ C2 ) @ B2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(23)
% 0.25/0.47 thf(fact_112_semiring__normalization__rules_I24_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( plus_plus @ A )
% 0.25/0.47 = ( ^ [A5: A,C4: A] : ( plus_plus @ A @ C4 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(24)
% 0.25/0.47 thf(fact_113_semiring__normalization__rules_I25_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,C2: A,D2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ A4 @ ( plus_plus @ A @ C2 @ D2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( plus_plus @ A @ A4 @ C2 ) @ D2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(25)
% 0.25/0.47 thf(fact_114_add__mono__thms__linordered__semiring_I4_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [I: A,J: A,K: A,L: A] :
% 0.25/0.47 ( ( ( I = J )
% 0.25/0.47 & ( K = L ) )
% 0.25/0.47 => ( ( plus_plus @ A @ I @ K )
% 0.25/0.47 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_mono_thms_linordered_semiring(4)
% 0.25/0.47 thf(fact_115_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ab_semigroup_add_class.add_ac(1)
% 0.25/0.47 thf(fact_116_mult_Oleft__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ B2 @ ( times_times @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult.left_commute
% 0.25/0.47 thf(fact_117_mult_Ocommute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( times_times @ A )
% 0.25/0.47 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult.commute
% 0.25/0.47 thf(fact_118_mult_Oassoc,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semigroup_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult.assoc
% 0.25/0.47 thf(fact_119_semiring__normalization__rules_I7_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( times_times @ A )
% 0.25/0.47 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(7)
% 0.25/0.47 thf(fact_120_semiring__normalization__rules_I13_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.25/0.47 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ ( times_times @ A @ Ly @ Ry ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(13)
% 0.25/0.47 thf(fact_121_semiring__normalization__rules_I14_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.25/0.47 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ ( times_times @ A @ Rx @ Ry ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(14)
% 0.25/0.47 thf(fact_122_semiring__normalization__rules_I15_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.25/0.47 = ( times_times @ A @ Rx @ ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Ry ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(15)
% 0.25/0.47 thf(fact_123_semiring__normalization__rules_I16_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Ly: A,Rx: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 0.25/0.47 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ly ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(16)
% 0.25/0.47 thf(fact_124_semiring__normalization__rules_I17_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Ly: A,Rx: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 0.25/0.47 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ Rx ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(17)
% 0.25/0.47 thf(fact_125_semiring__normalization__rules_I18_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Rx: A,Ry: A] :
% 0.25/0.47 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 0.25/0.47 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ry ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(18)
% 0.25/0.47 thf(fact_126_semiring__normalization__rules_I19_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Lx: A,Rx: A,Ry: A] :
% 0.25/0.47 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 0.25/0.47 = ( times_times @ A @ Rx @ ( times_times @ A @ Lx @ Ry ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(19)
% 0.25/0.47 thf(fact_127_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.25/0.47 thf(fact_128_semiring__normalization__rules_I34_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A,Z: A] :
% 0.25/0.47 ( ( times_times @ A @ X @ ( plus_plus @ A @ Y @ Z ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ X @ Y ) @ ( times_times @ A @ X @ Z ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(34)
% 0.25/0.47 thf(fact_129_semiring__normalization__rules_I8_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(8)
% 0.25/0.47 thf(fact_130_semiring__normalization__rules_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,M2: A,B2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( times_times @ A @ A4 @ M2 ) @ ( times_times @ A @ B2 @ M2 ) )
% 0.25/0.47 = ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ M2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(1)
% 0.25/0.47 thf(fact_131_add__mult__distrib,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat,K: nat] :
% 0.25/0.47 ( ( times_times @ nat @ ( plus_plus @ nat @ M2 @ N2 ) @ K )
% 0.25/0.47 = ( plus_plus @ nat @ ( times_times @ nat @ M2 @ K ) @ ( times_times @ nat @ N2 @ K ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_mult_distrib
% 0.25/0.47 thf(fact_132_add__mult__distrib2,axiom,
% 0.25/0.47 ! [K: nat,M2: nat,N2: nat] :
% 0.25/0.47 ( ( times_times @ nat @ K @ ( plus_plus @ nat @ M2 @ N2 ) )
% 0.25/0.47 = ( plus_plus @ nat @ ( times_times @ nat @ K @ M2 ) @ ( times_times @ nat @ K @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_mult_distrib2
% 0.25/0.47 thf(fact_133_ring__class_Oring__distribs_I2_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ring_class.ring_distribs(2)
% 0.25/0.47 thf(fact_134_ring__class_Oring__distribs_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ B2 ) @ ( times_times @ A @ A4 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % ring_class.ring_distribs(1)
% 0.25/0.47 thf(fact_135_linordered__field__class_Osign__simps_I36_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ B2 ) @ ( times_times @ A @ A4 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(36)
% 0.25/0.47 thf(fact_136_linordered__field__class_Osign__simps_I28_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(28)
% 0.25/0.47 thf(fact_137_linordered__field__class_Osign__simps_I27_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( plus_plus @ A )
% 0.25/0.47 = ( ^ [A5: A,B5: A] : ( plus_plus @ A @ B5 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(27)
% 0.25/0.47 thf(fact_138_linordered__field__class_Osign__simps_I26_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(26)
% 0.25/0.47 thf(fact_139_linordered__field__class_Osign__simps_I25_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [B2: A,A4: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ B2 @ ( times_times @ A @ A4 @ C2 ) )
% 0.25/0.47 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(25)
% 0.25/0.47 thf(fact_140_linordered__field__class_Osign__simps_I24_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( times_times @ A )
% 0.25/0.47 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(24)
% 0.25/0.47 thf(fact_141_linordered__field__class_Osign__simps_I23_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( times_times @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(23)
% 0.25/0.47 thf(fact_142_nat__add__right__cancel,axiom,
% 0.25/0.47 ! [M2: nat,K: nat,N2: nat] :
% 0.25/0.47 ( ( ( plus_plus @ nat @ M2 @ K )
% 0.25/0.47 = ( plus_plus @ nat @ N2 @ K ) )
% 0.25/0.47 = ( M2 = N2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % nat_add_right_cancel
% 0.25/0.47 thf(fact_143_nat__add__left__cancel,axiom,
% 0.25/0.47 ! [K: nat,M2: nat,N2: nat] :
% 0.25/0.47 ( ( ( plus_plus @ nat @ K @ M2 )
% 0.25/0.47 = ( plus_plus @ nat @ K @ N2 ) )
% 0.25/0.47 = ( M2 = N2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % nat_add_left_cancel
% 0.25/0.47 thf(fact_144_combine__common__factor,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,E: A,B2: A,C2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( times_times @ A @ A4 @ E ) @ ( plus_plus @ A @ ( times_times @ A @ B2 @ E ) @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ E ) @ C2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % combine_common_factor
% 0.25/0.47 thf(fact_145_distrib__right,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % distrib_right
% 0.25/0.47 thf(fact_146_distrib__left,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ B2 ) @ ( times_times @ A @ A4 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % distrib_left
% 0.25/0.47 thf(fact_147_comm__semiring__class_Odistrib,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % comm_semiring_class.distrib
% 0.25/0.47 thf(fact_148_linordered__field__class_Osign__simps_I35_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( linordered_field @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A,C2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 0.25/0.47 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % linordered_field_class.sign_simps(35)
% 0.25/0.47 thf(fact_149_dbl__simps_I3_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % dbl_simps(3)
% 0.25/0.47 thf(fact_150_numeral__plus__one,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N2 ) @ ( one_one @ A ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ N2 @ one2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_plus_one
% 0.25/0.47 thf(fact_151_one__plus__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % one_plus_numeral
% 0.25/0.47 thf(fact_152_one__add__one,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % one_add_one
% 0.25/0.47 thf(fact_153_nat__1__eq__mult__iff,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat] :
% 0.25/0.47 ( ( ( one_one @ nat )
% 0.25/0.47 = ( times_times @ nat @ M2 @ N2 ) )
% 0.25/0.47 = ( ( M2
% 0.25/0.47 = ( one_one @ nat ) )
% 0.25/0.47 & ( N2
% 0.25/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % nat_1_eq_mult_iff
% 0.25/0.47 thf(fact_154_nat__mult__eq__1__iff,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat] :
% 0.25/0.47 ( ( ( times_times @ nat @ M2 @ N2 )
% 0.25/0.47 = ( one_one @ nat ) )
% 0.25/0.47 = ( ( M2
% 0.25/0.47 = ( one_one @ nat ) )
% 0.25/0.47 & ( N2
% 0.25/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % nat_mult_eq_1_iff
% 0.25/0.47 thf(fact_155_mult_Oright__neutral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( one_one @ A ) )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult.right_neutral
% 0.25/0.47 thf(fact_156_mult_Oleft__neutral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A4 )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult.left_neutral
% 0.25/0.47 thf(fact_157_one__eq__numeral__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( ( one_one @ A )
% 0.25/0.47 = ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( one2 = N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % one_eq_numeral_iff
% 0.25/0.47 thf(fact_158_numeral__eq__one__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( ( numeral_numeral @ A @ N2 )
% 0.25/0.47 = ( one_one @ A ) )
% 0.25/0.47 = ( N2 = one2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_eq_one_iff
% 0.25/0.47 thf(fact_159_nat__mult__1__right,axiom,
% 0.25/0.47 ! [N2: nat] :
% 0.25/0.47 ( ( times_times @ nat @ N2 @ ( one_one @ nat ) )
% 0.25/0.47 = N2 ) ).
% 0.25/0.47
% 0.25/0.47 % nat_mult_1_right
% 0.25/0.47 thf(fact_160_nat__mult__1,axiom,
% 0.25/0.47 ! [N2: nat] :
% 0.25/0.47 ( ( times_times @ nat @ ( one_one @ nat ) @ N2 )
% 0.25/0.47 = N2 ) ).
% 0.25/0.47
% 0.25/0.47 % nat_mult_1
% 0.25/0.47 thf(fact_161_mult_Ocomm__neutral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( one_one @ A ) )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult.comm_neutral
% 0.25/0.47 thf(fact_162_comm__monoid__mult__class_Omult__1,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A4 )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % comm_monoid_mult_class.mult_1
% 0.25/0.47 thf(fact_163_semiring__normalization__rules_I11_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A4 )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(11)
% 0.25/0.47 thf(fact_164_semiring__normalization__rules_I12_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( one_one @ A ) )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(12)
% 0.25/0.47 thf(fact_165_one__reorient,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( one @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( ( one_one @ A )
% 0.25/0.47 = X )
% 0.25/0.47 = ( X
% 0.25/0.47 = ( one_one @ A ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % one_reorient
% 0.25/0.47 thf(fact_166_one__plus__numeral__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: num] :
% 0.25/0.47 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X ) )
% 0.25/0.47 = ( plus_plus @ A @ ( numeral_numeral @ A @ X ) @ ( one_one @ A ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % one_plus_numeral_commute
% 0.25/0.47 thf(fact_167_semiring__normalization__rules_I2_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,M2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( times_times @ A @ A4 @ M2 ) @ M2 )
% 0.25/0.47 = ( times_times @ A @ ( plus_plus @ A @ A4 @ ( one_one @ A ) ) @ M2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(2)
% 0.25/0.47 thf(fact_168_semiring__normalization__rules_I3_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: A,A4: A] :
% 0.25/0.47 ( ( plus_plus @ A @ M2 @ ( times_times @ A @ A4 @ M2 ) )
% 0.25/0.47 = ( times_times @ A @ ( plus_plus @ A @ A4 @ ( one_one @ A ) ) @ M2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(3)
% 0.25/0.47 thf(fact_169_semiring__normalization__rules_I4_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ M2 @ M2 )
% 0.25/0.47 = ( times_times @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) @ M2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_normalization_rules(4)
% 0.25/0.47 thf(fact_170_numeral__One,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( numeral_numeral @ A @ one2 )
% 0.25/0.47 = ( one_one @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_One
% 0.25/0.47 thf(fact_171_numerals_I1_J,axiom,
% 0.25/0.47 ( ( numeral_numeral @ nat @ one2 )
% 0.25/0.47 = ( one_one @ nat ) ) ).
% 0.25/0.47
% 0.25/0.47 % numerals(1)
% 0.25/0.47 thf(fact_172_nat__1__add__1,axiom,
% 0.25/0.47 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 0.25/0.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % nat_1_add_1
% 0.25/0.47 thf(fact_173_dbl__simps_I4_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % dbl_simps(4)
% 0.25/0.47 thf(fact_174_add__neg__numeral__special_I9_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_neg_numeral_special(9)
% 0.25/0.47 thf(fact_175_add__2__eq__Suc_H,axiom,
% 0.25/0.47 ! [N2: nat] :
% 0.25/0.47 ( ( plus_plus @ nat @ N2 @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
% 0.25/0.47 = ( suc @ ( suc @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_2_eq_Suc'
% 0.25/0.47 thf(fact_176_neg__equal__iff__equal,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( ( uminus_uminus @ A @ A4 )
% 0.25/0.47 = ( uminus_uminus @ A @ B2 ) )
% 0.25/0.47 = ( A4 = B2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % neg_equal_iff_equal
% 0.25/0.47 thf(fact_177_add_Oinverse__inverse,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A] :
% 0.25/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A4 ) )
% 0.25/0.47 = A4 ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.inverse_inverse
% 0.25/0.47 thf(fact_178_compl__eq__compl__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A] :
% 0.25/0.47 ( ( ( uminus_uminus @ A @ X )
% 0.25/0.47 = ( uminus_uminus @ A @ Y ) )
% 0.25/0.47 = ( X = Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % compl_eq_compl_iff
% 0.25/0.47 thf(fact_179_double__compl,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.25/0.47 = X ) ) ).
% 0.25/0.47
% 0.25/0.47 % double_compl
% 0.25/0.47 thf(fact_180_uminus__apply,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType] :
% 0.25/0.47 ( ( uminus @ B @ ( type2 @ B ) )
% 0.25/0.47 => ( ( uminus_uminus @ ( A > B ) )
% 0.25/0.47 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % uminus_apply
% 0.25/0.47 thf(fact_181_old_Onat_Oinject,axiom,
% 0.25/0.47 ! [Nat: nat,Nat2: nat] :
% 0.25/0.47 ( ( ( suc @ Nat )
% 0.25/0.47 = ( suc @ Nat2 ) )
% 0.25/0.47 = ( Nat = Nat2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % old.nat.inject
% 0.25/0.47 thf(fact_182_nat_Oinject,axiom,
% 0.25/0.47 ! [X22: nat,Y22: nat] :
% 0.25/0.47 ( ( ( suc @ X22 )
% 0.25/0.47 = ( suc @ Y22 ) )
% 0.25/0.47 = ( X22 = Y22 ) ) ).
% 0.25/0.47
% 0.25/0.47 % nat.inject
% 0.25/0.47 thf(fact_183_add__minus__cancel,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ A4 @ ( plus_plus @ A @ ( uminus_uminus @ A @ A4 ) @ B2 ) )
% 0.25/0.47 = B2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_minus_cancel
% 0.25/0.47 thf(fact_184_minus__add__cancel,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ A4 ) @ ( plus_plus @ A @ A4 @ B2 ) )
% 0.25/0.47 = B2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % minus_add_cancel
% 0.25/0.47 thf(fact_185_minus__add__distrib,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A4 @ B2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ A4 ) @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % minus_add_distrib
% 0.25/0.47 thf(fact_186_neg__numeral__eq__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 0.25/0.47 = ( M2 = N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % neg_numeral_eq_iff
% 0.25/0.47 thf(fact_187_mult__minus__left,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ A4 ) @ B2 )
% 0.25/0.47 = ( uminus_uminus @ A @ ( times_times @ A @ A4 @ B2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_minus_left
% 0.25/0.47 thf(fact_188_minus__mult__minus,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ A4 ) @ ( uminus_uminus @ A @ B2 ) )
% 0.25/0.47 = ( times_times @ A @ A4 @ B2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % minus_mult_minus
% 0.25/0.47 thf(fact_189_mult__minus__right,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( times_times @ A @ A4 @ ( uminus_uminus @ A @ B2 ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( times_times @ A @ A4 @ B2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_minus_right
% 0.25/0.47 thf(fact_190_add__Suc__right,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat] :
% 0.25/0.47 ( ( plus_plus @ nat @ M2 @ ( suc @ N2 ) )
% 0.25/0.47 = ( suc @ ( plus_plus @ nat @ M2 @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_Suc_right
% 0.25/0.47 thf(fact_191_add__neg__numeral__simps_I3_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ M2 ) @ ( numeral_numeral @ A @ N2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_neg_numeral_simps(3)
% 0.25/0.47 thf(fact_192_mult__minus1,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Z: A] :
% 0.25/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ Z )
% 0.25/0.47 = ( uminus_uminus @ A @ Z ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_minus1
% 0.25/0.47 thf(fact_193_mult__minus1__right,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [Z: A] :
% 0.25/0.47 ( ( times_times @ A @ Z @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.25/0.47 = ( uminus_uminus @ A @ Z ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_minus1_right
% 0.25/0.47 thf(fact_194_compl__sup__top,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ X )
% 0.25/0.47 = ( top_top @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % compl_sup_top
% 0.25/0.47 thf(fact_195_sup__compl__top,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( uminus_uminus @ A @ X ) )
% 0.25/0.47 = ( top_top @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_compl_top
% 0.25/0.47 thf(fact_196_sup__compl__top__left1,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A] :
% 0.25/0.47 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ ( sup_sup @ A @ X @ Y ) )
% 0.25/0.47 = ( top_top @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_compl_top_left1
% 0.25/0.47 thf(fact_197_sup__compl__top__left2,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [X: A,Y: A] :
% 0.25/0.47 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 0.25/0.47 = ( top_top @ A ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % sup_compl_top_left2
% 0.25/0.47 thf(fact_198_mult__Suc__right,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat] :
% 0.25/0.47 ( ( times_times @ nat @ M2 @ ( suc @ N2 ) )
% 0.25/0.47 = ( plus_plus @ nat @ M2 @ ( times_times @ nat @ M2 @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_Suc_right
% 0.25/0.47 thf(fact_199_dbl__simps_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [K: num] :
% 0.25/0.47 ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K ) ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % dbl_simps(1)
% 0.25/0.47 thf(fact_200_numeral__eq__neg__one__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.25/0.47 = ( N2 = one2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_eq_neg_one_iff
% 0.25/0.47 thf(fact_201_neg__one__eq__numeral__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( ( uminus_uminus @ A @ ( one_one @ A ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 0.25/0.47 = ( N2 = one2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % neg_one_eq_numeral_iff
% 0.25/0.47 thf(fact_202_semiring__norm_I168_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [V: num,W: num,Y: A] :
% 0.25/0.47 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ V ) ) @ ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) @ Y ) )
% 0.25/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(168)
% 0.25/0.47 thf(fact_203_Suc__numeral,axiom,
% 0.25/0.47 ! [N2: num] :
% 0.25/0.47 ( ( suc @ ( numeral_numeral @ nat @ N2 ) )
% 0.25/0.47 = ( numeral_numeral @ nat @ ( plus_plus @ num @ N2 @ one2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Suc_numeral
% 0.25/0.47 thf(fact_204_semiring__norm_I172_J,axiom,
% 0.25/0.47 ! [B: $tType] :
% 0.25/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.25/0.47 => ! [V: num,W: num,Y: B] :
% 0.25/0.47 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 0.25/0.47 = ( times_times @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) @ Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(172)
% 0.25/0.47 thf(fact_205_semiring__norm_I171_J,axiom,
% 0.25/0.47 ! [B: $tType] :
% 0.25/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.25/0.47 => ! [V: num,W: num,Y: B] :
% 0.25/0.47 ( ( times_times @ B @ ( numeral_numeral @ B @ V ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 0.25/0.47 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(171)
% 0.25/0.47 thf(fact_206_semiring__norm_I170_J,axiom,
% 0.25/0.47 ! [B: $tType] :
% 0.25/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.25/0.47 => ! [V: num,W: num,Y: B] :
% 0.25/0.47 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( numeral_numeral @ B @ W ) @ Y ) )
% 0.25/0.47 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % semiring_norm(170)
% 0.25/0.47 thf(fact_207_mult__neg__numeral__simps_I3_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ M2 ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_neg_numeral_simps(3)
% 0.25/0.47 thf(fact_208_mult__neg__numeral__simps_I2_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( numeral_numeral @ A @ N2 ) )
% 0.25/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_neg_numeral_simps(2)
% 0.25/0.47 thf(fact_209_mult__neg__numeral__simps_I1_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 0.25/0.47 = ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % mult_neg_numeral_simps(1)
% 0.25/0.47 thf(fact_210_add__2__eq__Suc,axiom,
% 0.25/0.47 ! [N2: nat] :
% 0.25/0.47 ( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N2 )
% 0.25/0.47 = ( suc @ ( suc @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_2_eq_Suc
% 0.25/0.47 thf(fact_211_Suc__1,axiom,
% 0.25/0.47 ( ( suc @ ( one_one @ nat ) )
% 0.25/0.47 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Suc_1
% 0.25/0.47 thf(fact_212_Suc__eq__plus1,axiom,
% 0.25/0.47 ( suc
% 0.25/0.47 = ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Suc_eq_plus1
% 0.25/0.47 thf(fact_213_Suc__eq__plus1__left,axiom,
% 0.25/0.47 ( suc
% 0.25/0.47 = ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % Suc_eq_plus1_left
% 0.25/0.47 thf(fact_214_one__neq__neg__one,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ( ( one_one @ A )
% 0.25/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % one_neq_neg_one
% 0.25/0.47 thf(fact_215_add_Oinverse__distrib__swap,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A4 @ B2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add.inverse_distrib_swap
% 0.25/0.47 thf(fact_216_minus__equation__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( ( uminus_uminus @ A @ A4 )
% 0.25/0.47 = B2 )
% 0.25/0.47 = ( ( uminus_uminus @ A @ B2 )
% 0.25/0.47 = A4 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % minus_equation_iff
% 0.25/0.47 thf(fact_217_equation__minus__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( A4
% 0.25/0.47 = ( uminus_uminus @ A @ B2 ) )
% 0.25/0.47 = ( B2
% 0.25/0.47 = ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % equation_minus_iff
% 0.25/0.47 thf(fact_218_numeral__neq__neg__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( numeral_numeral @ A @ M2 )
% 0.25/0.47 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_neq_neg_numeral
% 0.25/0.47 thf(fact_219_neg__numeral__neq__numeral,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [M2: num,N2: num] :
% 0.25/0.47 ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) )
% 0.25/0.47 != ( numeral_numeral @ A @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % neg_numeral_neq_numeral
% 0.25/0.47 thf(fact_220_is__num__normalize_I8_J,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A4 @ B2 ) )
% 0.25/0.47 = ( plus_plus @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % is_num_normalize(8)
% 0.25/0.47 thf(fact_221_fun__Compl__def,axiom,
% 0.25/0.47 ! [B: $tType,A: $tType] :
% 0.25/0.47 ( ( uminus @ B @ ( type2 @ B ) )
% 0.25/0.47 => ( ( uminus_uminus @ ( A > B ) )
% 0.25/0.47 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % fun_Compl_def
% 0.25/0.47 thf(fact_222_n__not__Suc__n,axiom,
% 0.25/0.47 ! [N2: nat] :
% 0.25/0.47 ( N2
% 0.25/0.47 != ( suc @ N2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % n_not_Suc_n
% 0.25/0.47 thf(fact_223_Suc__inject,axiom,
% 0.25/0.47 ! [X: nat,Y: nat] :
% 0.25/0.47 ( ( ( suc @ X )
% 0.25/0.47 = ( suc @ Y ) )
% 0.25/0.47 => ( X = Y ) ) ).
