%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP084^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n017.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 08:55:25 AM UTC 2026
% Result : Theorem 16.52s 3.84s
% Output : Refutation 16.52s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP084^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n017.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Tue Feb 24 08:24:26 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.47 ---- Original DTF file ---
% 0.21/0.47 thf(spec,logic,$$dhol).
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % File : ITP084^2 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.47 % Domain : Interactive Theorem Proving
% 0.21/0.47 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_119__3292052_1
% 0.21/0.47 % Version : Especial.
% 0.21/0.47 % English :
% 0.21/0.47
% 0.21/0.47 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.47 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.47 % Source : [Des21]
% 0.21/0.47 % Names : KnowledgeKeysSecrets/prob_119__3292052_1 [Des21]
% 0.21/0.47
% 0.21/0.47 % Status : Theorem
% 0.21/0.47 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.21/0.47 % Syntax : Number of formulae : 344 ( 139 unt; 78 typ; 0 def)
% 0.21/0.47 % Number of atoms : 744 ( 433 equ; 0 cnn)
% 0.21/0.47 % Maximal formula atoms : 13 ( 2 avg)
% 0.21/0.47 % Number of connectives : 4042 ( 141 ~; 45 |; 86 &;3444 @)
% 0.21/0.47 % ( 0 <=>; 326 =>; 0 <=; 0 <~>)
% 0.21/0.47 % Maximal formula depth : 23 ( 7 avg)
% 0.21/0.47 % Number of types : 6 ( 5 usr)
% 0.21/0.47 % Number of type conns : 284 ( 284 >; 0 *; 0 +; 0 <<)
% 0.21/0.47 % Number of symbols : 76 ( 73 usr; 4 con; 0-5 aty)
% 0.21/0.47 % Number of variables : 1123 ( 30 ^; 965 !; 72 ?;1123 :)
% 0.21/0.47 % ( 56 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.47 % SPC : TH1_THM_EQU_NAR
% 0.21/0.47
% 0.21/0.47 % Comments : This file was generated by Sledgehammer 2021-02-23 16:18:54.283
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 % Could-be-implicit typings (7)
% 0.21/0.47 thf(ty_t_Secrecy__types_OExpression,type,
% 0.21/0.47 secrecy_Expression: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Secrecy__types_OSecrets,type,
% 0.21/0.47 secrecy_Secrets: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Secrecy__types_OspecID,type,
% 0.21/0.47 secrecy_specID: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Secrecy__types_OKeys,type,
% 0.21/0.47 secrecy_Keys: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Secrecy__types_OKS,type,
% 0.21/0.47 secrecy_KS: $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_List_Olist,type,
% 0.21/0.47 list: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 thf(ty_t_Set_Oset,type,
% 0.21/0.47 set: $tType > $tType ).
% 0.21/0.47
% 0.21/0.47 % Explicit typings (71)
% 0.21/0.47 thf(sy_cl_HOL_Otype,type,
% 0.21/0.47 type:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.47 ord:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Oorder,type,
% 0.21/0.47 order:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.47 linorder:
% 0.21/0.47 !>[A: $tType] : $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 0.21/0.47 bNF_Greatest_Shift:
% 0.21/0.47 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_BNF__Greatest__Fixpoint_OSucc,type,
% 0.21/0.47 bNF_Greatest_Succ:
% 0.21/0.47 !>[A: $tType] : ( ( set @ ( list @ A ) ) > ( list @ A ) > ( set @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 0.21/0.47 bNF_Greatest_shift:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.21/0.47 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_Groups_Omonoid,type,
% 0.21/0.47 monoid:
% 0.21/0.47 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_If,type,
% 0.21/0.47 if:
% 0.21/0.47 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 0.21/0.47 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowsECorrect,type,
% 0.21/0.47 knowle1893229345orrect: secrecy_specID > secrecy_Expression > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 0.21/0.47 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows,type,
% 0.21/0.47 knowle2055185861_knows: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ListExtras_Odisjoint,type,
% 0.21/0.47 disjoint:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ListExtras_Omem,type,
% 0.21/0.47 mem:
% 0.21/0.47 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_ListExtras_OmemS,type,
% 0.21/0.47 memS:
% 0.21/0.47 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oappend,type,
% 0.21/0.47 append:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oarg__min__list,type,
% 0.21/0.47 arg_min_list:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Obind,type,
% 0.21/0.47 bind:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Obutlast,type,
