%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT160^1 : 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 : n011.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 08:44:58 AM UTC 2026
% Result : Theorem 2.68s 1.88s
% Output : Refutation 2.68s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT160^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n011.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:09:47 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : DAT160^1 : TPTP v9.2.1. Released v7.0.0.
% 0.20/0.46 % Domain : Data Structures
% 0.20/0.46 % Problem : Hamming stream 260
% 0.20/0.46 % Version : [Bla16] axioms : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Loc10] Lochbihler (2010), Coinductive
% 0.20/0.46 % : [RB15] Reynolds & Blanchette (2015), A Decision Procedure for
% 0.20/0.46 % : [Bla16] Blanchette (2016), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bla16]
% 0.20/0.46 % Names : hamming_stream__260.p [Bla16]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.00 v8.1.0, 0.25 v7.5.0, 0.00 v7.2.0, 0.25 v7.1.0
% 0.20/0.46 % Syntax : Number of formulae : 363 ( 112 unt; 60 typ; 0 def)
% 0.20/0.46 % Number of atoms : 700 ( 251 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.20/0.46 % Number of connectives : 3197 ( 41 ~; 3 |; 13 &;2849 @)
% 0.20/0.46 % ( 0 <=>; 291 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 17 ( 6 avg)
% 0.20/0.46 % Number of types : 5 ( 4 usr)
% 0.20/0.46 % Number of type conns : 116 ( 116 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 57 ( 56 usr; 4 con; 0-4 aty)
% 0.20/0.46 % Number of variables : 758 ( 37 ^; 671 !; 5 ?; 758 :)
% 0.20/0.46 % ( 45 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 0.20/0.46 % 2016-07-13 14:42:48.427
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 %----Could-be-implicit typings (6)
% 0.20/0.46 thf(ty_t_Coinductive__List_Ollist,type,
% 0.20/0.46 coinductive_llist: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Product__Type_Ounit,type,
% 0.20/0.46 product_unit: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Extended__Nat_Oenat,type,
% 0.20/0.46 extended_enat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Num_Onum,type,
% 0.20/0.46 num: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Nat_Onat,type,
% 0.20/0.46 nat: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_itself,type,
% 0.20/0.46 itself: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 %----Explicit typings (54)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oone,type,
% 0.20/0.46 one:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Num_Onumeral,type,
% 0.20/0.46 numeral:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Oring__1,type,
% 0.20/0.46 ring_1:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ouminus,type,
% 0.20/0.46 uminus:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.20/0.46 ord:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Nat_Oring__char__0,type,
% 0.20/0.46 ring_char_0:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Num_Oneg__numeral,type,
% 0.20/0.46 neg_numeral:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.20/0.46 order:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ogroup__add,type,
% 0.20/0.46 group_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Lattices_Olattice,type,
% 0.20/0.46 lattice:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Ocomm__ring__1,type,
% 0.20/0.46 comm_ring_1:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.20/0.46 monoid_mult:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.20/0.46 preorder:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.20/0.46 semiring_char_0:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Num_Osemiring__numeral,type,
% 0.20/0.46 semiring_numeral:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.20/0.46 semigroup_mult:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.20/0.46 comm_semiring_1:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.20/0.46 linordered_idom:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.20/0.46 comm_monoid_mult:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.20/0.46 ab_semigroup_mult:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.20/0.46 boolean_algebra:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.20/0.46 semilattice_inf:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.20/0.46 linordered_semidom:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.20/0.46 ordered_ab_group_add:
% 0.20/0.46 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.20/0.46 coinductive_lfinite:
% 0.20/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Coinductive__List_Ollength,type,
% 0.20/0.46 coinductive_llength:
% 0.20/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > extended_enat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.20/0.46 coinductive_LCons:
% 0.20/0.46 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Coinductive__List_Ollist_Olmap,type,
% 0.20/0.46 coinductive_lmap:
% 0.20/0.46 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coinductive_llist @ A ) > ( coinductive_llist @ Aa ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Coinductive__List_Ollist_Oltl,type,
% 0.20/0.46 coinductive_ltl:
% 0.20/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Extended__Nat_Oenat,type,
% 0.20/0.46 extended_enat2: nat > extended_enat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Extended__Nat_Oenat_Orec__enat,type,
% 0.20/0.46 extended_rec_enat:
% 0.20/0.46 !>[T: $tType] : ( ( nat > T ) > T > extended_enat > T ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.20/0.46 one_one:
% 0.20/0.46 !>[A: $tType] : A ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.20/0.46 times_times:
% 0.20/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.20/0.46 uminus_uminus:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Ohamming,type,
% 0.20/0.46 hammin2015774020amming: coinductive_llist @ nat ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Ohamming_H,type,
% 0.20/0.46 hammin1630468845amming: product_unit > ( coinductive_llist @ nat ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Oord__class_Olmerge,type,
% 0.20/0.46 hammin1138290136lmerge:
% 0.20/0.46 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Osmooth,type,
% 0.20/0.46 hammin1195055315smooth: nat > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.20/0.46 inf_inf:
% 0.20/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_OBitM,type,
% 0.20/0.46 bitM: num > num ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 0.20/0.46 neg_numeral_dbl:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 0.20/0.46 neg_numeral_dbl_dec:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 0.20/0.46 neg_numeral_dbl_inc:
% 0.20/0.46 !>[A: $tType] : ( A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Oneg__numeral__class_Osub,type,
% 0.20/0.46 neg_numeral_sub:
% 0.20/0.46 !>[A: $tType] : ( num > num > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Onum_OBit0,type,
% 0.20/0.46 bit0: num > num ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Onum_OBit1,type,
% 0.20/0.46 bit1: num > num ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Onum_OOne,type,
% 0.20/0.46 one2: num ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.20/0.46 numeral_numeral:
% 0.20/0.46 !>[A: $tType] : ( num > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.20/0.46 ord_less_eq:
% 0.20/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Product__Type_OUnity,type,
% 0.20/0.46 product_Unity: product_unit ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Pure_Otype,type,
% 0.20/0.46 type2:
% 0.20/0.46 !>[A: $tType] : ( itself @ A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_n____,type,
% 0.20/0.46 n: nat ).
% 0.20/0.46
% 0.20/0.46 %----Relevant facts (252)
% 0.20/0.46 thf(fact_0__092_060open_062lfinite_Ahamming_092_060close_062,axiom,
% 0.20/0.46 coinductive_lfinite @ nat @ hammin2015774020amming ).
% 0.20/0.46
% 0.20/0.46 % \<open>lfinite hamming\<close>
% 0.20/0.46 thf(fact_1_llength__lmerge__above,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ A @ Xs ) @ ( coinductive_llength @ A @ Ys ) ) @ ( coinductive_llength @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % llength_lmerge_above
% 0.20/0.46 thf(fact_2_n,axiom,
% 0.20/0.46 ( ( coinductive_llength @ nat @ hammin2015774020amming )
% 0.20/0.46 = ( extended_enat2 @ n ) ) ).
% 0.20/0.46
% 0.20/0.46 % n
% 0.20/0.46 thf(fact_3_llength__lmap,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.20/0.46 ( ( coinductive_llength @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.20/0.46 = ( coinductive_llength @ B @ Xs ) ) ).
% 0.20/0.46
% 0.20/0.46 % llength_lmap
% 0.20/0.46 thf(fact_4_le__inf__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A,Z: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.20/0.46 = ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.46 & ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_inf_iff
% 0.20/0.46 thf(fact_5_inf_Obounded__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A,C: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.20/0.46 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.46 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.bounded_iff
% 0.20/0.46 thf(fact_6_semiring__norm_I169_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [V: num,W: num,Z: A] :
% 0.20/0.46 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( times_times @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.20/0.46 = ( times_times @ A @ ( numeral_numeral @ A @ ( times_times @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(169)
% 0.20/0.46 thf(fact_7_numeral__times__numeral,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [M: num,N: num] :
% 0.20/0.46 ( ( times_times @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.20/0.46 = ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % numeral_times_numeral
% 0.20/0.46 thf(fact_8_numeral__le__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [M: num,N: num] :
% 0.20/0.46 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.20/0.46 = ( ord_less_eq @ num @ M @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % numeral_le_iff
% 0.20/0.46 thf(fact_9_semiring__norm_I85_J,axiom,
% 0.20/0.46 ! [M: num] :
% 0.20/0.46 ( ( bit0 @ M )
% 0.20/0.46 != one2 ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(85)
% 0.20/0.46 thf(fact_10_semiring__norm_I83_J,axiom,
% 0.20/0.46 ! [N: num] :
% 0.20/0.46 ( one2
% 0.20/0.46 != ( bit0 @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(83)
% 0.20/0.46 thf(fact_11_semiring__norm_I86_J,axiom,
% 0.20/0.46 ! [M: num] :
% 0.20/0.46 ( ( bit1 @ M )
% 0.20/0.46 != one2 ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(86)
% 0.20/0.46 thf(fact_12_semiring__norm_I84_J,axiom,
% 0.20/0.46 ! [N: num] :
% 0.20/0.46 ( one2
% 0.20/0.46 != ( bit1 @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(84)
% 0.20/0.46 thf(fact_13_semiring__norm_I89_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( bit1 @ M )
% 0.20/0.46 != ( bit0 @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(89)
% 0.20/0.46 thf(fact_14_semiring__norm_I90_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( ( bit1 @ M )
% 0.20/0.46 = ( bit1 @ N ) )
% 0.20/0.46 = ( M = N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(90)
% 0.20/0.46 thf(fact_15_num_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X3: num,Y3: num] :
% 0.20/0.46 ( ( ( bit1 @ X3 )
% 0.20/0.46 = ( bit1 @ Y3 ) )
% 0.20/0.46 = ( X3 = Y3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.inject(2)
% 0.20/0.46 thf(fact_16_semiring__norm_I87_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( ( bit0 @ M )
% 0.20/0.46 = ( bit0 @ N ) )
% 0.20/0.46 = ( M = N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(87)
% 0.20/0.46 thf(fact_17_num_Oinject_I1_J,axiom,
% 0.20/0.46 ! [X2: num,Y2: num] :
% 0.20/0.46 ( ( ( bit0 @ X2 )
% 0.20/0.46 = ( bit0 @ Y2 ) )
% 0.20/0.46 = ( X2 = Y2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.inject(1)
% 0.20/0.46 thf(fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_Ahamming_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.20/0.46 ~ ! [N2: nat] :
% 0.20/0.46 ( ( coinductive_llength @ nat @ hammin2015774020amming )
% 0.20/0.46 != ( extended_enat2 @ N2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % \<open>\<And>thesis. (\<And>n. llength hamming = enat n \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 0.20/0.46 thf(fact_19_numeral__eq__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [M: num,N: num] :
% 0.20/0.46 ( ( ( numeral_numeral @ A @ M )
% 0.20/0.46 = ( numeral_numeral @ A @ N ) )
% 0.20/0.46 = ( M = N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % numeral_eq_iff
% 0.20/0.46 thf(fact_20_inf__right__idem,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] :
% 0.20/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.20/0.46 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_right_idem
% 0.20/0.46 thf(fact_21_inf_Oright__idem,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] :
% 0.20/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.20/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.right_idem
% 0.20/0.46 thf(fact_22_inf__left__idem,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] :
% 0.20/0.46 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.20/0.46 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_left_idem
% 0.20/0.46 thf(fact_23_inf_Oleft__idem,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] :
% 0.20/0.46 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.20/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.left_idem
% 0.20/0.46 thf(fact_24_inf__idem,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A] :
% 0.20/0.46 ( ( inf_inf @ A @ X @ X )
% 0.20/0.46 = X ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_idem
% 0.20/0.46 thf(fact_25_inf_Oidem,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( inf_inf @ A @ A2 @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.idem
% 0.20/0.46 thf(fact_26_inf__apply,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.20/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.20/0.46 = ( ^ [F2: A > B,G: A > B,X4: A] : ( inf_inf @ B @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_apply
% 0.20/0.46 thf(fact_27_semiring__norm_I88_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( bit0 @ M )
% 0.20/0.46 != ( bit1 @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(88)
% 0.20/0.46 thf(fact_28_semiring__norm_I13_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( times_times @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.20/0.46 = ( bit0 @ ( bit0 @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(13)
% 0.20/0.46 thf(fact_29_lfinite__lmap,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.20/0.46 ( ( coinductive_lfinite @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.20/0.46 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.20/0.46
% 0.20/0.46 % lfinite_lmap
% 0.20/0.46 thf(fact_30_semiring__norm_I11_J,axiom,
% 0.20/0.46 ! [M: num] :
% 0.20/0.46 ( ( times_times @ num @ M @ one2 )
% 0.20/0.46 = M ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(11)
% 0.20/0.46 thf(fact_31_semiring__norm_I12_J,axiom,
% 0.20/0.46 ! [N: num] :
% 0.20/0.46 ( ( times_times @ num @ one2 @ N )
% 0.20/0.46 = N ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(12)
% 0.20/0.46 thf(fact_32_semiring__norm_I73_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( ord_less_eq @ num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.20/0.46 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(73)
% 0.20/0.46 thf(fact_33_semiring__norm_I71_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( ord_less_eq @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.20/0.46 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(71)
% 0.20/0.46 thf(fact_34_semiring__norm_I68_J,axiom,
% 0.20/0.46 ! [N: num] : ( ord_less_eq @ num @ one2 @ N ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(68)
% 0.20/0.46 thf(fact_35_semiring__norm_I14_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( times_times @ num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.20/0.46 = ( bit0 @ ( times_times @ num @ M @ ( bit1 @ N ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(14)
% 0.20/0.46 thf(fact_36_semiring__norm_I15_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( times_times @ num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.20/0.46 = ( bit0 @ ( times_times @ num @ ( bit1 @ M ) @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(15)
% 0.20/0.46 thf(fact_37_semiring__norm_I72_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( ord_less_eq @ num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.20/0.46 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(72)
% 0.20/0.46 thf(fact_38_semiring__norm_I70_J,axiom,
% 0.20/0.46 ! [M: num] :
% 0.20/0.46 ~ ( ord_less_eq @ num @ ( bit1 @ M ) @ one2 ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(70)
% 0.20/0.46 thf(fact_39_semiring__norm_I69_J,axiom,
% 0.20/0.46 ! [M: num] :
% 0.20/0.46 ~ ( ord_less_eq @ num @ ( bit0 @ M ) @ one2 ) ).
% 0.20/0.46
% 0.20/0.46 % semiring_norm(69)
% 0.20/0.46 thf(fact_40_lfinite__llength__enat,axiom,
% 0.20/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.20/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.20/0.46 => ? [N2: nat] :
% 0.20/0.46 ( ( coinductive_llength @ A @ Xs )
% 0.20/0.46 = ( extended_enat2 @ N2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lfinite_llength_enat
% 0.20/0.46 thf(fact_41_llength__eq__enat__lfiniteD,axiom,
% 0.20/0.46 ! [A: $tType,Xs: coinductive_llist @ A,N: nat] :
% 0.20/0.46 ( ( ( coinductive_llength @ A @ Xs )
% 0.20/0.46 = ( extended_enat2 @ N ) )
% 0.20/0.46 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.20/0.46
% 0.20/0.46 % llength_eq_enat_lfiniteD
% 0.20/0.46 thf(fact_42_lfinite__conv__llength__enat,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( coinductive_lfinite @ A )
% 0.20/0.46 = ( ^ [Xs2: coinductive_llist @ A] :
% 0.20/0.46 ? [N3: nat] :
% 0.20/0.46 ( ( coinductive_llength @ A @ Xs2 )
% 0.20/0.46 = ( extended_enat2 @ N3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lfinite_conv_llength_enat
% 0.20/0.46 thf(fact_43_le__num__One__iff,axiom,
% 0.20/0.46 ! [X: num] :
% 0.20/0.46 ( ( ord_less_eq @ num @ X @ one2 )
% 0.20/0.46 = ( X = one2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_num_One_iff
% 0.20/0.46 thf(fact_44_ext,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.20/0.46 ( ! [X5: A] :
% 0.20/0.46 ( ( F @ X5 )
% 0.20/0.46 = ( G2 @ X5 ) )
% 0.20/0.46 => ( F = G2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % ext
% 0.20/0.46 thf(fact_45_linfinite__lmerge,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.20/0.46 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.20/0.46 => ( ~ ( coinductive_lfinite @ A @ Ys )
% 0.20/0.46 => ~ ( coinductive_lfinite @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % linfinite_lmerge
% 0.20/0.46 thf(fact_46_lfinite__lmergeI,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.20/0.46 ( ( coinductive_lfinite @ A @ Xs )
% 0.20/0.46 => ( ( coinductive_lfinite @ A @ Ys )
% 0.20/0.46 => ( coinductive_lfinite @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lfinite_lmergeI
% 0.20/0.46 thf(fact_47_lfinite__lmergeD,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.20/0.46 ( ( coinductive_lfinite @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) )
% 0.20/0.46 => ( ( coinductive_lfinite @ A @ Xs )
% 0.20/0.46 | ( coinductive_lfinite @ A @ Ys ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % lfinite_lmergeD
% 0.20/0.46 thf(fact_48_wlog__linorder__le,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [P: A > A > $o,B2: A,A2: A] :
% 0.20/0.46 ( ! [A3: A,B3: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.20/0.46 => ( P @ A3 @ B3 ) )
% 0.20/0.46 => ( ( ( P @ B2 @ A2 )
% 0.20/0.46 => ( P @ A2 @ B2 ) )
% 0.20/0.46 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % wlog_linorder_le
% 0.20/0.46 thf(fact_49_inf__left__commute,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A,Z: A] :
% 0.20/0.46 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.20/0.46 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_left_commute
% 0.20/0.46 thf(fact_50_inf_Oleft__commute,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B2: A,A2: A,C: A] :
% 0.20/0.46 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C ) )
% 0.20/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.left_commute
% 0.20/0.46 thf(fact_51_inf__commute,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( inf_inf @ A )
% 0.20/0.46 = ( ^ [X4: A,Y4: A] : ( inf_inf @ A @ Y4 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_commute
% 0.20/0.46 thf(fact_52_inf_Ocommute,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( inf_inf @ A )
% 0.20/0.46 = ( ^ [A4: A,B4: A] : ( inf_inf @ A @ B4 @ A4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.commute
% 0.20/0.46 thf(fact_53_inf__assoc,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A,Z: A] :
% 0.20/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.20/0.46 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_assoc
% 0.20/0.46 thf(fact_54_inf_Oassoc,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A,C: A] :
% 0.20/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C )
% 0.20/0.46 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.assoc
% 0.20/0.46 thf(fact_55_inf__fun__def,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.20/0.46 => ( ( inf_inf @ ( A > B ) )
% 0.20/0.46 = ( ^ [F2: A > B,G: A > B,X4: A] : ( inf_inf @ B @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_fun_def
% 0.20/0.46 thf(fact_56_inf__sup__aci_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( inf_inf @ A )
% 0.20/0.46 = ( ^ [X4: A,Y4: A] : ( inf_inf @ A @ Y4 @ X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(1)
% 0.20/0.46 thf(fact_57_inf__sup__aci_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A,Z: A] :
% 0.20/0.46 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.20/0.46 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(2)
% 0.20/0.46 thf(fact_58_inf__sup__aci_I3_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A,Z: A] :
% 0.20/0.46 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.20/0.46 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(3)
% 0.20/0.46 thf(fact_59_inf__sup__aci_I4_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] :
% 0.20/0.46 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.20/0.46 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_aci(4)
% 0.20/0.46 thf(fact_60_num_Odistinct_I5_J,axiom,
% 0.20/0.46 ! [X2: num,X3: num] :
% 0.20/0.46 ( ( bit0 @ X2 )
% 0.20/0.46 != ( bit1 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.distinct(5)
% 0.20/0.46 thf(fact_61_num_Odistinct_I3_J,axiom,
% 0.20/0.46 ! [X3: num] :
% 0.20/0.46 ( one2
% 0.20/0.46 != ( bit1 @ X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.distinct(3)
% 0.20/0.46 thf(fact_62_num_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [X2: num] :
% 0.20/0.46 ( one2
% 0.20/0.46 != ( bit0 @ X2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.distinct(1)
% 0.20/0.46 thf(fact_63_inf_OcoboundedI2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B2: A,C: A,A2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ B2 @ C )
% 0.20/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.coboundedI2
% 0.20/0.46 thf(fact_64_inf_OcoboundedI1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,C: A,B2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ C )
% 0.20/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.coboundedI1
% 0.20/0.46 thf(fact_65_inf_Oabsorb__iff2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( ord_less_eq @ A )
% 0.20/0.46 = ( ^ [B4: A,A4: A] :
% 0.20/0.46 ( ( inf_inf @ A @ A4 @ B4 )
% 0.20/0.46 = B4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.absorb_iff2
% 0.20/0.46 thf(fact_66_inf_Oabsorb__iff1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( ord_less_eq @ A )
% 0.20/0.46 = ( ^ [A4: A,B4: A] :
% 0.20/0.46 ( ( inf_inf @ A @ A4 @ B4 )
% 0.20/0.46 = A4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.absorb_iff1
% 0.20/0.46 thf(fact_67_inf_Ocobounded2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.cobounded2
% 0.20/0.46 thf(fact_68_inf_Ocobounded1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.cobounded1
% 0.20/0.46 thf(fact_69_inf_Oorder__iff,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( ord_less_eq @ A )
% 0.20/0.46 = ( ^ [A4: A,B4: A] :
% 0.20/0.46 ( A4
% 0.20/0.46 = ( inf_inf @ A @ A4 @ B4 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.order_iff
% 0.20/0.46 thf(fact_70_inf__greatest,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A,Z: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.46 => ( ( ord_less_eq @ A @ X @ Z )
% 0.20/0.46 => ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_greatest
% 0.20/0.46 thf(fact_71_inf_OboundedI,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A,C: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ A2 @ C )
% 0.20/0.46 => ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.boundedI
% 0.20/0.46 thf(fact_72_inf_OboundedE,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A,C: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.20/0.46 => ~ ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.46 => ~ ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.boundedE
% 0.20/0.46 thf(fact_73_inf__absorb2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [Y: A,X: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ Y @ X )
% 0.20/0.46 => ( ( inf_inf @ A @ X @ Y )
% 0.20/0.46 = Y ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_absorb2
% 0.20/0.46 thf(fact_74_inf__absorb1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.46 => ( ( inf_inf @ A @ X @ Y )
% 0.20/0.46 = X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_absorb1
% 0.20/0.46 thf(fact_75_inf_Oabsorb2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B2: A,A2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.20/0.46 => ( ( inf_inf @ A @ A2 @ B2 )
% 0.20/0.46 = B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.absorb2
% 0.20/0.46 thf(fact_76_inf_Oabsorb1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.46 => ( ( inf_inf @ A @ A2 @ B2 )
% 0.20/0.46 = A2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.absorb1
% 0.20/0.46 thf(fact_77_le__iff__inf,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ( ( ord_less_eq @ A )
% 0.20/0.46 = ( ^ [X4: A,Y4: A] :
% 0.20/0.46 ( ( inf_inf @ A @ X4 @ Y4 )
% 0.20/0.46 = X4 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_iff_inf
% 0.20/0.46 thf(fact_78_inf__unique,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [F: A > A > A,X: A,Y: A] :
% 0.20/0.46 ( ! [X5: A,Y5: A] : ( ord_less_eq @ A @ ( F @ X5 @ Y5 ) @ X5 )
% 0.20/0.46 => ( ! [X5: A,Y5: A] : ( ord_less_eq @ A @ ( F @ X5 @ Y5 ) @ Y5 )
% 0.20/0.46 => ( ! [X5: A,Y5: A,Z2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ X5 @ Z2 )
% 0.20/0.46 => ( ord_less_eq @ A @ X5 @ ( F @ Y5 @ Z2 ) ) ) )
% 0.20/0.46 => ( ( inf_inf @ A @ X @ Y )
% 0.20/0.46 = ( F @ X @ Y ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_unique
% 0.20/0.46 thf(fact_79_inf_OorderI,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] :
% 0.20/0.46 ( ( A2
% 0.20/0.46 = ( inf_inf @ A @ A2 @ B2 ) )
% 0.20/0.46 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.orderI
% 0.20/0.46 thf(fact_80_inf_OorderE,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,B2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.46 => ( A2
% 0.20/0.46 = ( inf_inf @ A @ A2 @ B2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf.orderE
% 0.20/0.46 thf(fact_81_le__infI2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [B2: A,X: A,A2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ B2 @ X )
% 0.20/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_infI2
% 0.20/0.46 thf(fact_82_le__infI1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,X: A,B2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ X )
% 0.20/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_infI1
% 0.20/0.46 thf(fact_83_inf__mono,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A,C: A,B2: A,D: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ A2 @ C )
% 0.20/0.46 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.20/0.46 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ ( inf_inf @ A @ C @ D ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_mono
% 0.20/0.46 thf(fact_84_le__infI,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,A2: A,B2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X @ A2 )
% 0.20/0.46 => ( ( ord_less_eq @ A @ X @ B2 )
% 0.20/0.46 => ( ord_less_eq @ A @ X @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_infI
% 0.20/0.46 thf(fact_85_le__infE,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,A2: A,B2: A] :
% 0.20/0.46 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.20/0.46 => ~ ( ( ord_less_eq @ A @ X @ A2 )
% 0.20/0.46 => ~ ( ord_less_eq @ A @ X @ B2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % le_infE
% 0.20/0.46 thf(fact_86_inf__le2,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_le2
% 0.20/0.46 thf(fact_87_inf__le1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ X ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_le1
% 0.20/0.46 thf(fact_88_inf__sup__ord_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ X ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_ord(1)
% 0.20/0.46 thf(fact_89_inf__sup__ord_I2_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lattice @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ Y ) ) ).