% 0.25/0.47
% 0.25/0.47 % Suc_inject
% 0.25/0.47 thf(fact_224_Suc__mult__cancel1,axiom,
% 0.25/0.47 ! [K: nat,M2: nat,N2: nat] :
% 0.25/0.47 ( ( ( times_times @ nat @ ( suc @ K ) @ M2 )
% 0.25/0.47 = ( times_times @ nat @ ( suc @ K ) @ N2 ) )
% 0.25/0.47 = ( M2 = N2 ) ) ).
% 0.25/0.47
% 0.25/0.47 % Suc_mult_cancel1
% 0.25/0.47 thf(fact_225_square__eq__iff,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( idom @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( ( times_times @ A @ A4 @ A4 )
% 0.25/0.47 = ( times_times @ A @ B2 @ B2 ) )
% 0.25/0.47 = ( ( A4 = B2 )
% 0.25/0.47 | ( A4
% 0.25/0.47 = ( uminus_uminus @ A @ B2 ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % square_eq_iff
% 0.25/0.47 thf(fact_226_minus__mult__commute,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [A4: A,B2: A] :
% 0.25/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ A4 ) @ B2 )
% 0.25/0.47 = ( times_times @ A @ A4 @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % minus_mult_commute
% 0.25/0.47 thf(fact_227_add__Suc,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat] :
% 0.25/0.47 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N2 )
% 0.25/0.47 = ( suc @ ( plus_plus @ nat @ M2 @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_Suc
% 0.25/0.47 thf(fact_228_add__Suc__shift,axiom,
% 0.25/0.47 ! [M2: nat,N2: nat] :
% 0.25/0.47 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N2 )
% 0.25/0.47 = ( plus_plus @ nat @ M2 @ ( suc @ N2 ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % add_Suc_shift
% 0.25/0.47 thf(fact_229_numeral__times__minus__swap,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [W: num,X: A] :
% 0.25/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ W ) @ ( uminus_uminus @ A @ X ) )
% 0.25/0.47 = ( times_times @ A @ X @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) ) ) ) ).
% 0.25/0.47
% 0.25/0.47 % numeral_times_minus_swap
% 0.25/0.47 thf(fact_230_numeral__neq__neg__one,axiom,
% 0.25/0.47 ! [A: $tType] :
% 0.25/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.47 => ! [N2: num] :
% 0.25/0.47 ( ( numeral_numeral @ A @ N2 )
% 0.25/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % numeral_neq_neg_one
% 0.25/0.48 thf(fact_231_one__neq__neg__numeral,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.25/0.48 => ! [N2: num] :
% 0.25/0.48 ( ( one_one @ A )
% 0.25/0.48 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % one_neq_neg_numeral
% 0.25/0.48 thf(fact_232_ring__normalization__rules_I1_J,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 0.25/0.48 => ( ( uminus_uminus @ A )
% 0.25/0.48 = ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ring_normalization_rules(1)
% 0.25/0.48 thf(fact_233_square__eq__1__iff,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( ring_11004092258visors @ A @ ( type2 @ A ) )
% 0.25/0.48 => ! [X: A] :
% 0.25/0.48 ( ( ( times_times @ A @ X @ X )
% 0.25/0.48 = ( one_one @ A ) )
% 0.25/0.48 = ( ( X
% 0.25/0.48 = ( one_one @ A ) )
% 0.25/0.48 | ( X
% 0.25/0.48 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % square_eq_1_iff
% 0.25/0.48 thf(fact_234_sup__cancel__left1,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.48 => ! [X: A,A4: A,B2: A] :
% 0.25/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ A4 ) @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ B2 ) )
% 0.25/0.48 = ( top_top @ A ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % sup_cancel_left1
% 0.25/0.48 thf(fact_235_sup__cancel__left2,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.25/0.48 => ! [X: A,A4: A,B2: A] :
% 0.25/0.48 ( ( sup_sup @ A @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ A4 ) @ ( sup_sup @ A @ X @ B2 ) )
% 0.25/0.48 = ( top_top @ A ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % sup_cancel_left2
% 0.25/0.48 thf(fact_236_Compl__partition,axiom,
% 0.25/0.48 ! [A: $tType,A2: set @ A] :
% 0.25/0.48 ( ( sup_sup @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.25/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % Compl_partition
% 0.25/0.48 thf(fact_237_Compl__partition2,axiom,
% 0.25/0.48 ! [A: $tType,A2: set @ A] :
% 0.25/0.48 ( ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ A2 )
% 0.25/0.48 = ( top_top @ ( set @ A ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % Compl_partition2
% 0.25/0.48 thf(fact_238_mult__Suc,axiom,
% 0.25/0.48 ! [M2: nat,N2: nat] :
% 0.25/0.48 ( ( times_times @ nat @ ( suc @ M2 ) @ N2 )
% 0.25/0.48 = ( plus_plus @ nat @ N2 @ ( times_times @ nat @ M2 @ N2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_Suc
% 0.25/0.48 thf(fact_239_mult__1s_I4_J,axiom,
% 0.25/0.48 ! [B: $tType] :
% 0.25/0.48 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.25/0.48 => ! [B2: B] :
% 0.25/0.48 ( ( times_times @ B @ B2 @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) )
% 0.25/0.48 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_1s(4)
% 0.25/0.48 thf(fact_240_mult__1s_I3_J,axiom,
% 0.25/0.48 ! [B: $tType] :
% 0.25/0.48 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.25/0.48 => ! [B2: B] :
% 0.25/0.48 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) @ B2 )
% 0.25/0.48 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % mult_1s(3)
% 0.25/0.48 thf(fact_241_uminus__numeral__One,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.48 => ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ one2 ) )
% 0.25/0.48 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % uminus_numeral_One
% 0.25/0.48 thf(fact_242_Suc__nat__number__of__add,axiom,
% 0.25/0.48 ! [V: num,N2: nat] :
% 0.25/0.48 ( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V ) @ N2 ) )
% 0.25/0.48 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V @ one2 ) ) @ N2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % Suc_nat_number_of_add
% 0.25/0.48 thf(fact_243_Suc__double__not__eq__double,axiom,
% 0.25/0.48 ! [M2: nat,N2: nat] :
% 0.25/0.48 ( ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ M2 ) )
% 0.25/0.48 != ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N2 ) ) ).
% 0.25/0.48
% 0.25/0.48 % Suc_double_not_eq_double
% 0.25/0.48 thf(fact_244_double__not__eq__Suc__double,axiom,
% 0.25/0.48 ! [M2: nat,N2: nat] :
% 0.25/0.48 ( ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ M2 )
% 0.25/0.48 != ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % double_not_eq_Suc_double
% 0.25/0.48 thf(fact_245_add__neg__numeral__special_I6_J,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.48 => ! [M2: num] :
% 0.25/0.48 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.25/0.48 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ M2 ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_neg_numeral_special(6)
% 0.25/0.48 thf(fact_246_Compl__eq__Compl__iff,axiom,
% 0.25/0.48 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 0.25/0.48 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 0.25/0.48 = ( uminus_uminus @ ( set @ A ) @ B3 ) )
% 0.25/0.48 = ( A2 = B3 ) ) ).
% 0.25/0.48
% 0.25/0.48 % Compl_eq_Compl_iff
% 0.25/0.48 thf(fact_247_Compl__iff,axiom,
% 0.25/0.48 ! [A: $tType,C2: A,A2: set @ A] :
% 0.25/0.48 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.25/0.48 = ( ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % Compl_iff
% 0.25/0.48 thf(fact_248_ComplI,axiom,
% 0.25/0.48 ! [A: $tType,C2: A,A2: set @ A] :
% 0.25/0.48 ( ~ ( member @ A @ C2 @ A2 )
% 0.25/0.48 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % ComplI
% 0.25/0.48 thf(fact_249_add__neg__numeral__special_I5_J,axiom,
% 0.25/0.48 ! [A: $tType] :
% 0.25/0.48 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.25/0.48 => ! [N2: num] :
% 0.25/0.48 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 0.25/0.48 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ N2 ) ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 % add_neg_numeral_special(5)
% 0.25/0.48 thf(fact_250_double__complement,axiom,
% 0.25/0.48 ! [A: $tType,A2: set @ A] :
% 0.25/0.48 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 0.25/0.48 = A2 ) ).
% 0.25/0.48
% 0.25/0.48 % double_complement
% 0.25/0.48
% 0.25/0.48 %----Type constructors (39)
% 0.25/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.25/0.48 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.25/0.48 ! [A6: $tType] : ( bounded_lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( bounded_lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( bounded_lattice_top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( semilattice_sup @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( semilattice_sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( boolean_algebra @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( boolean_algebra @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Orderings_Otop,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( top @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.25/0.48 ! [A6: $tType,A7: $tType] :
% 0.25/0.48 ( ( uminus @ A7 @ ( type2 @ A7 ) )
% 0.25/0.48 => ( uminus @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 0.25/0.48 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 0.25/0.48 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 0.25/0.48 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 0.25/0.48 semilattice_sup @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.25/0.48 ab_semigroup_mult @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.25/0.48 comm_monoid_mult @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 0.25/0.48 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.25/0.48 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.25/0.48 semigroup_mult @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Num_Osemiring__numeral,axiom,
% 0.25/0.48 semiring_numeral @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 0.25/0.48 semigroup_add @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Rings_Ocomm__semiring,axiom,
% 0.25/0.48 comm_semiring @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.25/0.48 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.25/0.48 monoid_mult @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Lattices_Olattice_4,axiom,
% 0.25/0.48 lattice @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Rings_Osemiring,axiom,
% 0.25/0.48 semiring @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.25/0.48 numeral @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.25/0.48 one @ nat @ ( type2 @ nat ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5,axiom,
% 0.25/0.48 ! [A6: $tType] : ( bounded_lattice_top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_6,axiom,
% 0.25/0.48 ! [A6: $tType] : ( semilattice_sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_7,axiom,
% 0.25/0.48 ! [A6: $tType] : ( boolean_algebra @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Lattices_Olattice_8,axiom,
% 0.25/0.48 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Orderings_Otop_9,axiom,
% 0.25/0.48 ! [A6: $tType] : ( top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_Set_Oset___Groups_Ouminus_10,axiom,
% 0.25/0.48 ! [A6: $tType] : ( uminus @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_11,axiom,
% 0.25/0.48 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_12,axiom,
% 0.25/0.48 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_13,axiom,
% 0.25/0.48 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_HOL_Obool___Lattices_Olattice_14,axiom,
% 0.25/0.48 lattice @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_HOL_Obool___Orderings_Otop_15,axiom,
% 0.25/0.48 top @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 thf(tcon_HOL_Obool___Groups_Ouminus_16,axiom,
% 0.25/0.48 uminus @ $o @ ( type2 @ $o ) ).
% 0.25/0.48
% 0.25/0.48 %----Conjectures (1)
% 0.25/0.48 thf(conj_0,conjecture,
% 0.25/0.48 member @ a @ x @ ( image @ nat @ a @ ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) ) @ ( top_top @ ( set @ nat ) ) ) ).
% 0.25/0.48
% 0.25/0.48 %------------------------------------------------------------------------------
% 0.25/0.48 ------------------------
% 2.48/1.49 ---- Embedded in THF ---
% 2.48/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.48/1.49 %%% Generated on Tue Feb 24 06:11:41 EST 2026
% 2.48/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 2.48/1.49 %%% Logic specification used:
% 2.48/1.49 %%% thf(spec, logic, $$dhol).
% 2.48/1.49
% 2.48/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.H3y4OZI0Un/DTF2DTF9624.p
% 2.48/1.49 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream, type, stream170649215stream: ($tType > $tType)).
% 2.48/1.49 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.48/1.49 thf(ty_t_Num_Onum, type, num: $tType).
% 2.48/1.49 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.48/1.49 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 2.48/1.49 thf(ty_tf_a, type, a: $tType).
% 2.48/1.49 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Oidom, type, idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Oring, type, ring: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Num_Onumeral, type, numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Orderings_Otop, type, top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Osemiring, type, semiring: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Ocomm__ring__1, type, comm_ring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Oab__group__add, type, ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Ocomm__semiring, type, comm_semiring: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Osemigroup__add, type, semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Num_Osemiring__numeral, type, semiring_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Fields_Olinordered__field, type, linordered_field: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Oab__semigroup__add, type, ab_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Ocomm__monoid__mult, type, comm_monoid_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Lattices_Osemilattice__sup, type, semilattice_sup: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Ocancel__semigroup__add, type, cancel_semigroup_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Lattices_Obounded__lattice__top, type, bounded_lattice_top: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Rings_Oring__1__no__zero__divisors, type, ring_11004092258visors: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Groups_Oordered__ab__semigroup__add, type, ordere779506340up_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, type, semiri456707255roduct: (!> [A:$tType]: (((itself @ A) > $o)))).
% 2.48/1.49 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 2.48/1.49 thf(sy_c_Groups_Oplus__class_Oplus, type, plus_plus: (!> [A:$tType]: ((A > (A > A))))).
% 2.48/1.49 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 2.48/1.49 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 2.48/1.49 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.48/1.49 thf(sy_c_Nat_OSuc, type, suc: (nat > nat)).
% 2.48/1.49 thf(sy_c_Num_Oinc, type, inc: (num > num)).
% 2.48/1.49 thf(sy_c_Num_Oneg__numeral__class_Odbl, type, neg_numeral_dbl: (!> [A:$tType]: ((A > A)))).
% 2.48/1.49 thf(sy_c_Num_Onum_OBit0, type, bit0: (num > num)).
% 2.48/1.49 thf(sy_c_Num_Onum_OOne, type, one2: num).
% 2.48/1.49 thf(sy_c_Num_Onumeral__class_Onumeral, type, numeral_numeral: (!> [A:$tType]: ((num > A)))).
% 2.48/1.49 thf(sy_c_Orderings_Otop__class_Otop, type, top_top: (!> [A:$tType]: (A))).
% 2.48/1.49 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 2.48/1.49 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.48/1.49 thf(sy_c_Set_Oimage, type, image: (!> [A:$tType,B:$tType]: (((A > B) > ((set @ A) > (set @ B)))))).
% 2.48/1.49 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osinterleave, type, stream865922174rleave: (!> [A:$tType]: (((stream170649215stream @ A) > ((stream170649215stream @ A) > (stream170649215stream @ A)))))).
% 2.48/1.49 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember, type, stream1586597341member: (!> [A:$tType]: ((A > ((stream170649215stream @ A) > $o))))).
% 2.48/1.49 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmerge, type, stream857257621smerge: (!> [A:$tType]: (((stream170649215stream @ (stream170649215stream @ A)) > (stream170649215stream @ A))))).
% 2.48/1.49 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osnth, type, stream370371455e_snth: (!> [A:$tType]: (((stream170649215stream @ A) > (nat > A))))).
% 2.48/1.49 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osset, type, stream30925839e_sset: (!> [A:$tType]: (((stream170649215stream @ A) > (set @ A))))).
% 2.48/1.49 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.48/1.49 thf(sy_v_n____, type, n: nat).
% 2.48/1.49 thf(sy_v_s1, type, s1: (stream170649215stream @ a)).
% 2.48/1.49 thf(sy_v_s2, type, s2: (stream170649215stream @ a)).
% 2.48/1.49 thf(sy_v_x____, type, x: a).
% 2.48/1.49 thf(fact_0__092_060open_062x_A_061_As1_A_B_B_An_092_060close_062, axiom, (x = (((stream370371455e_snth @ a) @ s1) @ n))).
% 2.48/1.49 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Ax_A_061_As1_A_B_B_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [N:nat]: ((x != (((stream370371455e_snth @ a) @ s1) @ N))))))).
% 2.48/1.49 thf(fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062, axiom, ((((stream370371455e_snth @ a) @ (((stream865922174rleave @ a) @ s1) @ s2)) @ (((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ n)) = x)).
% 2.48/1.49 thf(fact_3__092_060open_062x_A_092_060in_062_Asset_As1_092_060close_062, axiom, (((member @ a) @ x) @ ((stream30925839e_sset @ a) @ s1))).
% 2.48/1.49 thf(fact_4__092_060open_062x_A_092_060in_062_Asset_As1_A_092_060union_062_Asset_As2_092_060close_062, axiom, (((member @ a) @ x) @ (((sup_sup @ (set @ a)) @ ((stream30925839e_sset @ a) @ s1)) @ ((stream30925839e_sset @ a) @ s2)))).
% 2.48/1.49 thf(fact_5_UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.48/1.49 thf(fact_6_iso__tuple__UNIV__I, axiom, (! [A:$tType,X:A]: ((((member @ A) @ X) @ (top_top @ (set @ A)))))).
% 2.48/1.49 thf(fact_7_top__apply, axiom, (! [C:$tType,D:$tType]: ((((top @ C) @ (type2 @ C)) => ((top_top @ (D > C)) = (^ [X2:D]: ((top_top @ C)))))))).
% 2.48/1.49 thf(fact_8_image__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X:B,A2:(set @ B)]: (((B2 = (F @ X)) => ((((member @ B) @ X) @ A2) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ A2))))))).
% 2.48/1.49 thf(fact_9_surjD, axiom, (! [A:$tType,B:$tType,F:(B > A),Y:A]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (? [X3:B]: ((Y = (F @ X3)))))))).
% 2.48/1.49 thf(fact_10_surjE, axiom, (! [A:$tType,B:$tType,F:(B > A),Y:A]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) => (~ ((! [X3:B]: ((Y != (F @ X3)))))))))).
% 2.48/1.49 thf(fact_11_surjI, axiom, (! [B:$tType,A:$tType,G:(B > A),F:(A > B)]: (((! [X3:A]: (((G @ (F @ X3)) = X3))) => (((((image @ B) @ A) @ G) @ (top_top @ (set @ B))) = (top_top @ (set @ A))))))).
% 2.48/1.49 thf(fact_12_rangeI, axiom, (! [A:$tType,B:$tType,F:(B > A),X:B]: ((((member @ A) @ (F @ X)) @ ((((image @ B) @ A) @ F) @ (top_top @ (set @ B))))))).
% 2.48/1.49 thf(fact_13_surj__def, axiom, (! [B:$tType,A:$tType,F:(B > A)]: (((((((image @ B) @ A) @ F) @ (top_top @ (set @ B))) = (top_top @ (set @ A))) = (! [Y2:A]: ((? [X2:B]: ((Y2 = (F @ X2)))))))))).
% 2.48/1.49 thf(fact_14_range__eqI, axiom, (! [A:$tType,B:$tType,B2:A,F:(B > A),X:B]: (((B2 = (F @ X)) => (((member @ A) @ B2) @ ((((image @ B) @ A) @ F) @ (top_top @ (set @ B)))))))).
% 2.48/1.49 thf(fact_15_sset__range, axiom, (! [A:$tType]: (((stream30925839e_sset @ A) = (^ [S:(stream170649215stream @ A)]: (((((image @ nat) @ A) @ ((stream370371455e_snth @ A) @ S)) @ (top_top @ (set @ nat))))))))).
% 2.48/1.49 thf(fact_16_UnCI, axiom, (! [A:$tType,C2:A,B3:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C2) @ B3))) => (((member @ A) @ C2) @ A2)) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)))))).
% 2.48/1.49 thf(fact_17_Un__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)) = ((((member @ A) @ C2) @ A2) | (((member @ A) @ C2) @ B3)))))).
% 2.48/1.49 thf(fact_18_UnE, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)) => ((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ B3)))))).
% 2.48/1.49 thf(fact_19_UnI1, axiom, (! [A:$tType,C2:A,A2:(set @ A),B3:(set @ A)]: (((((member @ A) @ C2) @ A2) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)))))).
% 2.48/1.49 thf(fact_20_UnI2, axiom, (! [A:$tType,C2:A,B3:(set @ A),A2:(set @ A)]: (((((member @ A) @ C2) @ B3) => (((member @ A) @ C2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)))))).
% 2.48/1.49 thf(fact_21_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B3) & (P @ X2))))))))).
% 2.48/1.49 thf(fact_22_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A2) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B3) => (P @ X2))))))))).