% 0.21/0.47 butlast:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oconcat,type,
% 0.21/0.47 concat:
% 0.21/0.47 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Odistinct__adj,type,
% 0.21/0.47 distinct_adj:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Ofoldr,type,
% 0.21/0.47 foldr:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oinsert,type,
% 0.21/0.47 insert:
% 0.21/0.47 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olast,type,
% 0.21/0.47 last:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_OCons,type,
% 0.21/0.47 cons:
% 0.21/0.47 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_ONil,type,
% 0.21/0.47 nil:
% 0.21/0.47 !>[A: $tType] : ( list @ A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Ocase__list,type,
% 0.21/0.47 case_list:
% 0.21/0.47 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Ohd,type,
% 0.21/0.47 hd:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist_Otl,type,
% 0.21/0.47 tl:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olist__ex1,type,
% 0.21/0.47 list_ex1:
% 0.21/0.47 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Olistrelp,type,
% 0.21/0.47 listrelp:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Omap__tailrec,type,
% 0.21/0.47 map_tailrec:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Omap__tailrec__rev,type,
% 0.21/0.47 map_tailrec_rev:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Omaps,type,
% 0.21/0.47 maps:
% 0.21/0.47 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Omember,type,
% 0.21/0.47 member:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.21/0.47 lexordp_eq:
% 0.21/0.47 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oord__class_Olexordp,type,
% 0.21/0.47 ord_lexordp:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 0.21/0.47 ord_lexordp_eq:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oproduct__lists,type,
% 0.21/0.47 product_lists:
% 0.21/0.47 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Orev,type,
% 0.21/0.47 rev:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Orotate1,type,
% 0.21/0.47 rotate1:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Oshuffles,type,
% 0.21/0.47 shuffles:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( set @ ( list @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Osplice,type,
% 0.21/0.47 splice:
% 0.21/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(sy_c_List_Osubseqs,type,
% 0.32/0.47 subseqs:
% 0.32/0.47 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_List_Osuccessively,type,
% 0.32/0.47 successively:
% 0.32/0.47 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.32/0.47 ord_less:
% 0.32/0.47 !>[A: $tType] : ( A > A > $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_ODecr,type,
% 0.32/0.47 decr: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OEnc,type,
% 0.32/0.47 enc: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.32/0.47 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OExt,type,
% 0.32/0.47 ext: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OSign,type,
% 0.32/0.47 sign: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_Oeout,type,
% 0.32/0.47 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_Oine,type,
% 0.32/0.47 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.32/0.47 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OspecKeys,type,
% 0.32/0.47 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.32/0.47 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.32/0.47 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 0.32/0.47 secrec1371625429on2KSL: ( list @ secrecy_Expression ) > ( list @ secrecy_KS ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.32/0.47 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.32/0.47 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.32/0.47 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 0.32/0.47 secrecy_case_KS:
% 0.32/0.47 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.32/0.47 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 0.32/0.47 secrecy_rec_KS:
% 0.32/0.47 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.32/0.47 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_Set_OCollect,type,
% 0.32/0.47 collect:
% 0.32/0.47 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_c_member,type,
% 0.32/0.47 member2:
% 0.32/0.47 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_A,type,
% 0.32/0.47 a: secrecy_specID ).
% 0.32/0.47
% 0.32/0.47 thf(sy_v_m,type,
% 0.32/0.47 m: secrecy_Keys ).
% 0.32/0.47
% 0.32/0.47 % Relevant facts (255)
% 0.32/0.47 thf(fact_0_assms,axiom,
% 0.32/0.47 knowle2055185861_knows @ a @ ( cons @ secrecy_Expression @ ( secrecy_kE @ m ) @ ( nil @ secrecy_Expression ) ) ).