% 0.20/0.46
% 0.20/0.46 % inf_sup_ord(2)
% 0.20/0.46 thf(fact_90_num_Oexhaust,axiom,
% 0.20/0.46 ! [Y: num] :
% 0.20/0.46 ( ( Y != one2 )
% 0.20/0.46 => ( ! [X22: num] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( bit0 @ X22 ) )
% 0.20/0.46 => ~ ! [X32: num] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( bit1 @ X32 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.exhaust
% 0.20/0.46 thf(fact_91_num_Oinduct,axiom,
% 0.20/0.46 ! [P: num > $o,Num: num] :
% 0.20/0.46 ( ( P @ one2 )
% 0.20/0.46 => ( ! [X5: num] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( P @ ( bit0 @ X5 ) ) )
% 0.20/0.46 => ( ! [X5: num] :
% 0.20/0.46 ( ( P @ X5 )
% 0.20/0.46 => ( P @ ( bit1 @ X5 ) ) )
% 0.20/0.46 => ( P @ Num ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % num.induct
% 0.20/0.46 thf(fact_92_mult__numeral__1__right,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( times_times @ A @ A2 @ ( numeral_numeral @ A @ one2 ) )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % mult_numeral_1_right
% 0.20/0.46 thf(fact_93_mult__numeral__1,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [A2: A] :
% 0.20/0.46 ( ( times_times @ A @ ( numeral_numeral @ A @ one2 ) @ A2 )
% 0.20/0.46 = A2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % mult_numeral_1
% 0.20/0.46 thf(fact_94_numeral__le__enat__iff,axiom,
% 0.20/0.46 ! [M: num,N: nat] :
% 0.20/0.46 ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ M ) @ ( extended_enat2 @ N ) )
% 0.20/0.46 = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ M ) @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % numeral_le_enat_iff
% 0.20/0.46 thf(fact_95_enat__ord__simps_I1_J,axiom,
% 0.20/0.46 ! [M: nat,N: nat] :
% 0.20/0.46 ( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.20/0.46 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.20/0.46
% 0.20/0.46 % enat_ord_simps(1)
% 0.20/0.46 thf(fact_96_times__enat__simps_I1_J,axiom,
% 0.20/0.46 ! [M: nat,N: nat] :
% 0.20/0.46 ( ( times_times @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.20/0.46 = ( extended_enat2 @ ( times_times @ nat @ M @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % times_enat_simps(1)
% 0.20/0.46 thf(fact_97_enat__ord__number_I1_J,axiom,
% 0.20/0.46 ! [M: num,N: num] :
% 0.20/0.46 ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ M ) @ ( numeral_numeral @ extended_enat @ N ) )
% 0.20/0.46 = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % enat_ord_number(1)
% 0.20/0.46 thf(fact_98_ltl__hamming,axiom,
% 0.20/0.46 ( ( coinductive_ltl @ nat @ hammin2015774020amming )
% 0.20/0.46 = ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ltl_hamming
% 0.20/0.46 thf(fact_99_enat_Oinject,axiom,
% 0.20/0.46 ! [Nat: nat,Nat2: nat] :
% 0.20/0.46 ( ( ( extended_enat2 @ Nat )
% 0.20/0.46 = ( extended_enat2 @ Nat2 ) )
% 0.20/0.46 = ( Nat = Nat2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % enat.inject
% 0.20/0.46 thf(fact_100_order__refl,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( preorder @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.20/0.46
% 0.20/0.46 % order_refl
% 0.20/0.46 thf(fact_101_enat__ile,axiom,
% 0.20/0.46 ! [N: extended_enat,M: nat] :
% 0.20/0.46 ( ( ord_less_eq @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 0.20/0.46 => ? [K: nat] :
% 0.20/0.46 ( N
% 0.20/0.46 = ( extended_enat2 @ K ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % enat_ile
% 0.20/0.46 thf(fact_102_numeral__eq__enat,axiom,
% 0.20/0.46 ( ( numeral_numeral @ extended_enat )
% 0.20/0.46 = ( ^ [K2: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ K2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % numeral_eq_enat
% 0.20/0.46 thf(fact_103_smooth5,axiom,
% 0.20/0.46 hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % smooth5
% 0.20/0.46 thf(fact_104_dbl__inc__simps_I5_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.46 => ! [K3: num] :
% 0.20/0.46 ( ( neg_numeral_dbl_inc @ A @ ( numeral_numeral @ A @ K3 ) )
% 0.20/0.46 = ( numeral_numeral @ A @ ( bit1 @ K3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % dbl_inc_simps(5)
% 0.20/0.46 thf(fact_105_lfinite__ltl,axiom,
% 0.20/0.46 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.20/0.46 ( ( coinductive_lfinite @ A @ ( coinductive_ltl @ A @ Xs ) )
% 0.20/0.47 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.20/0.47
% 0.20/0.47 % lfinite_ltl
% 0.20/0.47 thf(fact_106_ltl__lmap,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.20/0.47 ( ( coinductive_ltl @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.20/0.47 = ( coinductive_lmap @ B @ A @ F @ ( coinductive_ltl @ B @ Xs ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ltl_lmap
% 0.20/0.47 thf(fact_107_smooth__times,axiom,
% 0.20/0.47 ! [X: nat,Y: nat] :
% 0.20/0.47 ( ( hammin1195055315smooth @ ( times_times @ nat @ X @ Y ) )
% 0.20/0.47 = ( ( hammin1195055315smooth @ X )
% 0.20/0.47 & ( hammin1195055315smooth @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % smooth_times
% 0.20/0.47 thf(fact_108_le__funD,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [F: A > B,G2: A > B,X: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funD
% 0.20/0.47 thf(fact_109_le__funE,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [F: A > B,G2: A > B,X: A] :
% 0.20/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funE
% 0.20/0.47 thf(fact_110_le__funI,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [F: A > B,G2: A > B] :
% 0.20/0.47 ( ! [X5: A] : ( ord_less_eq @ B @ ( F @ X5 ) @ ( G2 @ X5 ) )
% 0.20/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_funI
% 0.20/0.47 thf(fact_111_le__fun__def,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( ord @ B @ ( type2 @ B ) )
% 0.20/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.20/0.47 = ( ^ [F2: A > B,G: A > B] :
% 0.20/0.47 ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_fun_def
% 0.20/0.47 thf(fact_112_order__subst1,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( ( order @ B @ ( type2 @ B ) )
% 0.20/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.20/0.47 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.20/0.47 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.20/0.47 => ( ! [X5: B,Y5: B] :
% 0.20/0.47 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 0.20/0.47 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst1
% 0.20/0.47 thf(fact_113_order__subst2,axiom,
% 0.20/0.47 ! [A: $tType,C2: $tType] :
% 0.20/0.47 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.20/0.47 & ( order @ A @ ( type2 @ A ) ) )
% 0.20/0.47 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.20/0.47 => ( ! [X5: A,Y5: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.20/0.47 => ( ord_less_eq @ C2 @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.47 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_subst2
% 0.20/0.47 thf(fact_114_ord__eq__le__subst,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.20/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.20/0.47 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.20/0.47 ( ( A2
% 0.20/0.47 = ( F @ B2 ) )
% 0.20/0.47 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.20/0.47 => ( ! [X5: B,Y5: B] :
% 0.20/0.47 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 0.20/0.47 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.47 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_eq_le_subst
% 0.20/0.47 thf(fact_115_ord__le__eq__subst,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType] :
% 0.20/0.47 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.20/0.47 & ( ord @ A @ ( type2 @ A ) ) )
% 0.20/0.47 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( ( ( F @ B2 )
% 0.20/0.47 = C )
% 0.20/0.47 => ( ! [X5: A,Y5: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.20/0.47 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_le_eq_subst
% 0.20/0.47 thf(fact_116_eq__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( ^ [Y6: A,Z3: A] : ( Y6 = Z3 ) )
% 0.20/0.47 = ( ^ [X4: A,Y4: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.20/0.47 & ( ord_less_eq @ A @ Y4 @ X4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_iff
% 0.20/0.47 thf(fact_117_antisym,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 => ( ( ord_less_eq @ A @ Y @ X )
% 0.20/0.47 => ( X = Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym
% 0.20/0.47 thf(fact_118_linear,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % linear
% 0.20/0.47 thf(fact_119_eq__refl,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( X = Y )
% 0.20/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_refl
% 0.20/0.47 thf(fact_120_le__cases,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_cases
% 0.20/0.47 thf(fact_121_order_Otrans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A,C: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.20/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order.trans
% 0.20/0.47 thf(fact_122_le__cases3,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A,Z: A] :
% 0.20/0.47 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.20/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.20/0.47 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_cases3
% 0.20/0.47 thf(fact_123_antisym__conv,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Y: A,X: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.20/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 = ( X = Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % antisym_conv
% 0.20/0.47 thf(fact_124_ord__eq__le__trans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A,C: A] :
% 0.20/0.47 ( ( A2 = B2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.20/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_eq_le_trans
% 0.20/0.47 thf(fact_125_ord__le__eq__trans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A,C: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( ( B2 = C )
% 0.20/0.47 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord_le_eq_trans
% 0.20/0.47 thf(fact_126_order__class_Oorder_Oantisym,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.20/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_class.order.antisym
% 0.20/0.47 thf(fact_127_order__trans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( preorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A,Z: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.20/0.47 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % order_trans
% 0.20/0.47 thf(fact_128_dual__order_Orefl,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.refl
% 0.20/0.47 thf(fact_129_linorder__wlog,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.20/0.47 ( ! [A3: A,B3: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.20/0.47 => ( P @ A3 @ B3 ) )
% 0.20/0.47 => ( ! [A3: A,B3: A] :
% 0.20/0.47 ( ( P @ B3 @ A3 )
% 0.20/0.47 => ( P @ A3 @ B3 ) )
% 0.20/0.47 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % linorder_wlog
% 0.20/0.47 thf(fact_130_dual__order_Otrans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B2: A,A2: A,C: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.20/0.47 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.trans
% 0.20/0.47 thf(fact_131_dual__order_Oantisym,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( order @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B2: A,A2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.20/0.47 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( A2 = B2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dual_order.antisym
% 0.20/0.47 thf(fact_132_smooth3,axiom,
% 0.20/0.47 hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % smooth3
% 0.20/0.47 thf(fact_133_smooth2,axiom,
% 0.20/0.47 hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % smooth2
% 0.20/0.47 thf(fact_134_le__cube,axiom,
% 0.20/0.47 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_cube
% 0.20/0.47 thf(fact_135_le__square,axiom,
% 0.20/0.47 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_square
% 0.20/0.47 thf(fact_136_mult__le__mono,axiom,
% 0.20/0.47 ! [I: nat,J: nat,K3: nat,L: nat] :
% 0.20/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.20/0.47 => ( ( ord_less_eq @ nat @ K3 @ L )
% 0.20/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K3 ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_le_mono
% 0.20/0.47 thf(fact_137_mult__le__mono1,axiom,
% 0.20/0.47 ! [I: nat,J: nat,K3: nat] :
% 0.20/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.20/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K3 ) @ ( times_times @ nat @ J @ K3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_le_mono1
% 0.20/0.47 thf(fact_138_mult__le__mono2,axiom,
% 0.20/0.47 ! [I: nat,J: nat,K3: nat] :
% 0.20/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.20/0.47 => ( ord_less_eq @ nat @ ( times_times @ nat @ K3 @ I ) @ ( times_times @ nat @ K3 @ J ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_le_mono2
% 0.20/0.47 thf(fact_139_nat__le__linear,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.20/0.47 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_le_linear
% 0.20/0.47 thf(fact_140_le__antisym,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( ord_less_eq @ nat @ M @ N )
% 0.20/0.47 => ( ( ord_less_eq @ nat @ N @ M )
% 0.20/0.47 => ( M = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_antisym
% 0.20/0.47 thf(fact_141_eq__imp__le,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( M = N )
% 0.20/0.47 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_imp_le
% 0.20/0.47 thf(fact_142_le__trans,axiom,
% 0.20/0.47 ! [I: nat,J: nat,K3: nat] :
% 0.20/0.47 ( ( ord_less_eq @ nat @ I @ J )
% 0.20/0.47 => ( ( ord_less_eq @ nat @ J @ K3 )
% 0.20/0.47 => ( ord_less_eq @ nat @ I @ K3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_trans
% 0.20/0.47 thf(fact_143_le__refl,axiom,
% 0.20/0.47 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.20/0.47
% 0.20/0.47 % le_refl
% 0.20/0.47 thf(fact_144_enat_Osimps_I6_J,axiom,
% 0.20/0.47 ! [T: $tType,F1: nat > T,F22: T,Nat: nat] :
% 0.20/0.47 ( ( extended_rec_enat @ T @ F1 @ F22 @ ( extended_enat2 @ Nat ) )
% 0.20/0.47 = ( F1 @ Nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % enat.simps(6)
% 0.20/0.47 thf(fact_145_sub__num__simps_I5_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ ( bit1 @ K3 ) @ one2 )
% 0.20/0.47 = ( numeral_numeral @ A @ ( bit0 @ K3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(5)
% 0.20/0.47 thf(fact_146_dbl__inc__simps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( neg_numeral_dbl_inc @ A @ ( one_one @ A ) )
% 0.20/0.47 = ( numeral_numeral @ A @ ( bit1 @ one2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_inc_simps(3)
% 0.20/0.47 thf(fact_147_dbl__simps_I5_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K3 ) )
% 0.20/0.47 = ( numeral_numeral @ A @ ( bit0 @ K3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_simps(5)
% 0.20/0.47 thf(fact_148_nat__1__eq__mult__iff,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( ( one_one @ nat )
% 0.20/0.47 = ( times_times @ nat @ M @ N ) )
% 0.20/0.47 = ( ( M
% 0.20/0.47 = ( one_one @ nat ) )
% 0.20/0.47 & ( N
% 0.20/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_1_eq_mult_iff
% 0.20/0.47 thf(fact_149_nat__mult__eq__1__iff,axiom,
% 0.20/0.47 ! [M: nat,N: nat] :
% 0.20/0.47 ( ( ( times_times @ nat @ M @ N )
% 0.20/0.47 = ( one_one @ nat ) )
% 0.20/0.47 = ( ( M
% 0.20/0.47 = ( one_one @ nat ) )
% 0.20/0.47 & ( N
% 0.20/0.47 = ( one_one @ nat ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % nat_mult_eq_1_iff
% 0.20/0.47 thf(fact_150_numeral__eq__one__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( ( numeral_numeral @ A @ N )
% 0.20/0.47 = ( one_one @ A ) )
% 0.20/0.47 = ( N = one2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_eq_one_iff
% 0.20/0.47 thf(fact_151_one__eq__numeral__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( ( one_one @ A )
% 0.20/0.47 = ( numeral_numeral @ A @ N ) )
% 0.20/0.47 = ( one2 = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % one_eq_numeral_iff
% 0.20/0.47 thf(fact_152_sub__num__simps_I9_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num,L: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ ( bit1 @ K3 ) @ ( bit1 @ L ) )
% 0.20/0.47 = ( neg_numeral_dbl @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(9)
% 0.20/0.47 thf(fact_153_sub__num__simps_I6_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num,L: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ ( bit0 @ K3 ) @ ( bit0 @ L ) )
% 0.20/0.47 = ( neg_numeral_dbl @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(6)
% 0.20/0.47 thf(fact_154_sub__num__simps_I8_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num,L: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ ( bit1 @ K3 ) @ ( bit0 @ L ) )
% 0.20/0.47 = ( neg_numeral_dbl_inc @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(8)
% 0.20/0.47 thf(fact_155_numeral__le__one__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.20/0.47 = ( ord_less_eq @ num @ N @ one2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_le_one_iff
% 0.20/0.47 thf(fact_156_dbl__simps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 0.20/0.47 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_simps(3)
% 0.20/0.47 thf(fact_157_nat__mult__1,axiom,
% 0.20/0.47 ! [N: nat] :
% 0.20/0.47 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 0.20/0.47 = N ) ).
% 0.20/0.47
% 0.20/0.47 % nat_mult_1
% 0.20/0.47 thf(fact_158_nat__mult__1__right,axiom,
% 0.20/0.47 ! [N: nat] :
% 0.20/0.47 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 0.20/0.47 = N ) ).
% 0.20/0.47
% 0.20/0.47 % nat_mult_1_right
% 0.20/0.47 thf(fact_159_le__numeral__extra_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_numeral_extra(4)
% 0.20/0.47 thf(fact_160_one__enat__def,axiom,
% 0.20/0.47 ( ( one_one @ extended_enat )
% 0.20/0.47 = ( extended_enat2 @ ( one_one @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % one_enat_def
% 0.20/0.47 thf(fact_161_enat__1__iff_I1_J,axiom,
% 0.20/0.47 ! [X: nat] :
% 0.20/0.47 ( ( ( extended_enat2 @ X )
% 0.20/0.47 = ( one_one @ extended_enat ) )
% 0.20/0.47 = ( X
% 0.20/0.47 = ( one_one @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % enat_1_iff(1)
% 0.20/0.47 thf(fact_162_enat__1__iff_I2_J,axiom,
% 0.20/0.47 ! [X: nat] :
% 0.20/0.47 ( ( ( one_one @ extended_enat )
% 0.20/0.47 = ( extended_enat2 @ X ) )
% 0.20/0.47 = ( X
% 0.20/0.47 = ( one_one @ nat ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % enat_1_iff(2)
% 0.20/0.47 thf(fact_163_one__le__numeral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] : ( ord_less_eq @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % one_le_numeral
% 0.20/0.47 thf(fact_164_numeral__One,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( numeral_numeral @ A @ one2 )
% 0.20/0.47 = ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_One
% 0.20/0.47 thf(fact_165_numerals_I1_J,axiom,
% 0.20/0.47 ( ( numeral_numeral @ nat @ one2 )
% 0.20/0.47 = ( one_one @ nat ) ) ).
% 0.20/0.47
% 0.20/0.47 % numerals(1)
% 0.20/0.47 thf(fact_166_mult_Oright__neutral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult.right_neutral
% 0.20/0.47 thf(fact_167_mult_Oleft__neutral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult.left_neutral
% 0.20/0.47 thf(fact_168_sub__num__simps_I7_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num,L: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ ( bit0 @ K3 ) @ ( bit1 @ L ) )
% 0.20/0.47 = ( neg_numeral_dbl_dec @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(7)
% 0.20/0.47 thf(fact_169_dbl__dec__simps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 0.20/0.47 = ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_dec_simps(3)
% 0.20/0.47 thf(fact_170_mult_Oleft__commute,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B2: A,A2: A,C: A] :
% 0.20/0.47 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C ) )
% 0.20/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult.left_commute
% 0.20/0.47 thf(fact_171_mult_Ocommute,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( times_times @ A )
% 0.20/0.47 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult.commute
% 0.20/0.47 thf(fact_172_mult_Oassoc,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( semigroup_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A,C: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.20/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult.assoc
% 0.20/0.47 thf(fact_173_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A,C: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.20/0.47 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ab_semigroup_mult_class.mult_ac(1)
% 0.20/0.47 thf(fact_174_one__reorient,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( one @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A] :
% 0.20/0.47 ( ( ( one_one @ A )
% 0.20/0.47 = X )
% 0.20/0.47 = ( X
% 0.20/0.47 = ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % one_reorient
% 0.20/0.47 thf(fact_175_comm__monoid__mult__class_Omult__1,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % comm_monoid_mult_class.mult_1
% 0.20/0.47 thf(fact_176_mult_Ocomm__neutral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult.comm_neutral
% 0.20/0.47 thf(fact_177_hamming__unfold,axiom,
% 0.20/0.47 ( hammin2015774020amming
% 0.20/0.47 = ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % hamming_unfold
% 0.20/0.47 thf(fact_178_sub__num__simps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ ( bit0 @ K3 ) @ one2 )
% 0.20/0.47 = ( numeral_numeral @ A @ ( bitM @ K3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(4)
% 0.20/0.47 thf(fact_179_semiring__normalization__rules_I12_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(12)
% 0.20/0.47 thf(fact_180_llist_Oinject,axiom,
% 0.20/0.47 ! [A: $tType,X21: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.20/0.47 ( ( ( coinductive_LCons @ A @ X21 @ X222 )
% 0.20/0.47 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.20/0.47 = ( ( X21 = Y21 )
% 0.20/0.47 & ( X222 = Y22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % llist.inject
% 0.20/0.47 thf(fact_181_lfinite__code_I2_J,axiom,
% 0.20/0.47 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.20/0.47 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.20/0.47 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.20/0.47
% 0.20/0.47 % lfinite_code(2)
% 0.20/0.47 thf(fact_182_lfinite__LCons,axiom,
% 0.20/0.47 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.20/0.47 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.20/0.47 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.20/0.47
% 0.20/0.47 % lfinite_LCons
% 0.20/0.47 thf(fact_183_dbl__dec__simps_I5_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_dbl_dec @ A @ ( numeral_numeral @ A @ K3 ) )
% 0.20/0.47 = ( numeral_numeral @ A @ ( bitM @ K3 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_dec_simps(5)
% 0.20/0.47 thf(fact_184_ltl__simps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,X21: A,X222: coinductive_llist @ A] :
% 0.20/0.47 ( ( coinductive_ltl @ A @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.20/0.47 = X222 ) ).
% 0.20/0.47
% 0.20/0.47 % ltl_simps(2)
% 0.20/0.47 thf(fact_185_lmap__eq__LCons__conv,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B,Y: A,Ys: coinductive_llist @ A] :
% 0.20/0.47 ( ( ( coinductive_lmap @ B @ A @ F @ Xs )
% 0.20/0.47 = ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.20/0.47 = ( ? [X4: B,Xs3: coinductive_llist @ B] :
% 0.20/0.47 ( ( Xs
% 0.20/0.47 = ( coinductive_LCons @ B @ X4 @ Xs3 ) )
% 0.20/0.47 & ( Y
% 0.20/0.47 = ( F @ X4 ) )
% 0.20/0.47 & ( Ys
% 0.20/0.47 = ( coinductive_lmap @ B @ A @ F @ Xs3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lmap_eq_LCons_conv
% 0.20/0.47 thf(fact_186_llist_Osimps_I13_J,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType,F: A > B,X21: A,X222: coinductive_llist @ A] :
% 0.20/0.47 ( ( coinductive_lmap @ A @ B @ F @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.20/0.47 = ( coinductive_LCons @ B @ ( F @ X21 ) @ ( coinductive_lmap @ A @ B @ F @ X222 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % llist.simps(13)
% 0.20/0.47 thf(fact_187_lfinite__LConsI,axiom,
% 0.20/0.47 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.20/0.47 ( ( coinductive_lfinite @ A @ Xs )
% 0.20/0.47 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lfinite_LConsI
% 0.20/0.47 thf(fact_188_semiring__norm_I26_J,axiom,
% 0.20/0.47 ( ( bitM @ one2 )
% 0.20/0.47 = one2 ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_norm(26)
% 0.20/0.47 thf(fact_189_semiring__norm_I28_J,axiom,
% 0.20/0.47 ! [N: num] :
% 0.20/0.47 ( ( bitM @ ( bit1 @ N ) )
% 0.20/0.47 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_norm(28)
% 0.20/0.47 thf(fact_190_semiring__norm_I27_J,axiom,
% 0.20/0.47 ! [N: num] :
% 0.20/0.47 ( ( bitM @ ( bit0 @ N ) )
% 0.20/0.47 = ( bit1 @ ( bitM @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_norm(27)
% 0.20/0.47 thf(fact_191_semiring__normalization__rules_I19_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Rx: A,Ry: A] :
% 0.20/0.47 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 0.20/0.47 = ( times_times @ A @ Rx @ ( times_times @ A @ Lx @ Ry ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(19)
% 0.20/0.47 thf(fact_192_semiring__normalization__rules_I18_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Rx: A,Ry: A] :
% 0.20/0.47 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 0.20/0.47 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ry ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(18)
% 0.20/0.47 thf(fact_193_semiring__normalization__rules_I17_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Ly: A,Rx: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 0.20/0.47 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ Rx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(17)
% 0.20/0.47 thf(fact_194_semiring__normalization__rules_I16_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Ly: A,Rx: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 0.20/0.47 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ly ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(16)
% 0.20/0.47 thf(fact_195_semiring__normalization__rules_I15_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.20/0.47 = ( times_times @ A @ Rx @ ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Ry ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(15)
% 0.20/0.47 thf(fact_196_semiring__normalization__rules_I14_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.20/0.47 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ ( times_times @ A @ Rx @ Ry ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(14)
% 0.20/0.47 thf(fact_197_semiring__normalization__rules_I13_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.20/0.47 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.20/0.47 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ ( times_times @ A @ Ly @ Ry ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(13)
% 0.20/0.47 thf(fact_198_semiring__normalization__rules_I7_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( times_times @ A )
% 0.20/0.47 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(7)
% 0.20/0.47 thf(fact_199_semiring__normalization__rules_I11_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_normalization_rules(11)
% 0.20/0.47 thf(fact_200_hamming_H_Osimps,axiom,
% 0.20/0.47 ( hammin1630468845amming
% 0.20/0.47 = ( ^ [Uu: product_unit] : ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % hamming'.simps
% 0.20/0.47 thf(fact_201_sub__num__simps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [L: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ one2 @ ( bit0 @ L ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bitM @ L ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(2)
% 0.20/0.47 thf(fact_202_dbl__dec__simps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( neg_numeral_dbl_dec @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit1 @ one2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_dec_simps(4)
% 0.20/0.47 thf(fact_203_compl__eq__compl__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( ( uminus_uminus @ A @ X )
% 0.20/0.47 = ( uminus_uminus @ A @ Y ) )
% 0.20/0.47 = ( X = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % compl_eq_compl_iff
% 0.20/0.47 thf(fact_204_double__compl,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A] :
% 0.20/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.20/0.47 = X ) ) ).
% 0.20/0.47
% 0.20/0.47 % double_compl
% 0.20/0.47 thf(fact_205_uminus__apply,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( uminus @ B @ ( type2 @ B ) )
% 0.20/0.47 => ( ( uminus_uminus @ ( A > B ) )
% 0.20/0.47 = ( ^ [A5: A > B,X4: A] : ( uminus_uminus @ B @ ( A5 @ X4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % uminus_apply
% 0.20/0.47 thf(fact_206_neg__equal__iff__equal,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.20/0.47 = ( uminus_uminus @ A @ B2 ) )
% 0.20/0.47 = ( A2 = B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_equal_iff_equal
% 0.20/0.47 thf(fact_207_add_Oinverse__inverse,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A] :
% 0.20/0.47 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 0.20/0.47 = A2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % add.inverse_inverse
% 0.20/0.47 thf(fact_208_compl__le__compl__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) )
% 0.20/0.47 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % compl_le_compl_iff
% 0.20/0.47 thf(fact_209_neg__le__iff__le,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [B2: A,A2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) )
% 0.20/0.47 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_le_iff_le
% 0.20/0.47 thf(fact_210_neg__numeral__eq__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.20/0.47 = ( M = N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_numeral_eq_iff
% 0.20/0.47 thf(fact_211_mult__minus1__right,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Z: A] :
% 0.20/0.47 ( ( times_times @ A @ Z @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ Z ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_minus1_right
% 0.20/0.47 thf(fact_212_mult__minus1,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Z: A] :
% 0.20/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ Z )
% 0.20/0.47 = ( uminus_uminus @ A @ Z ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_minus1
% 0.20/0.47 thf(fact_213_dbl__simps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K3 ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_simps(1)
% 0.20/0.47 thf(fact_214_dbl__inc__simps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( neg_numeral_dbl_inc @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_inc_simps(4)
% 0.20/0.47 thf(fact_215_neg__one__eq__numeral__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( ( uminus_uminus @ A @ ( one_one @ A ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.20/0.47 = ( N = one2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_one_eq_numeral_iff
% 0.20/0.47 thf(fact_216_numeral__eq__neg__one__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.20/0.47 = ( N = one2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_eq_neg_one_iff
% 0.20/0.47 thf(fact_217_mult__neg__numeral__simps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.20/0.47 = ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_neg_numeral_simps(1)
% 0.20/0.47 thf(fact_218_mult__neg__numeral__simps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_neg_numeral_simps(2)
% 0.20/0.47 thf(fact_219_mult__neg__numeral__simps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_neg_numeral_simps(3)
% 0.20/0.47 thf(fact_220_semiring__norm_I170_J,axiom,
% 0.20/0.47 ! [B: $tType] :
% 0.20/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [V: num,W: num,Y: B] :
% 0.20/0.47 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( numeral_numeral @ B @ W ) @ Y ) )
% 0.20/0.47 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_norm(170)
% 0.20/0.47 thf(fact_221_semiring__norm_I171_J,axiom,
% 0.20/0.47 ! [B: $tType] :
% 0.20/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [V: num,W: num,Y: B] :
% 0.20/0.47 ( ( times_times @ B @ ( numeral_numeral @ B @ V ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 0.20/0.47 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_norm(171)
% 0.20/0.47 thf(fact_222_semiring__norm_I172_J,axiom,
% 0.20/0.47 ! [B: $tType] :
% 0.20/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [V: num,W: num,Y: B] :
% 0.20/0.47 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 0.20/0.47 = ( times_times @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % semiring_norm(172)
% 0.20/0.47 thf(fact_223_neg__numeral__le__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.20/0.47 = ( ord_less_eq @ num @ N @ M ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_numeral_le_iff
% 0.20/0.47 thf(fact_224_not__neg__one__le__neg__numeral__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num] :
% 0.20/0.47 ( ( ~ ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) ) )
% 0.20/0.47 = ( M != one2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_neg_one_le_neg_numeral_iff
% 0.20/0.47 thf(fact_225_dbl__dec__simps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_dbl_dec @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K3 ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( neg_numeral_dbl_inc @ A @ ( numeral_numeral @ A @ K3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_dec_simps(1)
% 0.20/0.47 thf(fact_226_dbl__inc__simps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [K3: num] :
% 0.20/0.47 ( ( neg_numeral_dbl_inc @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K3 ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( neg_numeral_dbl_dec @ A @ ( numeral_numeral @ A @ K3 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_inc_simps(1)
% 0.20/0.47 thf(fact_227_sub__num__simps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [L: num] :
% 0.20/0.47 ( ( neg_numeral_sub @ A @ one2 @ ( bit1 @ L ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ L ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % sub_num_simps(3)
% 0.20/0.47 thf(fact_228_dbl__simps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.20/0.47 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % dbl_simps(4)
% 0.20/0.47 thf(fact_229_ring__normalization__rules_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( uminus_uminus @ A )
% 0.20/0.47 = ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ring_normalization_rules(1)
% 0.20/0.47 thf(fact_230_numeral__times__minus__swap,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [W: num,X: A] :
% 0.20/0.47 ( ( times_times @ A @ ( numeral_numeral @ A @ W ) @ ( uminus_uminus @ A @ X ) )
% 0.20/0.47 = ( times_times @ A @ X @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_times_minus_swap
% 0.20/0.47 thf(fact_231_numeral__neq__neg__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( numeral_numeral @ A @ N )
% 0.20/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_neq_neg_one
% 0.20/0.47 thf(fact_232_one__neq__neg__numeral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [N: num] :
% 0.20/0.47 ( ( one_one @ A )
% 0.20/0.47 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % one_neq_neg_numeral
% 0.20/0.47 thf(fact_233_hamming__def,axiom,
% 0.20/0.47 ( hammin2015774020amming
% 0.20/0.47 = ( hammin1630468845amming @ product_Unity ) ) ).