% 2.48/1.49 thf(fact_23_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B3)) @ C3) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B3) @ C3)))))).
% 2.48/1.49 thf(fact_24_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.48/1.49 thf(fact_25_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A3:(set @ A),B4:(set @ A)]: ((((sup_sup @ (set @ A)) @ B4) @ A3))))))).
% 2.48/1.49 thf(fact_26_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B3)) = (((sup_sup @ (set @ A)) @ A2) @ B3))))).
% 2.48/1.49 thf(fact_27_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A),C3:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B3) @ C3)) = (((sup_sup @ (set @ A)) @ B3) @ (((sup_sup @ (set @ A)) @ A2) @ C3)))))).
% 2.48/1.49 thf(fact_28_image__Un, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B),B3:(set @ B)]: ((((((image @ B) @ A) @ F) @ (((sup_sup @ (set @ B)) @ A2) @ B3)) = (((sup_sup @ (set @ A)) @ ((((image @ B) @ A) @ F) @ A2)) @ ((((image @ B) @ A) @ F) @ B3)))))).
% 2.48/1.49 thf(fact_29_top__set__def, axiom, (! [A:$tType]: (((top_top @ (set @ A)) = ((collect @ A) @ (top_top @ (A > $o))))))).
% 2.48/1.49 thf(fact_30_Un__UNIV__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (top_top @ (set @ A))) = (top_top @ (set @ A)))))).
% 2.48/1.49 thf(fact_31_Un__UNIV__left, axiom, (! [A:$tType,B3:(set @ A)]: (((((sup_sup @ (set @ A)) @ (top_top @ (set @ A))) @ B3) = (top_top @ (set @ A)))))).
% 2.48/1.49 thf(fact_32_snth__sset, axiom, (! [A:$tType,S2:(stream170649215stream @ A),N2:nat]: ((((member @ A) @ (((stream370371455e_snth @ A) @ S2) @ N2)) @ ((stream30925839e_sset @ A) @ S2))))).
% 2.48/1.49 thf(fact_33_rev__image__eqI, axiom, (! [B:$tType,A:$tType,X:A,A2:(set @ A),B2:B,F:(A > B)]: (((((member @ A) @ X) @ A2) => ((B2 = (F @ X)) => (((member @ B) @ B2) @ ((((image @ A) @ B) @ F) @ A2))))))).
% 2.48/1.49 thf(fact_34_ball__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ ((((image @ B) @ A) @ F) @ A2)) => (P @ X3)))) => (! [X4:B]: (((((member @ B) @ X4) @ A2) => (P @ (F @ X4))))))))).
% 2.48/1.49 thf(fact_35_image__cong, axiom, (! [B:$tType,A:$tType,M:(set @ A),N3:(set @ A),F:(A > B),G:(A > B)]: (((M = N3) => ((! [X3:A]: (((((member @ A) @ X3) @ N3) => ((F @ X3) = (G @ X3))))) => (((((image @ A) @ B) @ F) @ M) = ((((image @ A) @ B) @ G) @ N3))))))).
% 2.48/1.49 thf(fact_36_bex__imageD, axiom, (! [A:$tType,B:$tType,F:(B > A),A2:(set @ B),P:(A > $o)]: (((? [X4:A]: (((((member @ A) @ X4) @ ((((image @ B) @ A) @ F) @ A2)) & (P @ X4)))) => (? [X3:B]: (((((member @ B) @ X3) @ A2) & (P @ (F @ X3))))))))).
% 2.48/1.49 thf(fact_37_image__iff, axiom, (! [A:$tType,B:$tType,Z:A,F:(B > A),A2:(set @ B)]: (((((member @ A) @ Z) @ ((((image @ B) @ A) @ F) @ A2)) = (? [X2:B]: (((((member @ B) @ X2) @ A2) & (Z = (F @ X2))))))))).
% 2.48/1.49 thf(fact_38_imageI, axiom, (! [B:$tType,A:$tType,X:A,A2:(set @ A),F:(A > B)]: (((((member @ A) @ X) @ A2) => (((member @ B) @ (F @ X)) @ ((((image @ A) @ B) @ F) @ A2)))))).
% 2.48/1.49 thf(fact_39_UNIV__witness, axiom, (! [A:$tType]: ((? [X3:A]: ((((member @ A) @ X3) @ (top_top @ (set @ A)))))))).
% 2.48/1.49 thf(fact_40_UNIV__eq__I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((((member @ A) @ X3) @ A2))) => ((top_top @ (set @ A)) = A2))))).
% 2.48/1.49 thf(fact_41_sup__top__right, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ (top_top @ A)) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_42_sup__top__left, axiom, (! [A:$tType]: ((((bounded_lattice_top @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ (top_top @ A)) @ X) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_43_semiring__norm_I169_J, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [V:num,W:num,Z:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ (((times_times @ A) @ ((numeral_numeral @ A) @ W)) @ Z)) = (((times_times @ A) @ ((numeral_numeral @ A) @ (((times_times @ num) @ V) @ W))) @ Z)))))))).
% 2.48/1.49 thf(fact_44_numeral__times__numeral, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((times_times @ A) @ ((numeral_numeral @ A) @ M2)) @ ((numeral_numeral @ A) @ N2)) = ((numeral_numeral @ A) @ (((times_times @ num) @ M2) @ N2))))))))).
% 2.48/1.49 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 2.48/1.49 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.48/1.49 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.48/1.49 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.48/1.49 thf(fact_49_semiring__norm_I85_J, axiom, (! [M2:num]: (((bit0 @ M2) != one2)))).
% 2.48/1.49 thf(fact_50_semiring__norm_I83_J, axiom, (! [N2:num]: ((one2 != (bit0 @ N2))))).
% 2.48/1.49 thf(fact_51_mult__numeral__1, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ one2)) @ A4) = A4))))))).
% 2.48/1.49 thf(fact_52_mult__numeral__1__right, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ A4) @ ((numeral_numeral @ A) @ one2)) = A4))))))).
% 2.48/1.49 thf(fact_53_sup__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.48/1.49 thf(fact_54_sup_Oidem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A]: (((((sup_sup @ A) @ A4) @ A4) = A4))))))).
% 2.48/1.49 thf(fact_55_semiring__norm_I87_J, axiom, (! [M2:num,N2:num]: ((((bit0 @ M2) = (bit0 @ N2)) = (M2 = N2))))).
% 2.48/1.49 thf(fact_56_num_Oinject_I1_J, axiom, (! [X22:num,Y22:num]: ((((bit0 @ X22) = (bit0 @ Y22)) = (X22 = Y22))))).
% 2.48/1.49 thf(fact_57_numeral__eq__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((numeral_numeral @ A) @ M2) = ((numeral_numeral @ A) @ N2)) = (M2 = N2)))))))).
% 2.48/1.49 thf(fact_58_sup_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B2)) @ B2) = (((sup_sup @ A) @ A4) @ B2)))))))).
% 2.48/1.49 thf(fact_59_sup__left__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.48/1.49 thf(fact_60_sup_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ A4) @ B2)) = (((sup_sup @ A) @ A4) @ B2)))))))).
% 2.48/1.49 thf(fact_61_sup__idem, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ X) = X))))))).
% 2.48/1.49 thf(fact_62_top1I, axiom, (! [A:$tType,X:A]: (((top_top @ (A > $o)) @ X)))).
% 2.48/1.49 thf(fact_63_semiring__norm_I13_J, axiom, (! [M2:num,N2:num]: (((((times_times @ num) @ (bit0 @ M2)) @ (bit0 @ N2)) = (bit0 @ (bit0 @ (((times_times @ num) @ M2) @ N2))))))).
% 2.48/1.49 thf(fact_64_semiring__norm_I11_J, axiom, (! [M2:num]: (((((times_times @ num) @ M2) @ one2) = M2)))).
% 2.48/1.49 thf(fact_65_semiring__norm_I12_J, axiom, (! [N2:num]: (((((times_times @ num) @ one2) @ N2) = N2)))).
% 2.48/1.49 thf(fact_66_sup__left__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 2.48/1.49 thf(fact_67_sup_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((sup_sup @ A) @ B2) @ (((sup_sup @ A) @ A4) @ C2)) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_68_sup__commute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X2)))))))).
% 2.48/1.49 thf(fact_69_sup_Ocommute, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [A5:A,B5:A]: ((((sup_sup @ A) @ B5) @ A5)))))))).
% 2.48/1.49 thf(fact_70_sup__assoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 2.48/1.49 thf(fact_71_sup_Oassoc, axiom, (! [A:$tType]: ((((semilattice_sup @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ A4) @ B2)) @ C2) = (((sup_sup @ A) @ A4) @ (((sup_sup @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_72_sup__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_sup @ B) @ (type2 @ B)) => ((sup_sup @ (A > B)) = (^ [F2:(A > B),G2:(A > B),X2:A]: ((((sup_sup @ B) @ (F2 @ X2)) @ (G2 @ X2))))))))).
% 2.48/1.49 thf(fact_73_inf__sup__aci_I5_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((sup_sup @ A) = (^ [X2:A,Y2:A]: ((((sup_sup @ A) @ Y2) @ X2)))))))).
% 2.48/1.49 thf(fact_74_inf__sup__aci_I6_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ Y)) @ Z) = (((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z))))))))).
% 2.48/1.49 thf(fact_75_inf__sup__aci_I7_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ Y) @ Z)) = (((sup_sup @ A) @ Y) @ (((sup_sup @ A) @ X) @ Z))))))))).
% 2.48/1.49 thf(fact_76_inf__sup__aci_I8_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ X) @ Y)) = (((sup_sup @ A) @ X) @ Y)))))))).
% 2.48/1.49 thf(fact_77_num_Odistinct_I1_J, axiom, (! [X22:num]: ((one2 != (bit0 @ X22))))).
% 2.48/1.49 thf(fact_78_top__empty__eq, axiom, (! [A:$tType]: (((top_top @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (top_top @ (set @ A))))))))).
% 2.48/1.49 thf(fact_79_snth__sset__smerge, axiom, (! [A:$tType,Ss:(stream170649215stream @ (stream170649215stream @ A)),N2:nat,M2:nat]: ((((member @ A) @ (((stream370371455e_snth @ A) @ (((stream370371455e_snth @ (stream170649215stream @ A)) @ Ss) @ N2)) @ M2)) @ ((stream30925839e_sset @ A) @ ((stream857257621smerge @ A) @ Ss)))))).
% 2.48/1.49 thf(fact_80_dbl__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num]: ((((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K)) = ((numeral_numeral @ A) @ (bit0 @ K))))))))).
% 2.48/1.49 thf(fact_81_top__conj_I2_J, axiom, (! [A:$tType,P:$o,X:A]: (((P & ((top_top @ (A > $o)) @ X)) = P)))).
% 2.48/1.49 thf(fact_82_top__conj_I1_J, axiom, (! [A:$tType,X:A,P:$o]: (((((top_top @ (A > $o)) @ X) & P) = P)))).
% 2.48/1.49 thf(fact_83_Stream__Mirabelle__hbrgyiwlrc_Osmember__def, axiom, (! [A:$tType]: (((stream1586597341member @ A) = (^ [X2:A,S:(stream170649215stream @ A)]: ((((member @ A) @ X2) @ ((stream30925839e_sset @ A) @ S)))))))).
% 2.48/1.49 thf(fact_84_mult__2__right, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [Z:A]: (((((times_times @ A) @ Z) @ ((numeral_numeral @ A) @ (bit0 @ one2))) = (((plus_plus @ A) @ Z) @ Z)))))))).
% 2.48/1.49 thf(fact_85_mult__2, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [Z:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2))) @ Z) = (((plus_plus @ A) @ Z) @ Z)))))))).
% 2.48/1.49 thf(fact_86_semiring__norm_I6_J, axiom, (! [M2:num,N2:num]: (((((plus_plus @ num) @ (bit0 @ M2)) @ (bit0 @ N2)) = (bit0 @ (((plus_plus @ num) @ M2) @ N2)))))).
% 2.48/1.49 thf(fact_87_semiring__norm_I2_J, axiom, ((((plus_plus @ num) @ one2) @ one2) = (bit0 @ one2))).
% 2.48/1.49 thf(fact_88_add__numeral__left, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [V:num,W:num,Z:A]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ V)) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ W)) @ Z)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ V) @ W))) @ Z)))))))).
% 2.48/1.49 thf(fact_89_numeral__plus__numeral, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ M2)) @ ((numeral_numeral @ A) @ N2)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ M2) @ N2))))))))).
% 2.48/1.49 thf(fact_90_dbl__def, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => ((neg_numeral_dbl @ A) = (^ [X2:A]: ((((plus_plus @ A) @ X2) @ X2)))))))).
% 2.48/1.49 thf(fact_91_is__num__normalize_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_92_add__One__commute, axiom, (! [N2:num]: (((((plus_plus @ num) @ one2) @ N2) = (((plus_plus @ num) @ N2) @ one2))))).
% 2.48/1.49 thf(fact_93_left__add__mult__distrib, axiom, (! [I:nat,U:nat,J:nat,K:nat]: (((((plus_plus @ nat) @ (((times_times @ nat) @ I) @ U)) @ (((plus_plus @ nat) @ (((times_times @ nat) @ J) @ U)) @ K)) = (((plus_plus @ nat) @ (((times_times @ nat) @ (((plus_plus @ nat) @ I) @ J)) @ U)) @ K))))).
% 2.48/1.49 thf(fact_94_numeral__Bit0, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N2:num]: ((((numeral_numeral @ A) @ (bit0 @ N2)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ N2)) @ ((numeral_numeral @ A) @ N2))))))))).
% 2.48/1.49 thf(fact_95_distrib__left__numeral, axiom, (! [A:$tType]: (((((numeral @ A) @ (type2 @ A)) & ((semiring @ A) @ (type2 @ A))) => (! [V:num,B2:A,C2:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ (((plus_plus @ A) @ B2) @ C2)) = (((plus_plus @ A) @ (((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ B2)) @ (((times_times @ A) @ ((numeral_numeral @ A) @ V)) @ C2))))))))).
% 2.48/1.49 thf(fact_96_distrib__right__numeral, axiom, (! [A:$tType]: (((((numeral @ A) @ (type2 @ A)) & ((semiring @ A) @ (type2 @ A))) => (! [A4:A,B2:A,V:num]: (((((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ ((numeral_numeral @ A) @ V)) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ ((numeral_numeral @ A) @ V))) @ (((times_times @ A) @ B2) @ ((numeral_numeral @ A) @ V)))))))))).
% 2.48/1.49 thf(fact_97_add__left__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A4) @ B2) = (((plus_plus @ A) @ A4) @ C2)) = (B2 = C2)))))))).
% 2.48/1.49 thf(fact_98_add__right__cancel, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A4) = (((plus_plus @ A) @ C2) @ A4)) = (B2 = C2)))))))).
% 2.48/1.49 thf(fact_99_crossproduct__noteq, axiom, (! [A:$tType]: ((((semiri456707255roduct @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A,D2:A]: ((((A4 != B2) & (C2 != D2)) = ((((plus_plus @ A) @ (((times_times @ A) @ A4) @ C2)) @ (((times_times @ A) @ B2) @ D2)) != (((plus_plus @ A) @ (((times_times @ A) @ A4) @ D2)) @ (((times_times @ A) @ B2) @ C2)))))))))).
% 2.48/1.49 thf(fact_100_crossproduct__eq, axiom, (! [A:$tType]: ((((semiri456707255roduct @ A) @ (type2 @ A)) => (! [W:A,Y:A,X:A,Z:A]: ((((((plus_plus @ A) @ (((times_times @ A) @ W) @ Y)) @ (((times_times @ A) @ X) @ Z)) = (((plus_plus @ A) @ (((times_times @ A) @ W) @ Z)) @ (((times_times @ A) @ X) @ Y))) = ((W = X) | (Y = Z))))))))).
% 2.48/1.49 thf(fact_101_add__right__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A4) = (((plus_plus @ A) @ C2) @ A4)) => (B2 = C2)))))))).
% 2.48/1.49 thf(fact_102_add__left__imp__eq, axiom, (! [A:$tType]: ((((cancel_semigroup_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A4) @ B2) = (((plus_plus @ A) @ A4) @ C2)) => (B2 = C2)))))))).
% 2.48/1.49 thf(fact_103_add_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A4) @ C2)) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_104_add_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A5:A,B5:A]: ((((plus_plus @ A) @ B5) @ A5)))))))).
% 2.48/1.49 thf(fact_105_add_Oright__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: ((((((plus_plus @ A) @ B2) @ A4) = (((plus_plus @ A) @ C2) @ A4)) = (B2 = C2)))))))).
% 2.48/1.49 thf(fact_106_add_Oleft__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: ((((((plus_plus @ A) @ A4) @ B2) = (((plus_plus @ A) @ A4) @ C2)) = (B2 = C2)))))))).
% 2.48/1.49 thf(fact_107_add_Oassoc, axiom, (! [A:$tType]: ((((semigroup_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_108_semiring__normalization__rules_I20_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A,D2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ (((plus_plus @ A) @ C2) @ D2)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ C2)) @ (((plus_plus @ A) @ B2) @ D2))))))))).
% 2.48/1.49 thf(fact_109_semiring__normalization__rules_I21_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_110_semiring__normalization__rules_I22_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,C2:A,D2:A]: (((((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ C2) @ D2)) = (((plus_plus @ A) @ C2) @ (((plus_plus @ A) @ A4) @ D2))))))))).
% 2.48/1.49 thf(fact_111_semiring__normalization__rules_I23_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ C2)) @ B2)))))))).
% 2.48/1.49 thf(fact_112_semiring__normalization__rules_I24_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A5:A,C4:A]: ((((plus_plus @ A) @ C4) @ A5)))))))).
% 2.48/1.49 thf(fact_113_semiring__normalization__rules_I25_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,C2:A,D2:A]: (((((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ C2) @ D2)) = (((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ C2)) @ D2)))))))).
% 2.48/1.49 thf(fact_114_add__mono__thms__linordered__semiring_I4_J, axiom, (! [A:$tType]: ((((ordere779506340up_add @ A) @ (type2 @ A)) => (! [I:A,J:A,K:A,L:A]: ((((I = J) & (K = L)) => ((((plus_plus @ A) @ I) @ K) = (((plus_plus @ A) @ J) @ L))))))))).
% 2.48/1.49 thf(fact_115_ab__semigroup__add__class_Oadd__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_116_mult_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_mult @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A4) @ C2)) = (((times_times @ A) @ A4) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_117_mult_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_mult @ A) @ (type2 @ A)) => ((times_times @ A) = (^ [A5:A,B5:A]: ((((times_times @ A) @ B5) @ A5)))))))).
% 2.48/1.49 thf(fact_118_mult_Oassoc, axiom, (! [A:$tType]: ((((semigroup_mult @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((times_times @ A) @ A4) @ B2)) @ C2) = (((times_times @ A) @ A4) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_119_semiring__normalization__rules_I7_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((times_times @ A) = (^ [A5:A,B5:A]: ((((times_times @ A) @ B5) @ A5)))))))).
% 2.48/1.49 thf(fact_120_semiring__normalization__rules_I13_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A,Ry:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ (((times_times @ A) @ Lx) @ Rx)) @ (((times_times @ A) @ Ly) @ Ry))))))))).
% 2.48/1.49 thf(fact_121_semiring__normalization__rules_I14_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A,Ry:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ Lx) @ (((times_times @ A) @ Ly) @ (((times_times @ A) @ Rx) @ Ry)))))))))).
% 2.48/1.49 thf(fact_122_semiring__normalization__rules_I15_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A,Ry:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ Rx) @ (((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ Ry))))))))).
% 2.48/1.49 thf(fact_123_semiring__normalization__rules_I16_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ Rx) = (((times_times @ A) @ (((times_times @ A) @ Lx) @ Rx)) @ Ly)))))))).
% 2.48/1.49 thf(fact_124_semiring__normalization__rules_I17_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ Rx) = (((times_times @ A) @ Lx) @ (((times_times @ A) @ Ly) @ Rx))))))))).
% 2.48/1.49 thf(fact_125_semiring__normalization__rules_I18_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Rx:A,Ry:A]: (((((times_times @ A) @ Lx) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ (((times_times @ A) @ Lx) @ Rx)) @ Ry)))))))).
% 2.48/1.49 thf(fact_126_semiring__normalization__rules_I19_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Rx:A,Ry:A]: (((((times_times @ A) @ Lx) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ Rx) @ (((times_times @ A) @ Lx) @ Ry))))))))).
% 2.48/1.49 thf(fact_127_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_mult @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((times_times @ A) @ A4) @ B2)) @ C2) = (((times_times @ A) @ A4) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_128_semiring__normalization__rules_I34_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((times_times @ A) @ X) @ (((plus_plus @ A) @ Y) @ Z)) = (((plus_plus @ A) @ (((times_times @ A) @ X) @ Y)) @ (((times_times @ A) @ X) @ Z))))))))).
% 2.48/1.49 thf(fact_129_semiring__normalization__rules_I8_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ C2)) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_130_semiring__normalization__rules_I1_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,M2:A,B2:A]: (((((plus_plus @ A) @ (((times_times @ A) @ A4) @ M2)) @ (((times_times @ A) @ B2) @ M2)) = (((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ M2)))))))).
% 2.48/1.49 thf(fact_131_add__mult__distrib, axiom, (! [M2:nat,N2:nat,K:nat]: (((((times_times @ nat) @ (((plus_plus @ nat) @ M2) @ N2)) @ K) = (((plus_plus @ nat) @ (((times_times @ nat) @ M2) @ K)) @ (((times_times @ nat) @ N2) @ K)))))).
% 2.48/1.49 thf(fact_132_add__mult__distrib2, axiom, (! [K:nat,M2:nat,N2:nat]: (((((times_times @ nat) @ K) @ (((plus_plus @ nat) @ M2) @ N2)) = (((plus_plus @ nat) @ (((times_times @ nat) @ K) @ M2)) @ (((times_times @ nat) @ K) @ N2)))))).