% 0.32/0.47
% 0.32/0.47 % assms
% 0.32/0.47 thf(fact_1_KS_Oinject_I1_J,axiom,
% 0.32/0.47 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.32/0.47 ( ( ( secrecy_kKS @ X1 )
% 0.32/0.47 = ( secrecy_kKS @ Y1 ) )
% 0.32/0.47 = ( X1 = Y1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.inject(1)
% 0.32/0.47 thf(fact_2_knows4,axiom,
% 0.32/0.47 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 0.32/0.47 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.32/0.47 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K2 ) )
% 0.32/0.47 & ( knowle2055185861_knows @ A2 @ ( enc @ K1 @ E ) ) )
% 0.32/0.47 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.32/0.47
% 0.32/0.47 % knows4
% 0.32/0.47 thf(fact_3_knows5,axiom,
% 0.32/0.47 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 0.32/0.47 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.32/0.47 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K1 ) )
% 0.32/0.47 & ( knowle2055185861_knows @ A2 @ ( sign @ K2 @ E ) ) )
% 0.32/0.47 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.32/0.47
% 0.32/0.47 % knows5
% 0.32/0.47 thf(fact_4_knows6,axiom,
% 0.32/0.47 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 0.32/0.47 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 0.32/0.47 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 0.32/0.47 => ( knowle2055185861_knows @ A2 @ ( enc @ K @ E1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % knows6
% 0.32/0.47 thf(fact_5_knows7,axiom,
% 0.32/0.47 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 0.32/0.47 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 0.32/0.47 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 0.32/0.47 => ( knowle2055185861_knows @ A2 @ ( sign @ K @ E1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % knows7
% 0.32/0.47 thf(fact_6_know2knows__k,axiom,
% 0.32/0.47 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.32/0.47 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.32/0.47 => ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % know2knows_k
% 0.32/0.47 thf(fact_7_know1k,axiom,
% 0.32/0.47 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 0.32/0.47 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ ( nil @ secrecy_Expression ) ) )
% 0.32/0.47 = ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % know1k
% 0.32/0.47 thf(fact_8_KS_Osimps_I7_J,axiom,
% 0.32/0.47 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.32/0.47 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.32/0.47 = ( F1 @ X1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.simps(7)
% 0.32/0.47 thf(fact_9_KS_Osimps_I5_J,axiom,
% 0.32/0.47 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.32/0.47 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.32/0.47 = ( F1 @ X1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.simps(5)
% 0.32/0.47 thf(fact_10_eoutKnowCorrect__L1k,axiom,
% 0.32/0.47 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.32/0.47 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 0.32/0.47 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.32/0.47 => ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.32/0.47 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eoutKnowCorrect_L1k
% 0.32/0.47 thf(fact_11_eout__know__k,axiom,
% 0.32/0.47 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.32/0.47 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 0.32/0.47 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.32/0.47 = ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.32/0.47 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eout_know_k
% 0.32/0.47 thf(fact_12_know_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.32/0.47 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.32/0.47 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 0.32/0.47 | ( member2 @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % know.simps(1)
% 0.32/0.47 thf(fact_13_Expression_Oinject_I1_J,axiom,
% 0.32/0.47 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.32/0.47 ( ( ( secrecy_kE @ X1 )
% 0.32/0.47 = ( secrecy_kE @ Y1 ) )
% 0.32/0.47 = ( X1 = Y1 ) ) ).
% 0.32/0.47
% 0.32/0.47 % Expression.inject(1)
% 0.32/0.47 thf(fact_14_knows__emptyexpression,axiom,
% 0.32/0.47 ! [C: secrecy_specID] : ( knowle2055185861_knows @ C @ ( nil @ secrecy_Expression ) ) ).
% 0.32/0.47
% 0.32/0.47 % knows_emptyexpression
% 0.32/0.47 thf(fact_15_KS2Expression_Osimps_I1_J,axiom,
% 0.32/0.47 ! [M: secrecy_Keys] :
% 0.32/0.47 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.32/0.47 = ( secrecy_kE @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS2Expression.simps(1)
% 0.32/0.47 thf(fact_16_list_Oinject,axiom,
% 0.32/0.47 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 0.32/0.47 ( ( ( cons @ A @ X21 @ X22 )
% 0.32/0.47 = ( cons @ A @ Y21 @ Y22 ) )
% 0.32/0.47 = ( ( X21 = Y21 )