% 0.20/0.47
% 0.20/0.47 % hamming_def
% 0.20/0.47 thf(fact_234_neg__numeral__neq__numeral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 0.20/0.47 != ( numeral_numeral @ A @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_numeral_neq_numeral
% 0.20/0.47 thf(fact_235_numeral__neq__neg__numeral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ( ( numeral_numeral @ A @ M )
% 0.20/0.47 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % numeral_neq_neg_numeral
% 0.20/0.47 thf(fact_236_fun__Compl__def,axiom,
% 0.20/0.47 ! [B: $tType,A: $tType] :
% 0.20/0.47 ( ( uminus @ B @ ( type2 @ B ) )
% 0.20/0.47 => ( ( uminus_uminus @ ( A > B ) )
% 0.20/0.47 = ( ^ [A5: A > B,X4: A] : ( uminus_uminus @ B @ ( A5 @ X4 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % fun_Compl_def
% 0.20/0.47 thf(fact_237_compl__le__swap2,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Y: A,X: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ X )
% 0.20/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % compl_le_swap2
% 0.20/0.47 thf(fact_238_compl__le__swap1,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [Y: A,X: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ Y @ ( uminus_uminus @ A @ X ) )
% 0.20/0.47 => ( ord_less_eq @ A @ X @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % compl_le_swap1
% 0.20/0.47 thf(fact_239_compl__mono,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [X: A,Y: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.20/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ ( uminus_uminus @ A @ X ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % compl_mono
% 0.20/0.47 thf(fact_240_le__minus__one__simps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_minus_one_simps(2)
% 0.20/0.47 thf(fact_241_le__minus__one__simps_I4_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_minus_one_simps(4)
% 0.20/0.47 thf(fact_242_neg__numeral__le__numeral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] : ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % neg_numeral_le_numeral
% 0.20/0.47 thf(fact_243_not__numeral__le__neg__numeral,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [M: num,N: num] :
% 0.20/0.47 ~ ( ord_less_eq @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % not_numeral_le_neg_numeral
% 0.20/0.47 thf(fact_244_le__minus__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ ( uminus_uminus @ A @ B2 ) )
% 0.20/0.47 = ( ord_less_eq @ A @ B2 @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_minus_iff
% 0.20/0.47 thf(fact_245_minus__le__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A2 ) @ B2 )
% 0.20/0.47 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % minus_le_iff
% 0.20/0.47 thf(fact_246_le__imp__neg__le,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.20/0.47 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % le_imp_neg_le
% 0.20/0.47 thf(fact_247_minus__equation__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( ( uminus_uminus @ A @ A2 )
% 0.20/0.47 = B2 )
% 0.20/0.47 = ( ( uminus_uminus @ A @ B2 )
% 0.20/0.47 = A2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % minus_equation_iff
% 0.20/0.47 thf(fact_248_equation__minus__iff,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( group_add @ A @ ( type2 @ A ) )
% 0.20/0.47 => ! [A2: A,B2: A] :
% 0.20/0.47 ( ( A2
% 0.20/0.47 = ( uminus_uminus @ A @ B2 ) )
% 0.20/0.47 = ( B2
% 0.20/0.47 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % equation_minus_iff
% 0.20/0.47 thf(fact_249_one__neq__neg__one,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.20/0.47 => ( ( one_one @ A )
% 0.20/0.47 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % one_neq_neg_one
% 0.20/0.47 thf(fact_250_mult__1s_I3_J,axiom,
% 0.20/0.47 ! [B: $tType] :
% 0.20/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [B2: B] :
% 0.20/0.47 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) @ B2 )
% 0.20/0.47 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_1s(3)
% 0.20/0.47 thf(fact_251_mult__1s_I4_J,axiom,
% 0.20/0.47 ! [B: $tType] :
% 0.20/0.47 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.20/0.47 => ! [B2: B] :
% 0.20/0.47 ( ( times_times @ B @ B2 @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) )
% 0.20/0.47 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % mult_1s(4)
% 0.20/0.47
% 0.20/0.47 %----Type constructors (50)
% 0.20/0.47 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( semilattice_inf @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( semilattice_inf @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( boolean_algebra @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( boolean_algebra @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( preorder @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( preorder @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( order @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( ord @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( ord @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.20/0.47 ! [A6: $tType,A7: $tType] :
% 0.20/0.47 ( ( uminus @ A7 @ ( type2 @ A7 ) )
% 0.20/0.47 => ( uminus @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.20/0.47 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_1,axiom,
% 0.20/0.47 semilattice_inf @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.20/0.47 ab_semigroup_mult @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.20/0.47 comm_monoid_mult @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.20/0.47 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.20/0.47 semigroup_mult @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Num_Osemiring__numeral,axiom,
% 0.20/0.47 semiring_numeral @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.20/0.47 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 0.20/0.47 preorder @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.20/0.47 linorder @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.20/0.47 monoid_mult @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Lattices_Olattice_3,axiom,
% 0.20/0.47 lattice @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 0.20/0.47 order @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 0.20/0.47 ord @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.20/0.47 numeral @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.20/0.47 one @ nat @ ( type2 @ nat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Num_Onum___Orderings_Opreorder_6,axiom,
% 0.20/0.47 preorder @ num @ ( type2 @ num ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Num_Onum___Orderings_Olinorder_7,axiom,
% 0.20/0.47 linorder @ num @ ( type2 @ num ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Num_Onum___Orderings_Oorder_8,axiom,
% 0.20/0.47 order @ num @ ( type2 @ num ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Num_Onum___Orderings_Oord_9,axiom,
% 0.20/0.47 ord @ num @ ( type2 @ num ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_10,axiom,
% 0.20/0.47 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11,axiom,
% 0.20/0.47 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 0.20/0.47 preorder @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_13,axiom,
% 0.20/0.47 linorder @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Lattices_Olattice_14,axiom,
% 0.20/0.47 lattice @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.20/0.47 order @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.20/0.47 ord @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_HOL_Obool___Groups_Ouminus_17,axiom,
% 0.20/0.47 uminus @ $o @ ( type2 @ $o ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_18,axiom,
% 0.20/0.47 semilattice_inf @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_19,axiom,
% 0.20/0.47 ab_semigroup_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__mult_20,axiom,
% 0.20/0.47 comm_monoid_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_21,axiom,
% 0.20/0.47 comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_22,axiom,
% 0.20/0.47 semigroup_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_23,axiom,
% 0.20/0.47 semiring_numeral @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_24,axiom,
% 0.20/0.47 semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_25,axiom,
% 0.20/0.47 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_26,axiom,
% 0.20/0.47 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Omonoid__mult_27,axiom,
% 0.20/0.47 monoid_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Lattices_Olattice_28,axiom,
% 0.20/0.47 lattice @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_29,axiom,
% 0.20/0.47 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_30,axiom,
% 0.20/0.47 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Num_Onumeral_31,axiom,
% 0.20/0.47 numeral @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 thf(tcon_Extended__Nat_Oenat___Groups_Oone_32,axiom,
% 0.20/0.47 one @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.20/0.47
% 0.20/0.47 %----Conjectures (1)
% 0.20/0.47 thf(conj_0,conjecture,
% 0.20/0.47 ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) ) @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) @ ( coinductive_llength @ nat @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.32/1.51 ---- Embedded in THF ---
% 0.32/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.32/1.51 %%% Generated on Tue Feb 24 06:09:48 EST 2026
% 0.32/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 0.32/1.51 %%% Logic specification used:
% 0.32/1.51 %%% thf(spec, logic, $$dhol).
% 0.32/1.51
% 0.32/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2DTF16461.p
% 0.32/1.51 thf(ty_t_Coinductive__List_Ollist, type, coinductive_llist: ($tType > $tType)).
% 0.32/1.51 thf(ty_t_Product__Type_Ounit, type, product_unit: $tType).
% 0.32/1.51 thf(ty_t_Extended__Nat_Oenat, type, extended_enat: $tType).
% 0.32/1.51 thf(ty_t_Num_Onum, type, num: $tType).
% 0.32/1.51 thf(ty_t_Nat_Onat, type, nat: $tType).
% 0.32/1.51 thf(ty_t_itself, type, itself: ($tType > $tType)).
% 0.32/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Oone, type, one: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Num_Onumeral, type, numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Rings_Oring__1, type, ring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Ouminus, type, uminus: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Nat_Oring__char__0, type, ring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Num_Oneg__numeral, type, neg_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Ogroup__add, type, group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Lattices_Olattice, type, lattice: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Rings_Ocomm__ring__1, type, comm_ring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Omonoid__mult, type, monoid_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Nat_Osemiring__char__0, type, semiring_char_0: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Num_Osemiring__numeral, type, semiring_numeral: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Osemigroup__mult, type, semigroup_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Rings_Ocomm__semiring__1, type, comm_semiring_1: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Rings_Olinordered__idom, type, linordered_idom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Ocomm__monoid__mult, type, comm_monoid_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Oab__semigroup__mult, type, ab_semigroup_mult: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Lattices_Oboolean__algebra, type, boolean_algebra: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Lattices_Osemilattice__inf, type, semilattice_inf: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Rings_Olinordered__semidom, type, linordered_semidom: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_cl_Groups_Oordered__ab__group__add, type, ordered_ab_group_add: (!> [A:$tType]: (((itself @ A) > $o)))).
% 0.32/1.51 thf(sy_c_Coinductive__List_Olfinite, type, coinductive_lfinite: (!> [A:$tType]: (((coinductive_llist @ A) > $o)))).
% 0.32/1.51 thf(sy_c_Coinductive__List_Ollength, type, coinductive_llength: (!> [A:$tType]: (((coinductive_llist @ A) > extended_enat)))).
% 0.32/1.51 thf(sy_c_Coinductive__List_Ollist_OLCons, type, coinductive_LCons: (!> [A:$tType]: ((A > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 0.32/1.51 thf(sy_c_Coinductive__List_Ollist_Olmap, type, coinductive_lmap: (!> [A:$tType,Aa:$tType]: (((A > Aa) > ((coinductive_llist @ A) > (coinductive_llist @ Aa)))))).
% 0.32/1.51 thf(sy_c_Coinductive__List_Ollist_Oltl, type, coinductive_ltl: (!> [A:$tType]: (((coinductive_llist @ A) > (coinductive_llist @ A))))).
% 0.32/1.51 thf(sy_c_Extended__Nat_Oenat, type, extended_enat2: (nat > extended_enat)).
% 0.32/1.51 thf(sy_c_Extended__Nat_Oenat_Orec__enat, type, extended_rec_enat: (!> [T:$tType]: (((nat > T) > (T > (extended_enat > T)))))).
% 0.32/1.51 thf(sy_c_Groups_Oone__class_Oone, type, one_one: (!> [A:$tType]: (A))).
% 0.32/1.51 thf(sy_c_Groups_Otimes__class_Otimes, type, times_times: (!> [A:$tType]: ((A > (A > A))))).
% 0.32/1.51 thf(sy_c_Groups_Ouminus__class_Ouminus, type, uminus_uminus: (!> [A:$tType]: ((A > A)))).
% 0.32/1.51 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Ohamming, type, hammin2015774020amming: (coinductive_llist @ nat)).
% 0.32/1.51 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Ohamming_H, type, hammin1630468845amming: (product_unit > (coinductive_llist @ nat))).
% 0.32/1.51 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Oord__class_Olmerge, type, hammin1138290136lmerge: (!> [A:$tType]: (((coinductive_llist @ A) > ((coinductive_llist @ A) > (coinductive_llist @ A)))))).
% 0.32/1.51 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Osmooth, type, hammin1195055315smooth: (nat > $o)).
% 0.32/1.51 thf(sy_c_Lattices_Oinf__class_Oinf, type, inf_inf: (!> [A:$tType]: ((A > (A > A))))).
% 0.32/1.51 thf(sy_c_Num_OBitM, type, bitM: (num > num)).
% 0.32/1.51 thf(sy_c_Num_Oneg__numeral__class_Odbl, type, neg_numeral_dbl: (!> [A:$tType]: ((A > A)))).
% 0.32/1.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec, type, neg_numeral_dbl_dec: (!> [A:$tType]: ((A > A)))).
% 0.32/1.51 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc, type, neg_numeral_dbl_inc: (!> [A:$tType]: ((A > A)))).
% 0.32/1.51 thf(sy_c_Num_Oneg__numeral__class_Osub, type, neg_numeral_sub: (!> [A:$tType]: ((num > (num > A))))).
% 0.32/1.51 thf(sy_c_Num_Onum_OBit0, type, bit0: (num > num)).
% 0.32/1.51 thf(sy_c_Num_Onum_OBit1, type, bit1: (num > num)).
% 0.32/1.51 thf(sy_c_Num_Onum_OOne, type, one2: num).
% 0.32/1.51 thf(sy_c_Num_Onumeral__class_Onumeral, type, numeral_numeral: (!> [A:$tType]: ((num > A)))).
% 0.32/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 0.32/1.51 thf(sy_c_Product__Type_OUnity, type, product_Unity: product_unit).
% 0.32/1.51 thf(sy_c_Pure_Otype, type, type2: (!> [A:$tType]: ((itself @ A)))).
% 0.32/1.51 thf(sy_v_n____, type, n: nat).
% 0.32/1.51 thf(fact_0__092_060open_062lfinite_Ahamming_092_060close_062, axiom, ((coinductive_lfinite @ nat) @ hammin2015774020amming)).
% 0.32/1.51 thf(fact_1_llength__lmerge__above, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((ord_less_eq @ extended_enat) @ (((inf_inf @ extended_enat) @ ((coinductive_llength @ A) @ Xs)) @ ((coinductive_llength @ A) @ Ys))) @ ((coinductive_llength @ A) @ (((hammin1138290136lmerge @ A) @ Xs) @ Ys))))))))).
% 0.32/1.51 thf(fact_2_n, axiom, (((coinductive_llength @ nat) @ hammin2015774020amming) = (extended_enat2 @ n))).
% 0.32/1.51 thf(fact_3_llength__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coinductive_llist @ B)]: ((((coinductive_llength @ A) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)) = ((coinductive_llength @ B) @ Xs))))).
% 0.32/1.51 thf(fact_4_le__inf__iff, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = ((((ord_less_eq @ A) @ X) @ Y) & (((ord_less_eq @ A) @ X) @ Z))))))))).
% 0.32/1.51 thf(fact_5_inf_Obounded__iff, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C)) = ((((ord_less_eq @ A) @ A2) @ B2) & (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.51 thf(fact_6_semiring__norm_I169_J, axiom, (! [A:$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)))))))).
% 0.32/1.51 thf(fact_7_numeral__times__numeral, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((times_times @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = ((numeral_numeral @ A) @ (((times_times @ num) @ M) @ N))))))))).
% 0.32/1.51 thf(fact_8_numeral__le__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((ord_less_eq @ A) @ ((numeral_numeral @ A) @ M)) @ ((numeral_numeral @ A) @ N)) = (((ord_less_eq @ num) @ M) @ N)))))))).
% 0.32/1.51 thf(fact_9_semiring__norm_I85_J, axiom, (! [M:num]: (((bit0 @ M) != one2)))).
% 0.32/1.51 thf(fact_10_semiring__norm_I83_J, axiom, (! [N:num]: ((one2 != (bit0 @ N))))).
% 0.32/1.51 thf(fact_11_semiring__norm_I86_J, axiom, (! [M:num]: (((bit1 @ M) != one2)))).
% 0.32/1.51 thf(fact_12_semiring__norm_I84_J, axiom, (! [N:num]: ((one2 != (bit1 @ N))))).
% 0.32/1.51 thf(fact_13_semiring__norm_I89_J, axiom, (! [M:num,N:num]: (((bit1 @ M) != (bit0 @ N))))).
% 0.32/1.51 thf(fact_14_semiring__norm_I90_J, axiom, (! [M:num,N:num]: ((((bit1 @ M) = (bit1 @ N)) = (M = N))))).
% 0.32/1.51 thf(fact_15_num_Oinject_I2_J, axiom, (! [X3:num,Y3:num]: ((((bit1 @ X3) = (bit1 @ Y3)) = (X3 = Y3))))).
% 0.32/1.51 thf(fact_16_semiring__norm_I87_J, axiom, (! [M:num,N:num]: ((((bit0 @ M) = (bit0 @ N)) = (M = N))))).
% 0.32/1.51 thf(fact_17_num_Oinject_I1_J, axiom, (! [X2:num,Y2:num]: ((((bit0 @ X2) = (bit0 @ Y2)) = (X2 = Y2))))).
% 0.32/1.51 thf(fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_Ahamming_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062, axiom, (~ ((! [N2:nat]: ((((coinductive_llength @ nat) @ hammin2015774020amming) != (extended_enat2 @ N2))))))).
% 0.32/1.51 thf(fact_19_numeral__eq__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((numeral_numeral @ A) @ M) = ((numeral_numeral @ A) @ N)) = (M = N)))))))).
% 0.32/1.51 thf(fact_20_inf__right__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y) = (((inf_inf @ A) @ X) @ Y)))))))).
% 0.32/1.51 thf(fact_21_inf_Oright__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 0.32/1.51 thf(fact_22_inf__left__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 0.32/1.51 thf(fact_23_inf_Oleft__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ A2) @ B2)) = (((inf_inf @ A) @ A2) @ B2)))))))).
% 0.32/1.51 thf(fact_24_inf__idem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A]: (((((inf_inf @ A) @ X) @ X) = X))))))).
% 0.32/1.51 thf(fact_25_inf_Oidem, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A]: (((((inf_inf @ A) @ A2) @ A2) = A2))))))).
% 0.32/1.51 thf(fact_26_inf__apply, axiom, (! [B:$tType,A:$tType]: ((((semilattice_inf @ B) @ (type2 @ B)) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G:(A > B),X4:A]: ((((inf_inf @ B) @ (F2 @ X4)) @ (G @ X4))))))))).
% 0.32/1.51 thf(fact_27_semiring__norm_I88_J, axiom, (! [M:num,N:num]: (((bit0 @ M) != (bit1 @ N))))).
% 0.32/1.51 thf(fact_28_semiring__norm_I13_J, axiom, (! [M:num,N:num]: (((((times_times @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (bit0 @ (bit0 @ (((times_times @ num) @ M) @ N))))))).
% 0.32/1.51 thf(fact_29_lfinite__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ A) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 0.32/1.51 thf(fact_30_semiring__norm_I11_J, axiom, (! [M:num]: (((((times_times @ num) @ M) @ one2) = M)))).
% 0.32/1.51 thf(fact_31_semiring__norm_I12_J, axiom, (! [N:num]: (((((times_times @ num) @ one2) @ N) = N)))).
% 0.32/1.51 thf(fact_32_semiring__norm_I73_J, axiom, (! [M:num,N:num]: (((((ord_less_eq @ num) @ (bit1 @ M)) @ (bit1 @ N)) = (((ord_less_eq @ num) @ M) @ N))))).
% 0.32/1.51 thf(fact_33_semiring__norm_I71_J, axiom, (! [M:num,N:num]: (((((ord_less_eq @ num) @ (bit0 @ M)) @ (bit0 @ N)) = (((ord_less_eq @ num) @ M) @ N))))).
% 0.32/1.51 thf(fact_34_semiring__norm_I68_J, axiom, (! [N:num]: ((((ord_less_eq @ num) @ one2) @ N)))).
% 0.32/1.51 thf(fact_35_semiring__norm_I14_J, axiom, (! [M:num,N:num]: (((((times_times @ num) @ (bit0 @ M)) @ (bit1 @ N)) = (bit0 @ (((times_times @ num) @ M) @ (bit1 @ N))))))).
% 0.32/1.51 thf(fact_36_semiring__norm_I15_J, axiom, (! [M:num,N:num]: (((((times_times @ num) @ (bit1 @ M)) @ (bit0 @ N)) = (bit0 @ (((times_times @ num) @ (bit1 @ M)) @ N)))))).
% 0.32/1.51 thf(fact_37_semiring__norm_I72_J, axiom, (! [M:num,N:num]: (((((ord_less_eq @ num) @ (bit0 @ M)) @ (bit1 @ N)) = (((ord_less_eq @ num) @ M) @ N))))).
% 0.32/1.51 thf(fact_38_semiring__norm_I70_J, axiom, (! [M:num]: ((~ ((((ord_less_eq @ num) @ (bit1 @ M)) @ one2)))))).
% 0.32/1.51 thf(fact_39_semiring__norm_I69_J, axiom, (! [M:num]: ((~ ((((ord_less_eq @ num) @ (bit0 @ M)) @ one2)))))).
% 0.32/1.51 thf(fact_40_lfinite__llength__enat, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (? [N2:nat]: ((((coinductive_llength @ A) @ Xs) = (extended_enat2 @ N2)))))))).
% 0.32/1.51 thf(fact_41_llength__eq__enat__lfiniteD, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),N:nat]: (((((coinductive_llength @ A) @ Xs) = (extended_enat2 @ N)) => ((coinductive_lfinite @ A) @ Xs))))).
% 0.32/1.51 thf(fact_42_lfinite__conv__llength__enat, axiom, (! [A:$tType]: (((coinductive_lfinite @ A) = (^ [Xs2:(coinductive_llist @ A)]: ((? [N3:nat]: ((((coinductive_llength @ A) @ Xs2) = (extended_enat2 @ N3)))))))))).
% 0.32/1.51 thf(fact_43_le__num__One__iff, axiom, (! [X:num]: (((((ord_less_eq @ num) @ X) @ one2) = (X = one2))))).
% 0.32/1.51 thf(fact_44_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G2:(A > B)]: (((! [X5:A]: (((F @ X5) = (G2 @ X5)))) => (F = G2))))).
% 0.32/1.51 thf(fact_45_linfinite__lmerge, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: (((~ (((coinductive_lfinite @ A) @ Xs))) => ((~ (((coinductive_lfinite @ A) @ Ys))) => (~ (((coinductive_lfinite @ A) @ (((hammin1138290136lmerge @ A) @ Xs) @ Ys)))))))))))).
% 0.32/1.51 thf(fact_46_lfinite__lmergeI, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ Xs) => (((coinductive_lfinite @ A) @ Ys) => ((coinductive_lfinite @ A) @ (((hammin1138290136lmerge @ A) @ Xs) @ Ys)))))))))).
% 0.32/1.51 thf(fact_47_lfinite__lmergeD, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [Xs:(coinductive_llist @ A),Ys:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((hammin1138290136lmerge @ A) @ Xs) @ Ys)) => (((coinductive_lfinite @ A) @ Xs) | ((coinductive_lfinite @ A) @ Ys))))))))).
% 0.32/1.51 thf(fact_48_wlog__linorder__le, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),B2:A,A2:A]: (((! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((P @ A3) @ B3)))) => ((((P @ B2) @ A2) => ((P @ A2) @ B2)) => ((P @ A2) @ B2))))))))).
% 0.32/1.51 thf(fact_49_inf__left__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ Y) @ (((inf_inf @ A) @ X) @ Z))))))))).
% 0.32/1.51 thf(fact_50_inf_Oleft__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((inf_inf @ A) @ B2) @ (((inf_inf @ A) @ A2) @ C)) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C))))))))).
% 0.32/1.51 thf(fact_51_inf__commute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [X4:A,Y4:A]: ((((inf_inf @ A) @ Y4) @ X4)))))))).
% 0.32/1.51 thf(fact_52_inf_Ocommute, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [A4:A,B4:A]: ((((inf_inf @ A) @ B4) @ A4)))))))).
% 0.32/1.51 thf(fact_53_inf__assoc, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Z) = (((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z))))))))).
% 0.32/1.51 thf(fact_54_inf_Oassoc, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C) = (((inf_inf @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C))))))))).
% 0.32/1.51 thf(fact_55_inf__fun__def, axiom, (! [B:$tType,A:$tType]: ((((semilattice_inf @ B) @ (type2 @ B)) => ((inf_inf @ (A > B)) = (^ [F2:(A > B),G:(A > B),X4:A]: ((((inf_inf @ B) @ (F2 @ X4)) @ (G @ X4))))))))).
% 0.32/1.51 thf(fact_56_inf__sup__aci_I1_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => ((inf_inf @ A) = (^ [X4:A,Y4:A]: ((((inf_inf @ A) @ Y4) @ X4)))))))).
% 0.32/1.51 thf(fact_57_inf__sup__aci_I2_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Z) = (((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z))))))))).
% 0.32/1.51 thf(fact_58_inf__sup__aci_I3_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)) = (((inf_inf @ A) @ Y) @ (((inf_inf @ A) @ X) @ Z))))))))).
% 0.32/1.51 thf(fact_59_inf__sup__aci_I4_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((inf_inf @ A) @ X) @ (((inf_inf @ A) @ X) @ Y)) = (((inf_inf @ A) @ X) @ Y)))))))).
% 0.32/1.51 thf(fact_60_num_Odistinct_I5_J, axiom, (! [X2:num,X3:num]: (((bit0 @ X2) != (bit1 @ X3))))).
% 0.32/1.51 thf(fact_61_num_Odistinct_I3_J, axiom, (! [X3:num]: ((one2 != (bit1 @ X3))))).
% 0.32/1.51 thf(fact_62_num_Odistinct_I1_J, axiom, (! [X2:num]: ((one2 != (bit0 @ X2))))).
% 0.32/1.51 thf(fact_63_inf_OcoboundedI2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [B2:A,C:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C)))))))).
% 0.32/1.51 thf(fact_64_inf_OcoboundedI1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ C) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ C)))))))).
% 0.32/1.51 thf(fact_65_inf_Oabsorb__iff2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [B4:A,A4:A]: (((((inf_inf @ A) @ A4) @ B4) = B4)))))))).
% 0.32/1.51 thf(fact_66_inf_Oabsorb__iff1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A4:A,B4:A]: (((((inf_inf @ A) @ A4) @ B4) = A4)))))))).
% 0.32/1.51 thf(fact_67_inf_Ocobounded2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ B2))))))).
% 0.32/1.51 thf(fact_68_inf_Ocobounded1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ A2))))))).
% 0.32/1.51 thf(fact_69_inf_Oorder__iff, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [A4:A,B4:A]: ((A4 = (((inf_inf @ A) @ A4) @ B4))))))))).
% 0.32/1.51 thf(fact_70_inf__greatest, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ X) @ Z) => (((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ Y) @ Z)))))))))).
% 0.32/1.51 thf(fact_71_inf_OboundedI, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ A2) @ C) => (((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C)))))))))).
% 0.32/1.51 thf(fact_72_inf_OboundedE, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ (((inf_inf @ A) @ B2) @ C)) => (~ (((((ord_less_eq @ A) @ A2) @ B2) => (~ ((((ord_less_eq @ A) @ A2) @ C))))))))))))).
% 0.32/1.51 thf(fact_73_inf__absorb2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((inf_inf @ A) @ X) @ Y) = Y)))))))).
% 0.32/1.51 thf(fact_74_inf__absorb1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((inf_inf @ A) @ X) @ Y) = X)))))))).
% 0.32/1.51 thf(fact_75_inf_Oabsorb2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((inf_inf @ A) @ A2) @ B2) = B2)))))))).
% 0.32/1.51 thf(fact_76_inf_Oabsorb1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((inf_inf @ A) @ A2) @ B2) = A2)))))))).
% 0.32/1.51 thf(fact_77_le__iff__inf, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => ((ord_less_eq @ A) = (^ [X4:A,Y4:A]: (((((inf_inf @ A) @ X4) @ Y4) = X4)))))))).
% 0.32/1.51 thf(fact_78_inf__unique, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [F:(A > (A > A)),X:A,Y:A]: (((! [X5:A,Y5:A]: ((((ord_less_eq @ A) @ ((F @ X5) @ Y5)) @ X5))) => ((! [X5:A,Y5:A]: ((((ord_less_eq @ A) @ ((F @ X5) @ Y5)) @ Y5))) => ((! [X5:A,Y5:A,Z2:A]: (((((ord_less_eq @ A) @ X5) @ Y5) => ((((ord_less_eq @ A) @ X5) @ Z2) => (((ord_less_eq @ A) @ X5) @ ((F @ Y5) @ Z2)))))) => ((((inf_inf @ A) @ X) @ Y) = ((F @ X) @ Y))))))))))).
% 0.32/1.51 thf(fact_79_inf_OorderI, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = (((inf_inf @ A) @ A2) @ B2)) => (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.32/1.51 thf(fact_80_inf_OorderE, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (A2 = (((inf_inf @ A) @ A2) @ B2))))))))).
% 0.32/1.51 thf(fact_81_le__infI2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [B2:A,X:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ X) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ X)))))))).
% 0.32/1.51 thf(fact_82_le__infI1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,X:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ X) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ X)))))))).
% 0.32/1.51 thf(fact_83_inf__mono, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [A2:A,C:A,B2:A,D:A]: (((((ord_less_eq @ A) @ A2) @ C) => ((((ord_less_eq @ A) @ B2) @ D) => (((ord_less_eq @ A) @ (((inf_inf @ A) @ A2) @ B2)) @ (((inf_inf @ A) @ C) @ D)))))))))).
% 0.32/1.51 thf(fact_84_le__infI, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X) @ A2) => ((((ord_less_eq @ A) @ X) @ B2) => (((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ A2) @ B2)))))))))).
% 0.32/1.51 thf(fact_85_le__infE, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,A2:A,B2:A]: (((((ord_less_eq @ A) @ X) @ (((inf_inf @ A) @ A2) @ B2)) => (~ (((((ord_less_eq @ A) @ X) @ A2) => (~ ((((ord_less_eq @ A) @ X) @ B2))))))))))))).
% 0.32/1.51 thf(fact_86_inf__le2, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y))))))).
% 0.32/1.51 thf(fact_87_inf__le1, axiom, (! [A:$tType]: ((((semilattice_inf @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X) @ Y)) @ X))))))).
% 0.32/1.51 thf(fact_88_inf__sup__ord_I1_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X) @ Y)) @ X))))))).
% 0.32/1.51 thf(fact_89_inf__sup__ord_I2_J, axiom, (! [A:$tType]: ((((lattice @ A) @ (type2 @ A)) => (! [X:A,Y:A]: ((((ord_less_eq @ A) @ (((inf_inf @ A) @ X) @ Y)) @ Y))))))).
% 0.32/1.51 thf(fact_90_num_Oexhaust, axiom, (! [Y:num]: (((Y != one2) => ((! [X22:num]: ((Y != (bit0 @ X22)))) => (~ ((! [X32:num]: ((Y != (bit1 @ X32))))))))))).
% 0.32/1.51 thf(fact_91_num_Oinduct, axiom, (! [P:(num > $o),Num:num]: (((P @ one2) => ((! [X5:num]: (((P @ X5) => (P @ (bit0 @ X5))))) => ((! [X5:num]: (((P @ X5) => (P @ (bit1 @ X5))))) => (P @ Num))))))).
% 0.32/1.51 thf(fact_92_mult__numeral__1__right, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ A2) @ ((numeral_numeral @ A) @ one2)) = A2))))))).
% 0.32/1.51 thf(fact_93_mult__numeral__1, axiom, (! [A:$tType]: ((((semiring_numeral @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ ((numeral_numeral @ A) @ one2)) @ A2) = A2))))))).