% 2.48/1.49 thf(fact_133_ring__class_Oring__distribs_I2_J, axiom, (! [A:$tType]: ((((ring @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ C2)) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_134_ring__class_Oring__distribs_I1_J, axiom, (! [A:$tType]: ((((ring @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2)) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ B2)) @ (((times_times @ A) @ A4) @ C2))))))))).
% 2.48/1.49 thf(fact_135_linordered__field__class_Osign__simps_I36_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2)) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ B2)) @ (((times_times @ A) @ A4) @ C2))))))))).
% 2.48/1.49 thf(fact_136_linordered__field__class_Osign__simps_I28_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((plus_plus @ A) @ B2) @ (((plus_plus @ A) @ A4) @ C2)) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_137_linordered__field__class_Osign__simps_I27_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((plus_plus @ A) = (^ [A5:A,B5:A]: ((((plus_plus @ A) @ B5) @ A5)))))))).
% 2.48/1.49 thf(fact_138_linordered__field__class_Osign__simps_I26_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_139_linordered__field__class_Osign__simps_I25_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [B2:A,A4:A,C2:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A4) @ C2)) = (((times_times @ A) @ A4) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_140_linordered__field__class_Osign__simps_I24_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => ((times_times @ A) = (^ [A5:A,B5:A]: ((((times_times @ A) @ B5) @ A5)))))))).
% 2.48/1.49 thf(fact_141_linordered__field__class_Osign__simps_I23_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((times_times @ A) @ A4) @ B2)) @ C2) = (((times_times @ A) @ A4) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_142_nat__add__right__cancel, axiom, (! [M2:nat,K:nat,N2:nat]: ((((((plus_plus @ nat) @ M2) @ K) = (((plus_plus @ nat) @ N2) @ K)) = (M2 = N2))))).
% 2.48/1.49 thf(fact_143_nat__add__left__cancel, axiom, (! [K:nat,M2:nat,N2:nat]: ((((((plus_plus @ nat) @ K) @ M2) = (((plus_plus @ nat) @ K) @ N2)) = (M2 = N2))))).
% 2.48/1.49 thf(fact_144_combine__common__factor, axiom, (! [A:$tType]: ((((semiring @ A) @ (type2 @ A)) => (! [A4:A,E:A,B2:A,C2:A]: (((((plus_plus @ A) @ (((times_times @ A) @ A4) @ E)) @ (((plus_plus @ A) @ (((times_times @ A) @ B2) @ E)) @ C2)) = (((plus_plus @ A) @ (((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ E)) @ C2)))))))).
% 2.48/1.49 thf(fact_145_distrib__right, axiom, (! [A:$tType]: ((((semiring @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ C2)) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_146_distrib__left, axiom, (! [A:$tType]: ((((semiring @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ A4) @ (((plus_plus @ A) @ B2) @ C2)) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ B2)) @ (((times_times @ A) @ A4) @ C2))))))))).
% 2.48/1.49 thf(fact_147_comm__semiring__class_Odistrib, axiom, (! [A:$tType]: ((((comm_semiring @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ C2)) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_148_linordered__field__class_Osign__simps_I35_J, axiom, (! [A:$tType]: ((((linordered_field @ A) @ (type2 @ A)) => (! [A4:A,B2:A,C2:A]: (((((times_times @ A) @ (((plus_plus @ A) @ A4) @ B2)) @ C2) = (((plus_plus @ A) @ (((times_times @ A) @ A4) @ C2)) @ (((times_times @ A) @ B2) @ C2))))))))).
% 2.48/1.49 thf(fact_149_dbl__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl @ A) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 2.48/1.49 thf(fact_150_numeral__plus__one, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N2:num]: (((((plus_plus @ A) @ ((numeral_numeral @ A) @ N2)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ N2) @ one2))))))))).
% 2.48/1.49 thf(fact_151_one__plus__numeral, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [N2:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N2)) = ((numeral_numeral @ A) @ (((plus_plus @ num) @ one2) @ N2))))))))).
% 2.48/1.49 thf(fact_152_one__add__one, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => ((((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 2.48/1.49 thf(fact_153_nat__1__eq__mult__iff, axiom, (! [M2:nat,N2:nat]: ((((one_one @ nat) = (((times_times @ nat) @ M2) @ N2)) = ((M2 = (one_one @ nat)) & (N2 = (one_one @ nat))))))).
% 2.48/1.49 thf(fact_154_nat__mult__eq__1__iff, axiom, (! [M2:nat,N2:nat]: ((((((times_times @ nat) @ M2) @ N2) = (one_one @ nat)) = ((M2 = (one_one @ nat)) & (N2 = (one_one @ nat))))))).
% 2.48/1.49 thf(fact_155_mult_Oright__neutral, axiom, (! [A:$tType]: ((((monoid_mult @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ A4) @ (one_one @ A)) = A4))))))).
% 2.48/1.49 thf(fact_156_mult_Oleft__neutral, axiom, (! [A:$tType]: ((((monoid_mult @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ (one_one @ A)) @ A4) = A4))))))).
% 2.48/1.49 thf(fact_157_one__eq__numeral__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N2:num]: ((((one_one @ A) = ((numeral_numeral @ A) @ N2)) = (one2 = N2)))))))).
% 2.48/1.49 thf(fact_158_numeral__eq__one__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N2:num]: (((((numeral_numeral @ A) @ N2) = (one_one @ A)) = (N2 = one2)))))))).
% 2.48/1.49 thf(fact_159_nat__mult__1__right, axiom, (! [N2:nat]: (((((times_times @ nat) @ N2) @ (one_one @ nat)) = N2)))).
% 2.48/1.49 thf(fact_160_nat__mult__1, axiom, (! [N2:nat]: (((((times_times @ nat) @ (one_one @ nat)) @ N2) = N2)))).
% 2.48/1.49 thf(fact_161_mult_Ocomm__neutral, axiom, (! [A:$tType]: ((((comm_monoid_mult @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ A4) @ (one_one @ A)) = A4))))))).
% 2.48/1.49 thf(fact_162_comm__monoid__mult__class_Omult__1, axiom, (! [A:$tType]: ((((comm_monoid_mult @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ (one_one @ A)) @ A4) = A4))))))).
% 2.48/1.49 thf(fact_163_semiring__normalization__rules_I11_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ (one_one @ A)) @ A4) = A4))))))).
% 2.48/1.49 thf(fact_164_semiring__normalization__rules_I12_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A]: (((((times_times @ A) @ A4) @ (one_one @ A)) = A4))))))).
% 2.48/1.49 thf(fact_165_one__reorient, axiom, (! [A:$tType]: ((((one @ A) @ (type2 @ A)) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 2.48/1.49 thf(fact_166_one__plus__numeral__commute, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (! [X:num]: (((((plus_plus @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ X)) = (((plus_plus @ A) @ ((numeral_numeral @ A) @ X)) @ (one_one @ A))))))))).
% 2.48/1.49 thf(fact_167_semiring__normalization__rules_I2_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A4:A,M2:A]: (((((plus_plus @ A) @ (((times_times @ A) @ A4) @ M2)) @ M2) = (((times_times @ A) @ (((plus_plus @ A) @ A4) @ (one_one @ A))) @ M2)))))))).
% 2.48/1.49 thf(fact_168_semiring__normalization__rules_I3_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [M2:A,A4:A]: (((((plus_plus @ A) @ M2) @ (((times_times @ A) @ A4) @ M2)) = (((times_times @ A) @ (((plus_plus @ A) @ A4) @ (one_one @ A))) @ M2)))))))).
% 2.48/1.49 thf(fact_169_semiring__normalization__rules_I4_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [M2:A]: (((((plus_plus @ A) @ M2) @ M2) = (((times_times @ A) @ (((plus_plus @ A) @ (one_one @ A)) @ (one_one @ A))) @ M2)))))))).
% 2.48/1.49 thf(fact_170_numeral__One, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (((numeral_numeral @ A) @ one2) = (one_one @ A)))))).
% 2.48/1.49 thf(fact_171_numerals_I1_J, axiom, (((numeral_numeral @ nat) @ one2) = (one_one @ nat))).
% 2.48/1.49 thf(fact_172_nat__1__add__1, axiom, ((((plus_plus @ nat) @ (one_one @ nat)) @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 2.48/1.49 thf(fact_173_dbl__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2)))))))).
% 2.48/1.49 thf(fact_174_add__neg__numeral__special_I9_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => ((((plus_plus @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2)))))))).
% 2.48/1.49 thf(fact_175_add__2__eq__Suc_H, axiom, (! [N2:nat]: (((((plus_plus @ nat) @ N2) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) = (suc @ (suc @ N2)))))).
% 2.48/1.49 thf(fact_176_neg__equal__iff__equal, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((uminus_uminus @ A) @ A4) = ((uminus_uminus @ A) @ B2)) = (A4 = B2)))))))).
% 2.48/1.49 thf(fact_177_add_Oinverse__inverse, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A4)) = A4))))))).
% 2.48/1.49 thf(fact_178_compl__eq__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((uminus_uminus @ A) @ X) = ((uminus_uminus @ A) @ Y)) = (X = Y)))))))).
% 2.48/1.49 thf(fact_179_double__compl, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X)) = X))))))).
% 2.48/1.49 thf(fact_180_uminus__apply, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A3:(A > B),X2:A]: (((uminus_uminus @ B) @ (A3 @ X2))))))))).
% 2.48/1.49 thf(fact_181_old_Onat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((suc @ Nat) = (suc @ Nat2)) = (Nat = Nat2))))).
% 2.48/1.49 thf(fact_182_nat_Oinject, axiom, (! [X22:nat,Y22:nat]: ((((suc @ X22) = (suc @ Y22)) = (X22 = Y22))))).
% 2.48/1.49 thf(fact_183_add__minus__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((plus_plus @ A) @ A4) @ (((plus_plus @ A) @ ((uminus_uminus @ A) @ A4)) @ B2)) = B2))))))).
% 2.48/1.49 thf(fact_184_minus__add__cancel, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ A4)) @ (((plus_plus @ A) @ A4) @ B2)) = B2))))))).
% 2.48/1.49 thf(fact_185_minus__add__distrib, axiom, (! [A:$tType]: ((((ab_group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: ((((uminus_uminus @ A) @ (((plus_plus @ A) @ A4) @ B2)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ A4)) @ ((uminus_uminus @ A) @ B2))))))))).
% 2.48/1.49 thf(fact_186_neg__numeral__eq__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M2)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))) = (M2 = N2)))))))).
% 2.48/1.49 thf(fact_187_mult__minus__left, axiom, (! [A:$tType]: ((((ring @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A4)) @ B2) = ((uminus_uminus @ A) @ (((times_times @ A) @ A4) @ B2))))))))).
% 2.48/1.49 thf(fact_188_minus__mult__minus, axiom, (! [A:$tType]: ((((ring @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A4)) @ ((uminus_uminus @ A) @ B2)) = (((times_times @ A) @ A4) @ B2)))))))).
% 2.48/1.49 thf(fact_189_mult__minus__right, axiom, (! [A:$tType]: ((((ring @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((times_times @ A) @ A4) @ ((uminus_uminus @ A) @ B2)) = ((uminus_uminus @ A) @ (((times_times @ A) @ A4) @ B2))))))))).
% 2.48/1.49 thf(fact_190_add__Suc__right, axiom, (! [M2:nat,N2:nat]: (((((plus_plus @ nat) @ M2) @ (suc @ N2)) = (suc @ (((plus_plus @ nat) @ M2) @ N2)))))).
% 2.48/1.49 thf(fact_191_add__neg__numeral__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M2))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))) = ((uminus_uminus @ A) @ (((plus_plus @ A) @ ((numeral_numeral @ A) @ M2)) @ ((numeral_numeral @ A) @ N2)))))))))).
% 2.48/1.49 thf(fact_192_mult__minus1, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [Z:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ Z) = ((uminus_uminus @ A) @ Z)))))))).
% 2.48/1.49 thf(fact_193_mult__minus1__right, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [Z:A]: (((((times_times @ A) @ Z) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ Z)))))))).
% 2.48/1.49 thf(fact_194_compl__sup__top, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ X) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_195_sup__compl__top, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: (((((sup_sup @ A) @ X) @ ((uminus_uminus @ A) @ X)) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_196_sup__compl__top__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ (((sup_sup @ A) @ X) @ Y)) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_197_sup__compl__top__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((sup_sup @ A) @ X) @ (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ Y)) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_198_mult__Suc__right, axiom, (! [M2:nat,N2:nat]: (((((times_times @ nat) @ M2) @ (suc @ N2)) = (((plus_plus @ nat) @ M2) @ (((times_times @ nat) @ M2) @ N2)))))).
% 2.48/1.49 thf(fact_199_dbl__simps_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K:num]: ((((neg_numeral_dbl @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ K))) = ((uminus_uminus @ A) @ ((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K)))))))))).
% 2.48/1.49 thf(fact_200_numeral__eq__neg__one__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N2:num]: (((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2)) = ((uminus_uminus @ A) @ (one_one @ A))) = (N2 = one2)))))))).
% 2.48/1.49 thf(fact_201_neg__one__eq__numeral__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N2:num]: (((((uminus_uminus @ A) @ (one_one @ A)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))) = (N2 = one2)))))))).
% 2.48/1.49 thf(fact_202_semiring__norm_I168_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [V:num,W:num,Y:A]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ V))) @ (((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ W))) @ Y)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (((plus_plus @ num) @ V) @ W)))) @ Y)))))))).
% 2.48/1.49 thf(fact_203_Suc__numeral, axiom, (! [N2:num]: (((suc @ ((numeral_numeral @ nat) @ N2)) = ((numeral_numeral @ nat) @ (((plus_plus @ num) @ N2) @ one2)))))).
% 2.48/1.49 thf(fact_204_semiring__norm_I172_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [V:num,W:num,Y:B]: (((((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ V))) @ (((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ W))) @ Y)) = (((times_times @ B) @ ((numeral_numeral @ B) @ (((times_times @ num) @ V) @ W))) @ Y)))))))).
% 2.48/1.49 thf(fact_205_semiring__norm_I171_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [V:num,W:num,Y:B]: (((((times_times @ B) @ ((numeral_numeral @ B) @ V)) @ (((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ W))) @ Y)) = (((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ (((times_times @ num) @ V) @ W)))) @ Y)))))))).
% 2.48/1.49 thf(fact_206_semiring__norm_I170_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [V:num,W:num,Y:B]: (((((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ V))) @ (((times_times @ B) @ ((numeral_numeral @ B) @ W)) @ Y)) = (((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ (((times_times @ num) @ V) @ W)))) @ Y)))))))).
% 2.48/1.49 thf(fact_207_mult__neg__numeral__simps_I3_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((times_times @ A) @ ((numeral_numeral @ A) @ M2)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (((times_times @ num) @ M2) @ N2)))))))))).
% 2.48/1.49 thf(fact_208_mult__neg__numeral__simps_I2_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((times_times @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M2))) @ ((numeral_numeral @ A) @ N2)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (((times_times @ num) @ M2) @ N2)))))))))).
% 2.48/1.49 thf(fact_209_mult__neg__numeral__simps_I1_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: (((((times_times @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M2))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))) = ((numeral_numeral @ A) @ (((times_times @ num) @ M2) @ N2))))))))).
% 2.48/1.49 thf(fact_210_add__2__eq__Suc, axiom, (! [N2:nat]: (((((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ N2) = (suc @ (suc @ N2)))))).
% 2.48/1.49 thf(fact_211_Suc__1, axiom, ((suc @ (one_one @ nat)) = ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 2.48/1.49 thf(fact_212_Suc__eq__plus1, axiom, (suc = (^ [N4:nat]: ((((plus_plus @ nat) @ N4) @ (one_one @ nat)))))).
% 2.48/1.49 thf(fact_213_Suc__eq__plus1__left, axiom, (suc = ((plus_plus @ nat) @ (one_one @ nat)))).
% 2.48/1.49 thf(fact_214_one__neq__neg__one, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => ((one_one @ A) != ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.48/1.49 thf(fact_215_add_Oinverse__distrib__swap, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: ((((uminus_uminus @ A) @ (((plus_plus @ A) @ A4) @ B2)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A4))))))))).
% 2.48/1.49 thf(fact_216_minus__equation__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((uminus_uminus @ A) @ A4) = B2) = (((uminus_uminus @ A) @ B2) = A4)))))))).
% 2.48/1.49 thf(fact_217_equation__minus__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((A4 = ((uminus_uminus @ A) @ B2)) = (B2 = ((uminus_uminus @ A) @ A4))))))))).
% 2.48/1.49 thf(fact_218_numeral__neq__neg__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: ((((numeral_numeral @ A) @ M2) != ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))))))))).
% 2.48/1.49 thf(fact_219_neg__numeral__neq__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M2:num,N2:num]: ((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M2)) != ((numeral_numeral @ A) @ N2)))))))).
% 2.48/1.49 thf(fact_220_is__num__normalize_I8_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: ((((uminus_uminus @ A) @ (((plus_plus @ A) @ A4) @ B2)) = (((plus_plus @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A4))))))))).
% 2.48/1.49 thf(fact_221_fun__Compl__def, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A3:(A > B),X2:A]: (((uminus_uminus @ B) @ (A3 @ X2))))))))).
% 2.48/1.49 thf(fact_222_n__not__Suc__n, axiom, (! [N2:nat]: ((N2 != (suc @ N2))))).
% 2.48/1.49 thf(fact_223_Suc__inject, axiom, (! [X:nat,Y:nat]: ((((suc @ X) = (suc @ Y)) => (X = Y))))).
% 2.48/1.49 thf(fact_224_Suc__mult__cancel1, axiom, (! [K:nat,M2:nat,N2:nat]: ((((((times_times @ nat) @ (suc @ K)) @ M2) = (((times_times @ nat) @ (suc @ K)) @ N2)) = (M2 = N2))))).
% 2.48/1.49 thf(fact_225_square__eq__iff, axiom, (! [A:$tType]: ((((idom @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: ((((((times_times @ A) @ A4) @ A4) = (((times_times @ A) @ B2) @ B2)) = ((A4 = B2) | (A4 = ((uminus_uminus @ A) @ B2)))))))))).
% 2.48/1.49 thf(fact_226_minus__mult__commute, axiom, (! [A:$tType]: ((((ring @ A) @ (type2 @ A)) => (! [A4:A,B2:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ A4)) @ B2) = (((times_times @ A) @ A4) @ ((uminus_uminus @ A) @ B2))))))))).
% 2.48/1.49 thf(fact_227_add__Suc, axiom, (! [M2:nat,N2:nat]: (((((plus_plus @ nat) @ (suc @ M2)) @ N2) = (suc @ (((plus_plus @ nat) @ M2) @ N2)))))).
% 2.48/1.49 thf(fact_228_add__Suc__shift, axiom, (! [M2:nat,N2:nat]: (((((plus_plus @ nat) @ (suc @ M2)) @ N2) = (((plus_plus @ nat) @ M2) @ (suc @ N2)))))).
% 2.48/1.49 thf(fact_229_numeral__times__minus__swap, axiom, (! [A:$tType]: ((((comm_ring_1 @ A) @ (type2 @ A)) => (! [W:num,X:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ W)) @ ((uminus_uminus @ A) @ X)) = (((times_times @ A) @ X) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ W)))))))))).
% 2.48/1.49 thf(fact_230_numeral__neq__neg__one, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N2:num]: ((((numeral_numeral @ A) @ N2) != ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 2.48/1.49 thf(fact_231_one__neq__neg__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N2:num]: (((one_one @ A) != ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))))))))).
% 2.48/1.49 thf(fact_232_ring__normalization__rules_I1_J, axiom, (! [A:$tType]: ((((comm_ring_1 @ A) @ (type2 @ A)) => ((uminus_uminus @ A) = ((times_times @ A) @ ((uminus_uminus @ A) @ (one_one @ A)))))))).
% 2.48/1.49 thf(fact_233_square__eq__1__iff, axiom, (! [A:$tType]: ((((ring_11004092258visors @ A) @ (type2 @ A)) => (! [X:A]: ((((((times_times @ A) @ X) @ X) = (one_one @ A)) = ((X = (one_one @ A)) | (X = ((uminus_uminus @ A) @ (one_one @ A))))))))))).
% 2.48/1.49 thf(fact_234_sup__cancel__left1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,A4:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ X) @ A4)) @ (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ B2)) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_235_sup__cancel__left2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,A4:A,B2:A]: (((((sup_sup @ A) @ (((sup_sup @ A) @ ((uminus_uminus @ A) @ X)) @ A4)) @ (((sup_sup @ A) @ X) @ B2)) = (top_top @ A)))))))).
% 2.48/1.49 thf(fact_236_Compl__partition, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (top_top @ (set @ A)))))).
% 2.48/1.49 thf(fact_237_Compl__partition2, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) @ A2) = (top_top @ (set @ A)))))).
% 2.48/1.49 thf(fact_238_mult__Suc, axiom, (! [M2:nat,N2:nat]: (((((times_times @ nat) @ (suc @ M2)) @ N2) = (((plus_plus @ nat) @ N2) @ (((times_times @ nat) @ M2) @ N2)))))).
% 2.48/1.49 thf(fact_239_mult__1s_I4_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [B2:B]: (((((times_times @ B) @ B2) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ one2))) = ((uminus_uminus @ B) @ B2)))))))).
% 2.48/1.49 thf(fact_240_mult__1s_I3_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [B2:B]: (((((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ one2))) @ B2) = ((uminus_uminus @ B) @ B2)))))))).
% 2.48/1.49 thf(fact_241_uminus__numeral__One, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((uminus_uminus @ A) @ ((numeral_numeral @ A) @ one2)) = ((uminus_uminus @ A) @ (one_one @ A))))))).