% 0.32/0.47 & ( X22 = Y22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.inject
% 0.32/0.47 thf(fact_17_know1s,axiom,
% 0.32/0.47 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 0.32/0.47 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ ( nil @ secrecy_Expression ) ) )
% 0.32/0.47 = ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % know1s
% 0.32/0.47 thf(fact_18_list_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X21: A,X22: list @ A] :
% 0.32/0.47 ( ( nil @ A )
% 0.32/0.47 != ( cons @ A @ X21 @ X22 ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.distinct(1)
% 0.32/0.47 thf(fact_19_list_OdiscI,axiom,
% 0.32/0.47 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 0.32/0.47 ( ( List
% 0.32/0.47 = ( cons @ A @ X21 @ X22 ) )
% 0.32/0.47 => ( List
% 0.32/0.47 != ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.discI
% 0.32/0.47 thf(fact_20_list_Oexhaust,axiom,
% 0.32/0.47 ! [A: $tType,Y: list @ A] :
% 0.32/0.47 ( ( Y
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ~ ! [X212: A,X222: list @ A] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.exhaust
% 0.32/0.47 thf(fact_21_list_Oinducts,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X12: A,X2: list @ A] :
% 0.32/0.47 ( ( P @ X2 )
% 0.32/0.47 => ( P @ ( cons @ A @ X12 @ X2 ) ) )
% 0.32/0.47 => ( P @ List ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.inducts
% 0.32/0.47 thf(fact_22_neq__Nil__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 = ( ? [Y2: A,Ys: list @ A] :
% 0.32/0.47 ( Xs
% 0.32/0.47 = ( cons @ A @ Y2 @ Ys ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % neq_Nil_conv
% 0.32/0.47 thf(fact_23_list__induct2_H,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 0.32/0.47 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.32/0.47 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 0.32/0.47 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 0.32/0.47 => ( ! [X: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 0.32/0.47 ( ( P @ Xs2 @ Ys3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 0.32/0.47 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_induct2'
% 0.32/0.47 thf(fact_24_splice_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.32/0.47 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.32/0.47 => ( ! [X: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ( P @ Ys3 @ Xs2 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % splice.induct
% 0.32/0.47 thf(fact_25_induct__list012,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [X: A,Y3: A,Zs: list @ A] :
% 0.32/0.47 ( ( P @ Zs )
% 0.32/0.47 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 0.32/0.47 => ( P @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % induct_list012
% 0.32/0.47 thf(fact_26_min__list_Ocases,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [X3: list @ A] :
% 0.32/0.47 ( ! [X: A,Xs2: list @ A] :
% 0.32/0.47 ( X3
% 0.32/0.47 != ( cons @ A @ X @ Xs2 ) )
% 0.32/0.47 => ( X3
% 0.32/0.47 = ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % min_list.cases
% 0.32/0.47 thf(fact_27_KS_Oinject_I2_J,axiom,
% 0.32/0.47 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 0.32/0.47 ( ( ( secrecy_sKS @ X23 )
% 0.32/0.47 = ( secrecy_sKS @ Y23 ) )
% 0.32/0.47 = ( X23 = Y23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.inject(2)
% 0.32/0.47 thf(fact_28_KS_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 0.32/0.47 ( ( secrecy_kKS @ X1 )
% 0.32/0.47 != ( secrecy_sKS @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.distinct(1)
% 0.32/0.47 thf(fact_29_KS_Oinduct,axiom,
% 0.32/0.47 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.32/0.47 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.32/0.47 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.32/0.47 => ( P @ KS ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.induct
% 0.32/0.47 thf(fact_30_KS_Oexhaust,axiom,
% 0.32/0.47 ! [Y: secrecy_KS] :
% 0.32/0.47 ( ! [X12: secrecy_Keys] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( secrecy_kKS @ X12 ) )
% 0.32/0.47 => ~ ! [X2: secrecy_Secrets] :
% 0.32/0.47 ( Y
% 0.32/0.47 != ( secrecy_sKS @ X2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.exhaust
% 0.32/0.47 thf(fact_31_KS_Osimps_I6_J,axiom,
% 0.32/0.47 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X23: secrecy_Secrets] :
% 0.32/0.47 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X23 ) )
% 0.32/0.47 = ( F2 @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.simps(6)
% 0.32/0.47 thf(fact_32_KS_Osimps_I8_J,axiom,
% 0.32/0.47 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X23: secrecy_Secrets] :
% 0.32/0.47 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X23 ) )
% 0.32/0.47 = ( F2 @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS.simps(8)
% 0.32/0.47 thf(fact_33_not__Cons__self2,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( cons @ A @ X3 @ Xs )
% 0.32/0.47 != Xs ) ).