% 0.32/1.51 thf(fact_94_numeral__le__enat__iff, axiom, (! [M:num,N:nat]: (((((ord_less_eq @ extended_enat) @ ((numeral_numeral @ extended_enat) @ M)) @ (extended_enat2 @ N)) = (((ord_less_eq @ nat) @ ((numeral_numeral @ nat) @ M)) @ N))))).
% 0.32/1.51 thf(fact_95_enat__ord__simps_I1_J, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ extended_enat) @ (extended_enat2 @ M)) @ (extended_enat2 @ N)) = (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.51 thf(fact_96_times__enat__simps_I1_J, axiom, (! [M:nat,N:nat]: (((((times_times @ extended_enat) @ (extended_enat2 @ M)) @ (extended_enat2 @ N)) = (extended_enat2 @ (((times_times @ nat) @ M) @ N)))))).
% 0.32/1.51 thf(fact_97_enat__ord__number_I1_J, axiom, (! [M:num,N:num]: (((((ord_less_eq @ extended_enat) @ ((numeral_numeral @ extended_enat) @ M)) @ ((numeral_numeral @ extended_enat) @ N)) = (((ord_less_eq @ nat) @ ((numeral_numeral @ nat) @ M)) @ ((numeral_numeral @ nat) @ N)))))).
% 0.32/1.51 thf(fact_98_ltl__hamming, axiom, (((coinductive_ltl @ nat) @ hammin2015774020amming) = (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2)))) @ hammin2015774020amming)) @ (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2)))) @ hammin2015774020amming)) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ (bit0 @ one2))))) @ hammin2015774020amming))))).
% 0.32/1.51 thf(fact_99_enat_Oinject, axiom, (! [Nat:nat,Nat2:nat]: ((((extended_enat2 @ Nat) = (extended_enat2 @ Nat2)) = (Nat = Nat2))))).
% 0.32/1.51 thf(fact_100_order__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 0.32/1.51 thf(fact_101_enat__ile, axiom, (! [N:extended_enat,M:nat]: (((((ord_less_eq @ extended_enat) @ N) @ (extended_enat2 @ M)) => (? [K:nat]: ((N = (extended_enat2 @ K)))))))).
% 0.32/1.51 thf(fact_102_numeral__eq__enat, axiom, ((numeral_numeral @ extended_enat) = (^ [K2:num]: ((extended_enat2 @ ((numeral_numeral @ nat) @ K2)))))).
% 0.32/1.51 thf(fact_103_smooth5, axiom, (hammin1195055315smooth @ ((numeral_numeral @ nat) @ (bit1 @ (bit0 @ one2))))).
% 0.32/1.51 thf(fact_104_dbl__inc__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: ((((neg_numeral_dbl_inc @ A) @ ((numeral_numeral @ A) @ K3)) = ((numeral_numeral @ A) @ (bit1 @ K3))))))))).
% 0.32/1.51 thf(fact_105_lfinite__ltl, axiom, (! [A:$tType,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ ((coinductive_ltl @ A) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 0.32/1.51 thf(fact_106_ltl__lmap, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coinductive_llist @ B)]: ((((coinductive_ltl @ A) @ ((((coinductive_lmap @ B) @ A) @ F) @ Xs)) = ((((coinductive_lmap @ B) @ A) @ F) @ ((coinductive_ltl @ B) @ Xs)))))).
% 0.32/1.51 thf(fact_107_smooth__times, axiom, (! [X:nat,Y:nat]: (((hammin1195055315smooth @ (((times_times @ nat) @ X) @ Y)) = ((hammin1195055315smooth @ X) & (hammin1195055315smooth @ Y)))))).
% 0.32/1.51 thf(fact_108_le__funD, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X)) @ (G2 @ X))))))))).
% 0.32/1.51 thf(fact_109_le__funE, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G2:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G2) => (((ord_less_eq @ B) @ (F @ X)) @ (G2 @ X))))))))).
% 0.32/1.51 thf(fact_110_le__funI, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => (! [F:(A > B),G2:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F @ X5)) @ (G2 @ X5)))) => (((ord_less_eq @ (A > B)) @ F) @ G2)))))))).
% 0.32/1.51 thf(fact_111_le__fun__def, axiom, (! [B:$tType,A:$tType]: ((((ord @ B) @ (type2 @ B)) => ((ord_less_eq @ (A > B)) = (^ [F2:(A > B),G:(A > B)]: ((! [X4:A]: ((((ord_less_eq @ B) @ (F2 @ X4)) @ (G @ X4))))))))))).
% 0.32/1.51 thf(fact_112_order__subst1, axiom, (! [A:$tType,B:$tType]: (((((order @ B) @ (type2 @ B)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((((ord_less_eq @ A) @ A2) @ (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X5:B,Y5:B]: (((((ord_less_eq @ B) @ X5) @ Y5) => (((ord_less_eq @ A) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 0.32/1.51 thf(fact_113_order__subst2, axiom, (! [A:$tType,C2:$tType]: (((((order @ C2) @ (type2 @ C2)) & ((order @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > C2),C:C2]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ C2) @ (F @ B2)) @ C) => ((! [X5:A,Y5:A]: (((((ord_less_eq @ A) @ X5) @ Y5) => (((ord_less_eq @ C2) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ C2) @ (F @ A2)) @ C)))))))))).
% 0.32/1.51 thf(fact_114_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,F:(B > A),B2:B,C:B]: (((A2 = (F @ B2)) => ((((ord_less_eq @ B) @ B2) @ C) => ((! [X5:B,Y5:B]: (((((ord_less_eq @ B) @ X5) @ Y5) => (((ord_less_eq @ A) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A2) @ (F @ C))))))))))).
% 0.32/1.51 thf(fact_115_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: (((((ord @ B) @ (type2 @ B)) & ((ord @ A) @ (type2 @ A))) => (! [A2:A,B2:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A2) @ B2) => (((F @ B2) = C) => ((! [X5:A,Y5:A]: (((((ord_less_eq @ A) @ X5) @ Y5) => (((ord_less_eq @ B) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ B) @ (F @ A2)) @ C)))))))))).
% 0.32/1.51 thf(fact_116_eq__iff, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => ((^ [Y6:A,Z3:A]: ((Y6 = Z3))) = (^ [X4:A,Y4:A]: (((((ord_less_eq @ A) @ X4) @ Y4) & (((ord_less_eq @ A) @ Y4) @ X4))))))))).
% 0.32/1.51 thf(fact_117_antisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 0.32/1.51 thf(fact_118_linear, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.32/1.51 thf(fact_119_eq__refl, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 0.32/1.51 thf(fact_120_le__cases, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.32/1.51 thf(fact_121_order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.51 thf(fact_122_le__cases3, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z)))) => (((((ord_less_eq @ A) @ X) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ Y)))) => (((((ord_less_eq @ A) @ Z) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z) => (~ ((((ord_less_eq @ A) @ Z) @ X)))) => (~ (((((ord_less_eq @ A) @ Z) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 0.32/1.51 thf(fact_123_antisym__conv, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 0.32/1.51 thf(fact_124_ord__eq__le__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((A2 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.51 thf(fact_125_ord__le__eq__trans, axiom, (! [A:$tType]: ((((ord @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A2) @ C))))))))).
% 0.32/1.51 thf(fact_126_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => ((((ord_less_eq @ A) @ B2) @ A2) => (A2 = B2))))))))).
% 0.32/1.51 thf(fact_127_order__trans, axiom, (! [A:$tType]: ((((preorder @ A) @ (type2 @ A)) => (! [X:A,Y:A,Z:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z) => (((ord_less_eq @ A) @ X) @ Z))))))))).
% 0.32/1.51 thf(fact_128_dual__order_Orefl, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [A2:A]: ((((ord_less_eq @ A) @ A2) @ A2))))))).
% 0.32/1.51 thf(fact_129_linorder__wlog, axiom, (! [A:$tType]: ((((linorder @ A) @ (type2 @ A)) => (! [P:(A > (A > $o)),A2:A,B2:A]: (((! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((P @ A3) @ B3)))) => ((! [A3:A,B3:A]: ((((P @ B3) @ A3) => ((P @ A3) @ B3)))) => ((P @ A2) @ B2))))))))).
% 0.32/1.51 thf(fact_130_dual__order_Otrans, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A2))))))))).
% 0.32/1.51 thf(fact_131_dual__order_Oantisym, axiom, (! [A:$tType]: ((((order @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ B2) @ A2) => ((((ord_less_eq @ A) @ A2) @ B2) => (A2 = B2))))))))).
% 0.32/1.51 thf(fact_132_smooth3, axiom, (hammin1195055315smooth @ ((numeral_numeral @ nat) @ (bit1 @ one2)))).
% 0.32/1.51 thf(fact_133_smooth2, axiom, (hammin1195055315smooth @ ((numeral_numeral @ nat) @ (bit0 @ one2)))).
% 0.32/1.51 thf(fact_134_le__cube, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ (((times_times @ nat) @ M) @ M)))))).
% 0.32/1.51 thf(fact_135_le__square, axiom, (! [M:nat]: ((((ord_less_eq @ nat) @ M) @ (((times_times @ nat) @ M) @ M))))).
% 0.32/1.51 thf(fact_136_mult__le__mono, axiom, (! [I:nat,J:nat,K3:nat,L:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ K3) @ L) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I) @ K3)) @ (((times_times @ nat) @ J) @ L))))))).
% 0.32/1.51 thf(fact_137_mult__le__mono1, axiom, (! [I:nat,J:nat,K3:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ I) @ K3)) @ (((times_times @ nat) @ J) @ K3)))))).
% 0.32/1.51 thf(fact_138_mult__le__mono2, axiom, (! [I:nat,J:nat,K3:nat]: (((((ord_less_eq @ nat) @ I) @ J) => (((ord_less_eq @ nat) @ (((times_times @ nat) @ K3) @ I)) @ (((times_times @ nat) @ K3) @ J)))))).
% 0.32/1.51 thf(fact_139_nat__le__linear, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) | (((ord_less_eq @ nat) @ N) @ M))))).
% 0.32/1.51 thf(fact_140_le__antisym, axiom, (! [M:nat,N:nat]: (((((ord_less_eq @ nat) @ M) @ N) => ((((ord_less_eq @ nat) @ N) @ M) => (M = N)))))).
% 0.32/1.51 thf(fact_141_eq__imp__le, axiom, (! [M:nat,N:nat]: (((M = N) => (((ord_less_eq @ nat) @ M) @ N))))).
% 0.32/1.51 thf(fact_142_le__trans, axiom, (! [I:nat,J:nat,K3:nat]: (((((ord_less_eq @ nat) @ I) @ J) => ((((ord_less_eq @ nat) @ J) @ K3) => (((ord_less_eq @ nat) @ I) @ K3)))))).
% 0.32/1.51 thf(fact_143_le__refl, axiom, (! [N:nat]: ((((ord_less_eq @ nat) @ N) @ N)))).
% 0.32/1.51 thf(fact_144_enat_Osimps_I6_J, axiom, (! [T:$tType,F1:(nat > T),F22:T,Nat:nat]: ((((((extended_rec_enat @ T) @ F1) @ F22) @ (extended_enat2 @ Nat)) = (F1 @ Nat))))).
% 0.32/1.51 thf(fact_145_sub__num__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: (((((neg_numeral_sub @ A) @ (bit1 @ K3)) @ one2) = ((numeral_numeral @ A) @ (bit0 @ K3))))))))).
% 0.32/1.51 thf(fact_146_dbl__inc__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_inc @ A) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit1 @ one2))))))).
% 0.32/1.51 thf(fact_147_dbl__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: ((((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K3)) = ((numeral_numeral @ A) @ (bit0 @ K3))))))))).
% 0.32/1.51 thf(fact_148_nat__1__eq__mult__iff, axiom, (! [M:nat,N:nat]: ((((one_one @ nat) = (((times_times @ nat) @ M) @ N)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 0.32/1.51 thf(fact_149_nat__mult__eq__1__iff, axiom, (! [M:nat,N:nat]: ((((((times_times @ nat) @ M) @ N) = (one_one @ nat)) = ((M = (one_one @ nat)) & (N = (one_one @ nat))))))).
% 0.32/1.51 thf(fact_150_numeral__eq__one__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((((numeral_numeral @ A) @ N) = (one_one @ A)) = (N = one2)))))))).
% 0.32/1.51 thf(fact_151_one__eq__numeral__iff, axiom, (! [A:$tType]: ((((semiring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: ((((one_one @ A) = ((numeral_numeral @ A) @ N)) = (one2 = N)))))))).
% 0.32/1.51 thf(fact_152_sub__num__simps_I9_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num,L:num]: (((((neg_numeral_sub @ A) @ (bit1 @ K3)) @ (bit1 @ L)) = ((neg_numeral_dbl @ A) @ (((neg_numeral_sub @ A) @ K3) @ L))))))))).
% 0.32/1.51 thf(fact_153_sub__num__simps_I6_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num,L:num]: (((((neg_numeral_sub @ A) @ (bit0 @ K3)) @ (bit0 @ L)) = ((neg_numeral_dbl @ A) @ (((neg_numeral_sub @ A) @ K3) @ L))))))))).
% 0.32/1.51 thf(fact_154_sub__num__simps_I8_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num,L:num]: (((((neg_numeral_sub @ A) @ (bit1 @ K3)) @ (bit0 @ L)) = ((neg_numeral_dbl_inc @ A) @ (((neg_numeral_sub @ A) @ K3) @ L))))))))).
% 0.32/1.51 thf(fact_155_numeral__le__one__iff, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:num]: (((((ord_less_eq @ A) @ ((numeral_numeral @ A) @ N)) @ (one_one @ A)) = (((ord_less_eq @ num) @ N) @ one2)))))))).
% 0.32/1.51 thf(fact_156_dbl__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl @ A) @ (one_one @ A)) = ((numeral_numeral @ A) @ (bit0 @ one2))))))).
% 0.32/1.51 thf(fact_157_nat__mult__1, axiom, (! [N:nat]: (((((times_times @ nat) @ (one_one @ nat)) @ N) = N)))).
% 0.32/1.51 thf(fact_158_nat__mult__1__right, axiom, (! [N:nat]: (((((times_times @ nat) @ N) @ (one_one @ nat)) = N)))).
% 0.32/1.51 thf(fact_159_le__numeral__extra_I4_J, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (((ord_less_eq @ A) @ (one_one @ A)) @ (one_one @ A)))))).
% 0.32/1.51 thf(fact_160_one__enat__def, axiom, ((one_one @ extended_enat) = (extended_enat2 @ (one_one @ nat)))).
% 0.32/1.51 thf(fact_161_enat__1__iff_I1_J, axiom, (! [X:nat]: ((((extended_enat2 @ X) = (one_one @ extended_enat)) = (X = (one_one @ nat)))))).
% 0.32/1.51 thf(fact_162_enat__1__iff_I2_J, axiom, (! [X:nat]: ((((one_one @ extended_enat) = (extended_enat2 @ X)) = (X = (one_one @ nat)))))).
% 0.32/1.51 thf(fact_163_one__le__numeral, axiom, (! [A:$tType]: ((((linordered_semidom @ A) @ (type2 @ A)) => (! [N:num]: ((((ord_less_eq @ A) @ (one_one @ A)) @ ((numeral_numeral @ A) @ N)))))))).
% 0.32/1.51 thf(fact_164_numeral__One, axiom, (! [A:$tType]: ((((numeral @ A) @ (type2 @ A)) => (((numeral_numeral @ A) @ one2) = (one_one @ A)))))).
% 0.32/1.51 thf(fact_165_numerals_I1_J, axiom, (((numeral_numeral @ nat) @ one2) = (one_one @ nat))).
% 0.32/1.51 thf(fact_166_mult_Oright__neutral, axiom, (! [A:$tType]: ((((monoid_mult @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 0.32/1.51 thf(fact_167_mult_Oleft__neutral, axiom, (! [A:$tType]: ((((monoid_mult @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 0.32/1.51 thf(fact_168_sub__num__simps_I7_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num,L:num]: (((((neg_numeral_sub @ A) @ (bit0 @ K3)) @ (bit1 @ L)) = ((neg_numeral_dbl_dec @ A) @ (((neg_numeral_sub @ A) @ K3) @ L))))))))).
% 0.32/1.51 thf(fact_169_dbl__dec__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_dec @ A) @ (one_one @ A)) = (one_one @ A)))))).
% 0.32/1.51 thf(fact_170_mult_Oleft__commute, axiom, (! [A:$tType]: ((((ab_semigroup_mult @ A) @ (type2 @ A)) => (! [B2:A,A2:A,C:A]: (((((times_times @ A) @ B2) @ (((times_times @ A) @ A2) @ C)) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 0.32/1.51 thf(fact_171_mult_Ocommute, axiom, (! [A:$tType]: ((((ab_semigroup_mult @ A) @ (type2 @ A)) => ((times_times @ A) = (^ [A4:A,B4:A]: ((((times_times @ A) @ B4) @ A4)))))))).
% 0.32/1.51 thf(fact_172_mult_Oassoc, axiom, (! [A:$tType]: ((((semigroup_mult @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 0.32/1.51 thf(fact_173_ab__semigroup__mult__class_Omult__ac_I1_J, axiom, (! [A:$tType]: ((((ab_semigroup_mult @ A) @ (type2 @ A)) => (! [A2:A,B2:A,C:A]: (((((times_times @ A) @ (((times_times @ A) @ A2) @ B2)) @ C) = (((times_times @ A) @ A2) @ (((times_times @ A) @ B2) @ C))))))))).
% 0.32/1.51 thf(fact_174_one__reorient, axiom, (! [A:$tType]: ((((one @ A) @ (type2 @ A)) => (! [X:A]: ((((one_one @ A) = X) = (X = (one_one @ A))))))))).
% 0.32/1.51 thf(fact_175_comm__monoid__mult__class_Omult__1, axiom, (! [A:$tType]: ((((comm_monoid_mult @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 0.32/1.51 thf(fact_176_mult_Ocomm__neutral, axiom, (! [A:$tType]: ((((comm_monoid_mult @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 0.32/1.51 thf(fact_177_hamming__unfold, axiom, (hammin2015774020amming = (((coinductive_LCons @ nat) @ (one_one @ nat)) @ (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2)))) @ hammin2015774020amming)) @ (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2)))) @ hammin2015774020amming)) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ (bit0 @ one2))))) @ hammin2015774020amming)))))).
% 0.32/1.51 thf(fact_178_sub__num__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: (((((neg_numeral_sub @ A) @ (bit0 @ K3)) @ one2) = ((numeral_numeral @ A) @ (bitM @ K3))))))))).
% 0.32/1.51 thf(fact_179_semiring__normalization__rules_I12_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ A2) @ (one_one @ A)) = A2))))))).
% 0.32/1.51 thf(fact_180_llist_Oinject, axiom, (! [A:$tType,X21:A,X222:(coinductive_llist @ A),Y21:A,Y22:(coinductive_llist @ A)]: ((((((coinductive_LCons @ A) @ X21) @ X222) = (((coinductive_LCons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 0.32/1.51 thf(fact_181_lfinite__code_I2_J, axiom, (! [B:$tType,X:B,Xs:(coinductive_llist @ B)]: ((((coinductive_lfinite @ B) @ (((coinductive_LCons @ B) @ X) @ Xs)) = ((coinductive_lfinite @ B) @ Xs))))).
% 0.32/1.51 thf(fact_182_lfinite__LCons, axiom, (! [A:$tType,X:A,Xs:(coinductive_llist @ A)]: ((((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)) = ((coinductive_lfinite @ A) @ Xs))))).
% 0.32/1.51 thf(fact_183_dbl__dec__simps_I5_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: ((((neg_numeral_dbl_dec @ A) @ ((numeral_numeral @ A) @ K3)) = ((numeral_numeral @ A) @ (bitM @ K3))))))))).
% 0.32/1.51 thf(fact_184_ltl__simps_I2_J, axiom, (! [A:$tType,X21:A,X222:(coinductive_llist @ A)]: ((((coinductive_ltl @ A) @ (((coinductive_LCons @ A) @ X21) @ X222)) = X222)))).
% 0.32/1.51 thf(fact_185_lmap__eq__LCons__conv, axiom, (! [A:$tType,B:$tType,F:(B > A),Xs:(coinductive_llist @ B),Y:A,Ys:(coinductive_llist @ A)]: (((((((coinductive_lmap @ B) @ A) @ F) @ Xs) = (((coinductive_LCons @ A) @ Y) @ Ys)) = (? [X4:B,Xs3:(coinductive_llist @ B)]: (((Xs = (((coinductive_LCons @ B) @ X4) @ Xs3)) & ((Y = (F @ X4)) & (Ys = ((((coinductive_lmap @ B) @ A) @ F) @ Xs3)))))))))).
% 0.32/1.51 thf(fact_186_llist_Osimps_I13_J, axiom, (! [B:$tType,A:$tType,F:(A > B),X21:A,X222:(coinductive_llist @ A)]: ((((((coinductive_lmap @ A) @ B) @ F) @ (((coinductive_LCons @ A) @ X21) @ X222)) = (((coinductive_LCons @ B) @ (F @ X21)) @ ((((coinductive_lmap @ A) @ B) @ F) @ X222)))))).
% 0.32/1.51 thf(fact_187_lfinite__LConsI, axiom, (! [A:$tType,Xs:(coinductive_llist @ A),X:A]: ((((coinductive_lfinite @ A) @ Xs) => ((coinductive_lfinite @ A) @ (((coinductive_LCons @ A) @ X) @ Xs)))))).
% 0.32/1.51 thf(fact_188_semiring__norm_I26_J, axiom, ((bitM @ one2) = one2)).
% 0.32/1.51 thf(fact_189_semiring__norm_I28_J, axiom, (! [N:num]: (((bitM @ (bit1 @ N)) = (bit1 @ (bit0 @ N)))))).
% 0.32/1.51 thf(fact_190_semiring__norm_I27_J, axiom, (! [N:num]: (((bitM @ (bit0 @ N)) = (bit1 @ (bitM @ N)))))).
% 0.32/1.51 thf(fact_191_semiring__normalization__rules_I19_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Rx:A,Ry:A]: (((((times_times @ A) @ Lx) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ Rx) @ (((times_times @ A) @ Lx) @ Ry))))))))).
% 0.32/1.51 thf(fact_192_semiring__normalization__rules_I18_J, axiom, (! [A:$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)))))))).
% 0.32/1.51 thf(fact_193_semiring__normalization__rules_I17_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ Rx) = (((times_times @ A) @ Lx) @ (((times_times @ A) @ Ly) @ Rx))))))))).
% 0.32/1.51 thf(fact_194_semiring__normalization__rules_I16_J, axiom, (! [A:$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)))))))).
% 0.32/1.51 thf(fact_195_semiring__normalization__rules_I15_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A,Ry:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ Rx) @ (((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ Ry))))))))).
% 0.32/1.51 thf(fact_196_semiring__normalization__rules_I14_J, axiom, (! [A:$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)))))))))).
% 0.32/1.51 thf(fact_197_semiring__normalization__rules_I13_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [Lx:A,Ly:A,Rx:A,Ry:A]: (((((times_times @ A) @ (((times_times @ A) @ Lx) @ Ly)) @ (((times_times @ A) @ Rx) @ Ry)) = (((times_times @ A) @ (((times_times @ A) @ Lx) @ Rx)) @ (((times_times @ A) @ Ly) @ Ry))))))))).
% 0.32/1.51 thf(fact_198_semiring__normalization__rules_I7_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => ((times_times @ A) = (^ [A4:A,B4:A]: ((((times_times @ A) @ B4) @ A4)))))))).
% 0.32/1.51 thf(fact_199_semiring__normalization__rules_I11_J, axiom, (! [A:$tType]: ((((comm_semiring_1 @ A) @ (type2 @ A)) => (! [A2:A]: (((((times_times @ A) @ (one_one @ A)) @ A2) = A2))))))).
% 0.32/1.51 thf(fact_200_hamming_H_Osimps, axiom, (hammin1630468845amming = (^ [Uu:product_unit]: ((((coinductive_LCons @ nat) @ (one_one @ nat)) @ (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit0 @ one2)))) @ (hammin1630468845amming @ product_Unity))) @ (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2)))) @ (hammin1630468845amming @ product_Unity))) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ (bit0 @ one2))))) @ (hammin1630468845amming @ product_Unity))))))))).
% 0.32/1.51 thf(fact_201_sub__num__simps_I2_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [L:num]: (((((neg_numeral_sub @ A) @ one2) @ (bit0 @ L)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bitM @ L)))))))))).
% 0.32/1.51 thf(fact_202_dbl__dec__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_dec @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit1 @ one2)))))))).
% 0.32/1.51 thf(fact_203_compl__eq__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((uminus_uminus @ A) @ X) = ((uminus_uminus @ A) @ Y)) = (X = Y)))))))).
% 0.32/1.51 thf(fact_204_double__compl, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ X)) = X))))))).
% 0.32/1.51 thf(fact_205_uminus__apply, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A5:(A > B),X4:A]: (((uminus_uminus @ B) @ (A5 @ X4))))))))).
% 0.32/1.51 thf(fact_206_neg__equal__iff__equal, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((uminus_uminus @ A) @ A2) = ((uminus_uminus @ A) @ B2)) = (A2 = B2)))))))).
% 0.32/1.51 thf(fact_207_add_Oinverse__inverse, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A]: ((((uminus_uminus @ A) @ ((uminus_uminus @ A) @ A2)) = A2))))))).
% 0.32/1.51 thf(fact_208_compl__le__compl__iff, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X)) @ ((uminus_uminus @ A) @ Y)) = (((ord_less_eq @ A) @ Y) @ X)))))))).
% 0.32/1.51 thf(fact_209_neg__le__iff__le, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [B2:A,A2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A2)) = (((ord_less_eq @ A) @ A2) @ B2)))))))).
% 0.32/1.51 thf(fact_210_neg__numeral__eq__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (M = N)))))))).
% 0.32/1.51 thf(fact_211_mult__minus1__right, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [Z:A]: (((((times_times @ A) @ Z) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ Z)))))))).
% 0.32/1.51 thf(fact_212_mult__minus1, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [Z:A]: (((((times_times @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ Z) = ((uminus_uminus @ A) @ Z)))))))).
% 0.32/1.51 thf(fact_213_dbl__simps_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: ((((neg_numeral_dbl @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ K3))) = ((uminus_uminus @ A) @ ((neg_numeral_dbl @ A) @ ((numeral_numeral @ A) @ K3)))))))))).
% 0.32/1.51 thf(fact_214_dbl__inc__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl_inc @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ (one_one @ A))))))).
% 0.32/1.51 thf(fact_215_neg__one__eq__numeral__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((((uminus_uminus @ A) @ (one_one @ A)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (N = one2)))))))).
% 0.32/1.51 thf(fact_216_numeral__eq__neg__one__iff, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N)) = ((uminus_uminus @ A) @ (one_one @ A))) = (N = one2)))))))).
% 0.32/1.51 thf(fact_217_mult__neg__numeral__simps_I1_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((times_times @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = ((numeral_numeral @ A) @ (((times_times @ num) @ M) @ N))))))))).
% 0.32/1.51 thf(fact_218_mult__neg__numeral__simps_I2_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((times_times @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((numeral_numeral @ A) @ N)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (((times_times @ num) @ M) @ N)))))))))).
% 0.32/1.51 thf(fact_219_mult__neg__numeral__simps_I3_J, axiom, (! [A:$tType]: ((((ring_1 @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((times_times @ A) @ ((numeral_numeral @ A) @ M)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (((times_times @ num) @ M) @ N)))))))))).
% 0.32/1.51 thf(fact_220_semiring__norm_I170_J, axiom, (! [B:$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)))))))).
% 0.32/1.51 thf(fact_221_semiring__norm_I171_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [V:num,W:num,Y:B]: (((((times_times @ B) @ ((numeral_numeral @ B) @ V)) @ (((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ W))) @ Y)) = (((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ (((times_times @ num) @ V) @ W)))) @ Y)))))))).
% 0.32/1.51 thf(fact_222_semiring__norm_I172_J, axiom, (! [B:$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)))))))).
% 0.32/1.51 thf(fact_223_neg__numeral__le__iff, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num,N:num]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))) = (((ord_less_eq @ num) @ N) @ M)))))))).
% 0.32/1.51 thf(fact_224_not__neg__one__le__neg__numeral__iff, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num]: (((~ ((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))))) = (M != one2)))))))).
% 0.32/1.51 thf(fact_225_dbl__dec__simps_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: ((((neg_numeral_dbl_dec @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ K3))) = ((uminus_uminus @ A) @ ((neg_numeral_dbl_inc @ A) @ ((numeral_numeral @ A) @ K3)))))))))).
% 0.32/1.51 thf(fact_226_dbl__inc__simps_I1_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [K3:num]: ((((neg_numeral_dbl_inc @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ K3))) = ((uminus_uminus @ A) @ ((neg_numeral_dbl_dec @ A) @ ((numeral_numeral @ A) @ K3)))))))))).
% 0.32/1.51 thf(fact_227_sub__num__simps_I3_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (! [L:num]: (((((neg_numeral_sub @ A) @ one2) @ (bit1 @ L)) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit0 @ L)))))))))).
% 0.32/1.51 thf(fact_228_dbl__simps_I4_J, axiom, (! [A:$tType]: ((((neg_numeral @ A) @ (type2 @ A)) => (((neg_numeral_dbl @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) = ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ (bit0 @ one2)))))))).