% 2.48/1.49 thf(fact_242_Suc__nat__number__of__add, axiom, (! [V:num,N2:nat]: (((suc @ (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ V)) @ N2)) = (((plus_plus @ nat) @ ((numeral_numeral @ nat) @ (((plus_plus @ num) @ V) @ one2))) @ N2))))).
% 2.48/1.49 thf(fact_243_Suc__double__not__eq__double, axiom, (! [M2:nat,N2:nat]: (((suc @ (((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ M2)) != (((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ N2))))).
% 2.48/1.49 thf(fact_244_double__not__eq__Suc__double, axiom, (! [M2:nat,N2:nat]: (((((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ M2) != (suc @ (((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2))) @ N2)))))).
% 2.48/1.49 thf(fact_245_add__neg__numeral__special_I6_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [M2:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M2))) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (inc @ M2)))))))))).
% 2.48/1.49 thf(fact_246_Compl__eq__Compl__iff, axiom, (! [A:$tType,A2:(set @ A),B3:(set @ A)]: (((((uminus_uminus @ (set @ A)) @ A2) = ((uminus_uminus @ (set @ A)) @ B3)) = (A2 = B3))))).
% 2.48/1.49 thf(fact_247_Compl__iff, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)) = (~ ((((member @ A) @ C2) @ A2))))))).
% 2.48/1.49 thf(fact_248_ComplI, axiom, (! [A:$tType,C2:A,A2:(set @ A)]: (((~ ((((member @ A) @ C2) @ A2))) => (((member @ A) @ C2) @ ((uminus_uminus @ (set @ A)) @ A2)))))).
% 2.48/1.49 thf(fact_249_add__neg__numeral__special_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [N2:num]: (((((plus_plus @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N2))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (inc @ N2)))))))))).
% 2.48/1.49 thf(fact_250_double__complement, axiom, (! [A:$tType,A2:(set @ A)]: ((((uminus_uminus @ (set @ A)) @ ((uminus_uminus @ (set @ A)) @ A2)) = A2)))).
% 2.48/1.49 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, ((bounded_lattice @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A6:$tType]: (((bounded_lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounded_lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_fun___Lattices_Obounded__lattice__top, axiom, (! [A6:$tType,A7:$tType]: ((((bounded_lattice @ A7) @ (type2 @ A7)) => ((bounded_lattice_top @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_fun___Lattices_Osemilattice__sup, axiom, (! [A6:$tType,A7:$tType]: ((((semilattice_sup @ A7) @ (type2 @ A7)) => ((semilattice_sup @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A6:$tType,A7:$tType]: ((((boolean_algebra @ A7) @ (type2 @ A7)) => ((boolean_algebra @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_fun___Lattices_Olattice, axiom, (! [A6:$tType,A7:$tType]: ((((lattice @ A7) @ (type2 @ A7)) => ((lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_fun___Orderings_Otop, axiom, (! [A6:$tType,A7:$tType]: ((((top @ A7) @ (type2 @ A7)) => ((top @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_fun___Groups_Ouminus, axiom, (! [A6:$tType,A7:$tType]: ((((uminus @ A7) @ (type2 @ A7)) => ((uminus @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 2.48/1.49 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct, axiom, ((semiri456707255roduct @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add, axiom, ((ordere779506340up_add @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add, axiom, ((cancel_semigroup_add @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3, axiom, ((semilattice_sup @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, ((ab_semigroup_mult @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult, axiom, ((comm_monoid_mult @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add, axiom, ((ab_semigroup_add @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, ((comm_semiring_1 @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, ((semigroup_mult @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Num_Osemiring__numeral, axiom, ((semiring_numeral @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Osemigroup__add, axiom, ((semigroup_add @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Rings_Ocomm__semiring, axiom, ((comm_semiring @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Nat_Osemiring__char__0, axiom, ((semiring_char_0 @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Omonoid__mult, axiom, ((monoid_mult @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Lattices_Olattice_4, axiom, ((lattice @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Rings_Osemiring, axiom, ((semiring @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Num_Onumeral, axiom, ((numeral @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 2.48/1.49 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5, axiom, (! [A6:$tType]: (((bounded_lattice_top @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_6, axiom, (! [A6:$tType]: (((semilattice_sup @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_7, axiom, (! [A6:$tType]: (((boolean_algebra @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_Set_Oset___Lattices_Olattice_8, axiom, (! [A6:$tType]: (((lattice @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_Set_Oset___Orderings_Otop_9, axiom, (! [A6:$tType]: (((top @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_Set_Oset___Groups_Ouminus_10, axiom, (! [A6:$tType]: (((uminus @ (set @ A6)) @ (type2 @ (set @ A6)))))).
% 2.48/1.49 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_11, axiom, ((bounded_lattice_top @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_12, axiom, ((semilattice_sup @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_13, axiom, ((boolean_algebra @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(tcon_HOL_Obool___Lattices_Olattice_14, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(tcon_HOL_Obool___Orderings_Otop_15, axiom, ((top @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(tcon_HOL_Obool___Groups_Ouminus_16, axiom, ((uminus @ $o) @ (type2 @ $o))).
% 2.48/1.49 thf(conj_0, conjecture, (((member @ a) @ x) @ ((((image @ nat) @ a) @ ((stream370371455e_snth @ a) @ (((stream865922174rleave @ a) @ s1) @ s2))) @ (top_top @ (set @ nat))))).
% 2.48/1.49 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.H3y4OZI0Un/DTF2DTF9624.p
% 2.48/1.49 ------------------------
% 2.77/1.54 ---- Cleaned THF ---
% 2.77/1.54 thf(ty_t_Stream__Mirabelle__hbrgyiwlrc_Ostream,type,
% 2.77/1.54 stream170649215stream: $tType > $tType ).
% 2.77/1.54
% 2.77/1.54 thf(ty_t_Set_Oset,type,
% 2.77/1.54 set: $tType > $tType ).
% 2.77/1.54
% 2.77/1.54 thf(ty_t_Num_Onum,type,
% 2.77/1.54 num: $tType ).
% 2.77/1.54
% 2.77/1.54 thf(ty_t_Nat_Onat,type,
% 2.77/1.54 nat: $tType ).
% 2.77/1.54
% 2.77/1.54 thf(ty_t_itself,type,
% 2.77/1.54 itself: $tType > $tType ).
% 2.77/1.54
% 2.77/1.54 thf(ty_tf_a,type,
% 2.77/1.54 a: $tType ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.77/1.54 bounded_lattice:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_HOL_Otype,type,
% 2.77/1.54 type:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Oone,type,
% 2.77/1.54 one:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Oidom,type,
% 2.77/1.54 idom:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Oring,type,
% 2.77/1.54 ring:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Num_Onumeral,type,
% 2.77/1.54 numeral:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Oring__1,type,
% 2.77/1.54 ring_1:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Ouminus,type,
% 2.77/1.54 uminus:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Orderings_Otop,type,
% 2.77/1.54 top:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Osemiring,type,
% 2.77/1.54 semiring:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Nat_Oring__char__0,type,
% 2.77/1.54 ring_char_0:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Num_Oneg__numeral,type,
% 2.77/1.54 neg_numeral:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Ogroup__add,type,
% 2.77/1.54 group_add:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Lattices_Olattice,type,
% 2.77/1.54 lattice:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Ocomm__ring__1,type,
% 2.77/1.54 comm_ring_1:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Omonoid__mult,type,
% 2.77/1.54 monoid_mult:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Oab__group__add,type,
% 2.77/1.54 ab_group_add:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Nat_Osemiring__char__0,type,
% 2.77/1.54 semiring_char_0:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Ocomm__semiring,type,
% 2.77/1.54 comm_semiring:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Osemigroup__add,type,
% 2.77/1.54 semigroup_add:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Num_Osemiring__numeral,type,
% 2.77/1.54 semiring_numeral:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Osemigroup__mult,type,
% 2.77/1.54 semigroup_mult:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 2.77/1.54 comm_semiring_1:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Fields_Olinordered__field,type,
% 2.77/1.54 linordered_field:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Oab__semigroup__add,type,
% 2.77/1.54 ab_semigroup_add:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 2.77/1.54 comm_monoid_mult:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 2.77/1.54 ab_semigroup_mult:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 2.77/1.54 boolean_algebra:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Lattices_Osemilattice__sup,type,
% 2.77/1.54 semilattice_sup:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Ocancel__semigroup__add,type,
% 2.77/1.54 cancel_semigroup_add:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Lattices_Obounded__lattice__top,type,
% 2.77/1.54 bounded_lattice_top:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Rings_Oring__1__no__zero__divisors,type,
% 2.77/1.54 ring_11004092258visors:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Groups_Oordered__ab__semigroup__add,type,
% 2.77/1.54 ordere779506340up_add:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_cl_Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,type,
% 2.77/1.54 semiri456707255roduct:
% 2.77/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Groups_Oone__class_Oone,type,
% 2.77/1.54 one_one:
% 2.77/1.54 !>[A: $tType] : A ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Groups_Oplus__class_Oplus,type,
% 2.77/1.54 plus_plus:
% 2.77/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 2.77/1.54 times_times:
% 2.77/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 2.77/1.54 uminus_uminus:
% 2.77/1.54 !>[A: $tType] : ( A > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.77/1.54 sup_sup:
% 2.77/1.54 !>[A: $tType] : ( A > A > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Nat_OSuc,type,
% 2.77/1.54 suc: nat > nat ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Num_Oinc,type,
% 2.77/1.54 inc: num > num ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 2.77/1.54 neg_numeral_dbl:
% 2.77/1.54 !>[A: $tType] : ( A > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Num_Onum_OBit0,type,
% 2.77/1.54 bit0: num > num ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Num_Onum_OOne,type,
% 2.77/1.54 one2: num ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 2.77/1.54 numeral_numeral:
% 2.77/1.54 !>[A: $tType] : ( num > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Orderings_Otop__class_Otop,type,
% 2.77/1.54 top_top:
% 2.77/1.54 !>[A: $tType] : A ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Pure_Otype,type,
% 2.77/1.54 type2:
% 2.77/1.54 !>[A: $tType] : ( itself @ A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Set_OCollect,type,
% 2.77/1.54 collect:
% 2.77/1.54 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Set_Oimage,type,
% 2.77/1.54 image:
% 2.77/1.54 !>[A: $tType,B: $tType] : ( ( A > B ) > ( set @ A ) > ( set @ B ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osinterleave,type,
% 2.77/1.54 stream865922174rleave:
% 2.77/1.54 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( stream170649215stream @ A ) > ( stream170649215stream @ A ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmember,type,
% 2.77/1.54 stream1586597341member:
% 2.77/1.54 !>[A: $tType] : ( A > ( stream170649215stream @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osmerge,type,
% 2.77/1.54 stream857257621smerge:
% 2.77/1.54 !>[A: $tType] : ( ( stream170649215stream @ ( stream170649215stream @ A ) ) > ( stream170649215stream @ A ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Osnth,type,
% 2.77/1.54 stream370371455e_snth:
% 2.77/1.54 !>[A: $tType] : ( ( stream170649215stream @ A ) > nat > A ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_Stream__Mirabelle__hbrgyiwlrc_Ostream_Osset,type,
% 2.77/1.54 stream30925839e_sset:
% 2.77/1.54 !>[A: $tType] : ( ( stream170649215stream @ A ) > ( set @ A ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_c_member,type,
% 2.77/1.54 member:
% 2.77/1.54 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(sy_v_n____,type,
% 2.77/1.54 n: nat ).
% 2.77/1.54
% 2.77/1.54 thf(sy_v_s1,type,
% 2.77/1.54 s1: stream170649215stream @ a ).
% 2.77/1.54
% 2.77/1.54 thf(sy_v_s2,type,
% 2.77/1.54 s2: stream170649215stream @ a ).
% 2.77/1.54
% 2.77/1.54 thf(sy_v_x____,type,
% 2.77/1.54 x: a ).
% 2.77/1.54
% 2.77/1.54 thf(fact_0__092_060open_062x_A_061_As1_A_B_B_An_092_060close_062,axiom,
% 2.77/1.54 ( x
% 2.77/1.54 = ( stream370371455e_snth @ a @ s1 @ n ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_1__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Ax_A_061_As1_A_B_B_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 2.77/1.54 ~ ! [N: nat] :
% 2.77/1.54 ( x
% 2.77/1.54 != ( stream370371455e_snth @ a @ s1 @ N ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062,axiom,
% 2.77/1.54 ( ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ n ) )
% 2.77/1.54 = x ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_3__092_060open_062x_A_092_060in_062_Asset_As1_092_060close_062,axiom,
% 2.77/1.54 member @ a @ x @ ( stream30925839e_sset @ a @ s1 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_4__092_060open_062x_A_092_060in_062_Asset_As1_A_092_060union_062_Asset_As2_092_060close_062,axiom,
% 2.77/1.54 member @ a @ x @ ( sup_sup @ ( set @ a ) @ ( stream30925839e_sset @ a @ s1 ) @ ( stream30925839e_sset @ a @ s2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_5_UNIV__I,axiom,
% 2.77/1.54 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_6_iso__tuple__UNIV__I,axiom,
% 2.77/1.54 ! [A: $tType,X: A] : ( member @ A @ X @ ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_7_top__apply,axiom,
% 2.77/1.54 ! [C: $tType,D: $tType] :
% 2.77/1.54 ( ( top @ C @ ( type2 @ C ) )
% 2.77/1.54 => ( ( top_top @ ( D > C ) )
% 2.77/1.54 = ( ^ [X2: D] : ( top_top @ C ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_8_image__eqI,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,B2: A,F: B > A,X: B,A2: set @ B] :
% 2.77/1.54 ( ( B2
% 2.77/1.54 = ( F @ X ) )
% 2.77/1.54 => ( ( member @ B @ X @ A2 )
% 2.77/1.54 => ( member @ A @ B2 @ ( image @ B @ A @ F @ A2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_9_surjD,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 2.77/1.54 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) )
% 2.77/1.54 => ? [X3: B] :
% 2.77/1.54 ( Y
% 2.77/1.54 = ( F @ X3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_10_surjE,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,F: B > A,Y: A] :
% 2.77/1.54 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) )
% 2.77/1.54 => ~ ! [X3: B] :
% 2.77/1.54 ( Y
% 2.77/1.54 != ( F @ X3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_11_surjI,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType,G: B > A,F: A > B] :
% 2.77/1.54 ( ! [X3: A] :
% 2.77/1.54 ( ( G @ ( F @ X3 ) )
% 2.77/1.54 = X3 )
% 2.77/1.54 => ( ( image @ B @ A @ G @ ( top_top @ ( set @ B ) ) )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_12_rangeI,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,F: B > A,X: B] : ( member @ A @ ( F @ X ) @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_13_surj__def,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType,F: B > A] :
% 2.77/1.54 ( ( ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) )
% 2.77/1.54 = ( ! [Y2: A] :
% 2.77/1.54 ? [X2: B] :
% 2.77/1.54 ( Y2
% 2.77/1.54 = ( F @ X2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_14_range__eqI,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,B2: A,F: B > A,X: B] :
% 2.77/1.54 ( ( B2
% 2.77/1.54 = ( F @ X ) )
% 2.77/1.54 => ( member @ A @ B2 @ ( image @ B @ A @ F @ ( top_top @ ( set @ B ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_15_sset__range,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( stream30925839e_sset @ A )
% 2.77/1.54 = ( ^ [S: stream170649215stream @ A] : ( image @ nat @ A @ ( stream370371455e_snth @ A @ S ) @ ( top_top @ ( set @ nat ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_16_UnCI,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,B3: set @ A,A2: set @ A] :
% 2.77/1.54 ( ( ~ ( member @ A @ C2 @ B3 )
% 2.77/1.54 => ( member @ A @ C2 @ A2 ) )
% 2.77/1.54 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_17_Un__iff,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 2.77/1.54 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 2.77/1.54 = ( ( member @ A @ C2 @ A2 )
% 2.77/1.54 | ( member @ A @ C2 @ B3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_18_UnE,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 2.77/1.54 ( ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 2.77/1.54 => ( ~ ( member @ A @ C2 @ A2 )
% 2.77/1.54 => ( member @ A @ C2 @ B3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_19_UnI1,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,A2: set @ A,B3: set @ A] :
% 2.77/1.54 ( ( member @ A @ C2 @ A2 )
% 2.77/1.54 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_20_UnI2,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,B3: set @ A,A2: set @ A] :
% 2.77/1.54 ( ( member @ A @ C2 @ B3 )
% 2.77/1.54 => ( member @ A @ C2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_21_bex__Un,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A,B3: set @ A,P: A > $o] :
% 2.77/1.54 ( ( ? [X2: A] :
% 2.77/1.54 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 2.77/1.54 & ( P @ X2 ) ) )
% 2.77/1.54 = ( ? [X2: A] :
% 2.77/1.54 ( ( member @ A @ X2 @ A2 )
% 2.77/1.54 & ( P @ X2 ) )
% 2.77/1.54 | ? [X2: A] :
% 2.77/1.54 ( ( member @ A @ X2 @ B3 )
% 2.77/1.54 & ( P @ X2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_22_ball__Un,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A,B3: set @ A,P: A > $o] :
% 2.77/1.54 ( ( ! [X2: A] :
% 2.77/1.54 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 2.77/1.54 => ( P @ X2 ) ) )
% 2.77/1.54 = ( ! [X2: A] :
% 2.77/1.54 ( ( member @ A @ X2 @ A2 )
% 2.77/1.54 => ( P @ X2 ) )
% 2.77/1.54 & ! [X2: A] :
% 2.77/1.54 ( ( member @ A @ X2 @ B3 )
% 2.77/1.54 => ( P @ X2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_23_Un__assoc,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A,B3: set @ A,C3: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) @ C3 )
% 2.77/1.54 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B3 @ C3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_24_Un__absorb,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 2.77/1.54 = A2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_25_Un__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) )
% 2.77/1.54 = ( ^ [A3: set @ A,B4: set @ A] : ( sup_sup @ ( set @ A ) @ B4 @ A3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_26_Un__left__absorb,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B3 ) )
% 2.77/1.54 = ( sup_sup @ ( set @ A ) @ A2 @ B3 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_27_Un__left__commute,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A,B3: set @ A,C3: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B3 @ C3 ) )
% 2.77/1.54 = ( sup_sup @ ( set @ A ) @ B3 @ ( sup_sup @ ( set @ A ) @ A2 @ C3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_28_image__Un,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,B3: set @ B] :
% 2.77/1.54 ( ( image @ B @ A @ F @ ( sup_sup @ ( set @ B ) @ A2 @ B3 ) )
% 2.77/1.54 = ( sup_sup @ ( set @ A ) @ ( image @ B @ A @ F @ A2 ) @ ( image @ B @ A @ F @ B3 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_29_top__set__def,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( top_top @ ( set @ A ) )
% 2.77/1.54 = ( collect @ A @ ( top_top @ ( A > $o ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_30_Un__UNIV__right,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ A2 @ ( top_top @ ( set @ A ) ) )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_31_Un__UNIV__left,axiom,
% 2.77/1.54 ! [A: $tType,B3: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ ( top_top @ ( set @ A ) ) @ B3 )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_32_snth__sset,axiom,
% 2.77/1.54 ! [A: $tType,S2: stream170649215stream @ A,N2: nat] : ( member @ A @ ( stream370371455e_snth @ A @ S2 @ N2 ) @ ( stream30925839e_sset @ A @ S2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_33_rev__image__eqI,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType,X: A,A2: set @ A,B2: B,F: A > B] :
% 2.77/1.54 ( ( member @ A @ X @ A2 )
% 2.77/1.54 => ( ( B2
% 2.77/1.54 = ( F @ X ) )
% 2.77/1.54 => ( member @ B @ B2 @ ( image @ A @ B @ F @ A2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_34_ball__imageD,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P: A > $o] :
% 2.77/1.54 ( ! [X3: A] :
% 2.77/1.54 ( ( member @ A @ X3 @ ( image @ B @ A @ F @ A2 ) )
% 2.77/1.54 => ( P @ X3 ) )
% 2.77/1.54 => ! [X4: B] :
% 2.77/1.54 ( ( member @ B @ X4 @ A2 )
% 2.77/1.54 => ( P @ ( F @ X4 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_35_image__cong,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType,M: set @ A,N3: set @ A,F: A > B,G: A > B] :
% 2.77/1.54 ( ( M = N3 )
% 2.77/1.54 => ( ! [X3: A] :
% 2.77/1.54 ( ( member @ A @ X3 @ N3 )
% 2.77/1.54 => ( ( F @ X3 )
% 2.77/1.54 = ( G @ X3 ) ) )
% 2.77/1.54 => ( ( image @ A @ B @ F @ M )
% 2.77/1.54 = ( image @ A @ B @ G @ N3 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_36_bex__imageD,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,F: B > A,A2: set @ B,P: A > $o] :
% 2.77/1.54 ( ? [X4: A] :
% 2.77/1.54 ( ( member @ A @ X4 @ ( image @ B @ A @ F @ A2 ) )
% 2.77/1.54 & ( P @ X4 ) )
% 2.77/1.54 => ? [X3: B] :
% 2.77/1.54 ( ( member @ B @ X3 @ A2 )
% 2.77/1.54 & ( P @ ( F @ X3 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_37_image__iff,axiom,
% 2.77/1.54 ! [A: $tType,B: $tType,Z: A,F: B > A,A2: set @ B] :
% 2.77/1.54 ( ( member @ A @ Z @ ( image @ B @ A @ F @ A2 ) )
% 2.77/1.54 = ( ? [X2: B] :
% 2.77/1.54 ( ( member @ B @ X2 @ A2 )
% 2.77/1.54 & ( Z
% 2.77/1.54 = ( F @ X2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_38_imageI,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType,X: A,A2: set @ A,F: A > B] :
% 2.77/1.54 ( ( member @ A @ X @ A2 )
% 2.77/1.54 => ( member @ B @ ( F @ X ) @ ( image @ A @ B @ F @ A2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_39_UNIV__witness,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ? [X3: A] : ( member @ A @ X3 @ ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_40_UNIV__eq__I,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ! [X3: A] : ( member @ A @ X3 @ A2 )
% 2.77/1.54 => ( ( top_top @ ( set @ A ) )
% 2.77/1.54 = A2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_41_sup__top__right,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( top_top @ A ) )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_42_sup__top__left,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( bounded_lattice_top @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( top_top @ A ) @ X )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_43_semiring__norm_I169_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [V: num,W: num,Z: A] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( times_times @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 2.77/1.54 = ( times_times @ A @ ( numeral_numeral @ A @ ( times_times @ num @ V @ W ) ) @ Z ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_44_numeral__times__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ M2 ) @ ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_45_mem__Collect__eq,axiom,
% 2.77/1.54 ! [A: $tType,A4: A,P: A > $o] :
% 2.77/1.54 ( ( member @ A @ A4 @ ( collect @ A @ P ) )
% 2.77/1.54 = ( P @ A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_46_Collect__mem__eq,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ( collect @ A
% 2.77/1.54 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 2.77/1.54 = A2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_47_Collect__cong,axiom,
% 2.77/1.54 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.77/1.54 ( ! [X3: A] :
% 2.77/1.54 ( ( P @ X3 )
% 2.77/1.54 = ( Q @ X3 ) )
% 2.77/1.54 => ( ( collect @ A @ P )
% 2.77/1.54 = ( collect @ A @ Q ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_48_ext,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.77/1.54 ( ! [X3: A] :
% 2.77/1.54 ( ( F @ X3 )
% 2.77/1.54 = ( G @ X3 ) )
% 2.77/1.54 => ( F = G ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_49_semiring__norm_I85_J,axiom,
% 2.77/1.54 ! [M2: num] :
% 2.77/1.54 ( ( bit0 @ M2 )
% 2.77/1.54 != one2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_50_semiring__norm_I83_J,axiom,
% 2.77/1.54 ! [N2: num] :
% 2.77/1.54 ( one2