% 0.32/1.51 thf(fact_229_ring__normalization__rules_I1_J, axiom, (! [A:$tType]: ((((comm_ring_1 @ A) @ (type2 @ A)) => ((uminus_uminus @ A) = ((times_times @ A) @ ((uminus_uminus @ A) @ (one_one @ A)))))))).
% 0.32/1.51 thf(fact_230_numeral__times__minus__swap, axiom, (! [A:$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)))))))))).
% 0.32/1.51 thf(fact_231_numeral__neq__neg__one, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: ((((numeral_numeral @ A) @ N) != ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 0.32/1.51 thf(fact_232_one__neq__neg__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [N:num]: (((one_one @ A) != ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))))))))).
% 0.32/1.51 thf(fact_233_hamming__def, axiom, (hammin2015774020amming = (hammin1630468845amming @ product_Unity))).
% 0.32/1.51 thf(fact_234_neg__numeral__neq__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M)) != ((numeral_numeral @ A) @ N)))))))).
% 0.32/1.51 thf(fact_235_numeral__neq__neg__numeral, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((((numeral_numeral @ A) @ M) != ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))))))))).
% 0.32/1.51 thf(fact_236_fun__Compl__def, axiom, (! [B:$tType,A:$tType]: ((((uminus @ B) @ (type2 @ B)) => ((uminus_uminus @ (A > B)) = (^ [A5:(A > B),X4:A]: (((uminus_uminus @ B) @ (A5 @ X4))))))))).
% 0.32/1.51 thf(fact_237_compl__le__swap2, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y)) @ X) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ X)) @ Y)))))))).
% 0.32/1.51 thf(fact_238_compl__le__swap1, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ ((uminus_uminus @ A) @ X)) => (((ord_less_eq @ A) @ X) @ ((uminus_uminus @ A) @ Y))))))))).
% 0.32/1.51 thf(fact_239_compl__mono, axiom, (! [A:$tType]: ((((boolean_algebra @ A) @ (type2 @ A)) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ Y)) @ ((uminus_uminus @ A) @ X))))))))).
% 0.32/1.51 thf(fact_240_le__minus__one__simps_I2_J, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ (one_one @ A))) @ (one_one @ A)))))).
% 0.32/1.51 thf(fact_241_le__minus__one__simps_I4_J, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (~ ((((ord_less_eq @ A) @ (one_one @ A)) @ ((uminus_uminus @ A) @ (one_one @ A))))))))).
% 0.32/1.51 thf(fact_242_neg__numeral__le__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ M))) @ ((numeral_numeral @ A) @ N)))))))).
% 0.32/1.51 thf(fact_243_not__numeral__le__neg__numeral, axiom, (! [A:$tType]: ((((linordered_idom @ A) @ (type2 @ A)) => (! [M:num,N:num]: ((~ ((((ord_less_eq @ A) @ ((numeral_numeral @ A) @ M)) @ ((uminus_uminus @ A) @ ((numeral_numeral @ A) @ N))))))))))).
% 0.32/1.51 thf(fact_244_le__minus__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ ((uminus_uminus @ A) @ B2)) = (((ord_less_eq @ A) @ B2) @ ((uminus_uminus @ A) @ A2))))))))).
% 0.32/1.51 thf(fact_245_minus__le__iff, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ ((uminus_uminus @ A) @ A2)) @ B2) = (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ A2)))))))).
% 0.32/1.51 thf(fact_246_le__imp__neg__le, axiom, (! [A:$tType]: ((((ordered_ab_group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((ord_less_eq @ A) @ A2) @ B2) => (((ord_less_eq @ A) @ ((uminus_uminus @ A) @ B2)) @ ((uminus_uminus @ A) @ A2))))))))).
% 0.32/1.51 thf(fact_247_minus__equation__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((((uminus_uminus @ A) @ A2) = B2) = (((uminus_uminus @ A) @ B2) = A2)))))))).
% 0.32/1.51 thf(fact_248_equation__minus__iff, axiom, (! [A:$tType]: ((((group_add @ A) @ (type2 @ A)) => (! [A2:A,B2:A]: (((A2 = ((uminus_uminus @ A) @ B2)) = (B2 = ((uminus_uminus @ A) @ A2))))))))).
% 0.32/1.51 thf(fact_249_one__neq__neg__one, axiom, (! [A:$tType]: ((((ring_char_0 @ A) @ (type2 @ A)) => ((one_one @ A) != ((uminus_uminus @ A) @ (one_one @ A))))))).
% 0.32/1.51 thf(fact_250_mult__1s_I3_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [B2:B]: (((((times_times @ B) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ one2))) @ B2) = ((uminus_uminus @ B) @ B2)))))))).
% 0.32/1.51 thf(fact_251_mult__1s_I4_J, axiom, (! [B:$tType]: ((((ring_1 @ B) @ (type2 @ B)) => (! [B2:B]: (((((times_times @ B) @ B2) @ ((uminus_uminus @ B) @ ((numeral_numeral @ B) @ one2))) = ((uminus_uminus @ B) @ B2)))))))).
% 0.32/1.51 thf(tcon_fun___Lattices_Osemilattice__inf, axiom, (! [A6:$tType,A7:$tType]: ((((semilattice_inf @ A7) @ (type2 @ A7)) => ((semilattice_inf @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_fun___Lattices_Oboolean__algebra, axiom, (! [A6:$tType,A7:$tType]: ((((boolean_algebra @ A7) @ (type2 @ A7)) => ((boolean_algebra @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A6:$tType,A7:$tType]: ((((preorder @ A7) @ (type2 @ A7)) => ((preorder @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_fun___Lattices_Olattice, axiom, (! [A6:$tType,A7:$tType]: ((((lattice @ A7) @ (type2 @ A7)) => ((lattice @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: ((((order @ A7) @ (type2 @ A7)) => ((order @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: ((((ord @ A7) @ (type2 @ A7)) => ((ord @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_fun___Groups_Ouminus, axiom, (! [A6:$tType,A7:$tType]: ((((uminus @ A7) @ (type2 @ A7)) => ((uminus @ (A6 > A7)) @ (type2 @ (A6 > A7))))))).
% 0.32/1.51 thf(tcon_Nat_Onat___Rings_Olinordered__semidom, axiom, ((linordered_semidom @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_1, axiom, ((semilattice_inf @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult, axiom, ((ab_semigroup_mult @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult, axiom, ((comm_monoid_mult @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1, axiom, ((comm_semiring_1 @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Groups_Osemigroup__mult, axiom, ((semigroup_mult @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Num_Osemiring__numeral, axiom, ((semiring_numeral @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Nat_Osemiring__char__0, axiom, ((semiring_char_0 @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Orderings_Opreorder_2, axiom, ((preorder @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, ((linorder @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Groups_Omonoid__mult, axiom, ((monoid_mult @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Lattices_Olattice_3, axiom, ((lattice @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Orderings_Oorder_4, axiom, ((order @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Orderings_Oord_5, axiom, ((ord @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Num_Onumeral, axiom, ((numeral @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Nat_Onat___Groups_Oone, axiom, ((one @ nat) @ (type2 @ nat))).
% 0.32/1.51 thf(tcon_Num_Onum___Orderings_Opreorder_6, axiom, ((preorder @ num) @ (type2 @ num))).
% 0.32/1.51 thf(tcon_Num_Onum___Orderings_Olinorder_7, axiom, ((linorder @ num) @ (type2 @ num))).
% 0.32/1.51 thf(tcon_Num_Onum___Orderings_Oorder_8, axiom, ((order @ num) @ (type2 @ num))).
% 0.32/1.51 thf(tcon_Num_Onum___Orderings_Oord_9, axiom, ((ord @ num) @ (type2 @ num))).
% 0.32/1.51 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_10, axiom, ((semilattice_inf @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11, axiom, ((boolean_algebra @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Orderings_Opreorder_12, axiom, ((preorder @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder_13, axiom, ((linorder @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Lattices_Olattice_14, axiom, ((lattice @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Orderings_Oorder_15, axiom, ((order @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Orderings_Oord_16, axiom, ((ord @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_HOL_Obool___Groups_Ouminus_17, axiom, ((uminus @ $o) @ (type2 @ $o))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_18, axiom, ((semilattice_inf @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_19, axiom, ((ab_semigroup_mult @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__mult_20, axiom, ((comm_monoid_mult @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_21, axiom, ((comm_semiring_1 @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_22, axiom, ((semigroup_mult @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_23, axiom, ((semiring_numeral @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_24, axiom, ((semiring_char_0 @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_25, axiom, ((preorder @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_26, axiom, ((linorder @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Groups_Omonoid__mult_27, axiom, ((monoid_mult @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Lattices_Olattice_28, axiom, ((lattice @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_29, axiom, ((order @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_30, axiom, ((ord @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Num_Onumeral_31, axiom, ((numeral @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(tcon_Extended__Nat_Oenat___Groups_Oone_32, axiom, ((one @ extended_enat) @ (type2 @ extended_enat))).
% 0.32/1.51 thf(conj_0, conjecture, (((ord_less_eq @ extended_enat) @ (((inf_inf @ extended_enat) @ ((coinductive_llength @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2)))) @ hammin2015774020amming))) @ ((coinductive_llength @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ (bit0 @ one2))))) @ hammin2015774020amming)))) @ ((coinductive_llength @ nat) @ (((hammin1138290136lmerge @ nat) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ one2)))) @ hammin2015774020amming)) @ ((((coinductive_lmap @ nat) @ nat) @ ((times_times @ nat) @ ((numeral_numeral @ nat) @ (bit1 @ (bit0 @ one2))))) @ hammin2015774020amming))))).
% 0.32/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2DTF16461.p
% 0.32/1.51 ------------------------
% 0.32/1.53 ---- Cleaned THF ---
% 0.32/1.54 thf(ty_t_Coinductive__List_Ollist,type,
% 0.32/1.54 coinductive_llist: $tType > $tType ).
% 0.32/1.54
% 0.32/1.54 thf(ty_t_Product__Type_Ounit,type,
% 0.32/1.54 product_unit: $tType ).
% 0.32/1.54
% 0.32/1.54 thf(ty_t_Extended__Nat_Oenat,type,
% 0.32/1.54 extended_enat: $tType ).
% 0.32/1.54
% 0.32/1.54 thf(ty_t_Num_Onum,type,
% 0.32/1.54 num: $tType ).
% 0.32/1.54
% 0.32/1.54 thf(ty_t_Nat_Onat,type,
% 0.32/1.54 nat: $tType ).
% 0.32/1.54
% 0.32/1.54 thf(ty_t_itself,type,
% 0.32/1.54 itself: $tType > $tType ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_HOL_Otype,type,
% 0.32/1.54 type:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Oone,type,
% 0.32/1.54 one:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Num_Onumeral,type,
% 0.32/1.54 numeral:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Rings_Oring__1,type,
% 0.32/1.54 ring_1:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Ouminus,type,
% 0.32/1.54 uminus:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Orderings_Oord,type,
% 0.32/1.54 ord:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Nat_Oring__char__0,type,
% 0.32/1.54 ring_char_0:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Num_Oneg__numeral,type,
% 0.32/1.54 neg_numeral:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Orderings_Oorder,type,
% 0.32/1.54 order:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Ogroup__add,type,
% 0.32/1.54 group_add:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Lattices_Olattice,type,
% 0.32/1.54 lattice:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Rings_Ocomm__ring__1,type,
% 0.32/1.54 comm_ring_1:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Omonoid__mult,type,
% 0.32/1.54 monoid_mult:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Orderings_Olinorder,type,
% 0.32/1.54 linorder:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Orderings_Opreorder,type,
% 0.32/1.54 preorder:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Nat_Osemiring__char__0,type,
% 0.32/1.54 semiring_char_0:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Num_Osemiring__numeral,type,
% 0.32/1.54 semiring_numeral:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Osemigroup__mult,type,
% 0.32/1.54 semigroup_mult:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Rings_Ocomm__semiring__1,type,
% 0.32/1.54 comm_semiring_1:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Rings_Olinordered__idom,type,
% 0.32/1.54 linordered_idom:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Ocomm__monoid__mult,type,
% 0.32/1.54 comm_monoid_mult:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Oab__semigroup__mult,type,
% 0.32/1.54 ab_semigroup_mult:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Lattices_Oboolean__algebra,type,
% 0.32/1.54 boolean_algebra:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Lattices_Osemilattice__inf,type,
% 0.32/1.54 semilattice_inf:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Rings_Olinordered__semidom,type,
% 0.32/1.54 linordered_semidom:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_cl_Groups_Oordered__ab__group__add,type,
% 0.32/1.54 ordered_ab_group_add:
% 0.32/1.54 !>[A: $tType] : ( ( itself @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Coinductive__List_Olfinite,type,
% 0.32/1.54 coinductive_lfinite:
% 0.32/1.54 !>[A: $tType] : ( ( coinductive_llist @ A ) > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Coinductive__List_Ollength,type,
% 0.32/1.54 coinductive_llength:
% 0.32/1.54 !>[A: $tType] : ( ( coinductive_llist @ A ) > extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Coinductive__List_Ollist_OLCons,type,
% 0.32/1.54 coinductive_LCons:
% 0.32/1.54 !>[A: $tType] : ( A > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Coinductive__List_Ollist_Olmap,type,
% 0.32/1.54 coinductive_lmap:
% 0.32/1.54 !>[A: $tType,Aa: $tType] : ( ( A > Aa ) > ( coinductive_llist @ A ) > ( coinductive_llist @ Aa ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Coinductive__List_Ollist_Oltl,type,
% 0.32/1.54 coinductive_ltl:
% 0.32/1.54 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Extended__Nat_Oenat,type,
% 0.32/1.54 extended_enat2: nat > extended_enat ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Extended__Nat_Oenat_Orec__enat,type,
% 0.32/1.54 extended_rec_enat:
% 0.32/1.54 !>[T: $tType] : ( ( nat > T ) > T > extended_enat > T ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Groups_Oone__class_Oone,type,
% 0.32/1.54 one_one:
% 0.32/1.54 !>[A: $tType] : A ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Groups_Otimes__class_Otimes,type,
% 0.32/1.54 times_times:
% 0.32/1.54 !>[A: $tType] : ( A > A > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Groups_Ouminus__class_Ouminus,type,
% 0.32/1.54 uminus_uminus:
% 0.32/1.54 !>[A: $tType] : ( A > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Ohamming,type,
% 0.32/1.54 hammin2015774020amming: coinductive_llist @ nat ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Ohamming_H,type,
% 0.32/1.54 hammin1630468845amming: product_unit > ( coinductive_llist @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Oord__class_Olmerge,type,
% 0.32/1.54 hammin1138290136lmerge:
% 0.32/1.54 !>[A: $tType] : ( ( coinductive_llist @ A ) > ( coinductive_llist @ A ) > ( coinductive_llist @ A ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Hamming__Stream__Mirabelle__rwekfkwckg_Osmooth,type,
% 0.32/1.54 hammin1195055315smooth: nat > $o ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Lattices_Oinf__class_Oinf,type,
% 0.32/1.54 inf_inf:
% 0.32/1.54 !>[A: $tType] : ( A > A > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_OBitM,type,
% 0.32/1.54 bitM: num > num ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Oneg__numeral__class_Odbl,type,
% 0.32/1.54 neg_numeral_dbl:
% 0.32/1.54 !>[A: $tType] : ( A > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec,type,
% 0.32/1.54 neg_numeral_dbl_dec:
% 0.32/1.54 !>[A: $tType] : ( A > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc,type,
% 0.32/1.54 neg_numeral_dbl_inc:
% 0.32/1.54 !>[A: $tType] : ( A > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Oneg__numeral__class_Osub,type,
% 0.32/1.54 neg_numeral_sub:
% 0.32/1.54 !>[A: $tType] : ( num > num > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Onum_OBit0,type,
% 0.32/1.54 bit0: num > num ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Onum_OBit1,type,
% 0.32/1.54 bit1: num > num ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Onum_OOne,type,
% 0.32/1.54 one2: num ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Num_Onumeral__class_Onumeral,type,
% 0.32/1.54 numeral_numeral:
% 0.32/1.54 !>[A: $tType] : ( num > A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.32/1.54 ord_less_eq:
% 0.32/1.54 !>[A: $tType] : ( A > A > $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Product__Type_OUnity,type,
% 0.32/1.54 product_Unity: product_unit ).
% 0.32/1.54
% 0.32/1.54 thf(sy_c_Pure_Otype,type,
% 0.32/1.54 type2:
% 0.32/1.54 !>[A: $tType] : ( itself @ A ) ).
% 0.32/1.54
% 0.32/1.54 thf(sy_v_n____,type,
% 0.32/1.54 n: nat ).
% 0.32/1.54
% 0.32/1.54 thf(fact_0__092_060open_062lfinite_Ahamming_092_060close_062,axiom,
% 0.32/1.54 coinductive_lfinite @ nat @ hammin2015774020amming ).
% 0.32/1.54
% 0.32/1.54 thf(fact_1_llength__lmerge__above,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] : ( ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ A @ Xs ) @ ( coinductive_llength @ A @ Ys ) ) @ ( coinductive_llength @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_2_n,axiom,
% 0.32/1.54 ( ( coinductive_llength @ nat @ hammin2015774020amming )
% 0.32/1.54 = ( extended_enat2 @ n ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_3_llength__lmap,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.32/1.54 ( ( coinductive_llength @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.32/1.54 = ( coinductive_llength @ B @ Xs ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_4_le__inf__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/1.54 = ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 & ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_5_inf_Obounded__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.32/1.54 = ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 & ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_6_semiring__norm_I169_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [V: num,W: num,Z: A] :
% 0.32/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ V ) @ ( times_times @ A @ ( numeral_numeral @ A @ W ) @ Z ) )
% 0.32/1.54 = ( times_times @ A @ ( numeral_numeral @ A @ ( times_times @ num @ V @ W ) ) @ Z ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_7_numeral__times__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_8_numeral__le__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ M ) @ ( numeral_numeral @ A @ N ) )
% 0.32/1.54 = ( ord_less_eq @ num @ M @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_9_semiring__norm_I85_J,axiom,
% 0.32/1.54 ! [M: num] :
% 0.32/1.54 ( ( bit0 @ M )
% 0.32/1.54 != one2 ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_10_semiring__norm_I83_J,axiom,
% 0.32/1.54 ! [N: num] :
% 0.32/1.54 ( one2
% 0.32/1.54 != ( bit0 @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_11_semiring__norm_I86_J,axiom,
% 0.32/1.54 ! [M: num] :
% 0.32/1.54 ( ( bit1 @ M )
% 0.32/1.54 != one2 ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_12_semiring__norm_I84_J,axiom,
% 0.32/1.54 ! [N: num] :
% 0.32/1.54 ( one2
% 0.32/1.54 != ( bit1 @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_13_semiring__norm_I89_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( bit1 @ M )
% 0.32/1.54 != ( bit0 @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_14_semiring__norm_I90_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( ( bit1 @ M )
% 0.32/1.54 = ( bit1 @ N ) )
% 0.32/1.54 = ( M = N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_15_num_Oinject_I2_J,axiom,
% 0.32/1.54 ! [X3: num,Y3: num] :
% 0.32/1.54 ( ( ( bit1 @ X3 )
% 0.32/1.54 = ( bit1 @ Y3 ) )
% 0.32/1.54 = ( X3 = Y3 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_16_semiring__norm_I87_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( ( bit0 @ M )
% 0.32/1.54 = ( bit0 @ N ) )
% 0.32/1.54 = ( M = N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_17_num_Oinject_I1_J,axiom,
% 0.32/1.54 ! [X2: num,Y2: num] :
% 0.32/1.54 ( ( ( bit0 @ X2 )
% 0.32/1.54 = ( bit0 @ Y2 ) )
% 0.32/1.54 = ( X2 = Y2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_18__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062n_O_Allength_Ahamming_A_061_Aenat_An_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 0.32/1.54 ~ ! [N2: nat] :
% 0.32/1.54 ( ( coinductive_llength @ nat @ hammin2015774020amming )
% 0.32/1.54 != ( extended_enat2 @ N2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_19_numeral__eq__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( ( numeral_numeral @ A @ M )
% 0.32/1.54 = ( numeral_numeral @ A @ N ) )
% 0.32/1.54 = ( M = N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_20_inf__right__idem,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Y )
% 0.32/1.54 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_21_inf_Oright__idem,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 )
% 0.32/1.54 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_22_inf__left__idem,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.32/1.54 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_23_inf_Oleft__idem,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( inf_inf @ A @ A2 @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.32/1.54 = ( inf_inf @ A @ A2 @ B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_24_inf__idem,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A] :
% 0.32/1.54 ( ( inf_inf @ A @ X @ X )
% 0.32/1.54 = X ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_25_inf_Oidem,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( inf_inf @ A @ A2 @ A2 )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_26_inf__apply,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.32/1.54 => ( ( inf_inf @ ( A > B ) )
% 0.32/1.54 = ( ^ [F2: A > B,G: A > B,X4: A] : ( inf_inf @ B @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_27_semiring__norm_I88_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( bit0 @ M )
% 0.32/1.54 != ( bit1 @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_28_semiring__norm_I13_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/1.54 = ( bit0 @ ( bit0 @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_29_lfinite__lmap,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.32/1.54 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_30_semiring__norm_I11_J,axiom,
% 0.32/1.54 ! [M: num] :
% 0.32/1.54 ( ( times_times @ num @ M @ one2 )
% 0.32/1.54 = M ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_31_semiring__norm_I12_J,axiom,
% 0.32/1.54 ! [N: num] :
% 0.32/1.54 ( ( times_times @ num @ one2 @ N )
% 0.32/1.54 = N ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_32_semiring__norm_I73_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( ord_less_eq @ num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 0.32/1.54 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_33_semiring__norm_I71_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( ord_less_eq @ num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 0.32/1.54 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_34_semiring__norm_I68_J,axiom,
% 0.32/1.54 ! [N: num] : ( ord_less_eq @ num @ one2 @ N ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_35_semiring__norm_I14_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/1.54 = ( bit0 @ ( times_times @ num @ M @ ( bit1 @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_36_semiring__norm_I15_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 0.32/1.54 = ( bit0 @ ( times_times @ num @ ( bit1 @ M ) @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_37_semiring__norm_I72_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( ord_less_eq @ num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 0.32/1.54 = ( ord_less_eq @ num @ M @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_38_semiring__norm_I70_J,axiom,
% 0.32/1.54 ! [M: num] :
% 0.32/1.54 ~ ( ord_less_eq @ num @ ( bit1 @ M ) @ one2 ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_39_semiring__norm_I69_J,axiom,
% 0.32/1.54 ! [M: num] :
% 0.32/1.54 ~ ( ord_less_eq @ num @ ( bit0 @ M ) @ one2 ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_40_lfinite__llength__enat,axiom,
% 0.32/1.54 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ Xs )
% 0.32/1.54 => ? [N2: nat] :
% 0.32/1.54 ( ( coinductive_llength @ A @ Xs )
% 0.32/1.54 = ( extended_enat2 @ N2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_41_llength__eq__enat__lfiniteD,axiom,
% 0.32/1.54 ! [A: $tType,Xs: coinductive_llist @ A,N: nat] :
% 0.32/1.54 ( ( ( coinductive_llength @ A @ Xs )
% 0.32/1.54 = ( extended_enat2 @ N ) )
% 0.32/1.54 => ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_42_lfinite__conv__llength__enat,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( coinductive_lfinite @ A )
% 0.32/1.54 = ( ^ [Xs2: coinductive_llist @ A] :
% 0.32/1.54 ? [N3: nat] :
% 0.32/1.54 ( ( coinductive_llength @ A @ Xs2 )
% 0.32/1.54 = ( extended_enat2 @ N3 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_43_le__num__One__iff,axiom,
% 0.32/1.54 ! [X: num] :
% 0.32/1.54 ( ( ord_less_eq @ num @ X @ one2 )
% 0.32/1.54 = ( X = one2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_44_ext,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType,F: A > B,G2: A > B] :
% 0.32/1.54 ( ! [X5: A] :
% 0.32/1.54 ( ( F @ X5 )
% 0.32/1.54 = ( G2 @ X5 ) )
% 0.32/1.54 => ( F = G2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_45_linfinite__lmerge,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.32/1.54 ( ~ ( coinductive_lfinite @ A @ Xs )
% 0.32/1.54 => ( ~ ( coinductive_lfinite @ A @ Ys )
% 0.32/1.54 => ~ ( coinductive_lfinite @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_46_lfinite__lmergeI,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ Xs )
% 0.32/1.54 => ( ( coinductive_lfinite @ A @ Ys )
% 0.32/1.54 => ( coinductive_lfinite @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_47_lfinite__lmergeD,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Xs: coinductive_llist @ A,Ys: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ ( hammin1138290136lmerge @ A @ Xs @ Ys ) )
% 0.32/1.54 => ( ( coinductive_lfinite @ A @ Xs )
% 0.32/1.54 | ( coinductive_lfinite @ A @ Ys ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_48_wlog__linorder__le,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [P: A > A > $o,B2: A,A2: A] :
% 0.32/1.54 ( ! [A3: A,B3: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.54 => ( P @ A3 @ B3 ) )
% 0.32/1.54 => ( ( ( P @ B2 @ A2 )
% 0.32/1.54 => ( P @ A2 @ B2 ) )
% 0.32/1.54 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_49_inf__left__commute,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/1.54 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_50_inf_Oleft__commute,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,A2: A,C: A] :
% 0.32/1.54 ( ( inf_inf @ A @ B2 @ ( inf_inf @ A @ A2 @ C ) )
% 0.32/1.54 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_51_inf__commute,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( inf_inf @ A )
% 0.32/1.54 = ( ^ [X4: A,Y4: A] : ( inf_inf @ A @ Y4 @ X4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_52_inf_Ocommute,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( inf_inf @ A )
% 0.32/1.54 = ( ^ [A4: A,B4: A] : ( inf_inf @ A @ B4 @ A4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_53_inf__assoc,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.32/1.54 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_54_inf_Oassoc,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C )
% 0.32/1.54 = ( inf_inf @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_55_inf__fun__def,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ B @ ( type2 @ B ) )
% 0.32/1.54 => ( ( inf_inf @ ( A > B ) )
% 0.32/1.54 = ( ^ [F2: A > B,G: A > B,X4: A] : ( inf_inf @ B @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_56_inf__sup__aci_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( inf_inf @ A )
% 0.32/1.54 = ( ^ [X4: A,Y4: A] : ( inf_inf @ A @ Y4 @ X4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_57_inf__sup__aci_I2_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( inf_inf @ A @ ( inf_inf @ A @ X @ Y ) @ Z )
% 0.32/1.54 = ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_58_inf__sup__aci_I3_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ Y @ Z ) )
% 0.32/1.54 = ( inf_inf @ A @ Y @ ( inf_inf @ A @ X @ Z ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_59_inf__sup__aci_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( inf_inf @ A @ X @ ( inf_inf @ A @ X @ Y ) )
% 0.32/1.54 = ( inf_inf @ A @ X @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_60_num_Odistinct_I5_J,axiom,
% 0.32/1.54 ! [X2: num,X3: num] :
% 0.32/1.54 ( ( bit0 @ X2 )
% 0.32/1.54 != ( bit1 @ X3 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_61_num_Odistinct_I3_J,axiom,
% 0.32/1.54 ! [X3: num] :
% 0.32/1.54 ( one2
% 0.32/1.54 != ( bit1 @ X3 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_62_num_Odistinct_I1_J,axiom,
% 0.32/1.54 ! [X2: num] :
% 0.32/1.54 ( one2
% 0.32/1.54 != ( bit0 @ X2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_63_inf_OcoboundedI2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,C: A,A2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/1.54 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_64_inf_OcoboundedI1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,C: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ C )
% 0.32/1.54 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ C ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_65_inf_Oabsorb__iff2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( ord_less_eq @ A )
% 0.32/1.54 = ( ^ [B4: A,A4: A] :
% 0.32/1.54 ( ( inf_inf @ A @ A4 @ B4 )
% 0.32/1.54 = B4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_66_inf_Oabsorb__iff1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( ord_less_eq @ A )
% 0.32/1.54 = ( ^ [A4: A,B4: A] :
% 0.32/1.54 ( ( inf_inf @ A @ A4 @ B4 )
% 0.32/1.54 = A4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_67_inf_Ocobounded2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ B2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_68_inf_Ocobounded1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_69_inf_Oorder__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( ord_less_eq @ A )
% 0.32/1.54 = ( ^ [A4: A,B4: A] :
% 0.32/1.54 ( A4
% 0.32/1.54 = ( inf_inf @ A @ A4 @ B4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_70_inf__greatest,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ( ( ord_less_eq @ A @ X @ Z )
% 0.32/1.54 => ( ord_less_eq @ A @ X @ ( inf_inf @ A @ Y @ Z ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_71_inf_OboundedI,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ A2 @ C )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_72_inf_OboundedE,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ ( inf_inf @ A @ B2 @ C ) )
% 0.32/1.54 => ~ ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_73_inf__absorb2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Y: A,X: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ Y @ X )
% 0.32/1.54 => ( ( inf_inf @ A @ X @ Y )
% 0.32/1.54 = Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_74_inf__absorb1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ( ( inf_inf @ A @ X @ Y )
% 0.32/1.54 = X ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_75_inf_Oabsorb2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,A2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.54 => ( ( inf_inf @ A @ A2 @ B2 )
% 0.32/1.54 = B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_76_inf_Oabsorb1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( inf_inf @ A @ A2 @ B2 )
% 0.32/1.54 = A2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_77_le__iff__inf,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( ord_less_eq @ A )
% 0.32/1.54 = ( ^ [X4: A,Y4: A] :
% 0.32/1.54 ( ( inf_inf @ A @ X4 @ Y4 )
% 0.32/1.54 = X4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_78_inf__unique,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [F: A > A > A,X: A,Y: A] :
% 0.32/1.54 ( ! [X5: A,Y5: A] : ( ord_less_eq @ A @ ( F @ X5 @ Y5 ) @ X5 )
% 0.32/1.54 => ( ! [X5: A,Y5: A] : ( ord_less_eq @ A @ ( F @ X5 @ Y5 ) @ Y5 )
% 0.32/1.54 => ( ! [X5: A,Y5: A,Z2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ X5 @ Z2 )
% 0.32/1.54 => ( ord_less_eq @ A @ X5 @ ( F @ Y5 @ Z2 ) ) ) )
% 0.32/1.54 => ( ( inf_inf @ A @ X @ Y )
% 0.32/1.54 = ( F @ X @ Y ) ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_79_inf_OorderI,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( A2
% 0.32/1.54 = ( inf_inf @ A @ A2 @ B2 ) )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_80_inf_OorderE,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( A2
% 0.32/1.54 = ( inf_inf @ A @ A2 @ B2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_81_le__infI2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,X: A,A2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ B2 @ X )
% 0.32/1.54 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_82_le__infI1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,X: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ X )
% 0.32/1.54 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ X ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_83_inf__mono,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,C: A,B2: A,D: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ C )
% 0.32/1.54 => ( ( ord_less_eq @ A @ B2 @ D )
% 0.32/1.54 => ( ord_less_eq @ A @ ( inf_inf @ A @ A2 @ B2 ) @ ( inf_inf @ A @ C @ D ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_84_le__infI,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ A2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ X @ B2 )
% 0.32/1.54 => ( ord_less_eq @ A @ X @ ( inf_inf @ A @ A2 @ B2 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_85_le__infE,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ ( inf_inf @ A @ A2 @ B2 ) )
% 0.32/1.54 => ~ ( ( ord_less_eq @ A @ X @ A2 )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ X @ B2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_86_inf__le2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ Y ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_87_inf__le1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ X ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_88_inf__sup__ord_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ X ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_89_inf__sup__ord_I2_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( lattice @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] : ( ord_less_eq @ A @ ( inf_inf @ A @ X @ Y ) @ Y ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_90_num_Oexhaust,axiom,
% 0.32/1.54 ! [Y: num] :
% 0.32/1.54 ( ( Y != one2 )
% 0.32/1.54 => ( ! [X22: num] :
% 0.32/1.54 ( Y
% 0.32/1.54 != ( bit0 @ X22 ) )
% 0.32/1.54 => ~ ! [X32: num] :
% 0.32/1.54 ( Y
% 0.32/1.54 != ( bit1 @ X32 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_91_num_Oinduct,axiom,
% 0.32/1.54 ! [P: num > $o,Num: num] :
% 0.32/1.54 ( ( P @ one2 )
% 0.32/1.54 => ( ! [X5: num] :
% 0.32/1.54 ( ( P @ X5 )
% 0.32/1.54 => ( P @ ( bit0 @ X5 ) ) )
% 0.32/1.54 => ( ! [X5: num] :
% 0.32/1.54 ( ( P @ X5 )
% 0.32/1.54 => ( P @ ( bit1 @ X5 ) ) )
% 0.32/1.54 => ( P @ Num ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_92_mult__numeral__1__right,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ A2 @ ( numeral_numeral @ A @ one2 ) )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_93_mult__numeral__1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ one2 ) @ A2 )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_94_numeral__le__enat__iff,axiom,
% 0.32/1.54 ! [M: num,N: nat] :
% 0.32/1.54 ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ M ) @ ( extended_enat2 @ N ) )
% 0.32/1.54 = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ M ) @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_95_enat__ord__simps_I1_J,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( ord_less_eq @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.32/1.54 = ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_96_times__enat__simps_I1_J,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( times_times @ extended_enat @ ( extended_enat2 @ M ) @ ( extended_enat2 @ N ) )
% 0.32/1.54 = ( extended_enat2 @ ( times_times @ nat @ M @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_97_enat__ord__number_I1_J,axiom,
% 0.32/1.54 ! [M: num,N: num] :
% 0.32/1.54 ( ( ord_less_eq @ extended_enat @ ( numeral_numeral @ extended_enat @ M ) @ ( numeral_numeral @ extended_enat @ N ) )
% 0.32/1.54 = ( ord_less_eq @ nat @ ( numeral_numeral @ nat @ M ) @ ( numeral_numeral @ nat @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_98_ltl__hamming,axiom,
% 0.32/1.54 ( ( coinductive_ltl @ nat @ hammin2015774020amming )
% 0.32/1.54 = ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_99_enat_Oinject,axiom,
% 0.32/1.54 ! [Nat: nat,Nat2: nat] :
% 0.32/1.54 ( ( ( extended_enat2 @ Nat )
% 0.32/1.54 = ( extended_enat2 @ Nat2 ) )
% 0.32/1.54 = ( Nat = Nat2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_100_order__refl,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( preorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_101_enat__ile,axiom,
% 0.32/1.54 ! [N: extended_enat,M: nat] :
% 0.32/1.54 ( ( ord_less_eq @ extended_enat @ N @ ( extended_enat2 @ M ) )
% 0.32/1.54 => ? [K: nat] :
% 0.32/1.54 ( N
% 0.32/1.54 = ( extended_enat2 @ K ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_102_numeral__eq__enat,axiom,
% 0.32/1.54 ( ( numeral_numeral @ extended_enat )
% 0.32/1.54 = ( ^ [K2: num] : ( extended_enat2 @ ( numeral_numeral @ nat @ K2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_103_smooth5,axiom,
% 0.32/1.54 hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_104_dbl__inc__simps_I5_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_dbl_inc @ A @ ( numeral_numeral @ A @ K3 ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bit1 @ K3 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_105_lfinite__ltl,axiom,
% 0.32/1.54 ! [A: $tType,Xs: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ ( coinductive_ltl @ A @ Xs ) )
% 0.32/1.54 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_106_ltl__lmap,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B] :
% 0.32/1.54 ( ( coinductive_ltl @ A @ ( coinductive_lmap @ B @ A @ F @ Xs ) )
% 0.32/1.54 = ( coinductive_lmap @ B @ A @ F @ ( coinductive_ltl @ B @ Xs ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_107_smooth__times,axiom,
% 0.32/1.54 ! [X: nat,Y: nat] :
% 0.32/1.54 ( ( hammin1195055315smooth @ ( times_times @ nat @ X @ Y ) )
% 0.32/1.54 = ( ( hammin1195055315smooth @ X )
% 0.32/1.54 & ( hammin1195055315smooth @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_108_le__funD,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( ord @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [F: A > B,G2: A > B,X: A] :
% 0.32/1.54 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.32/1.54 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_109_le__funE,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( ord @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [F: A > B,G2: A > B,X: A] :
% 0.32/1.54 ( ( ord_less_eq @ ( A > B ) @ F @ G2 )
% 0.32/1.54 => ( ord_less_eq @ B @ ( F @ X ) @ ( G2 @ X ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_110_le__funI,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( ord @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [F: A > B,G2: A > B] :
% 0.32/1.54 ( ! [X5: A] : ( ord_less_eq @ B @ ( F @ X5 ) @ ( G2 @ X5 ) )
% 0.32/1.54 => ( ord_less_eq @ ( A > B ) @ F @ G2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_111_le__fun__def,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( ord @ B @ ( type2 @ B ) )
% 0.32/1.54 => ( ( ord_less_eq @ ( A > B ) )
% 0.32/1.54 = ( ^ [F2: A > B,G: A > B] :
% 0.32/1.54 ! [X4: A] : ( ord_less_eq @ B @ ( F2 @ X4 ) @ ( G @ X4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_112_order__subst1,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType] :
% 0.32/1.54 ( ( ( order @ B @ ( type2 @ B ) )
% 0.32/1.54 & ( order @ A @ ( type2 @ A ) ) )
% 0.32/1.54 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ ( F @ B2 ) )
% 0.32/1.54 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.32/1.54 => ( ! [X5: B,Y5: B] :
% 0.32/1.54 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 0.32/1.54 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_113_order__subst2,axiom,
% 0.32/1.54 ! [A: $tType,C2: $tType] :
% 0.32/1.54 ( ( ( order @ C2 @ ( type2 @ C2 ) )
% 0.32/1.54 & ( order @ A @ ( type2 @ A ) ) )
% 0.32/1.54 => ! [A2: A,B2: A,F: A > C2,C: C2] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( ord_less_eq @ C2 @ ( F @ B2 ) @ C )
% 0.32/1.54 => ( ! [X5: A,Y5: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.32/1.54 => ( ord_less_eq @ C2 @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.32/1.54 => ( ord_less_eq @ C2 @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_114_ord__eq__le__subst,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType] :
% 0.32/1.54 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.32/1.54 & ( ord @ A @ ( type2 @ A ) ) )
% 0.32/1.54 => ! [A2: A,F: B > A,B2: B,C: B] :
% 0.32/1.54 ( ( A2
% 0.32/1.54 = ( F @ B2 ) )
% 0.32/1.54 => ( ( ord_less_eq @ B @ B2 @ C )
% 0.32/1.54 => ( ! [X5: B,Y5: B] :
% 0.32/1.54 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 0.32/1.54 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ ( F @ C ) ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_115_ord__le__eq__subst,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType] :
% 0.32/1.54 ( ( ( ord @ B @ ( type2 @ B ) )
% 0.32/1.54 & ( ord @ A @ ( type2 @ A ) ) )
% 0.32/1.54 => ! [A2: A,B2: A,F: A > B,C: B] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( ( F @ B2 )
% 0.32/1.54 = C )
% 0.32/1.54 => ( ! [X5: A,Y5: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.32/1.54 => ( ord_less_eq @ B @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.32/1.54 => ( ord_less_eq @ B @ ( F @ A2 ) @ C ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_116_eq__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( ^ [Y6: A,Z3: A] : ( Y6 = Z3 ) )
% 0.32/1.54 = ( ^ [X4: A,Y4: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X4 @ Y4 )
% 0.32/1.54 & ( ord_less_eq @ A @ Y4 @ X4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_117_antisym,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ( ( ord_less_eq @ A @ Y @ X )
% 0.32/1.54 => ( X = Y ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_118_linear,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_119_eq__refl,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( preorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( X = Y )
% 0.32/1.54 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_120_le__cases,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_121_order_Otrans,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_122_le__cases3,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ Y @ Z ) )
% 0.32/1.54 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ X @ Z ) )
% 0.32/1.54 => ( ( ( ord_less_eq @ A @ X @ Z )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ Z @ Y ) )
% 0.32/1.54 => ( ( ( ord_less_eq @ A @ Z @ Y )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.32/1.54 => ( ( ( ord_less_eq @ A @ Y @ Z )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ Z @ X ) )
% 0.32/1.54 => ~ ( ( ord_less_eq @ A @ Z @ X )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_123_antisym__conv,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Y: A,X: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ Y @ X )
% 0.32/1.54 => ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 = ( X = Y ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_124_ord__eq__le__trans,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( A2 = B2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_125_ord__le__eq__trans,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ord @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( B2 = C )
% 0.32/1.54 => ( ord_less_eq @ A @ A2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_126_order__class_Oorder_Oantisym,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.54 => ( A2 = B2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_127_order__trans,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( preorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A,Z: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ( ( ord_less_eq @ A @ Y @ Z )
% 0.32/1.54 => ( ord_less_eq @ A @ X @ Z ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_128_dual__order_Orefl,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] : ( ord_less_eq @ A @ A2 @ A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_129_linorder__wlog,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linorder @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [P: A > A > $o,A2: A,B2: A] :
% 0.32/1.54 ( ! [A3: A,B3: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.32/1.54 => ( P @ A3 @ B3 ) )
% 0.32/1.54 => ( ! [A3: A,B3: A] :
% 0.32/1.54 ( ( P @ B3 @ A3 )
% 0.32/1.54 => ( P @ A3 @ B3 ) )
% 0.32/1.54 => ( P @ A2 @ B2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_130_dual__order_Otrans,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,A2: A,C: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.32/1.54 => ( ord_less_eq @ A @ C @ A2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_131_dual__order_Oantisym,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( order @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,A2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ B2 @ A2 )
% 0.32/1.54 => ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( A2 = B2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_132_smooth3,axiom,
% 0.32/1.54 hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_133_smooth2,axiom,
% 0.32/1.54 hammin1195055315smooth @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_134_le__cube,axiom,
% 0.32/1.54 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ ( times_times @ nat @ M @ M ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_135_le__square,axiom,
% 0.32/1.54 ! [M: nat] : ( ord_less_eq @ nat @ M @ ( times_times @ nat @ M @ M ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_136_mult__le__mono,axiom,
% 0.32/1.54 ! [I: nat,J: nat,K3: nat,L: nat] :
% 0.32/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.54 => ( ( ord_less_eq @ nat @ K3 @ L )
% 0.32/1.54 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K3 ) @ ( times_times @ nat @ J @ L ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_137_mult__le__mono1,axiom,
% 0.32/1.54 ! [I: nat,J: nat,K3: nat] :
% 0.32/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.54 => ( ord_less_eq @ nat @ ( times_times @ nat @ I @ K3 ) @ ( times_times @ nat @ J @ K3 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_138_mult__le__mono2,axiom,
% 0.32/1.54 ! [I: nat,J: nat,K3: nat] :
% 0.32/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.54 => ( ord_less_eq @ nat @ ( times_times @ nat @ K3 @ I ) @ ( times_times @ nat @ K3 @ J ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_139_nat__le__linear,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.54 | ( ord_less_eq @ nat @ N @ M ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_140_le__antisym,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( ord_less_eq @ nat @ M @ N )
% 0.32/1.54 => ( ( ord_less_eq @ nat @ N @ M )
% 0.32/1.54 => ( M = N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_141_eq__imp__le,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( M = N )
% 0.32/1.54 => ( ord_less_eq @ nat @ M @ N ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_142_le__trans,axiom,
% 0.32/1.54 ! [I: nat,J: nat,K3: nat] :
% 0.32/1.54 ( ( ord_less_eq @ nat @ I @ J )
% 0.32/1.54 => ( ( ord_less_eq @ nat @ J @ K3 )
% 0.32/1.54 => ( ord_less_eq @ nat @ I @ K3 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_143_le__refl,axiom,
% 0.32/1.54 ! [N: nat] : ( ord_less_eq @ nat @ N @ N ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_144_enat_Osimps_I6_J,axiom,
% 0.32/1.54 ! [T: $tType,F1: nat > T,F22: T,Nat: nat] :
% 0.32/1.54 ( ( extended_rec_enat @ T @ F1 @ F22 @ ( extended_enat2 @ Nat ) )
% 0.32/1.54 = ( F1 @ Nat ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_145_sub__num__simps_I5_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ ( bit1 @ K3 ) @ one2 )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bit0 @ K3 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_146_dbl__inc__simps_I3_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( neg_numeral_dbl_inc @ A @ ( one_one @ A ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bit1 @ one2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_147_dbl__simps_I5_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K3 ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bit0 @ K3 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_148_nat__1__eq__mult__iff,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( ( one_one @ nat )
% 0.32/1.54 = ( times_times @ nat @ M @ N ) )
% 0.32/1.54 = ( ( M
% 0.32/1.54 = ( one_one @ nat ) )
% 0.32/1.54 & ( N
% 0.32/1.54 = ( one_one @ nat ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_149_nat__mult__eq__1__iff,axiom,
% 0.32/1.54 ! [M: nat,N: nat] :
% 0.32/1.54 ( ( ( times_times @ nat @ M @ N )
% 0.32/1.54 = ( one_one @ nat ) )
% 0.32/1.54 = ( ( M
% 0.32/1.54 = ( one_one @ nat ) )
% 0.32/1.54 & ( N
% 0.32/1.54 = ( one_one @ nat ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_150_numeral__eq__one__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( ( numeral_numeral @ A @ N )
% 0.32/1.54 = ( one_one @ A ) )
% 0.32/1.54 = ( N = one2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_151_one__eq__numeral__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semiring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( ( one_one @ A )
% 0.32/1.54 = ( numeral_numeral @ A @ N ) )
% 0.32/1.54 = ( one2 = N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_152_sub__num__simps_I9_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num,L: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ ( bit1 @ K3 ) @ ( bit1 @ L ) )
% 0.32/1.54 = ( neg_numeral_dbl @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_153_sub__num__simps_I6_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num,L: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ ( bit0 @ K3 ) @ ( bit0 @ L ) )
% 0.32/1.54 = ( neg_numeral_dbl @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_154_sub__num__simps_I8_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num,L: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ ( bit1 @ K3 ) @ ( bit0 @ L ) )
% 0.32/1.54 = ( neg_numeral_dbl_inc @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_155_numeral__le__one__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( numeral_numeral @ A @ N ) @ ( one_one @ A ) )
% 0.32/1.54 = ( ord_less_eq @ num @ N @ one2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_156_dbl__simps_I3_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( neg_numeral_dbl @ A @ ( one_one @ A ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_157_nat__mult__1,axiom,
% 0.32/1.54 ! [N: nat] :
% 0.32/1.54 ( ( times_times @ nat @ ( one_one @ nat ) @ N )
% 0.32/1.54 = N ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_158_nat__mult__1__right,axiom,
% 0.32/1.54 ! [N: nat] :
% 0.32/1.54 ( ( times_times @ nat @ N @ ( one_one @ nat ) )
% 0.32/1.54 = N ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_159_le__numeral__extra_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ord_less_eq @ A @ ( one_one @ A ) @ ( one_one @ A ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_160_one__enat__def,axiom,
% 0.32/1.54 ( ( one_one @ extended_enat )
% 0.32/1.54 = ( extended_enat2 @ ( one_one @ nat ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_161_enat__1__iff_I1_J,axiom,
% 0.32/1.54 ! [X: nat] :
% 0.32/1.54 ( ( ( extended_enat2 @ X )
% 0.32/1.54 = ( one_one @ extended_enat ) )
% 0.32/1.54 = ( X
% 0.32/1.54 = ( one_one @ nat ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_162_enat__1__iff_I2_J,axiom,
% 0.32/1.54 ! [X: nat] :
% 0.32/1.54 ( ( ( one_one @ extended_enat )
% 0.32/1.54 = ( extended_enat2 @ X ) )
% 0.32/1.54 = ( X
% 0.32/1.54 = ( one_one @ nat ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_163_one__le__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_semidom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] : ( ord_less_eq @ A @ ( one_one @ A ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_164_numeral__One,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( numeral_numeral @ A @ one2 )
% 0.32/1.54 = ( one_one @ A ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_165_numerals_I1_J,axiom,
% 0.32/1.54 ( ( numeral_numeral @ nat @ one2 )
% 0.32/1.54 = ( one_one @ nat ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_166_mult_Oright__neutral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_167_mult_Oleft__neutral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( monoid_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_168_sub__num__simps_I7_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num,L: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ ( bit0 @ K3 ) @ ( bit1 @ L ) )
% 0.32/1.54 = ( neg_numeral_dbl_dec @ A @ ( neg_numeral_sub @ A @ K3 @ L ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_169_dbl__dec__simps_I3_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( neg_numeral_dbl_dec @ A @ ( one_one @ A ) )
% 0.32/1.54 = ( one_one @ A ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_170_mult_Oleft__commute,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,A2: A,C: A] :
% 0.32/1.54 ( ( times_times @ A @ B2 @ ( times_times @ A @ A2 @ C ) )
% 0.32/1.54 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_171_mult_Ocommute,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( times_times @ A )
% 0.32/1.54 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_172_mult_Oassoc,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( semigroup_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.32/1.54 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_173_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ab_semigroup_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A,C: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ A2 @ B2 ) @ C )
% 0.32/1.54 = ( times_times @ A @ A2 @ ( times_times @ A @ B2 @ C ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_174_one__reorient,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( one @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A] :
% 0.32/1.54 ( ( ( one_one @ A )
% 0.32/1.54 = X )
% 0.32/1.54 = ( X
% 0.32/1.54 = ( one_one @ A ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_175_comm__monoid__mult__class_Omult__1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_176_mult_Ocomm__neutral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_monoid_mult @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_177_hamming__unfold,axiom,
% 0.32/1.54 ( hammin2015774020amming
% 0.32/1.54 = ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ hammin2015774020amming ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_178_sub__num__simps_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ ( bit0 @ K3 ) @ one2 )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bitM @ K3 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_179_semiring__normalization__rules_I12_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ A2 @ ( one_one @ A ) )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_180_llist_Oinject,axiom,
% 0.32/1.54 ! [A: $tType,X21: A,X222: coinductive_llist @ A,Y21: A,Y22: coinductive_llist @ A] :
% 0.32/1.54 ( ( ( coinductive_LCons @ A @ X21 @ X222 )
% 0.32/1.54 = ( coinductive_LCons @ A @ Y21 @ Y22 ) )
% 0.32/1.54 = ( ( X21 = Y21 )
% 0.32/1.54 & ( X222 = Y22 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_181_lfinite__code_I2_J,axiom,
% 0.32/1.54 ! [B: $tType,X: B,Xs: coinductive_llist @ B] :
% 0.32/1.54 ( ( coinductive_lfinite @ B @ ( coinductive_LCons @ B @ X @ Xs ) )
% 0.32/1.54 = ( coinductive_lfinite @ B @ Xs ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_182_lfinite__LCons,axiom,
% 0.32/1.54 ! [A: $tType,X: A,Xs: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) )
% 0.32/1.54 = ( coinductive_lfinite @ A @ Xs ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_183_dbl__dec__simps_I5_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_dbl_dec @ A @ ( numeral_numeral @ A @ K3 ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( bitM @ K3 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_184_ltl__simps_I2_J,axiom,
% 0.32/1.54 ! [A: $tType,X21: A,X222: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_ltl @ A @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.32/1.54 = X222 ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_185_lmap__eq__LCons__conv,axiom,
% 0.32/1.54 ! [A: $tType,B: $tType,F: B > A,Xs: coinductive_llist @ B,Y: A,Ys: coinductive_llist @ A] :
% 0.32/1.54 ( ( ( coinductive_lmap @ B @ A @ F @ Xs )
% 0.32/1.54 = ( coinductive_LCons @ A @ Y @ Ys ) )
% 0.32/1.54 = ( ? [X4: B,Xs3: coinductive_llist @ B] :
% 0.32/1.54 ( ( Xs
% 0.32/1.54 = ( coinductive_LCons @ B @ X4 @ Xs3 ) )
% 0.32/1.54 & ( Y
% 0.32/1.54 = ( F @ X4 ) )
% 0.32/1.54 & ( Ys
% 0.32/1.54 = ( coinductive_lmap @ B @ A @ F @ Xs3 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_186_llist_Osimps_I13_J,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType,F: A > B,X21: A,X222: coinductive_llist @ A] :
% 0.32/1.54 ( ( coinductive_lmap @ A @ B @ F @ ( coinductive_LCons @ A @ X21 @ X222 ) )
% 0.32/1.54 = ( coinductive_LCons @ B @ ( F @ X21 ) @ ( coinductive_lmap @ A @ B @ F @ X222 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_187_lfinite__LConsI,axiom,
% 0.32/1.54 ! [A: $tType,Xs: coinductive_llist @ A,X: A] :
% 0.32/1.54 ( ( coinductive_lfinite @ A @ Xs )
% 0.32/1.54 => ( coinductive_lfinite @ A @ ( coinductive_LCons @ A @ X @ Xs ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_188_semiring__norm_I26_J,axiom,
% 0.32/1.54 ( ( bitM @ one2 )
% 0.32/1.54 = one2 ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_189_semiring__norm_I28_J,axiom,
% 0.32/1.54 ! [N: num] :
% 0.32/1.54 ( ( bitM @ ( bit1 @ N ) )
% 0.32/1.54 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_190_semiring__norm_I27_J,axiom,
% 0.32/1.54 ! [N: num] :
% 0.32/1.54 ( ( bitM @ ( bit0 @ N ) )
% 0.32/1.54 = ( bit1 @ ( bitM @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_191_semiring__normalization__rules_I19_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Rx: A,Ry: A] :
% 0.32/1.54 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 0.32/1.54 = ( times_times @ A @ Rx @ ( times_times @ A @ Lx @ Ry ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_192_semiring__normalization__rules_I18_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Rx: A,Ry: A] :
% 0.32/1.54 ( ( times_times @ A @ Lx @ ( times_times @ A @ Rx @ Ry ) )
% 0.32/1.54 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ry ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_193_semiring__normalization__rules_I17_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Ly: A,Rx: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 0.32/1.54 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ Rx ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_194_semiring__normalization__rules_I16_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Ly: A,Rx: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Rx )
% 0.32/1.54 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ Ly ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_195_semiring__normalization__rules_I15_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.32/1.54 = ( times_times @ A @ Rx @ ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ Ry ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_196_semiring__normalization__rules_I14_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.32/1.54 = ( times_times @ A @ Lx @ ( times_times @ A @ Ly @ ( times_times @ A @ Rx @ Ry ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_197_semiring__normalization__rules_I13_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Lx: A,Ly: A,Rx: A,Ry: A] :
% 0.32/1.54 ( ( times_times @ A @ ( times_times @ A @ Lx @ Ly ) @ ( times_times @ A @ Rx @ Ry ) )
% 0.32/1.54 = ( times_times @ A @ ( times_times @ A @ Lx @ Rx ) @ ( times_times @ A @ Ly @ Ry ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_198_semiring__normalization__rules_I7_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( times_times @ A )
% 0.32/1.54 = ( ^ [A4: A,B4: A] : ( times_times @ A @ B4 @ A4 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_199_semiring__normalization__rules_I11_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_semiring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( times_times @ A @ ( one_one @ A ) @ A2 )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_200_hamming_H_Osimps,axiom,
% 0.32/1.54 ( hammin1630468845amming
% 0.32/1.54 = ( ^ [Uu: product_unit] : ( coinductive_LCons @ nat @ ( one_one @ nat ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit0 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ ( hammin1630468845amming @ product_Unity ) ) ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_201_sub__num__simps_I2_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [L: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ one2 @ ( bit0 @ L ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bitM @ L ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_202_dbl__dec__simps_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( neg_numeral_dbl_dec @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit1 @ one2 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_203_compl__eq__compl__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( ( uminus_uminus @ A @ X )
% 0.32/1.54 = ( uminus_uminus @ A @ Y ) )
% 0.32/1.54 = ( X = Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_204_double__compl,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A] :
% 0.32/1.54 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ X ) )
% 0.32/1.54 = X ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_205_uminus__apply,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( uminus @ B @ ( type2 @ B ) )
% 0.32/1.54 => ( ( uminus_uminus @ ( A > B ) )
% 0.32/1.54 = ( ^ [A5: A > B,X4: A] : ( uminus_uminus @ B @ ( A5 @ X4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_206_neg__equal__iff__equal,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ( uminus_uminus @ A @ A2 )
% 0.32/1.54 = ( uminus_uminus @ A @ B2 ) )
% 0.32/1.54 = ( A2 = B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_207_add_Oinverse__inverse,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A] :
% 0.32/1.54 ( ( uminus_uminus @ A @ ( uminus_uminus @ A @ A2 ) )
% 0.32/1.54 = A2 ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_208_compl__le__compl__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ ( uminus_uminus @ A @ Y ) )
% 0.32/1.54 = ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_209_neg__le__iff__le,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [B2: A,A2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) )
% 0.32/1.54 = ( ord_less_eq @ A @ A2 @ B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_210_neg__numeral__eq__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/1.54 = ( M = N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_211_mult__minus1__right,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Z: A] :
% 0.32/1.54 ( ( times_times @ A @ Z @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ Z ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_212_mult__minus1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Z: A] :
% 0.32/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ Z )