% 2.77/1.54 != ( bit0 @ N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_51_mult__numeral__1,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ one2 ) @ A4 )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_52_mult__numeral__1__right,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( numeral_numeral @ A @ one2 ) )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_53_sup__apply,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.77/1.54 => ( ( sup_sup @ ( A > B ) )
% 2.77/1.54 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_54_sup_Oidem,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( sup_sup @ A @ A4 @ A4 )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_55_semiring__norm_I87_J,axiom,
% 2.77/1.54 ! [M2: num,N2: num] :
% 2.77/1.54 ( ( ( bit0 @ M2 )
% 2.77/1.54 = ( bit0 @ N2 ) )
% 2.77/1.54 = ( M2 = N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_56_num_Oinject_I1_J,axiom,
% 2.77/1.54 ! [X22: num,Y22: num] :
% 2.77/1.54 ( ( ( bit0 @ X22 )
% 2.77/1.54 = ( bit0 @ Y22 ) )
% 2.77/1.54 = ( X22 = Y22 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_57_numeral__eq__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( ( numeral_numeral @ A @ M2 )
% 2.77/1.54 = ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( M2 = N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_58_sup_Oright__idem,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B2 ) @ B2 )
% 2.77/1.54 = ( sup_sup @ A @ A4 @ B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_59_sup__left__idem,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.77/1.54 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_60_sup_Oleft__idem,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( sup_sup @ A @ A4 @ ( sup_sup @ A @ A4 @ B2 ) )
% 2.77/1.54 = ( sup_sup @ A @ A4 @ B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_61_sup__idem,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ X )
% 2.77/1.54 = X ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_62_top1I,axiom,
% 2.77/1.54 ! [A: $tType,X: A] : ( top_top @ ( A > $o ) @ X ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_63_semiring__norm_I13_J,axiom,
% 2.77/1.54 ! [M2: num,N2: num] :
% 2.77/1.54 ( ( times_times @ num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 2.77/1.54 = ( bit0 @ ( bit0 @ ( times_times @ num @ M2 @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_64_semiring__norm_I11_J,axiom,
% 2.77/1.54 ! [M2: num] :
% 2.77/1.54 ( ( times_times @ num @ M2 @ one2 )
% 2.77/1.54 = M2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_65_semiring__norm_I12_J,axiom,
% 2.77/1.54 ! [N2: num] :
% 2.77/1.54 ( ( times_times @ num @ one2 @ N2 )
% 2.77/1.54 = N2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_66_sup__left__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A,Z: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 2.77/1.54 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_67_sup_Oleft__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( sup_sup @ A @ B2 @ ( sup_sup @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_68_sup__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( sup_sup @ A )
% 2.77/1.54 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_69_sup_Ocommute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( sup_sup @ A )
% 2.77/1.54 = ( ^ [A5: A,B5: A] : ( sup_sup @ A @ B5 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_70_sup__assoc,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A,Z: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.77/1.54 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_71_sup_Oassoc,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( sup_sup @ A @ A4 @ ( sup_sup @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_72_sup__fun__def,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ B @ ( type2 @ B ) )
% 2.77/1.54 => ( ( sup_sup @ ( A > B ) )
% 2.77/1.54 = ( ^ [F2: A > B,G2: A > B,X2: A] : ( sup_sup @ B @ ( F2 @ X2 ) @ ( G2 @ X2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_73_inf__sup__aci_I5_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( sup_sup @ A )
% 2.77/1.54 = ( ^ [X2: A,Y2: A] : ( sup_sup @ A @ Y2 @ X2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_74_inf__sup__aci_I6_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A,Z: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ Y ) @ Z )
% 2.77/1.54 = ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_75_inf__sup__aci_I7_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A,Z: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ Y @ Z ) )
% 2.77/1.54 = ( sup_sup @ A @ Y @ ( sup_sup @ A @ X @ Z ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_76_inf__sup__aci_I8_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ X @ Y ) )
% 2.77/1.54 = ( sup_sup @ A @ X @ Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_77_num_Odistinct_I1_J,axiom,
% 2.77/1.54 ! [X22: num] :
% 2.77/1.54 ( one2
% 2.77/1.54 != ( bit0 @ X22 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_78_top__empty__eq,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( top_top @ ( A > $o ) )
% 2.77/1.54 = ( ^ [X2: A] : ( member @ A @ X2 @ ( top_top @ ( set @ A ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_79_snth__sset__smerge,axiom,
% 2.77/1.54 ! [A: $tType,Ss: stream170649215stream @ ( stream170649215stream @ A ),N2: nat,M2: nat] : ( member @ A @ ( stream370371455e_snth @ A @ ( stream370371455e_snth @ ( stream170649215stream @ A ) @ Ss @ N2 ) @ M2 ) @ ( stream30925839e_sset @ A @ ( stream857257621smerge @ A @ Ss ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_80_dbl__simps_I5_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [K: num] :
% 2.77/1.54 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( bit0 @ K ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_81_top__conj_I2_J,axiom,
% 2.77/1.54 ! [A: $tType,P: $o,X: A] :
% 2.77/1.54 ( ( P
% 2.77/1.54 & ( top_top @ ( A > $o ) @ X ) )
% 2.77/1.54 = P ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_82_top__conj_I1_J,axiom,
% 2.77/1.54 ! [A: $tType,X: A,P: $o] :
% 2.77/1.54 ( ( ( top_top @ ( A > $o ) @ X )
% 2.77/1.54 & P )
% 2.77/1.54 = P ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_83_Stream__Mirabelle__hbrgyiwlrc_Osmember__def,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( stream1586597341member @ A )
% 2.77/1.54 = ( ^ [X2: A,S: stream170649215stream @ A] : ( member @ A @ X2 @ ( stream30925839e_sset @ A @ S ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_84_mult__2__right,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Z: A] :
% 2.77/1.54 ( ( times_times @ A @ Z @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) )
% 2.77/1.54 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_85_mult__2,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Z: A] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) @ Z )
% 2.77/1.54 = ( plus_plus @ A @ Z @ Z ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_86_semiring__norm_I6_J,axiom,
% 2.77/1.54 ! [M2: num,N2: num] :
% 2.77/1.54 ( ( plus_plus @ num @ ( bit0 @ M2 ) @ ( bit0 @ N2 ) )
% 2.77/1.54 = ( bit0 @ ( plus_plus @ num @ M2 @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_87_semiring__norm_I2_J,axiom,
% 2.77/1.54 ( ( plus_plus @ num @ one2 @ one2 )
% 2.77/1.54 = ( bit0 @ one2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_88_add__numeral__left,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [V: num,W: num,Z: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 2.77/1.54 = ( plus_plus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) @ Z ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_89_numeral__plus__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( numeral_numeral @ A @ M2 ) @ ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( plus_plus @ num @ M2 @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_90_dbl__def,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( neg_numeral_dbl @ A )
% 2.77/1.54 = ( ^ [X2: A] : ( plus_plus @ A @ X2 @ X2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_91_is__num__normalize_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_92_add__One__commute,axiom,
% 2.77/1.54 ! [N2: num] :
% 2.77/1.54 ( ( plus_plus @ num @ one2 @ N2 )
% 2.77/1.54 = ( plus_plus @ num @ N2 @ one2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_93_left__add__mult__distrib,axiom,
% 2.77/1.54 ! [I: nat,U: nat,J: nat,K: nat] :
% 2.77/1.54 ( ( plus_plus @ nat @ ( times_times @ nat @ I @ U ) @ ( plus_plus @ nat @ ( times_times @ nat @ J @ U ) @ K ) )
% 2.77/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ ( plus_plus @ nat @ I @ J ) @ U ) @ K ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_94_numeral__Bit0,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( numeral_numeral @ A @ ( bit0 @ N2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( numeral_numeral @ A @ N2 ) @ ( numeral_numeral @ A @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_95_distrib__left__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 & ( semiring @ A @ ( type2 @ A ) ) )
% 2.77/1.54 => ! [V: num,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ B2 ) @ ( times_times @ A @ ( numeral_numeral @ A @ V ) @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_96_distrib__right__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 & ( semiring @ A @ ( type2 @ A ) ) )
% 2.77/1.54 => ! [A4: A,B2: A,V: num] :
% 2.77/1.54 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ ( numeral_numeral @ A @ V ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ ( numeral_numeral @ A @ V ) ) @ ( times_times @ A @ B2 @ ( numeral_numeral @ A @ V ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_97_add__left__cancel,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ A4 @ B2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( B2 = C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_98_add__right__cancel,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ B2 @ A4 )
% 2.77/1.54 = ( plus_plus @ A @ C2 @ A4 ) )
% 2.77/1.54 = ( B2 = C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_99_crossproduct__noteq,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A,D2: A] :
% 2.77/1.54 ( ( ( A4 != B2 )
% 2.77/1.54 & ( C2 != D2 ) )
% 2.77/1.54 = ( ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ D2 ) )
% 2.77/1.54 != ( plus_plus @ A @ ( times_times @ A @ A4 @ D2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_100_crossproduct__eq,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiri456707255roduct @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [W: A,Y: A,X: A,Z: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ ( times_times @ A @ W @ Y ) @ ( times_times @ A @ X @ Z ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ W @ Z ) @ ( times_times @ A @ X @ Y ) ) )
% 2.77/1.54 = ( ( W = X )
% 2.77/1.54 | ( Y = Z ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_101_add__right__imp__eq,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ B2 @ A4 )
% 2.77/1.54 = ( plus_plus @ A @ C2 @ A4 ) )
% 2.77/1.54 => ( B2 = C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_102_add__left__imp__eq,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( cancel_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ A4 @ B2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ C2 ) )
% 2.77/1.54 => ( B2 = C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_103_add_Oleft__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_104_add_Ocommute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( plus_plus @ A )
% 2.77/1.54 = ( ^ [A5: A,B5: A] : ( plus_plus @ A @ B5 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_105_add_Oright__cancel,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ B2 @ A4 )
% 2.77/1.54 = ( plus_plus @ A @ C2 @ A4 ) )
% 2.77/1.54 = ( B2 = C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_106_add_Oleft__cancel,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( ( plus_plus @ A @ A4 @ B2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( B2 = C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_107_add_Oassoc,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_108_semiring__normalization__rules_I20_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A,D2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ ( plus_plus @ A @ C2 @ D2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( plus_plus @ A @ A4 @ C2 ) @ ( plus_plus @ A @ B2 @ D2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_109_semiring__normalization__rules_I21_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_110_semiring__normalization__rules_I22_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,C2: A,D2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ A4 @ ( plus_plus @ A @ C2 @ D2 ) )
% 2.77/1.54 = ( plus_plus @ A @ C2 @ ( plus_plus @ A @ A4 @ D2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_111_semiring__normalization__rules_I23_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ ( plus_plus @ A @ A4 @ C2 ) @ B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_112_semiring__normalization__rules_I24_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( plus_plus @ A )
% 2.77/1.54 = ( ^ [A5: A,C4: A] : ( plus_plus @ A @ C4 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_113_semiring__normalization__rules_I25_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,C2: A,D2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ A4 @ ( plus_plus @ A @ C2 @ D2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( plus_plus @ A @ A4 @ C2 ) @ D2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_114_add__mono__thms__linordered__semiring_I4_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ordere779506340up_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [I: A,J: A,K: A,L: A] :
% 2.77/1.54 ( ( ( I = J )
% 2.77/1.54 & ( K = L ) )
% 2.77/1.54 => ( ( plus_plus @ A @ I @ K )
% 2.77/1.54 = ( plus_plus @ A @ J @ L ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_115_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_semigroup_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_116_mult_Oleft__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ B2 @ ( times_times @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_117_mult_Ocommute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( times_times @ A )
% 2.77/1.54 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_118_mult_Oassoc,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semigroup_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_119_semiring__normalization__rules_I7_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( times_times @ A )
% 2.77/1.54 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_120_semiring__normalization__rules_I13_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 2.77/1.54 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ ( times_times @ A @ Ly @ Ry ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_121_semiring__normalization__rules_I14_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 2.77/1.54 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ ( times_times @ A @ Rx @ Ry ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_122_semiring__normalization__rules_I15_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 2.77/1.54 = ( times_times @ A @ Rx @ ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Ry ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_123_semiring__normalization__rules_I16_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Ly: A,Rx: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 2.77/1.54 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ly ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_124_semiring__normalization__rules_I17_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Ly: A,Rx: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 2.77/1.54 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ Rx ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_125_semiring__normalization__rules_I18_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Rx: A,Ry: A] :
% 2.77/1.54 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 2.77/1.54 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ry ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_126_semiring__normalization__rules_I19_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Lx: A,Rx: A,Ry: A] :
% 2.77/1.54 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 2.77/1.54 = ( times_times @ A @ Rx @ ( times_times @ A @ Lx @ Ry ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_127_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_128_semiring__normalization__rules_I34_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A,Z: A] :
% 2.77/1.54 ( ( times_times @ A @ X @ ( plus_plus @ A @ Y @ Z ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ X @ Y ) @ ( times_times @ A @ X @ Z ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_129_semiring__normalization__rules_I8_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_130_semiring__normalization__rules_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,M2: A,B2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( times_times @ A @ A4 @ M2 ) @ ( times_times @ A @ B2 @ M2 ) )
% 2.77/1.54 = ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ M2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_131_add__mult__distrib,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat,K: nat] :
% 2.77/1.54 ( ( times_times @ nat @ ( plus_plus @ nat @ M2 @ N2 ) @ K )
% 2.77/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ M2 @ K ) @ ( times_times @ nat @ N2 @ K ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_132_add__mult__distrib2,axiom,
% 2.77/1.54 ! [K: nat,M2: nat,N2: nat] :
% 2.77/1.54 ( ( times_times @ nat @ K @ ( plus_plus @ nat @ M2 @ N2 ) )
% 2.77/1.54 = ( plus_plus @ nat @ ( times_times @ nat @ K @ M2 ) @ ( times_times @ nat @ K @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_133_ring__class_Oring__distribs_I2_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_134_ring__class_Oring__distribs_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ B2 ) @ ( times_times @ A @ A4 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_135_linordered__field__class_Osign__simps_I36_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ B2 ) @ ( times_times @ A @ A4 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_136_linordered__field__class_Osign__simps_I28_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ B2 @ ( plus_plus @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_137_linordered__field__class_Osign__simps_I27_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( plus_plus @ A )
% 2.77/1.54 = ( ^ [A5: A,B5: A] : ( plus_plus @ A @ B5 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_138_linordered__field__class_Osign__simps_I26_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_139_linordered__field__class_Osign__simps_I25_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [B2: A,A4: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ B2 @ ( times_times @ A @ A4 @ C2 ) )
% 2.77/1.54 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_140_linordered__field__class_Osign__simps_I24_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( times_times @ A )
% 2.77/1.54 = ( ^ [A5: A,B5: A] : ( times_times @ A @ B5 @ A5 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_141_linordered__field__class_Osign__simps_I23_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( times_times @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( times_times @ A @ A4 @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_142_nat__add__right__cancel,axiom,
% 2.77/1.54 ! [M2: nat,K: nat,N2: nat] :
% 2.77/1.54 ( ( ( plus_plus @ nat @ M2 @ K )
% 2.77/1.54 = ( plus_plus @ nat @ N2 @ K ) )
% 2.77/1.54 = ( M2 = N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_143_nat__add__left__cancel,axiom,
% 2.77/1.54 ! [K: nat,M2: nat,N2: nat] :
% 2.77/1.54 ( ( ( plus_plus @ nat @ K @ M2 )
% 2.77/1.54 = ( plus_plus @ nat @ K @ N2 ) )
% 2.77/1.54 = ( M2 = N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_144_combine__common__factor,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,E: A,B2: A,C2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( times_times @ A @ A4 @ E ) @ ( plus_plus @ A @ ( times_times @ A @ B2 @ E ) @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ E ) @ C2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_145_distrib__right,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_146_distrib__left,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( plus_plus @ A @ B2 @ C2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ B2 ) @ ( times_times @ A @ A4 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_147_comm__semiring__class_Odistrib,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_148_linordered__field__class_Osign__simps_I35_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( linordered_field @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A,C2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( plus_plus @ A @ A4 @ B2 ) @ C2 )
% 2.77/1.54 = ( plus_plus @ A @ ( times_times @ A @ A4 @ C2 ) @ ( times_times @ A @ B2 @ C2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_149_dbl__simps_I3_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_150_numeral__plus__one,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( numeral_numeral @ A @ N2 ) @ ( one_one @ A ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( plus_plus @ num @ N2 @ one2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_151_one__plus__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( plus_plus @ num @ one2 @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_152_one__add__one,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_153_nat__1__eq__mult__iff,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( ( one_one @ nat )
% 2.77/1.54 = ( times_times @ nat @ M2 @ N2 ) )
% 2.77/1.54 = ( ( M2
% 2.77/1.54 = ( one_one @ nat ) )
% 2.77/1.54 & ( N2
% 2.77/1.54 = ( one_one @ nat ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_154_nat__mult__eq__1__iff,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( ( times_times @ nat @ M2 @ N2 )
% 2.77/1.54 = ( one_one @ nat ) )
% 2.77/1.54 = ( ( M2
% 2.77/1.54 = ( one_one @ nat ) )
% 2.77/1.54 & ( N2
% 2.77/1.54 = ( one_one @ nat ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_155_mult_Oright__neutral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( one_one @ A ) )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_156_mult_Oleft__neutral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ ( one_one @ A ) @ A4 )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_157_one__eq__numeral__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( ( one_one @ A )
% 2.77/1.54 = ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( one2 = N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_158_numeral__eq__one__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( ( numeral_numeral @ A @ N2 )
% 2.77/1.54 = ( one_one @ A ) )
% 2.77/1.54 = ( N2 = one2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_159_nat__mult__1__right,axiom,
% 2.77/1.54 ! [N2: nat] :
% 2.77/1.54 ( ( times_times @ nat @ N2 @ ( one_one @ nat ) )
% 2.77/1.54 = N2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_160_nat__mult__1,axiom,
% 2.77/1.54 ! [N2: nat] :
% 2.77/1.54 ( ( times_times @ nat @ ( one_one @ nat ) @ N2 )
% 2.77/1.54 = N2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_161_mult_Ocomm__neutral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( one_one @ A ) )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_162_comm__monoid__mult__class_Omult__1,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ ( one_one @ A ) @ A4 )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_163_semiring__normalization__rules_I11_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ ( one_one @ A ) @ A4 )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_164_semiring__normalization__rules_I12_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( one_one @ A ) )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_165_one__reorient,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( one @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( ( one_one @ A )
% 2.77/1.54 = X )
% 2.77/1.54 = ( X
% 2.77/1.54 = ( one_one @ A ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_166_one__plus__numeral__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ X ) )
% 2.77/1.54 = ( plus_plus @ A @ ( numeral_numeral @ A @ X ) @ ( one_one @ A ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_167_semiring__normalization__rules_I2_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,M2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( times_times @ A @ A4 @ M2 ) @ M2 )
% 2.77/1.54 = ( times_times @ A @ ( plus_plus @ A @ A4 @ ( one_one @ A ) ) @ M2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_168_semiring__normalization__rules_I3_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: A,A4: A] :
% 2.77/1.54 ( ( plus_plus @ A @ M2 @ ( times_times @ A @ A4 @ M2 ) )
% 2.77/1.54 = ( times_times @ A @ ( plus_plus @ A @ A4 @ ( one_one @ A ) ) @ M2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_169_semiring__normalization__rules_I4_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ M2 @ M2 )
% 2.77/1.54 = ( times_times @ A @ ( plus_plus @ A @ ( one_one @ A ) @ ( one_one @ A ) ) @ M2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_170_numeral__One,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( numeral_numeral @ A @ one2 )
% 2.77/1.54 = ( one_one @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_171_numerals_I1_J,axiom,
% 2.77/1.54 ( ( numeral_numeral @ nat @ one2 )
% 2.77/1.54 = ( one_one @ nat ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_172_nat__1__add__1,axiom,
% 2.77/1.54 ( ( plus_plus @ nat @ ( one_one @ nat ) @ ( one_one @ nat ) )