% 0.32/1.54 = ( uminus_uminus @ A @ Z ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_213_dbl__simps_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K3 ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( neg_numeral_dbl @ A @ ( numeral_numeral @ A @ K3 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_214_dbl__inc__simps_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( neg_numeral_dbl_inc @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_215_neg__one__eq__numeral__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( ( uminus_uminus @ A @ ( one_one @ A ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/1.54 = ( N = one2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_216_numeral__eq__neg__one__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/1.54 = ( N = one2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_217_mult__neg__numeral__simps_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/1.54 = ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_218_mult__neg__numeral__simps_I2_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_219_mult__neg__numeral__simps_I3_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( times_times @ num @ M @ N ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_220_semiring__norm_I170_J,axiom,
% 0.32/1.54 ! [B: $tType] :
% 0.32/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [V: num,W: num,Y: B] :
% 0.32/1.54 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( numeral_numeral @ B @ W ) @ Y ) )
% 0.32/1.54 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_221_semiring__norm_I171_J,axiom,
% 0.32/1.54 ! [B: $tType] :
% 0.32/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [V: num,W: num,Y: B] :
% 0.32/1.54 ( ( times_times @ B @ ( numeral_numeral @ B @ V ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 0.32/1.54 = ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) ) @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_222_semiring__norm_I172_J,axiom,
% 0.32/1.54 ! [B: $tType] :
% 0.32/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [V: num,W: num,Y: B] :
% 0.32/1.54 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ V ) ) @ ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ W ) ) @ Y ) )
% 0.32/1.54 = ( times_times @ B @ ( numeral_numeral @ B @ ( times_times @ num @ V @ W ) ) @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_223_neg__numeral__le__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) )
% 0.32/1.54 = ( ord_less_eq @ num @ N @ M ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_224_not__neg__one__le__neg__numeral__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num] :
% 0.32/1.54 ( ( ~ ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) ) )
% 0.32/1.54 = ( M != one2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_225_dbl__dec__simps_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_dbl_dec @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K3 ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( neg_numeral_dbl_inc @ A @ ( numeral_numeral @ A @ K3 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_226_dbl__inc__simps_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [K3: num] :
% 0.32/1.54 ( ( neg_numeral_dbl_inc @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ K3 ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( neg_numeral_dbl_dec @ A @ ( numeral_numeral @ A @ K3 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_227_sub__num__simps_I3_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [L: num] :
% 0.32/1.54 ( ( neg_numeral_sub @ A @ one2 @ ( bit1 @ L ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ L ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_228_dbl__simps_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( neg_numeral @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( neg_numeral_dbl @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) )
% 0.32/1.54 = ( uminus_uminus @ A @ ( numeral_numeral @ A @ ( bit0 @ one2 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_229_ring__normalization__rules_I1_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( uminus_uminus @ A )
% 0.32/1.54 = ( times_times @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_230_numeral__times__minus__swap,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( comm_ring_1 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [W: num,X: A] :
% 0.32/1.54 ( ( times_times @ A @ ( numeral_numeral @ A @ W ) @ ( uminus_uminus @ A @ X ) )
% 0.32/1.54 = ( times_times @ A @ X @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ W ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_231_numeral__neq__neg__one,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( numeral_numeral @ A @ N )
% 0.32/1.54 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_232_one__neq__neg__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [N: num] :
% 0.32/1.54 ( ( one_one @ A )
% 0.32/1.54 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_233_hamming__def,axiom,
% 0.32/1.54 ( hammin2015774020amming
% 0.32/1.54 = ( hammin1630468845amming @ product_Unity ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_234_neg__numeral__neq__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) )
% 0.32/1.54 != ( numeral_numeral @ A @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_235_numeral__neq__neg__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ( ( numeral_numeral @ A @ M )
% 0.32/1.54 != ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_236_fun__Compl__def,axiom,
% 0.32/1.54 ! [B: $tType,A: $tType] :
% 0.32/1.54 ( ( uminus @ B @ ( type2 @ B ) )
% 0.32/1.54 => ( ( uminus_uminus @ ( A > B ) )
% 0.32/1.54 = ( ^ [A5: A > B,X4: A] : ( uminus_uminus @ B @ ( A5 @ X4 ) ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_237_compl__le__swap2,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Y: A,X: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ X )
% 0.32/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ X ) @ Y ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_238_compl__le__swap1,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [Y: A,X: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ Y @ ( uminus_uminus @ A @ X ) )
% 0.32/1.54 => ( ord_less_eq @ A @ X @ ( uminus_uminus @ A @ Y ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_239_compl__mono,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [X: A,Y: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ X @ Y )
% 0.32/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ Y ) @ ( uminus_uminus @ A @ X ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_240_le__minus__one__simps_I2_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( one_one @ A ) ) @ ( one_one @ A ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_241_le__minus__one__simps_I4_J,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ~ ( ord_less_eq @ A @ ( one_one @ A ) @ ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_242_neg__numeral__le__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] : ( ord_less_eq @ A @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ M ) ) @ ( numeral_numeral @ A @ N ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_243_not__numeral__le__neg__numeral,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( linordered_idom @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [M: num,N: num] :
% 0.32/1.54 ~ ( ord_less_eq @ A @ ( numeral_numeral @ A @ M ) @ ( uminus_uminus @ A @ ( numeral_numeral @ A @ N ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_244_le__minus__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ ( uminus_uminus @ A @ B2 ) )
% 0.32/1.54 = ( ord_less_eq @ A @ B2 @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_245_minus__le__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ ( uminus_uminus @ A @ A2 ) @ B2 )
% 0.32/1.54 = ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ A2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_246_le__imp__neg__le,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ordered_ab_group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ord_less_eq @ A @ A2 @ B2 )
% 0.32/1.54 => ( ord_less_eq @ A @ ( uminus_uminus @ A @ B2 ) @ ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_247_minus__equation__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( ( uminus_uminus @ A @ A2 )
% 0.32/1.54 = B2 )
% 0.32/1.54 = ( ( uminus_uminus @ A @ B2 )
% 0.32/1.54 = A2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_248_equation__minus__iff,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( group_add @ A @ ( type2 @ A ) )
% 0.32/1.54 => ! [A2: A,B2: A] :
% 0.32/1.54 ( ( A2
% 0.32/1.54 = ( uminus_uminus @ A @ B2 ) )
% 0.32/1.54 = ( B2
% 0.32/1.54 = ( uminus_uminus @ A @ A2 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_249_one__neq__neg__one,axiom,
% 0.32/1.54 ! [A: $tType] :
% 0.32/1.54 ( ( ring_char_0 @ A @ ( type2 @ A ) )
% 0.32/1.54 => ( ( one_one @ A )
% 0.32/1.54 != ( uminus_uminus @ A @ ( one_one @ A ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_250_mult__1s_I3_J,axiom,
% 0.32/1.54 ! [B: $tType] :
% 0.32/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [B2: B] :
% 0.32/1.54 ( ( times_times @ B @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) @ B2 )
% 0.32/1.54 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(fact_251_mult__1s_I4_J,axiom,
% 0.32/1.54 ! [B: $tType] :
% 0.32/1.54 ( ( ring_1 @ B @ ( type2 @ B ) )
% 0.32/1.54 => ! [B2: B] :
% 0.32/1.54 ( ( times_times @ B @ B2 @ ( uminus_uminus @ B @ ( numeral_numeral @ B @ one2 ) ) )
% 0.32/1.54 = ( uminus_uminus @ B @ B2 ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Lattices_Osemilattice__inf,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( semilattice_inf @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( semilattice_inf @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Lattices_Oboolean__algebra,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( boolean_algebra @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( boolean_algebra @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( preorder @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( preorder @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Lattices_Olattice,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( lattice @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( lattice @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( order @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( order @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( ord @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( ord @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_fun___Groups_Ouminus,axiom,
% 0.32/1.54 ! [A6: $tType,A7: $tType] :
% 0.32/1.54 ( ( uminus @ A7 @ ( type2 @ A7 ) )
% 0.32/1.54 => ( uminus @ ( A6 > A7 ) @ ( type2 @ ( A6 > A7 ) ) ) ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Rings_Olinordered__semidom,axiom,
% 0.32/1.54 linordered_semidom @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Lattices_Osemilattice__inf_1,axiom,
% 0.32/1.54 semilattice_inf @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Oab__semigroup__mult,axiom,
% 0.32/1.54 ab_semigroup_mult @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Ocomm__monoid__mult,axiom,
% 0.32/1.54 comm_monoid_mult @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Rings_Ocomm__semiring__1,axiom,
% 0.32/1.54 comm_semiring_1 @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Osemigroup__mult,axiom,
% 0.32/1.54 semigroup_mult @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Num_Osemiring__numeral,axiom,
% 0.32/1.54 semiring_numeral @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Nat_Osemiring__char__0,axiom,
% 0.32/1.54 semiring_char_0 @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Opreorder_2,axiom,
% 0.32/1.54 preorder @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.32/1.54 linorder @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Omonoid__mult,axiom,
% 0.32/1.54 monoid_mult @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Lattices_Olattice_3,axiom,
% 0.32/1.54 lattice @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 0.32/1.54 order @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 0.32/1.54 ord @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Num_Onumeral,axiom,
% 0.32/1.54 numeral @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Nat_Onat___Groups_Oone,axiom,
% 0.32/1.54 one @ nat @ ( type2 @ nat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Num_Onum___Orderings_Opreorder_6,axiom,
% 0.32/1.54 preorder @ num @ ( type2 @ num ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Num_Onum___Orderings_Olinorder_7,axiom,
% 0.32/1.54 linorder @ num @ ( type2 @ num ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Num_Onum___Orderings_Oorder_8,axiom,
% 0.32/1.54 order @ num @ ( type2 @ num ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Num_Onum___Orderings_Oord_9,axiom,
% 0.32/1.54 ord @ num @ ( type2 @ num ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Lattices_Osemilattice__inf_10,axiom,
% 0.32/1.54 semilattice_inf @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Lattices_Oboolean__algebra_11,axiom,
% 0.32/1.54 boolean_algebra @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Opreorder_12,axiom,
% 0.32/1.54 preorder @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Olinorder_13,axiom,
% 0.32/1.54 linorder @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Lattices_Olattice_14,axiom,
% 0.32/1.54 lattice @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.32/1.54 order @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.32/1.54 ord @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_HOL_Obool___Groups_Ouminus_17,axiom,
% 0.32/1.54 uminus @ $o @ ( type2 @ $o ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Lattices_Osemilattice__inf_18,axiom,
% 0.32/1.54 semilattice_inf @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Groups_Oab__semigroup__mult_19,axiom,
% 0.32/1.54 ab_semigroup_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Groups_Ocomm__monoid__mult_20,axiom,
% 0.32/1.54 comm_monoid_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Rings_Ocomm__semiring__1_21,axiom,
% 0.32/1.54 comm_semiring_1 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Groups_Osemigroup__mult_22,axiom,
% 0.32/1.54 semigroup_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Num_Osemiring__numeral_23,axiom,
% 0.32/1.54 semiring_numeral @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Nat_Osemiring__char__0_24,axiom,
% 0.32/1.54 semiring_char_0 @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Orderings_Opreorder_25,axiom,
% 0.32/1.54 preorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Orderings_Olinorder_26,axiom,
% 0.32/1.54 linorder @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Groups_Omonoid__mult_27,axiom,
% 0.32/1.54 monoid_mult @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Lattices_Olattice_28,axiom,
% 0.32/1.54 lattice @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Orderings_Oorder_29,axiom,
% 0.32/1.54 order @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Orderings_Oord_30,axiom,
% 0.32/1.54 ord @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Num_Onumeral_31,axiom,
% 0.32/1.54 numeral @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(tcon_Extended__Nat_Oenat___Groups_Oone_32,axiom,
% 0.32/1.54 one @ extended_enat @ ( type2 @ extended_enat ) ).
% 0.32/1.54
% 0.32/1.54 thf(conj_0,conjecture,
% 0.32/1.54 ord_less_eq @ extended_enat @ ( inf_inf @ extended_enat @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) ) @ ( coinductive_llength @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) @ ( coinductive_llength @ nat @ ( hammin1138290136lmerge @ nat @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ one2 ) ) ) @ hammin2015774020amming ) @ ( coinductive_lmap @ nat @ nat @ ( times_times @ nat @ ( numeral_numeral @ nat @ ( bit1 @ ( bit0 @ one2 ) ) ) ) @ hammin2015774020amming ) ) ) ).
% 0.32/1.54 ------------------------
% 0.32/1.56 % (16789)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/183Mi)
% 0.32/1.56 % (16795)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/18Mi)
% 0.32/1.56 % (16795)Instruction limit reached!
% 0.32/1.56 % (16795)------------------------------
% 0.32/1.56 % (16795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (16795)Termination reason: Unknown
% 0.32/1.56 % (16795)Termination phase: Property scanning
% 0.32/1.56
% 0.32/1.56 % (16795)Memory used [KB]: 1663
% 0.32/1.56 % (16795)Time elapsed: 0.008 s
% 0.32/1.56 % (16795)Instructions burned: 20 (million)
% 0.32/1.56 % (16795)------------------------------
% 0.32/1.56 % (16795)------------------------------
% 0.32/1.56 % (16790)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_16461 for (2999ds/4Mi)
% 0.32/1.56 % (16791)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_16461 for (2999ds/27Mi)
% 0.32/1.56 % (16792)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/2Mi)
% 0.32/1.56 % (16793)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_16461 for (2999ds/2Mi)
% 0.32/1.56 % (16794)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_16461 for (2999ds/275Mi)
% 0.32/1.56 % (16793)Instruction limit reached!
% 0.32/1.56 % (16793)------------------------------
% 0.32/1.56 % (16793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.56 % (16793)Termination reason: Unknown
% 0.32/1.56 % (16793)Termination phase: shuffling
% 0.32/1.56
% 0.32/1.56 % (16793)Memory used [KB]: 1279
% 0.32/1.56 % (16793)Time elapsed: 0.003 s
% 0.32/1.56 % (16793)Instructions burned: 2 (million)
% 0.32/1.56 % (16793)------------------------------
% 0.32/1.56 % (16793)------------------------------
% 0.32/1.57 % (16792)Instruction limit reached!
% 0.32/1.57 % (16792)------------------------------
% 0.32/1.57 % (16792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (16792)Termination reason: Unknown
% 0.32/1.57 % (16792)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (16792)Memory used [KB]: 1407
% 0.32/1.57 % (16792)Time elapsed: 0.004 s
% 0.32/1.57 % (16792)Instructions burned: 3 (million)
% 0.32/1.57 % (16792)------------------------------
% 0.32/1.57 % (16792)------------------------------
% 0.32/1.57 % (16790)Instruction limit reached!
% 0.32/1.57 % (16790)------------------------------
% 0.32/1.57 % (16790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.57 % (16790)Termination reason: Unknown
% 0.32/1.57 % (16790)Termination phase: shuffling
% 0.32/1.57
% 0.32/1.57 % (16790)Memory used [KB]: 1407
% 0.32/1.57 % (16790)Time elapsed: 0.005 s
% 0.32/1.57 % (16790)Instructions burned: 5 (million)
% 0.32/1.57 % (16790)------------------------------
% 0.32/1.57 % (16790)------------------------------
% 0.32/1.57 % (16796)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/3Mi)
% 0.32/1.58 % (16796)Instruction limit reached!
% 0.32/1.58 % (16796)------------------------------
% 0.32/1.58 % (16796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (16796)Termination reason: Unknown
% 0.32/1.58 % (16796)Termination phase: shuffling
% 0.32/1.58
% 0.32/1.58 % (16796)Memory used [KB]: 1407
% 0.32/1.58 % (16796)Time elapsed: 0.003 s
% 0.32/1.58 % (16796)Instructions burned: 4 (million)
% 0.32/1.58 % (16796)------------------------------
% 0.32/1.58 % (16796)------------------------------
% 0.32/1.58 % (16791)Instruction limit reached!
% 0.32/1.58 % (16791)------------------------------
% 0.32/1.58 % (16791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.58 % (16791)Termination reason: Unknown
% 0.32/1.58 % (16791)Termination phase: Preprocessing 1
% 0.32/1.58
% 0.32/1.58 % (16791)Memory used [KB]: 1663
% 0.32/1.58 % (16791)Time elapsed: 0.018 s
% 0.32/1.58 % (16791)Instructions burned: 28 (million)
% 0.32/1.58 % (16791)------------------------------
% 0.32/1.58 % (16791)------------------------------
% 0.32/1.58 % (16797)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_16461 for (2999ds/37Mi)
% 0.32/1.58 % (16799)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_16461 for (2999ds/3Mi)
% 0.32/1.58 % (16798)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_16461 for (2999ds/15Mi)
% 0.32/1.59 % (16799)Instruction limit reached!
% 0.32/1.59 % (16799)------------------------------
% 0.32/1.59 % (16799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (16799)Termination reason: Unknown
% 0.32/1.59 % (16799)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (16799)Memory used [KB]: 1407
% 0.32/1.59 % (16799)Time elapsed: 0.004 s
% 0.32/1.59 % (16799)Instructions burned: 5 (million)
% 0.32/1.59 % (16799)------------------------------
% 0.32/1.59 % (16799)------------------------------
% 0.32/1.59 % (16800)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_16461 for (2999ds/1041Mi)
% 0.32/1.59 % (16798)Instruction limit reached!
% 0.32/1.59 % (16798)------------------------------
% 0.32/1.59 % (16798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.32/1.59 % (16798)Termination reason: Unknown
% 0.32/1.59 % (16798)Termination phase: shuffling
% 0.32/1.59
% 0.32/1.59 % (16798)Memory used [KB]: 1663
% 0.32/1.59 % (16798)Time elapsed: 0.012 s
% 0.32/1.59 % (16798)Instructions burned: 16 (million)
% 0.32/1.59 % (16798)------------------------------
% 0.32/1.59 % (16798)------------------------------
% 0.32/1.59 % (16801)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/7Mi)
% 2.68/1.60 % (16801)Instruction limit reached!
% 2.68/1.60 % (16801)------------------------------
% 2.68/1.60 % (16801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.60 % (16801)Termination reason: Unknown
% 2.68/1.60 % (16801)Termination phase: shuffling
% 2.68/1.60
% 2.68/1.60 % (16801)Memory used [KB]: 1407
% 2.68/1.60 % (16801)Time elapsed: 0.005 s
% 2.68/1.60 % (16801)Instructions burned: 7 (million)
% 2.68/1.60 % (16801)------------------------------
% 2.68/1.60 % (16801)------------------------------
% 2.68/1.60 % (16797)Instruction limit reached!
% 2.68/1.60 % (16797)------------------------------
% 2.68/1.60 % (16797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.60 % (16797)Termination reason: Unknown
% 2.68/1.60 % (16797)Termination phase: Property scanning
% 2.68/1.60
% 2.68/1.60 % (16797)Memory used [KB]: 1791
% 2.68/1.60 % (16797)Time elapsed: 0.021 s
% 2.68/1.60 % (16797)Instructions burned: 38 (million)
% 2.68/1.60 % (16797)------------------------------
% 2.68/1.60 % (16797)------------------------------
% 2.68/1.60 % (16802)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/16Mi)
% 2.68/1.61 % (16804)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_16461 for (2999ds/3Mi)
% 2.68/1.61 % (16804)Instruction limit reached!
% 2.68/1.61 % (16804)------------------------------
% 2.68/1.61 % (16804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.61 % (16804)Termination reason: Unknown
% 2.68/1.61 % (16804)Termination phase: shuffling
% 2.68/1.61
% 2.68/1.61 % (16804)Memory used [KB]: 1279
% 2.68/1.61 % (16804)Time elapsed: 0.002 s
% 2.68/1.61 % (16804)Instructions burned: 3 (million)
% 2.68/1.61 % (16804)------------------------------
% 2.68/1.61 % (16804)------------------------------
% 2.68/1.61 % (16803)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_16461 for (2999ds/3Mi)
% 2.68/1.61 % (16802)Instruction limit reached!
% 2.68/1.61 % (16802)------------------------------
% 2.68/1.61 % (16802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.61 % (16802)Termination reason: Unknown
% 2.68/1.61 % (16802)Termination phase: shuffling
% 2.68/1.61
% 2.68/1.61 % (16802)Memory used [KB]: 1663
% 2.68/1.61 % (16802)Time elapsed: 0.012 s
% 2.68/1.61 % (16802)Instructions burned: 16 (million)
% 2.68/1.61 % (16802)------------------------------
% 2.68/1.61 % (16802)------------------------------
% 2.68/1.61 % (16803)Instruction limit reached!
% 2.68/1.61 % (16803)------------------------------
% 2.68/1.61 % (16803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.61 % (16803)Termination reason: Unknown
% 2.68/1.61 % (16803)Termination phase: shuffling
% 2.68/1.61
% 2.68/1.61 % (16803)Memory used [KB]: 1407
% 2.68/1.61 % (16803)Time elapsed: 0.004 s
% 2.68/1.61 % (16803)Instructions burned: 4 (million)
% 2.68/1.61 % (16803)------------------------------
% 2.68/1.61 % (16803)------------------------------
% 2.68/1.62 % (16789)Instruction limit reached!
% 2.68/1.62 % (16789)------------------------------
% 2.68/1.62 % (16789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.62 % (16789)Termination reason: Unknown
% 2.68/1.62 % (16789)Termination phase: Saturation
% 2.68/1.62
% 2.68/1.62 % (16789)Memory used [KB]: 6780
% 2.68/1.62 % (16789)Time elapsed: 0.062 s
% 2.68/1.62 % (16789)Instructions burned: 184 (million)
% 2.68/1.62 % (16789)------------------------------
% 2.68/1.62 % (16789)------------------------------
% 2.68/1.62 % (16806)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/3Mi)
% 2.68/1.62 % (16805)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/7Mi)
% 2.68/1.62 % (16806)Instruction limit reached!
% 2.68/1.62 % (16806)------------------------------
% 2.68/1.62 % (16806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.62 % (16806)Termination reason: Unknown
% 2.68/1.62 % (16806)Termination phase: shuffling
% 2.68/1.62
% 2.68/1.62 % (16806)Memory used [KB]: 1407
% 2.68/1.62 % (16806)Time elapsed: 0.003 s
% 2.68/1.62 % (16806)Instructions burned: 4 (million)
% 2.68/1.62 % (16806)------------------------------
% 2.68/1.62 % (16806)------------------------------
% 2.68/1.62 % (16805)Instruction limit reached!
% 2.68/1.62 % (16805)------------------------------
% 2.68/1.62 % (16805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.62 % (16805)Termination reason: Unknown
% 2.68/1.62 % (16805)Termination phase: shuffling
% 2.68/1.62
% 2.68/1.62 % (16805)Memory used [KB]: 1407
% 2.68/1.62 % (16805)Time elapsed: 0.006 s
% 2.68/1.62 % (16805)Instructions burned: 7 (million)
% 2.68/1.62 % (16805)------------------------------
% 2.68/1.62 % (16805)------------------------------
% 2.68/1.63 % (16809)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/710Mi)
% 2.68/1.63 % (16807)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/4Mi)
% 2.68/1.63 % (16810)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/6Mi)
% 2.68/1.63 % (16808)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/18Mi)
% 2.68/1.63 % (16807)Instruction limit reached!
% 2.68/1.63 % (16807)------------------------------
% 2.68/1.63 % (16807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.63 % (16807)Termination reason: Unknown
% 2.68/1.63 % (16807)Termination phase: shuffling
% 2.68/1.63
% 2.68/1.63 % (16807)Memory used [KB]: 1407
% 2.68/1.63 % (16807)Time elapsed: 0.004 s
% 2.68/1.63 % (16807)Instructions burned: 5 (million)
% 2.68/1.63 % (16807)------------------------------
% 2.68/1.63 % (16807)------------------------------
% 2.68/1.63 % (16810)Instruction limit reached!
% 2.68/1.63 % (16810)------------------------------
% 2.68/1.63 % (16810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.63 % (16810)Termination reason: Unknown
% 2.68/1.63 % (16810)Termination phase: shuffling
% 2.68/1.63
% 2.68/1.63 % (16810)Memory used [KB]: 1407
% 2.68/1.63 % (16810)Time elapsed: 0.004 s
% 2.68/1.63 % (16810)Instructions burned: 7 (million)
% 2.68/1.63 % (16810)------------------------------
% 2.68/1.63 % (16810)------------------------------
% 2.68/1.64 % (16811)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_16461 for (2999ds/902Mi)
% 2.68/1.64 % (16812)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_16461 for (2999ds/21Mi)
% 2.68/1.64 % (16808)Instruction limit reached!
% 2.68/1.64 % (16808)------------------------------
% 2.68/1.64 % (16808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.64 % (16808)Termination reason: Unknown
% 2.68/1.64 % (16808)Termination phase: Property scanning
% 2.68/1.64
% 2.68/1.64 % (16808)Memory used [KB]: 1663
% 2.68/1.64 % (16808)Time elapsed: 0.013 s
% 2.68/1.64 % (16808)Instructions burned: 18 (million)
% 2.68/1.64 % (16808)------------------------------
% 2.68/1.64 % (16808)------------------------------
% 2.68/1.64 % (16813)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/5Mi)
% 2.68/1.64 % (16813)Instruction limit reached!
% 2.68/1.64 % (16813)------------------------------
% 2.68/1.64 % (16813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.64 % (16813)Termination reason: Unknown
% 2.68/1.64 % (16813)Termination phase: shuffling
% 2.68/1.64
% 2.68/1.64 % (16813)Memory used [KB]: 1407
% 2.68/1.64 % (16813)Time elapsed: 0.004 s
% 2.68/1.64 % (16813)Instructions burned: 8 (million)
% 2.68/1.64 % (16813)------------------------------
% 2.68/1.64 % (16813)------------------------------
% 2.68/1.65 % (16812)Instruction limit reached!
% 2.68/1.65 % (16812)------------------------------
% 2.68/1.65 % (16812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.65 % (16812)Termination reason: Unknown
% 2.68/1.65 % (16812)Termination phase: Property scanning
% 2.68/1.65
% 2.68/1.65 % (16812)Memory used [KB]: 1663
% 2.68/1.65 % (16812)Time elapsed: 0.008 s
% 2.68/1.65 % (16812)Instructions burned: 22 (million)
% 2.68/1.65 % (16812)------------------------------
% 2.68/1.65 % (16812)------------------------------
% 2.68/1.65 % (16815)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/377Mi)
% 2.68/1.66 % (16816)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_16461 for (2999ds/779Mi)
% 2.68/1.66 % (16814)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_16461 for (2999ds/6Mi)
% 2.68/1.66 % (16814)Instruction limit reached!
% 2.68/1.66 % (16814)------------------------------
% 2.68/1.66 % (16814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.66 % (16814)Termination reason: Unknown
% 2.68/1.66 % (16814)Termination phase: shuffling
% 2.68/1.66
% 2.68/1.66 % (16814)Memory used [KB]: 1407
% 2.68/1.66 % (16814)Time elapsed: 0.004 s
% 2.68/1.66 % (16814)Instructions burned: 6 (million)
% 2.68/1.66 % (16814)------------------------------
% 2.68/1.66 % (16814)------------------------------
% 2.68/1.67 % (16817)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_16461 for (2998ds/19Mi)
% 2.68/1.67 % (16794)Instruction limit reached!
% 2.68/1.67 % (16794)------------------------------
% 2.68/1.67 % (16794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.67 % (16794)Termination reason: Unknown
% 2.68/1.67 % (16794)Termination phase: Saturation
% 2.68/1.67
% 2.68/1.67 % (16794)Memory used [KB]: 6908
% 2.68/1.67 % (16794)Time elapsed: 0.112 s
% 2.68/1.67 % (16794)Instructions burned: 276 (million)
% 2.68/1.67 % (16794)------------------------------
% 2.68/1.67 % (16794)------------------------------
% 2.68/1.68 % (16817)Instruction limit reached!
% 2.68/1.68 % (16817)------------------------------
% 2.68/1.68 % (16817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.68 % (16817)Termination reason: Unknown
% 2.68/1.68 % (16817)Termination phase: shuffling
% 2.68/1.68
% 2.68/1.68 % (16817)Memory used [KB]: 1663
% 2.68/1.68 % (16817)Time elapsed: 0.007 s
% 2.68/1.68 % (16817)Instructions burned: 21 (million)
% 2.68/1.68 % (16817)------------------------------
% 2.68/1.68 % (16817)------------------------------
% 2.68/1.68 % (16818)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_16461 for (2998ds/879Mi)
% 2.68/1.69 % (16819)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_16461 for (2998ds/17Mi)
% 2.68/1.69 % (16819)Instruction limit reached!
% 2.68/1.69 % (16819)------------------------------
% 2.68/1.69 % (16819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.69 % (16819)Termination reason: Unknown
% 2.68/1.69 % (16819)Termination phase: Property scanning
% 2.68/1.69
% 2.68/1.69 % (16819)Memory used [KB]: 1663
% 2.68/1.69 % (16819)Time elapsed: 0.008 s
% 2.68/1.69 % (16819)Instructions burned: 18 (million)
% 2.68/1.69 % (16819)------------------------------
% 2.68/1.69 % (16819)------------------------------
% 2.68/1.70 % (16820)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_16461 for (2998ds/3Mi)
% 2.68/1.70 % (16820)Instruction limit reached!
% 2.68/1.70 % (16820)------------------------------
% 2.68/1.70 % (16820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.70 % (16820)Termination reason: Unknown
% 2.68/1.70 % (16820)Termination phase: shuffling
% 2.68/1.70
% 2.68/1.70 % (16820)Memory used [KB]: 1407
% 2.68/1.70 % (16820)Time elapsed: 0.003 s
% 2.68/1.70 % (16820)Instructions burned: 4 (million)
% 2.68/1.70 % (16820)------------------------------
% 2.68/1.70 % (16820)------------------------------
% 2.68/1.71 % (16821)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_16461 for (2998ds/30Mi)
% 2.68/1.72 % (16821)Instruction limit reached!
% 2.68/1.72 % (16821)------------------------------
% 2.68/1.72 % (16821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.72 % (16821)Termination reason: Unknown
% 2.68/1.72 % (16821)Termination phase: Preprocessing 2
% 2.68/1.72
% 2.68/1.72 % (16821)Memory used [KB]: 1663
% 2.68/1.72 % (16821)Time elapsed: 0.012 s
% 2.68/1.72 % (16821)Instructions burned: 31 (million)
% 2.68/1.72 % (16821)------------------------------
% 2.68/1.72 % (16821)------------------------------
% 2.68/1.73 % (16822)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_16461 for (2998ds/127Mi)
% 2.68/1.78 % (16822)Instruction limit reached!
% 2.68/1.78 % (16822)------------------------------
% 2.68/1.78 % (16822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.78 % (16822)Termination reason: Unknown
% 2.68/1.78 % (16822)Termination phase: Saturation
% 2.68/1.78
% 2.68/1.78 % (16822)Memory used [KB]: 6780
% 2.68/1.78 % (16822)Time elapsed: 0.044 s
% 2.68/1.78 % (16822)Instructions burned: 129 (million)
% 2.68/1.78 % (16822)------------------------------
% 2.68/1.78 % (16822)------------------------------
% 2.68/1.79 % (16815)Instruction limit reached!
% 2.68/1.79 % (16815)------------------------------
% 2.68/1.79 % (16815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.79 % (16815)Termination reason: Unknown
% 2.68/1.79 % (16815)Termination phase: Saturation
% 2.68/1.79
% 2.68/1.79 % (16815)Memory used [KB]: 7419
% 2.68/1.79 % (16815)Time elapsed: 0.133 s
% 2.68/1.79 % (16815)Instructions burned: 379 (million)
% 2.68/1.79 % (16815)------------------------------
% 2.68/1.79 % (16815)------------------------------
% 2.68/1.79 % (16823)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/100Mi)
% 2.68/1.80 % (16824)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/3Mi)
% 2.68/1.81 % (16824)Instruction limit reached!
% 2.68/1.81 % (16824)------------------------------
% 2.68/1.81 % (16824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.81 % (16824)Termination reason: Unknown
% 2.68/1.81 % (16824)Termination phase: shuffling
% 2.68/1.81
% 2.68/1.81 % (16824)Memory used [KB]: 1407
% 2.68/1.81 % (16824)Time elapsed: 0.004 s
% 2.68/1.81 % (16824)Instructions burned: 4 (million)
% 2.68/1.81 % (16824)------------------------------
% 2.68/1.81 % (16824)------------------------------
% 2.68/1.82 % (16823)Instruction limit reached!
% 2.68/1.82 % (16823)------------------------------
% 2.68/1.82 % (16823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.82 % (16823)Termination reason: Unknown
% 2.68/1.82 % (16823)Termination phase: Saturation
% 2.68/1.82
% 2.68/1.82 % (16823)Memory used [KB]: 6524
% 2.68/1.82 % (16823)Time elapsed: 0.031 s
% 2.68/1.82 % (16823)Instructions burned: 103 (million)
% 2.68/1.82 % (16823)------------------------------
% 2.68/1.82 % (16823)------------------------------
% 2.68/1.82 % (16825)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/20Mi)
% 2.68/1.83 % (16826)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/86Mi)
% 2.68/1.83 % (16825)Instruction limit reached!
% 2.68/1.83 % (16825)------------------------------
% 2.68/1.83 % (16825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.83 % (16825)Termination reason: Unknown
% 2.68/1.83 % (16825)Termination phase: Property scanning
% 2.68/1.83
% 2.68/1.83 % (16825)Memory used [KB]: 1663
% 2.68/1.83 % (16825)Time elapsed: 0.014 s
% 2.68/1.83 % (16825)Instructions burned: 20 (million)
% 2.68/1.83 % (16825)------------------------------
% 2.68/1.83 % (16825)------------------------------
% 2.68/1.85 % (16827)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/107Mi)
% 2.68/1.85 % (16809)Instruction limit reached!
% 2.68/1.85 % (16809)------------------------------
% 2.68/1.85 % (16809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.85 % (16809)Termination reason: Unknown
% 2.68/1.85 % (16809)Termination phase: Saturation
% 2.68/1.85
% 2.68/1.85 % (16809)Memory used [KB]: 7931
% 2.68/1.85 % (16809)Time elapsed: 0.227 s
% 2.68/1.85 % (16809)Instructions burned: 712 (million)
% 2.68/1.85 % (16809)------------------------------
% 2.68/1.85 % (16809)------------------------------
% 2.68/1.85 % (16826)Instruction limit reached!
% 2.68/1.85 % (16826)------------------------------
% 2.68/1.85 % (16826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.85 % (16826)Termination reason: Unknown
% 2.68/1.85 % (16826)Termination phase: Saturation
% 2.68/1.85
% 2.68/1.85 % (16826)Memory used [KB]: 6524
% 2.68/1.85 % (16826)Time elapsed: 0.029 s
% 2.68/1.85 % (16826)Instructions burned: 86 (million)
% 2.68/1.85 % (16826)------------------------------
% 2.68/1.85 % (16826)------------------------------
% 2.68/1.86 % (16828)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/39Mi)
% 2.68/1.86 % (16829)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_16461 for (2997ds/448Mi)
% 2.68/1.87 % (16828)Instruction limit reached!
% 2.68/1.87 % (16828)------------------------------
% 2.68/1.87 % (16828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.87 % (16828)Termination reason: Unknown
% 2.68/1.87 % (16828)Termination phase: Property scanning
% 2.68/1.87
% 2.68/1.87 % (16828)Memory used [KB]: 1791
% 2.68/1.87 % (16828)Time elapsed: 0.012 s
% 2.68/1.87 % (16828)Instructions burned: 40 (million)
% 2.68/1.87 % (16828)------------------------------
% 2.68/1.87 % (16828)------------------------------
% 2.68/1.87 % (16811)First to succeed.
% 2.68/1.88 % (16811)Refutation found. Thanks to Tanya!
% 2.68/1.88 % SZS status Theorem for DTF2THF_16461
% 2.68/1.88 % SZS output start Proof for DTF2THF_16461
% 2.68/1.88 thf(type_def_5, type, itself: ($tType) > $tType).
% 2.68/1.88 thf(type_def_7, type, coinductive_llist: ($tType) > $tType).
% 2.68/1.88 thf(type_def_8, type, extended_enat: $tType).
% 2.68/1.88 thf(type_def_9, type, nat: $tType).
% 2.68/1.88 thf(type_def_10, type, product_unit: $tType).
% 2.68/1.88 thf(type_def_11, type, num: $tType).
% 2.68/1.88 thf(func_def_0, type, coinductive_llist: ($tType) > $tType).
% 2.68/1.88 thf(func_def_1, type, product_unit: $tType).
% 2.68/1.88 thf(func_def_2, type, extended_enat: $tType).
% 2.68/1.88 thf(func_def_3, type, num: $tType).
% 2.68/1.88 thf(func_def_4, type, nat: $tType).
% 2.68/1.88 thf(func_def_5, type, itself: ($tType) > $tType).
% 2.68/1.88 thf(func_def_6, type, type: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_7, type, one: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_8, type, numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_9, type, ring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_10, type, uminus: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_11, type, ord: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_12, type, ring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_13, type, neg_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_14, type, order: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_15, type, group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_16, type, lattice: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_17, type, comm_ring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_18, type, monoid_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_19, type, linorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_20, type, preorder: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_21, type, semiring_char_0: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_22, type, semiring_numeral: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_23, type, semigroup_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_24, type, comm_semiring_1: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_25, type, linordered_idom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_26, type, comm_monoid_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_27, type, ab_semigroup_mult: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_28, type, boolean_algebra: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_29, type, semilattice_inf: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_30, type, linordered_semidom: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_31, type, ordered_ab_group_add: !>[X0: $tType]:(itself @ X0 > $o)).
% 2.68/1.88 thf(func_def_32, type, coinductive_lfinite: !>[X0: $tType]:(coinductive_llist @ X0 > $o)).
% 2.68/1.88 thf(func_def_33, type, coinductive_llength: !>[X0: $tType]:(coinductive_llist @ X0 > extended_enat)).
% 2.68/1.88 thf(func_def_34, type, coinductive_LCons: !>[X0: $tType]:(X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.68/1.88 thf(func_def_35, type, coinductive_lmap: !>[X0: $tType, X1: $tType]:((X0 > X1) > coinductive_llist @ X0 > coinductive_llist @ X1)).
% 2.68/1.88 thf(func_def_36, type, coinductive_ltl: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.68/1.88 thf(func_def_37, type, extended_enat2: nat > extended_enat).
% 2.68/1.88 thf(func_def_38, type, extended_rec_enat: !>[X0: $tType]:((nat > X0) > X0 > extended_enat > X0)).
% 2.68/1.88 thf(func_def_39, type, one_one: !>[X0: $tType]:(X0)).
% 2.68/1.88 thf(func_def_40, type, times_times: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.68/1.88 thf(func_def_41, type, uminus_uminus: !>[X0: $tType]:(X0 > X0)).
% 2.68/1.88 thf(func_def_42, type, hammin2015774020amming: coinductive_llist @ nat).
% 2.68/1.88 thf(func_def_43, type, hammin1630468845amming: product_unit > coinductive_llist @ nat).
% 2.68/1.88 thf(func_def_44, type, hammin1138290136lmerge: !>[X0: $tType]:(coinductive_llist @ X0 > coinductive_llist @ X0 > coinductive_llist @ X0)).
% 2.68/1.88 thf(func_def_45, type, hammin1195055315smooth: nat > $o).
% 2.68/1.88 thf(func_def_46, type, inf_inf: !>[X0: $tType]:(X0 > X0 > X0)).
% 2.68/1.88 thf(func_def_47, type, bitM: num > num).
% 2.68/1.88 thf(func_def_48, type, neg_numeral_dbl: !>[X0: $tType]:(X0 > X0)).
% 2.68/1.88 thf(func_def_49, type, neg_numeral_dbl_dec: !>[X0: $tType]:(X0 > X0)).
% 2.68/1.88 thf(func_def_50, type, neg_numeral_dbl_inc: !>[X0: $tType]:(X0 > X0)).
% 2.68/1.88 thf(func_def_51, type, neg_numeral_sub: !>[X0: $tType]:(num > num > X0)).
% 2.68/1.88 thf(func_def_52, type, bit0: num > num).
% 2.68/1.88 thf(func_def_53, type, bit1: num > num).
% 2.68/1.88 thf(func_def_54, type, one2: num).
% 2.68/1.88 thf(func_def_55, type, numeral_numeral: !>[X0: $tType]:(num > X0)).
% 2.68/1.88 thf(func_def_56, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 2.68/1.88 thf(func_def_57, type, product_Unity: product_unit).
% 2.68/1.88 thf(func_def_58, type, type2: !>[X0: $tType]:(itself @ X0)).
% 2.68/1.88 thf(func_def_59, type, n: nat).
% 2.68/1.88 thf(func_def_71, type, sP0: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.68/1.88 thf(func_def_72, type, sP1: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.68/1.88 thf(func_def_73, type, sP2: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 2.68/1.88 thf(func_def_74, type, sK3: num > num).
% 2.68/1.88 thf(func_def_75, type, sK4: num > num).
% 2.68/1.88 thf(func_def_76, type, sK5: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.68/1.88 thf(func_def_77, type, sK6: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.68/1.88 thf(func_def_78, type, sK7: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.68/1.88 thf(func_def_79, type, sK8: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.68/1.88 thf(func_def_80, type, sK9: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.68/1.88 thf(func_def_81, type, sK10: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.68/1.88 thf(func_def_82, type, sK11: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_83, type, sK12: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_84, type, sK13: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_85, type, sK14: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_86, type, sK15: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_87, type, sK16: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_88, type, sK17: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 2.68/1.88 thf(func_def_89, type, sK18: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_90, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_91, type, sK20: (num > $o) > num).
% 2.68/1.88 thf(func_def_92, type, sK21: (num > $o) > num).
% 2.68/1.88 thf(func_def_93, type, sK22: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.68/1.88 thf(func_def_94, type, sK23: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 2.68/1.88 thf(func_def_95, type, sK24: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X1 > (X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_96, type, sK25: !>[X0: $tType, X1: $tType]:(coinductive_llist @ X0 > X0 > coinductive_llist @ X1 > (X1 > X0) > coinductive_llist @ X1)).
% 2.68/1.88 thf(func_def_97, type, sK26: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_98, type, sK27: nat).
% 2.68/1.88 thf(func_def_99, type, sK28: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_100, type, sK29: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_101, type, sK30: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 2.68/1.88 thf(func_def_102, type, sK31: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.68/1.88 thf(func_def_103, type, sK32: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 2.68/1.88 thf(func_def_104, type, sK33: extended_enat > nat).
% 2.68/1.88 thf(func_def_105, type, sK34: !>[X0: $tType]:(coinductive_llist @ X0 > nat)).
% 2.68/1.88 thf(func_def_107, type, ph36: !>[X0: $tType]:(X0)).
% 2.68/1.88 thf(f2950,plain,(
% 2.68/1.88 $false),
% 2.68/1.88 inference(trivial_inequality_removal,[status(thm)],[f2949])).
% 2.68/1.88 thf(f2949,plain,(
% 2.68/1.88 ($true != $true)),
% 2.68/1.88 inference(superposition,[status(thm)],[f2769,f1429])).
% 2.68/1.88 thf(f1429,plain,(
% 2.68/1.88 ((preorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f725])).
% 2.68/1.88 thf(f725,plain,(
% 2.68/1.88 ((preorder @ extended_enat @ type2 @ extended_enat) = $true)),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f724])).
% 2.68/1.88 thf(f724,plain,(
% 2.68/1.88 (preorder @ extended_enat @ type2 @ extended_enat)),
% 2.68/1.88 inference(rectify,[status(thm)],[f295])).
% 2.68/1.88 thf(f295,axiom,(
% 2.68/1.88 (preorder @ extended_enat @ type2 @ extended_enat)),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',tcon_Extended__Nat_Oenat___Orderings_Opreorder_25)).
% 2.68/1.88 thf(f2769,plain,(
% 2.68/1.88 ((preorder @ extended_enat @ type2 @ extended_enat) != $true)),
% 2.68/1.88 inference(trivial_inequality_removal,[status(thm)],[f2754])).
% 2.68/1.88 thf(f2754,plain,(
% 2.68/1.88 ($true != $true) | ((preorder @ extended_enat @ type2 @ extended_enat) != $true)),
% 2.68/1.88 inference(superposition,[status(thm)],[f2431,f1191])).
% 2.68/1.88 thf(f1191,plain,(
% 2.68/1.88 ( ! [X0 : $tType,X1 : X0] : (((ord_less_eq @ X0 @ X1 @ X1) = $true) | ((preorder @ X0 @ type2 @ X0) != $true)) )),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f912])).
% 2.68/1.88 thf(f912,plain,(
% 2.68/1.88 ! [X0 : $tType] : (! [X1 : X0] : ((ord_less_eq @ X0 @ X1 @ X1) = $true) | ((preorder @ X0 @ type2 @ X0) != $true))),
% 2.68/1.88 inference(ennf_transformation,[status(thm)],[f399])).
% 2.68/1.88 thf(f399,plain,(
% 2.68/1.88 ! [X0 : $tType] : (((preorder @ X0 @ type2 @ X0) = $true) => ! [X1 : X0] : ((ord_less_eq @ X0 @ X1 @ X1) = $true))),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f398])).
% 2.68/1.88 thf(f398,plain,(
% 2.68/1.88 ! [X0 : $tType] : ((preorder @ X0 @ type2 @ X0) => ! [X1 : X0] : (ord_less_eq @ X0 @ X1 @ X1))),
% 2.68/1.88 inference(rectify,[status(thm)],[f101])).
% 2.68/1.88 thf(f101,axiom,(
% 2.68/1.88 ! [X0 : $tType] : ((preorder @ X0 @ type2 @ X0) => ! [X7 : X0] : (ord_less_eq @ X0 @ X7 @ X7))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',fact_100_order__refl)).
% 2.68/1.88 thf(f2431,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n))) != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f2430,f1271])).
% 2.68/1.88 thf(f1271,plain,(
% 2.68/1.88 ((coinductive_llength @ nat @ hammin2015774020amming) = (extended_enat2 @ n))),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f3])).
% 2.68/1.88 thf(f3,axiom,(
% 2.68/1.88 ((coinductive_llength @ nat @ hammin2015774020amming) = (extended_enat2 @ n))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',fact_2_n)).
% 2.68/1.88 thf(f2430,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (coinductive_llength @ nat @ hammin2015774020amming))) != $true)),
% 2.68/1.88 inference(trivial_inequality_removal,[status(thm)],[f2429])).
% 2.68/1.88 thf(f2429,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (coinductive_llength @ nat @ hammin2015774020amming))) != $true) | ($true != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f2428,f1461])).
% 2.68/1.88 thf(f1461,plain,(
% 2.68/1.88 ((ord @ nat @ type2 @ nat) = $true)),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f775])).
% 2.68/1.88 thf(f775,plain,(
% 2.68/1.88 ((ord @ nat @ type2 @ nat) = $true)),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f774])).
% 2.68/1.88 thf(f774,plain,(
% 2.68/1.88 (ord @ nat @ type2 @ nat)),
% 2.68/1.88 inference(rectify,[status(thm)],[f273])).
% 2.68/1.88 thf(f273,axiom,(
% 2.68/1.88 (ord @ nat @ type2 @ nat)),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',tcon_Nat_Onat___Orderings_Oord_5)).
% 2.68/1.88 thf(f2428,plain,(
% 2.68/1.88 ((ord @ nat @ type2 @ nat) != $true) | ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (coinductive_llength @ nat @ hammin2015774020amming))) != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f2427,f1518])).
% 2.68/1.88 thf(f1518,plain,(
% 2.68/1.88 ( ! [X1 : $tType,X0 : $tType,X2 : X1 > X0,X3 : coinductive_llist @ X1] : (((coinductive_llength @ X0 @ (coinductive_lmap @ X1 @ X0 @ X2 @ X3)) = (coinductive_llength @ X1 @ X3))) )),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f854])).
% 2.68/1.88 thf(f854,plain,(
% 2.68/1.88 ! [X0 : $tType,X1 : $tType,X2 : X1 > X0,X3 : coinductive_llist @ X1] : ((coinductive_llength @ X0 @ (coinductive_lmap @ X1 @ X0 @ X2 @ X3)) = (coinductive_llength @ X1 @ X3))),
% 2.68/1.88 inference(rectify,[status(thm)],[f4])).
% 2.68/1.88 thf(f4,axiom,(
% 2.68/1.88 ! [X0 : $tType,X5 : $tType,X6 : X5 > X0,X3 : coinductive_llist @ X5] : ((coinductive_llength @ X0 @ (coinductive_lmap @ X5 @ X0 @ X6 @ X3)) = (coinductive_llength @ X5 @ X3))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',fact_3_llength__lmap)).
% 2.68/1.88 thf(f2427,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming)))) != $true) | ((ord @ nat @ type2 @ nat) != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f2426,f1271])).
% 2.68/1.88 thf(f2426,plain,(
% 2.68/1.88 ($true != (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ hammin2015774020amming) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming))))) | ((ord @ nat @ type2 @ nat) != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f2356,f1518])).
% 2.68/1.88 thf(f2356,plain,(
% 2.68/1.88 ($true != (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming))))) | ((ord @ nat @ type2 @ nat) != $true)),
% 2.68/1.88 inference(trivial_inequality_removal,[status(thm)],[f2326])).
% 2.68/1.88 thf(f2326,plain,(
% 2.68/1.88 ($true != (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming))))) | ((ord @ nat @ type2 @ nat) != $true) | ($true != $true)),
% 2.68/1.88 inference(superposition,[status(thm)],[f1643,f1524])).
% 2.68/1.88 thf(f1524,plain,(
% 2.68/1.88 ( ! [X0 : $tType,X2 : coinductive_llist @ X0,X1 : coinductive_llist @ X0] : (((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ X0 @ X1) @ (coinductive_llength @ X0 @ X2)) @ (coinductive_llength @ X0 @ (hammin1138290136lmerge @ X0 @ X1 @ X2))) = $true) | ((ord @ X0 @ type2 @ X0) != $true)) )),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f1089])).
% 2.68/1.88 thf(f1089,plain,(
% 2.68/1.88 ! [X0 : $tType] : (! [X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ X0 @ X1) @ (coinductive_llength @ X0 @ X2)) @ (coinductive_llength @ X0 @ (hammin1138290136lmerge @ X0 @ X1 @ X2))) = $true) | ((ord @ X0 @ type2 @ X0) != $true))),
% 2.68/1.88 inference(ennf_transformation,[status(thm)],[f575])).
% 2.68/1.88 thf(f575,plain,(
% 2.68/1.88 ! [X0 : $tType] : (((ord @ X0 @ type2 @ X0) = $true) => ! [X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ X0 @ X1) @ (coinductive_llength @ X0 @ X2)) @ (coinductive_llength @ X0 @ (hammin1138290136lmerge @ X0 @ X1 @ X2))) = $true))),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f574])).
% 2.68/1.88 thf(f574,plain,(
% 2.68/1.88 ! [X0 : $tType] : ((ord @ X0 @ type2 @ X0) => ! [X1 : coinductive_llist @ X0,X2 : coinductive_llist @ X0] : (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ X0 @ X1) @ (coinductive_llength @ X0 @ X2)) @ (coinductive_llength @ X0 @ (hammin1138290136lmerge @ X0 @ X1 @ X2))))),
% 2.68/1.88 inference(rectify,[status(thm)],[f2])).
% 2.68/1.88 thf(f2,axiom,(
% 2.68/1.88 ! [X0 : $tType] : ((ord @ X0 @ type2 @ X0) => ! [X3 : coinductive_llist @ X0,X4 : coinductive_llist @ X0] : (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ X0 @ X3) @ (coinductive_llength @ X0 @ X4)) @ (coinductive_llength @ X0 @ (hammin1138290136lmerge @ X0 @ X3 @ X4))))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',fact_1_llength__lmerge__above)).
% 2.68/1.88 thf(f1643,plain,(
% 2.68/1.88 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ X0 @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming)))) != $true) | ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ X0) != $true)) )),
% 2.68/1.88 inference(trivial_inequality_removal,[status(thm)],[f1642])).
% 2.68/1.88 thf(f1642,plain,(
% 2.68/1.88 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ X0 @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming)))) != $true) | ($true != $true) | ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ X0) != $true)) )),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f1616,f1393])).
% 2.68/1.88 thf(f1393,plain,(
% 2.68/1.88 ((order @ extended_enat @ type2 @ extended_enat) = $true)),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f785])).
% 2.68/1.88 thf(f785,plain,(
% 2.68/1.88 ((order @ extended_enat @ type2 @ extended_enat) = $true)),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f784])).
% 2.68/1.88 thf(f784,plain,(
% 2.68/1.88 (order @ extended_enat @ type2 @ extended_enat)),
% 2.68/1.88 inference(rectify,[status(thm)],[f299])).
% 2.68/1.88 thf(f299,axiom,(
% 2.68/1.88 (order @ extended_enat @ type2 @ extended_enat)),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',tcon_Extended__Nat_Oenat___Orderings_Oorder_29)).
% 2.68/1.88 thf(f1616,plain,(
% 2.68/1.88 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ X0 @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming)))) != $true) | ((order @ extended_enat @ type2 @ extended_enat) != $true) | ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ X0) != $true)) )),
% 2.68/1.88 inference(trivial_inequality_removal,[status(thm)],[f1608])).
% 2.68/1.88 thf(f1608,plain,(
% 2.68/1.88 ( ! [X0 : extended_enat] : (((ord_less_eq @ extended_enat @ X0 @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming)))) != $true) | ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ X0) != $true) | ((order @ extended_enat @ type2 @ extended_enat) != $true) | ($true != $true)) )),
% 2.68/1.88 inference(superposition,[status(thm)],[f1591,f1422])).
% 2.68/1.88 thf(f1422,plain,(
% 2.68/1.88 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0] : (((ord_less_eq @ X0 @ X1 @ X3) = $true) | ((order @ X0 @ type2 @ X0) != $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3)) | ((ord_less_eq @ X0 @ X1 @ X2) != $true)) )),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f945])).
% 2.68/1.88 thf(f945,plain,(
% 2.68/1.88 ! [X0 : $tType] : (((order @ X0 @ type2 @ X0) != $true) | ! [X1 : X0,X2 : X0,X3 : X0] : (((ord_less_eq @ X0 @ X1 @ X2) != $true) | ((ord_less_eq @ X0 @ X1 @ X3) = $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3))))),
% 2.68/1.88 inference(flattening,[status(thm)],[f944])).
% 2.68/1.88 thf(f944,plain,(
% 2.68/1.88 ! [X0 : $tType] : (! [X1 : X0,X2 : X0,X3 : X0] : ((((ord_less_eq @ X0 @ X1 @ X3) = $true) | ($true != (ord_less_eq @ X0 @ X2 @ X3))) | ((ord_less_eq @ X0 @ X1 @ X2) != $true)) | ((order @ X0 @ type2 @ X0) != $true))),
% 2.68/1.88 inference(ennf_transformation,[status(thm)],[f691])).
% 2.68/1.88 thf(f691,plain,(
% 2.68/1.88 ! [X0 : $tType] : (((order @ X0 @ type2 @ X0) = $true) => ! [X1 : X0,X2 : X0,X3 : X0] : (((ord_less_eq @ X0 @ X1 @ X2) = $true) => (($true = (ord_less_eq @ X0 @ X2 @ X3)) => ((ord_less_eq @ X0 @ X1 @ X3) = $true))))),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f690])).
% 2.68/1.88 thf(f690,plain,(
% 2.68/1.88 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X1 : X0,X2 : X0,X3 : X0] : ((ord_less_eq @ X0 @ X1 @ X2) => ((ord_less_eq @ X0 @ X2 @ X3) => (ord_less_eq @ X0 @ X1 @ X3))))),
% 2.68/1.88 inference(rectify,[status(thm)],[f122])).
% 2.68/1.88 thf(f122,axiom,(
% 2.68/1.88 ! [X0 : $tType] : ((order @ X0 @ type2 @ X0) => ! [X10 : X0,X11 : X0,X12 : X0] : ((ord_less_eq @ X0 @ X10 @ X11) => ((ord_less_eq @ X0 @ X11 @ X12) => (ord_less_eq @ X0 @ X10 @ X12))))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',fact_121_order_Otrans)).
% 2.68/1.88 thf(f1591,plain,(
% 2.68/1.88 ($true != (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bitM @ (bit1 @ one2)))) @ hammin2015774020amming)))))),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f1590,f1457])).
% 2.68/1.88 thf(f1457,plain,(
% 2.68/1.88 ( ! [X0 : num] : (((bit1 @ (bit0 @ X0)) = (bitM @ (bit1 @ X0)))) )),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f860])).
% 2.68/1.88 thf(f860,plain,(
% 2.68/1.88 ! [X0 : num] : ((bit1 @ (bit0 @ X0)) = (bitM @ (bit1 @ X0)))),
% 2.68/1.88 inference(rectify,[status(thm)],[f190])).
% 2.68/1.88 thf(f190,axiom,(
% 2.68/1.88 ! [X16 : num] : ((bitM @ (bit1 @ X16)) = (bit1 @ (bit0 @ X16)))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',fact_189_semiring__norm_I28_J)).
% 2.68/1.88 thf(f1590,plain,(
% 2.68/1.88 ($true != (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (extended_enat2 @ n)) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))))),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f1589,f1271])).
% 2.68/1.88 thf(f1589,plain,(
% 2.68/1.88 ($true != (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (coinductive_llength @ nat @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))))),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f1588,f1518])).
% 2.68/1.88 thf(f1588,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (extended_enat2 @ n) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))) != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f1587,f1271])).
% 2.68/1.88 thf(f1587,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ hammin2015774020amming) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))) != $true)),
% 2.68/1.88 inference(forward_demodulation,[status(thm)],[f1388,f1518])).
% 2.68/1.88 thf(f1388,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))) != $true)),
% 2.68/1.88 inference(cnf_transformation,[status(thm)],[f829])).
% 2.68/1.88 thf(f829,plain,(
% 2.68/1.88 ((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))) != $true)),
% 2.68/1.88 inference(flattening,[status(thm)],[f357])).
% 2.68/1.88 thf(f357,plain,(
% 2.68/1.88 ~((ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming)))) = $true)),
% 2.68/1.88 inference(fool_elimination,[status(thm)],[f356])).
% 2.68/1.88 thf(f356,plain,(
% 2.68/1.88 ~(ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))))),
% 2.68/1.88 inference(rectify,[status(thm)],[f304])).
% 2.68/1.88 thf(f304,negated_conjecture,(
% 2.68/1.88 ~(ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))))),
% 2.68/1.88 inference(negated_conjecture,[status(cth)],[f303])).
% 2.68/1.88 thf(f303,conjecture,(
% 2.68/1.88 (ord_less_eq @ extended_enat @ (inf_inf @ extended_enat @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming)) @ (coinductive_llength @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))) @ (coinductive_llength @ nat @ (hammin1138290136lmerge @ nat @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ one2))) @ hammin2015774020amming) @ (coinductive_lmap @ nat @ nat @ (times_times @ nat @ (numeral_numeral @ nat @ (bit1 @ (bit0 @ one2)))) @ hammin2015774020amming))))),
% 2.68/1.88 file('/export/starexec/sandbox/tmp/tmp.PB4dSepqoZ/DTF2THF_16461.p',conj_0)).
% 2.68/1.88 % SZS output end Proof for DTF2THF_16461
% 2.68/1.88 % (16811)------------------------------
% 2.68/1.88 % (16811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.68/1.88 % (16811)Termination reason: Refutation
% 2.68/1.88
% 2.68/1.88 % (16811)Memory used [KB]: 7036
% 2.68/1.88 % (16811)Time elapsed: 0.237 s
% 2.68/1.88 % (16811)Instructions burned: 747 (million)
% 2.68/1.88 % (16811)------------------------------
% 2.68/1.88 % (16811)------------------------------
% 2.68/1.88 % (16788)Success in time 0.32 s
%------------------------------------------------------------------------------