% 2.77/1.54 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_173_dbl__simps_I4_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_174_add__neg__numeral__special_I9_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_175_add__2__eq__Suc_H,axiom,
% 2.77/1.54 ! [N2: nat] :
% 2.77/1.54 ( ( plus_plus @ nat @ N2 @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) )
% 2.77/1.54 = ( suc @ ( suc @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_176_neg__equal__iff__equal,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( ( uminus_uminus @ A @ A4 )
% 2.77/1.54 = ( uminus_uminus @ A @ B2 ) )
% 2.77/1.54 = ( A4 = B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_177_add_Oinverse__inverse,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A] :
% 2.77/1.54 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A4 ) )
% 2.77/1.54 = A4 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_178_compl__eq__compl__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A] :
% 2.77/1.54 ( ( ( uminus_uminus @ A @ X )
% 2.77/1.54 = ( uminus_uminus @ A @ Y ) )
% 2.77/1.54 = ( X = Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_179_double__compl,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 2.77/1.54 = X ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_180_uminus__apply,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType] :
% 2.77/1.54 ( ( uminus @ B @ ( type2 @ B ) )
% 2.77/1.54 => ( ( uminus_uminus @ ( A > B ) )
% 2.77/1.54 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_181_old_Onat_Oinject,axiom,
% 2.77/1.54 ! [Nat: nat,Nat2: nat] :
% 2.77/1.54 ( ( ( suc @ Nat )
% 2.77/1.54 = ( suc @ Nat2 ) )
% 2.77/1.54 = ( Nat = Nat2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_182_nat_Oinject,axiom,
% 2.77/1.54 ! [X22: nat,Y22: nat] :
% 2.77/1.54 ( ( ( suc @ X22 )
% 2.77/1.54 = ( suc @ Y22 ) )
% 2.77/1.54 = ( X22 = Y22 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_183_add__minus__cancel,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ A4 @ ( plus_plus @ A @ ( uminus_uminus @ A @ A4 ) @ B2 ) )
% 2.77/1.54 = B2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_184_minus__add__cancel,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( uminus_uminus @ A @ A4 ) @ ( plus_plus @ A @ A4 @ B2 ) )
% 2.77/1.54 = B2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_185_minus__add__distrib,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ab_group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A4 @ B2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( uminus_uminus @ A @ A4 ) @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_186_neg__numeral__eq__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 2.77/1.54 = ( M2 = N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_187_mult__minus__left,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ A4 ) @ B2 )
% 2.77/1.54 = ( uminus_uminus @ A @ ( times_times @ A @ A4 @ B2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_188_minus__mult__minus,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ A4 ) @ ( uminus_uminus @ A @ B2 ) )
% 2.77/1.54 = ( times_times @ A @ A4 @ B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_189_mult__minus__right,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( times_times @ A @ A4 @ ( uminus_uminus @ A @ B2 ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( times_times @ A @ A4 @ B2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_190_add__Suc__right,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( plus_plus @ nat @ M2 @ ( suc @ N2 ) )
% 2.77/1.54 = ( suc @ ( plus_plus @ nat @ M2 @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_191_add__neg__numeral__simps_I3_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( plus_plus @ A @ ( numeral_numeral @ A @ M2 ) @ ( numeral_numeral @ A @ N2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_192_mult__minus1,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Z: A] :
% 2.77/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ Z )
% 2.77/1.54 = ( uminus_uminus @ A @ Z ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_193_mult__minus1__right,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [Z: A] :
% 2.77/1.54 ( ( times_times @ A @ Z @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ Z ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_194_compl__sup__top,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ X )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_195_sup__compl__top,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( uminus_uminus @ A @ X ) )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_196_sup__compl__top__left1,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ ( sup_sup @ A @ X @ Y ) )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_197_sup__compl__top__left2,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,Y: A] :
% 2.77/1.54 ( ( sup_sup @ A @ X @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ Y ) )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_198_mult__Suc__right,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( times_times @ nat @ M2 @ ( suc @ N2 ) )
% 2.77/1.54 = ( plus_plus @ nat @ M2 @ ( times_times @ nat @ M2 @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_199_dbl__simps_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [K: num] :
% 2.77/1.54 ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_200_numeral__eq__neg__one__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.77/1.54 = ( N2 = one2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_201_neg__one__eq__numeral__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( ( uminus_uminus @ A @ ( one_one @ A ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 2.77/1.54 = ( N2 = one2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_202_semiring__norm_I168_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [V: num,W: num,Y: A] :
% 2.77/1.54 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ V ) ) @ ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) @ Y ) )
% 2.77/1.54 = ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( plus_plus @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_203_Suc__numeral,axiom,
% 2.77/1.54 ! [N2: num] :
% 2.77/1.54 ( ( suc @ ( numeral_numeral @ nat @ N2 ) )
% 2.77/1.54 = ( numeral_numeral @ nat @ ( plus_plus @ num @ N2 @ one2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_204_semiring__norm_I172_J,axiom,
% 2.77/1.54 ! [B: $tType] :
% 2.77/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 2.77/1.54 => ! [V: num,W: num,Y: B] :
% 2.77/1.54 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 2.77/1.54 = ( times_times @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) @ Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_205_semiring__norm_I171_J,axiom,
% 2.77/1.54 ! [B: $tType] :
% 2.77/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 2.77/1.54 => ! [V: num,W: num,Y: B] :
% 2.77/1.54 ( ( times_times @ B @ ( numeral_numeral @ B @ V ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 2.77/1.54 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_206_semiring__norm_I170_J,axiom,
% 2.77/1.54 ! [B: $tType] :
% 2.77/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 2.77/1.54 => ! [V: num,W: num,Y: B] :
% 2.77/1.54 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( numeral_numeral @ B @ W ) @ Y ) )
% 2.77/1.54 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_207_mult__neg__numeral__simps_I3_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ M2 ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_208_mult__neg__numeral__simps_I2_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( numeral_numeral @ A @ N2 ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_209_mult__neg__numeral__simps_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 2.77/1.54 = ( numeral_numeral @ A @ ( times_times @ num @ M2 @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_210_add__2__eq__Suc,axiom,
% 2.77/1.54 ! [N2: nat] :
% 2.77/1.54 ( ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N2 )
% 2.77/1.54 = ( suc @ ( suc @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_211_Suc__1,axiom,
% 2.77/1.54 ( ( suc @ ( one_one @ nat ) )
% 2.77/1.54 = ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_212_Suc__eq__plus1,axiom,
% 2.77/1.54 ( suc
% 2.77/1.54 = ( ^ [N4: nat] : ( plus_plus @ nat @ N4 @ ( one_one @ nat ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_213_Suc__eq__plus1__left,axiom,
% 2.77/1.54 ( suc
% 2.77/1.54 = ( plus_plus @ nat @ ( one_one @ nat ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_214_one__neq__neg__one,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( one_one @ A )
% 2.77/1.54 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_215_add_Oinverse__distrib__swap,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A4 @ B2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_216_minus__equation__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( ( uminus_uminus @ A @ A4 )
% 2.77/1.54 = B2 )
% 2.77/1.54 = ( ( uminus_uminus @ A @ B2 )
% 2.77/1.54 = A4 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_217_equation__minus__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( A4
% 2.77/1.54 = ( uminus_uminus @ A @ B2 ) )
% 2.77/1.54 = ( B2
% 2.77/1.54 = ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_218_numeral__neq__neg__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( numeral_numeral @ A @ M2 )
% 2.77/1.54 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_219_neg__numeral__neq__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num,N2: num] :
% 2.77/1.54 ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) )
% 2.77/1.54 != ( numeral_numeral @ A @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_220_is__num__normalize_I8_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( uminus_uminus @ A @ ( plus_plus @ A @ A4 @ B2 ) )
% 2.77/1.54 = ( plus_plus @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A4 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_221_fun__Compl__def,axiom,
% 2.77/1.54 ! [B: $tType,A: $tType] :
% 2.77/1.54 ( ( uminus @ B @ ( type2 @ B ) )
% 2.77/1.54 => ( ( uminus_uminus @ ( A > B ) )
% 2.77/1.54 = ( ^ [A3: A > B,X2: A] : ( uminus_uminus @ B @ ( A3 @ X2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_222_n__not__Suc__n,axiom,
% 2.77/1.54 ! [N2: nat] :
% 2.77/1.54 ( N2
% 2.77/1.54 != ( suc @ N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_223_Suc__inject,axiom,
% 2.77/1.54 ! [X: nat,Y: nat] :
% 2.77/1.54 ( ( ( suc @ X )
% 2.77/1.54 = ( suc @ Y ) )
% 2.77/1.54 => ( X = Y ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_224_Suc__mult__cancel1,axiom,
% 2.77/1.54 ! [K: nat,M2: nat,N2: nat] :
% 2.77/1.54 ( ( ( times_times @ nat @ ( suc @ K ) @ M2 )
% 2.77/1.54 = ( times_times @ nat @ ( suc @ K ) @ N2 ) )
% 2.77/1.54 = ( M2 = N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_225_square__eq__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( idom @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( ( times_times @ A @ A4 @ A4 )
% 2.77/1.54 = ( times_times @ A @ B2 @ B2 ) )
% 2.77/1.54 = ( ( A4 = B2 )
% 2.77/1.54 | ( A4
% 2.77/1.54 = ( uminus_uminus @ A @ B2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_226_minus__mult__commute,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [A4: A,B2: A] :
% 2.77/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ A4 ) @ B2 )
% 2.77/1.54 = ( times_times @ A @ A4 @ ( uminus_uminus @ A @ B2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_227_add__Suc,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N2 )
% 2.77/1.54 = ( suc @ ( plus_plus @ nat @ M2 @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_228_add__Suc__shift,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( plus_plus @ nat @ ( suc @ M2 ) @ N2 )
% 2.77/1.54 = ( plus_plus @ nat @ M2 @ ( suc @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_229_numeral__times__minus__swap,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [W: num,X: A] :
% 2.77/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ W ) @ ( uminus_uminus @ A @ X ) )
% 2.77/1.54 = ( times_times @ A @ X @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_230_numeral__neq__neg__one,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( numeral_numeral @ A @ N2 )
% 2.77/1.54 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_231_one__neq__neg__numeral,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( one_one @ A )
% 2.77/1.54 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_232_ring__normalization__rules_I1_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( uminus_uminus @ A )
% 2.77/1.54 = ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_233_square__eq__1__iff,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( ring_11004092258visors @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A] :
% 2.77/1.54 ( ( ( times_times @ A @ X @ X )
% 2.77/1.54 = ( one_one @ A ) )
% 2.77/1.54 = ( ( X
% 2.77/1.54 = ( one_one @ A ) )
% 2.77/1.54 | ( X
% 2.77/1.54 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_234_sup__cancel__left1,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,A4: A,B2: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ X @ A4 ) @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ B2 ) )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_235_sup__cancel__left2,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [X: A,A4: A,B2: A] :
% 2.77/1.54 ( ( sup_sup @ A @ ( sup_sup @ A @ ( uminus_uminus @ A @ X ) @ A4 ) @ ( sup_sup @ A @ X @ B2 ) )
% 2.77/1.54 = ( top_top @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_236_Compl__partition,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ A2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_237_Compl__partition2,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ( sup_sup @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) @ A2 )
% 2.77/1.54 = ( top_top @ ( set @ A ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_238_mult__Suc,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( times_times @ nat @ ( suc @ M2 ) @ N2 )
% 2.77/1.54 = ( plus_plus @ nat @ N2 @ ( times_times @ nat @ M2 @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_239_mult__1s_I4_J,axiom,
% 2.77/1.54 ! [B: $tType] :
% 2.77/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 2.77/1.54 => ! [B2: B] :
% 2.77/1.54 ( ( times_times @ B @ B2 @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) )
% 2.77/1.54 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_240_mult__1s_I3_J,axiom,
% 2.77/1.54 ! [B: $tType] :
% 2.77/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 2.77/1.54 => ! [B2: B] :
% 2.77/1.54 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) @ B2 )
% 2.77/1.54 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_241_uminus__numeral__One,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ one2 ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_242_Suc__nat__number__of__add,axiom,
% 2.77/1.54 ! [V: num,N2: nat] :
% 2.77/1.54 ( ( suc @ ( plus_plus @ nat @ ( numeral_numeral @ nat @ V ) @ N2 ) )
% 2.77/1.54 = ( plus_plus @ nat @ ( numeral_numeral @ nat @ ( plus_plus @ num @ V @ one2 ) ) @ N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_243_Suc__double__not__eq__double,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ M2 ) )
% 2.77/1.54 != ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N2 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_244_double__not__eq__Suc__double,axiom,
% 2.77/1.54 ! [M2: nat,N2: nat] :
% 2.77/1.54 ( ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ M2 )
% 2.77/1.54 != ( suc @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) @ N2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_245_add__neg__numeral__special_I6_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [M2: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M2 ) ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ M2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_246_Compl__eq__Compl__iff,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A,B3: set @ A] :
% 2.77/1.54 ( ( ( uminus_uminus @ ( set @ A ) @ A2 )
% 2.77/1.54 = ( uminus_uminus @ ( set @ A ) @ B3 ) )
% 2.77/1.54 = ( A2 = B3 ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_247_Compl__iff,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,A2: set @ A] :
% 2.77/1.54 ( ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.77/1.54 = ( ~ ( member @ A @ C2 @ A2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_248_ComplI,axiom,
% 2.77/1.54 ! [A: $tType,C2: A,A2: set @ A] :
% 2.77/1.54 ( ~ ( member @ A @ C2 @ A2 )
% 2.77/1.54 => ( member @ A @ C2 @ ( uminus_uminus @ ( set @ A ) @ A2 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_249_add__neg__numeral__special_I5_J,axiom,
% 2.77/1.54 ! [A: $tType] :
% 2.77/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 2.77/1.54 => ! [N2: num] :
% 2.77/1.54 ( ( plus_plus @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N2 ) ) )
% 2.77/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( inc @ N2 ) ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(fact_250_double__complement,axiom,
% 2.77/1.54 ! [A: $tType,A2: set @ A] :
% 2.77/1.54 ( ( uminus_uminus @ ( set @ A ) @ ( uminus_uminus @ ( set @ A ) @ A2 ) )
% 2.77/1.54 = A2 ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.77/1.54 bounded_lattice @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.77/1.54 ! [A6: $tType] : ( bounded_lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( bounded_lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Lattices_Obounded__lattice__top,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( bounded_lattice @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( bounded_lattice_top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Lattices_Osemilattice__sup,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( semilattice_sup @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( semilattice_sup @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( boolean_algebra @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( boolean_algebra @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Lattices_Olattice,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Orderings_Otop,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( top @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( top @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_fun___Groups_Ouminus,axiom,
% 2.77/1.54 ! [A6: $tType,A7: $tType] :
% 2.77/1.54 ( ( uminus @ A7 @ ( type2 @ A7 ) )
% 2.77/1.54 => ( uminus @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Semiring__Normalization_Ocomm__semiring__1__cancel__crossproduct,axiom,
% 2.77/1.54 semiri456707255roduct @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Oordered__ab__semigroup__add,axiom,
% 2.77/1.54 ordere779506340up_add @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Ocancel__semigroup__add,axiom,
% 2.77/1.54 cancel_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Lattices_Osemilattice__sup_3,axiom,
% 2.77/1.54 semilattice_sup @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 2.77/1.54 ab_semigroup_mult @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 2.77/1.54 comm_monoid_mult @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__add,axiom,
% 2.77/1.54 ab_semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 2.77/1.54 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 2.77/1.54 semigroup_mult @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Num_Osemiring__numeral,axiom,
% 2.77/1.54 semiring_numeral @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__add,axiom,
% 2.77/1.54 semigroup_add @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Rings_Ocomm__semiring,axiom,
% 2.77/1.54 comm_semiring @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 2.77/1.54 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 2.77/1.54 monoid_mult @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Lattices_Olattice_4,axiom,
% 2.77/1.54 lattice @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Rings_Osemiring,axiom,
% 2.77/1.54 semiring @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 2.77/1.54 numeral @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 2.77/1.54 one @ nat @ ( type2 @ nat ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Lattices_Obounded__lattice__top_5,axiom,
% 2.77/1.54 ! [A6: $tType] : ( bounded_lattice_top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Lattices_Osemilattice__sup_6,axiom,
% 2.77/1.54 ! [A6: $tType] : ( semilattice_sup @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Lattices_Oboolean__algebra_7,axiom,
% 2.77/1.54 ! [A6: $tType] : ( boolean_algebra @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Lattices_Olattice_8,axiom,
% 2.77/1.54 ! [A6: $tType] : ( lattice @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Orderings_Otop_9,axiom,
% 2.77/1.54 ! [A6: $tType] : ( top @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_Set_Oset___Groups_Ouminus_10,axiom,
% 2.77/1.54 ! [A6: $tType] : ( uminus @ ( set @ A6 ) @ ( type2 @ ( set @ A6 ) ) ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Lattices_Obounded__lattice__top_11,axiom,
% 2.77/1.54 bounded_lattice_top @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__sup_12,axiom,
% 2.77/1.54 semilattice_sup @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_13,axiom,
% 2.77/1.54 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Lattices_Olattice_14,axiom,
% 2.77/1.54 lattice @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Orderings_Otop_15,axiom,
% 2.77/1.54 top @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(tcon_HOL_Obool___Groups_Ouminus_16,axiom,
% 2.77/1.54 uminus @ $o @ ( type2 @ $o ) ).
% 2.77/1.54
% 2.77/1.54 thf(conj_0,conjecture,
% 2.77/1.54 member @ a @ x @ ( image @ nat @ a @ ( stream370371455e_snth @ a @ ( stream865922174rleave @ a @ s1 @ s2 ) ) @ ( top_top @ ( set @ nat ) ) ) ).
% 2.77/1.54 ------------------------
% 2.77/1.57 % (9927)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/27Mi)
% 2.77/1.57 % (9929)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/2Mi)
% 2.77/1.57 % (9929)Instruction limit reached!
% 2.77/1.57 % (9929)------------------------------
% 2.77/1.57 % (9929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.57 % (9929)Termination reason: Unknown
% 2.77/1.57 % (9929)Termination phase: shuffling
% 2.77/1.57
% 2.77/1.57 % (9929)Memory used [KB]: 1279
% 2.77/1.57 % (9929)Time elapsed: 0.002 s
% 2.77/1.57 % (9929)Instructions burned: 3 (million)
% 2.77/1.57 % (9929)------------------------------
% 2.77/1.57 % (9929)------------------------------
% 2.77/1.57 % (9928)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/2Mi)
% 2.77/1.57 % (9928)Instruction limit reached!
% 2.77/1.57 % (9928)------------------------------
% 2.77/1.57 % (9928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.57 % (9928)Termination reason: Unknown
% 2.77/1.57 % (9928)Termination phase: shuffling
% 2.77/1.57
% 2.77/1.57 % (9928)Memory used [KB]: 1279
% 2.77/1.57 % (9928)Time elapsed: 0.003 s
% 2.77/1.57 % (9928)Instructions burned: 3 (million)
% 2.77/1.57 % (9928)------------------------------
% 2.77/1.57 % (9928)------------------------------
% 2.77/1.58 % (9926)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/4Mi)
% 2.77/1.58 % (9926)Instruction limit reached!
% 2.77/1.58 % (9926)------------------------------
% 2.77/1.58 % (9926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.58 % (9926)Termination reason: Unknown
% 2.77/1.58 % (9926)Termination phase: shuffling
% 2.77/1.58
% 2.77/1.58 % (9926)Memory used [KB]: 1279
% 2.77/1.58 % (9926)Time elapsed: 0.003 s
% 2.77/1.58 % (9926)Instructions burned: 4 (million)
% 2.77/1.58 % (9926)------------------------------
% 2.77/1.58 % (9926)------------------------------
% 2.77/1.58 % (9925)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/183Mi)
% 2.77/1.58 % (9930)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/275Mi)
% 2.77/1.58 % (9931)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/18Mi)
% 2.77/1.58 % (9927)Instruction limit reached!
% 2.77/1.58 % (9927)------------------------------
% 2.77/1.58 % (9927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.58 % (9927)Termination reason: Unknown
% 2.77/1.58 % (9927)Termination phase: Preprocessing 1
% 2.77/1.58
% 2.77/1.58 % (9927)Memory used [KB]: 1535
% 2.77/1.58 % (9927)Time elapsed: 0.010 s
% 2.77/1.58 % (9927)Instructions burned: 28 (million)
% 2.77/1.58 % (9927)------------------------------
% 2.77/1.58 % (9927)------------------------------
% 2.77/1.58 % (9932)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/3Mi)
% 2.77/1.58 % (9932)Instruction limit reached!
% 2.77/1.58 % (9932)------------------------------
% 2.77/1.58 % (9932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.58 % (9932)Termination reason: Unknown
% 2.77/1.58 % (9932)Termination phase: shuffling
% 2.77/1.58
% 2.77/1.58 % (9932)Memory used [KB]: 1279
% 2.77/1.58 % (9932)Time elapsed: 0.003 s
% 2.77/1.58 % (9932)Instructions burned: 4 (million)
% 2.77/1.58 % (9932)------------------------------
% 2.77/1.58 % (9932)------------------------------
% 2.77/1.59 % (9933)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/37Mi)
% 2.77/1.59 % (9935)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/3Mi)
% 2.77/1.59 % (9935)Instruction limit reached!
% 2.77/1.59 % (9935)------------------------------
% 2.77/1.59 % (9935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.59 % (9935)Termination reason: Unknown
% 2.77/1.59 % (9935)Termination phase: shuffling
% 2.77/1.59
% 2.77/1.59 % (9935)Memory used [KB]: 1279
% 2.77/1.59 % (9935)Time elapsed: 0.002 s
% 2.77/1.59 % (9935)Instructions burned: 3 (million)
% 2.77/1.59 % (9935)------------------------------
% 2.77/1.59 % (9935)------------------------------
% 2.77/1.59 % (9931)Instruction limit reached!
% 2.77/1.59 % (9931)------------------------------
% 2.77/1.59 % (9931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.77/1.59 % (9931)Termination reason: Unknown
% 2.77/1.59 % (9931)Termination phase: Property scanning
% 2.77/1.59
% 2.77/1.59 % (9931)Memory used [KB]: 1535
% 2.77/1.59 % (9931)Time elapsed: 0.014 s
% 2.77/1.59 % (9931)Instructions burned: 19 (million)
% 2.77/1.59 % (9931)------------------------------
% 2.77/1.59 % (9931)------------------------------
% 2.77/1.59 % (9936)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/1041Mi)
% 2.77/1.59 % (9934)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/15Mi)
% 2.82/1.60 % (9933)Instruction limit reached!
% 2.82/1.60 % (9933)------------------------------
% 2.82/1.60 % (9933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.60 % (9933)Termination reason: Unknown
% 2.82/1.60 % (9933)Termination phase: Property scanning
% 2.82/1.60
% 2.82/1.60 % (9933)Memory used [KB]: 1791
% 2.82/1.60 % (9933)Time elapsed: 0.013 s
% 2.82/1.60 % (9933)Instructions burned: 39 (million)
% 2.82/1.60 % (9933)------------------------------
% 2.82/1.60 % (9933)------------------------------
% 2.82/1.60 % (9937)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/7Mi)
% 2.82/1.60 % (9934)Instruction limit reached!
% 2.82/1.60 % (9934)------------------------------
% 2.82/1.60 % (9934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.60 % (9934)Termination reason: Unknown
% 2.82/1.60 % (9934)Termination phase: shuffling
% 2.82/1.60
% 2.82/1.60 % (9934)Memory used [KB]: 1535
% 2.82/1.60 % (9934)Time elapsed: 0.008 s
% 2.82/1.60 % (9934)Instructions burned: 15 (million)
% 2.82/1.60 % (9934)------------------------------
% 2.82/1.60 % (9934)------------------------------
% 2.82/1.60 % (9937)Instruction limit reached!
% 2.82/1.60 % (9937)------------------------------
% 2.82/1.60 % (9937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.60 % (9937)Termination reason: Unknown
% 2.82/1.60 % (9937)Termination phase: shuffling
% 2.82/1.60
% 2.82/1.60 % (9937)Memory used [KB]: 1407
% 2.82/1.60 % (9937)Time elapsed: 0.004 s
% 2.82/1.60 % (9937)Instructions burned: 8 (million)
% 2.82/1.60 % (9937)------------------------------
% 2.82/1.60 % (9937)------------------------------
% 2.82/1.61 % (9938)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/16Mi)
% 2.82/1.61 % (9939)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/3Mi)
% 2.82/1.61 % (9939)Instruction limit reached!
% 2.82/1.61 % (9939)------------------------------
% 2.82/1.61 % (9939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (9939)Termination reason: Unknown
% 2.82/1.61 % (9939)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (9939)Memory used [KB]: 1279
% 2.82/1.61 % (9939)Time elapsed: 0.003 s
% 2.82/1.61 % (9939)Instructions burned: 3 (million)
% 2.82/1.61 % (9939)------------------------------
% 2.82/1.61 % (9939)------------------------------
% 2.82/1.61 % (9941)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/7Mi)
% 2.82/1.61 % (9930)Refutation not found, incomplete strategy
% 2.82/1.61 % (9930)------------------------------
% 2.82/1.61 % (9930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (9930)Termination reason: Refutation not found, incomplete strategy
% 2.82/1.61
% 2.82/1.61
% 2.82/1.61 % (9930)Memory used [KB]: 6396
% 2.82/1.61 % (9930)Time elapsed: 0.035 s
% 2.82/1.61 % (9930)Instructions burned: 55 (million)
% 2.82/1.61 % (9930)------------------------------
% 2.82/1.61 % (9930)------------------------------
% 2.82/1.61 % (9941)Instruction limit reached!
% 2.82/1.61 % (9941)------------------------------
% 2.82/1.61 % (9941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (9941)Termination reason: Unknown
% 2.82/1.61 % (9941)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (9941)Memory used [KB]: 1407
% 2.82/1.61 % (9941)Time elapsed: 0.004 s
% 2.82/1.61 % (9941)Instructions burned: 9 (million)
% 2.82/1.61 % (9941)------------------------------
% 2.82/1.61 % (9941)------------------------------
% 2.82/1.61 % (9938)Instruction limit reached!
% 2.82/1.61 % (9938)------------------------------
% 2.82/1.61 % (9938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.61 % (9938)Termination reason: Unknown
% 2.82/1.61 % (9938)Termination phase: shuffling
% 2.82/1.61
% 2.82/1.61 % (9938)Memory used [KB]: 1535
% 2.82/1.61 % (9938)Time elapsed: 0.010 s
% 2.82/1.61 % (9938)Instructions burned: 16 (million)
% 2.82/1.61 % (9938)------------------------------
% 2.82/1.61 % (9938)------------------------------
% 2.82/1.61 % (9940)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/3Mi)
% 2.82/1.62 % (9940)Instruction limit reached!
% 2.82/1.62 % (9940)------------------------------
% 2.82/1.62 % (9940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (9940)Termination reason: Unknown
% 2.82/1.62 % (9940)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (9940)Memory used [KB]: 1279
% 2.82/1.62 % (9940)Time elapsed: 0.003 s
% 2.82/1.62 % (9940)Instructions burned: 4 (million)
% 2.82/1.62 % (9940)------------------------------
% 2.82/1.62 % (9940)------------------------------
% 2.82/1.62 % (9942)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/3Mi)
% 2.82/1.62 % (9942)Instruction limit reached!
% 2.82/1.62 % (9942)------------------------------
% 2.82/1.62 % (9942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.62 % (9942)Termination reason: Unknown
% 2.82/1.62 % (9942)Termination phase: shuffling
% 2.82/1.62
% 2.82/1.62 % (9942)Memory used [KB]: 1279
% 2.82/1.62 % (9942)Time elapsed: 0.003 s
% 2.82/1.62 % (9942)Instructions burned: 4 (million)
% 2.82/1.62 % (9942)------------------------------
% 2.82/1.62 % (9942)------------------------------
% 2.82/1.62 % (9944)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/18Mi)
% 2.82/1.62 % (9945)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/710Mi)
% 2.82/1.63 % (9944)Instruction limit reached!
% 2.82/1.63 % (9944)------------------------------
% 2.82/1.63 % (9944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.63 % (9944)Termination reason: Unknown
% 2.82/1.63 % (9944)Termination phase: Property scanning
% 2.82/1.63
% 2.82/1.63 % (9944)Memory used [KB]: 1535
% 2.82/1.63 % (9944)Time elapsed: 0.007 s
% 2.82/1.63 % (9944)Instructions burned: 19 (million)
% 2.82/1.63 % (9944)------------------------------
% 2.82/1.63 % (9944)------------------------------
% 2.82/1.63 % (9943)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/4Mi)
% 2.82/1.63 % (9947)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/902Mi)
% 2.82/1.63 % (9943)Instruction limit reached!
% 2.82/1.63 % (9943)------------------------------
% 2.82/1.63 % (9943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.63 % (9943)Termination reason: Unknown
% 2.82/1.63 % (9943)Termination phase: shuffling
% 2.82/1.63
% 2.82/1.63 % (9943)Memory used [KB]: 1407
% 2.82/1.63 % (9943)Time elapsed: 0.005 s
% 2.82/1.63 % (9943)Instructions burned: 5 (million)
% 2.82/1.63 % (9943)------------------------------
% 2.82/1.63 % (9943)------------------------------
% 2.82/1.63 % (9946)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/6Mi)
% 2.82/1.63 % (9946)Instruction limit reached!
% 2.82/1.63 % (9946)------------------------------
% 2.82/1.63 % (9946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.63 % (9946)Termination reason: Unknown
% 2.82/1.63 % (9946)Termination phase: shuffling
% 2.82/1.63
% 2.82/1.63 % (9946)Memory used [KB]: 1407
% 2.82/1.63 % (9946)Time elapsed: 0.004 s
% 2.82/1.63 % (9946)Instructions burned: 7 (million)
% 2.82/1.63 % (9946)------------------------------
% 2.82/1.63 % (9946)------------------------------
% 2.82/1.64 % (9948)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/21Mi)
% 2.82/1.64 % (9948)Instruction limit reached!
% 2.82/1.64 % (9948)------------------------------
% 2.82/1.64 % (9948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.64 % (9948)Termination reason: Unknown
% 2.82/1.64 % (9948)Termination phase: Property scanning
% 2.82/1.64
% 2.82/1.64 % (9948)Memory used [KB]: 1663
% 2.82/1.64 % (9948)Time elapsed: 0.008 s
% 2.82/1.64 % (9948)Instructions burned: 21 (million)
% 2.82/1.64 % (9948)------------------------------
% 2.82/1.64 % (9948)------------------------------
% 2.82/1.65 % (9949)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/5Mi)
% 2.82/1.65 % (9950)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/6Mi)
% 2.82/1.65 % (9949)Instruction limit reached!
% 2.82/1.65 % (9949)------------------------------
% 2.82/1.65 % (9949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.65 % (9949)Termination reason: Unknown
% 2.82/1.65 % (9949)Termination phase: shuffling
% 2.82/1.65
% 2.82/1.65 % (9949)Memory used [KB]: 1407
% 2.82/1.65 % (9949)Time elapsed: 0.005 s
% 2.82/1.65 % (9949)Instructions burned: 6 (million)
% 2.82/1.65 % (9949)------------------------------
% 2.82/1.65 % (9949)------------------------------
% 2.82/1.65 % (9950)Instruction limit reached!
% 2.82/1.65 % (9950)------------------------------
% 2.82/1.65 % (9950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.65 % (9950)Termination reason: Unknown
% 2.82/1.65 % (9950)Termination phase: shuffling
% 2.82/1.65
% 2.82/1.65 % (9950)Memory used [KB]: 1407
% 2.82/1.65 % (9950)Time elapsed: 0.004 s
% 2.82/1.65 % (9950)Instructions burned: 7 (million)
% 2.82/1.65 % (9950)------------------------------
% 2.82/1.65 % (9950)------------------------------
% 2.82/1.65 % (9951)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_9624 for (2999ds/377Mi)
% 2.82/1.66 % (9925)First to succeed.
% 2.82/1.67 % (9925)Refutation found. Thanks to Tanya!
% 2.82/1.67 % SZS status Theorem for DTF2THF_9624
% 2.82/1.67 % SZS output start Proof for DTF2THF_9624
% 2.82/1.67 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.82/1.67 thf(type_def_7, type, nat: $tType).
% 2.82/1.67 thf(type_def_8, type, num: $tType).
% 2.82/1.67 thf(type_def_9, type, set: ($tType) > $tType).
% 2.82/1.67 thf(type_def_10, type, stream170649215stream: ($tType) > $tType).
% 2.82/1.67 thf(type_def_11, type, a: $tType).
% 2.82/1.67 thf(func_def_0, type, stream170649215stream: ($tType) > $tType).
% 2.82/1.67 thf(func_def_1, type, set: ($tType) > $tType).
% 2.82/1.67 thf(func_def_2, type, num: $tType).
% 2.82/1.67 thf(func_def_3, type, nat: $tType).
% 2.82/1.67 thf(func_def_4, type, itself: ($tType) > $tType).
% 2.82/1.67 thf(func_def_5, type, a: $tType).
% 2.82/1.67 thf(func_def_6, type, bounded_lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_7, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_8, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_9, type, idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_10, type, ring: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_11, type, numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_12, type, ring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_13, type, uminus: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_14, type, top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_15, type, semiring: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_16, type, ring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_17, type, neg_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_18, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_19, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_20, type, comm_ring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_21, type, monoid_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_22, type, ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_23, type, semiring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_24, type, comm_semiring: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_25, type, semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_26, type, semiring_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_27, type, semigroup_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_28, type, comm_semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_29, type, linordered_field: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_30, type, ab_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_31, type, comm_monoid_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_32, type, ab_semigroup_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_33, type, boolean_algebra: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_34, type, semilattice_sup: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_35, type, cancel_semigroup_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_36, type, bounded_lattice_top: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_37, type, ring_11004092258visors: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_38, type, ordere779506340up_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_39, type, semiri456707255roduct: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.82/1.67 thf(func_def_40, type, one_one: !>[X0: $tType]:(X0)).
% 2.82/1.67 thf(func_def_41, type, plus_plus: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.82/1.67 thf(func_def_42, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.82/1.67 thf(func_def_43, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 2.82/1.67 thf(func_def_44, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.82/1.67 thf(func_def_45, type, suc: nat > nat).
% 2.82/1.67 thf(func_def_46, type, inc: num > num).
% 2.82/1.67 thf(func_def_47, type, neg_numeral_dbl: !>[X0: $tType]:(X0 > X0)).
% 2.82/1.67 thf(func_def_48, type, bit0: num > num).
% 2.82/1.67 thf(func_def_49, type, one2: num).
% 2.82/1.67 thf(func_def_50, type, numeral_numeral: !>[X0: $tType]:(num > X0)).
% 2.82/1.67 thf(func_def_51, type, top_top: !>[X0: $tType]:(X0)).
% 2.82/1.67 thf(func_def_52, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.82/1.67 thf(func_def_53, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 2.82/1.67 thf(func_def_54, type, image: !>[X0: $tType, X1: $tType]:((X0 > X1) > set @ X0 > set @ X1)).
% 2.82/1.67 thf(func_def_55, type, stream865922174rleave: !>[X0: $tType]:(stream170649215stream @ X0 > stream170649215stream @ X0 > stream170649215stream @ X0)).
% 2.82/1.67 thf(func_def_56, type, stream1586597341member: !>[X0: $tType]:(X0 > stream170649215stream @ X0 > $o)).
% 2.82/1.67 thf(func_def_57, type, stream857257621smerge: !>[X0: $tType]:(stream170649215stream @ stream170649215stream @ X0 > stream170649215stream @ X0)).
% 2.82/1.67 thf(func_def_58, type, stream370371455e_snth: !>[X0: $tType]:(stream170649215stream @ X0 > nat > X0)).
% 2.82/1.67 thf(func_def_59, type, stream30925839e_sset: !>[X0: $tType]:(stream170649215stream @ X0 > set @ X0)).
% 2.82/1.67 thf(func_def_60, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 2.82/1.67 thf(func_def_61, type, n: nat).
% 2.82/1.67 thf(func_def_62, type, s1: stream170649215stream @ a).
% 2.82/1.67 thf(func_def_63, type, s2: stream170649215stream @ a).
% 2.82/1.67 thf(func_def_64, type, x: a).
% 2.82/1.67 thf(func_def_79, type, sK0: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X1)).
% 2.82/1.67 thf(func_def_80, type, sK1: !>[X0: $tType]:(X0)).
% 2.82/1.67 thf(func_def_81, type, sK2: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_82, type, sK3: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 2.82/1.67 thf(func_def_83, type, sK4: !>[X0: $tType, X1: $tType]:(X0 > (X1 > X0) > X1)).
% 2.82/1.67 thf(func_def_84, type, sK5: !>[X0: $tType]:(set @ X0 > X0)).
% 2.82/1.67 thf(func_def_85, type, sK6: nat).
% 2.82/1.67 thf(func_def_86, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X0 > X1) > X1)).
% 2.82/1.67 thf(func_def_87, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > set @ X1 > X1)).
% 2.82/1.67 thf(func_def_88, type, sK9: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.82/1.67 thf(func_def_89, type, sK10: !>[X0: $tType, X1: $tType]:((X0 > $o) > set @ X1 > (X1 > X0) > X0)).
% 2.82/1.67 thf(func_def_91, type, sK12: !>[X0: $tType, X1: $tType]:(X1 > (X0 > X1) > X0)).
% 2.82/1.67 thf(func_def_92, type, sK13: !>[X0: $tType, X1: $tType]:((X0 > X1) > X1)).
% 2.82/1.67 thf(func_def_93, type, sK14: !>[X0: $tType]:(set @ X0 > set @ X0 > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_94, type, sK15: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 2.82/1.67 thf(func_def_95, type, sK16: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_96, type, sK17: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_97, type, sK18: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_98, type, sK19: !>[X0: $tType]:(set @ X0 > (X0 > $o) > set @ X0 > X0)).
% 2.82/1.67 thf(func_def_99, type, sK20: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_100, type, sK21: !>[X0: $tType]:(set @ X0 > (X0 > $o) > X0)).
% 2.82/1.67 thf(func_def_101, type, sK22: !>[X0: $tType, X1: $tType]:((X1 > X0) > set @ X1 > X0 > X1)).
% 2.82/1.67 thf(f1704,plain,(
% 2.82/1.67 $false),
% 2.82/1.67 inference(subsumption_resolution,[status(thm)],[f1330,f1356])).
% 2.82/1.67 thf(f1356,plain,(
% 2.82/1.67 ( ! [X1 : $tType,X0 : $tType,X3 : X1 > X0,X4 : X1] : (($true = (member @ X0 @ (X3 @ X4) @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1)))) )),
% 2.82/1.67 inference(equality_resolution,[status(thm)],[f1242])).
% 2.82/1.67 thf(f1242,plain,(
% 2.82/1.67 ( ! [X1 : $tType,X0 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : (((member @ X0 @ X2 @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1)) = $true) | ((X3 @ X4) != X2)) )),
% 2.82/1.67 inference(cnf_transformation,[status(thm)],[f909])).
% 2.82/1.67 thf(f909,plain,(
% 2.82/1.67 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : (((member @ X0 @ X2 @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1)) = $true) | ((X3 @ X4) != X2))),
% 2.82/1.67 inference(ennf_transformation,[status(thm)],[f541])).
% 2.82/1.67 thf(f541,plain,(
% 2.82/1.67 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : (((X3 @ X4) = X2) => ((member @ X0 @ X2 @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1)) = $true))),
% 2.82/1.67 inference(fool_elimination,[status(thm)],[f540])).
% 2.82/1.67 thf(f540,plain,(
% 2.82/1.67 ! [X0 : $tType,X1 : $tType,X2 : X0,X3 : X1 > X0,X4 : X1] : (((X3 @ X4) = X2) => (member @ X0 @ X2 @ (image @ X1 @ X0 @ X3 @ top_top @ set @ X1)))),
% 2.82/1.67 inference(rectify,[status(thm)],[f15])).
% 2.82/1.67 thf(f15,axiom,(
% 2.82/1.67 ! [X0 : $tType,X1 : $tType,X7 : X0,X8 : X1 > X0,X3 : X1] : (((X8 @ X3) = X7) => (member @ X0 @ X7 @ (image @ X1 @ X0 @ X8 @ top_top @ set @ X1)))),
% 2.82/1.67 file('/export/starexec/sandbox/tmp/tmp.H3y4OZI0Un/DTF2THF_9624.p',fact_14_range__eqI)).
% 2.82/1.67 thf(f1330,plain,(
% 2.82/1.67 ($true != (member @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n)) @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat)))),
% 2.82/1.67 inference(definition_unfolding,[status(thm)],[f1055,f1143])).
% 2.82/1.67 thf(f1143,plain,(
% 2.82/1.67 (x = (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n)))),
% 2.82/1.67 inference(cnf_transformation,[status(thm)],[f3])).
% 2.82/1.67 thf(f3,axiom,(
% 2.82/1.67 (x = (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2) @ (times_times @ nat @ (numeral_numeral @ nat @ (bit0 @ one2)) @ n)))),
% 2.82/1.67 file('/export/starexec/sandbox/tmp/tmp.H3y4OZI0Un/DTF2THF_9624.p',fact_2__092_060open_062sinterleave_As1_As2_A_B_B_A_I2_A_K_An_J_A_061_Ax_092_060close_062)).
% 2.82/1.67 thf(f1055,plain,(
% 2.82/1.67 ((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat)) != $true)),
% 2.82/1.67 inference(cnf_transformation,[status(thm)],[f796])).
% 2.82/1.67 thf(f796,plain,(
% 2.82/1.67 ((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat)) != $true)),
% 2.82/1.67 inference(flattening,[status(thm)],[f507])).
% 2.82/1.67 thf(f507,plain,(
% 2.82/1.67 ~((member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat)) = $true)),
% 2.82/1.67 inference(fool_elimination,[status(thm)],[f506])).
% 2.82/1.67 thf(f506,plain,(
% 2.82/1.67 ~(member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 2.82/1.67 inference(rectify,[status(thm)],[f292])).
% 2.82/1.67 thf(f292,negated_conjecture,(
% 2.82/1.67 ~(member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 2.82/1.67 inference(negated_conjecture,[status(cth)],[f291])).
% 2.82/1.67 thf(f291,conjecture,(
% 2.82/1.67 (member @ a @ x @ (image @ nat @ a @ (stream370371455e_snth @ a @ (stream865922174rleave @ a @ s1 @ s2)) @ top_top @ set @ nat))),
% 2.82/1.67 file('/export/starexec/sandbox/tmp/tmp.H3y4OZI0Un/DTF2THF_9624.p',conj_0)).
% 2.82/1.67 % SZS output end Proof for DTF2THF_9624
% 2.82/1.67 % (9925)------------------------------
% 2.82/1.67 % (9925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.82/1.67 % (9925)Termination reason: Refutation
% 2.82/1.67
% 2.82/1.67 % (9925)Memory used [KB]: 6652
% 2.82/1.67 % (9925)Time elapsed: 0.090 s
% 2.82/1.67 % (9925)Instructions burned: 171 (million)
% 2.82/1.67 % (9925)------------------------------
% 2.82/1.67 % (9925)------------------------------
% 2.82/1.67 % (9924)Success in time 0.109 s
%------------------------------------------------------------------------------