% 0.32/0.47
% 0.32/0.47 % not_Cons_self2
% 0.32/0.47 thf(fact_34_strict__sorted_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A,Ys3: list @ A] :
% 0.32/0.47 ( ( P @ Ys3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Ys3 ) ) )
% 0.32/0.47 => ( P @ A0 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % strict_sorted.induct
% 0.32/0.47 thf(fact_35_strict__sorted_Ocases,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [X3: list @ A] :
% 0.32/0.47 ( ( X3
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ~ ! [X: A,Ys3: list @ A] :
% 0.32/0.47 ( X3
% 0.32/0.47 != ( cons @ A @ X @ Ys3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % strict_sorted.cases
% 0.32/0.47 thf(fact_36_map__tailrec__rev_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.32/0.47 ( ! [F: A > B,X_1: list @ B] : ( P @ F @ ( nil @ A ) @ X_1 )
% 0.32/0.47 => ( ! [F: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.32/0.47 ( ( P @ F @ As @ ( cons @ B @ ( F @ A3 ) @ Bs ) )
% 0.32/0.47 => ( P @ F @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 0.32/0.47 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_tailrec_rev.induct
% 0.32/0.47 thf(fact_37_list__nonempty__induct,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [X: A,Xs2: list @ A] :
% 0.32/0.47 ( ( Xs2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( P @ Xs2 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 0.32/0.47 => ( P @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_nonempty_induct
% 0.32/0.47 thf(fact_38_successively_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.32/0.47 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.32/0.47 => ( ! [P2: A > A > $o,X: A] : ( P @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [P2: A > A > $o,X: A,Y3: A,Xs2: list @ A] :
% 0.32/0.47 ( ( P @ P2 @ ( cons @ A @ Y3 @ Xs2 ) )
% 0.32/0.47 => ( P @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.induct
% 0.32/0.47 thf(fact_39_arg__min__list_Oinduct,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( linorder @ B )
% 0.32/0.47 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.32/0.47 ( ! [F: A > B,X: A] : ( P @ F @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [F: A > B,X: A,Y3: A,Zs: list @ A] :
% 0.32/0.47 ( ( P @ F @ ( cons @ A @ Y3 @ Zs ) )
% 0.32/0.47 => ( P @ F @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 0.32/0.47 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % arg_min_list.induct
% 0.32/0.47 thf(fact_40_remdups__adj_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.32/0.47 ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ( ! [X: A,Y3: A,Xs2: list @ A] :
% 0.32/0.47 ( ( ( X = Y3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.32/0.47 => ( ( ( X != Y3 )
% 0.32/0.47 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 0.32/0.47 => ( P @ A0 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.induct
% 0.32/0.47 thf(fact_41_sorted__wrt_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.32/0.47 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.32/0.47 => ( ! [P2: A > A > $o,X: A,Ys3: list @ A] :
% 0.32/0.47 ( ( P @ P2 @ Ys3 )
% 0.32/0.47 => ( P @ P2 @ ( cons @ A @ X @ Ys3 ) ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % sorted_wrt.induct
% 0.32/0.47 thf(fact_42_remdups__adj_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,X3: list @ A] :
% 0.32/0.47 ( ( X3
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A] :
% 0.32/0.47 ( X3
% 0.32/0.47 != ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 0.32/0.47 ( X3
% 0.32/0.47 != ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.cases
% 0.32/0.47 thf(fact_43_transpose_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,X3: list @ ( list @ A )] :
% 0.32/0.47 ( ( X3
% 0.32/0.47 != ( nil @ ( list @ A ) ) )
% 0.32/0.47 => ( ! [Xss: list @ ( list @ A )] :
% 0.32/0.47 ( X3
% 0.32/0.47 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.32/0.47 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.32/0.47 ( X3
% 0.32/0.47 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % transpose.cases
% 0.32/0.47 thf(fact_44_mem__Collect__eq,axiom,
% 0.32/0.47 ! [A: $tType,A4: A,P: A > $o] :
% 0.32/0.47 ( ( member2 @ A @ A4 @ ( collect @ A @ P ) )
% 0.32/0.47 = ( P @ A4 ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_Collect_eq
% 0.32/0.47 thf(fact_45_Collect__mem__eq,axiom,
% 0.32/0.47 ! [A: $tType,A2: set @ A] :
% 0.32/0.47 ( ( collect @ A
% 0.32/0.47 @ ^ [X4: A] : ( member2 @ A @ X4 @ A2 ) )
% 0.32/0.47 = A2 ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_mem_eq
% 0.32/0.47 thf(fact_46_Collect__cong,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.32/0.47 ( ! [X: A] :
% 0.32/0.47 ( ( P @ X )
% 0.32/0.47 = ( Q @ X ) )
% 0.32/0.47 => ( ( collect @ A @ P )
% 0.32/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Collect_cong
% 0.32/0.47 thf(fact_47_ext,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 0.32/0.47 ( ! [X: A] :
% 0.32/0.47 ( ( F3 @ X )
% 0.32/0.47 = ( G @ X ) )
% 0.32/0.47 => ( F3 = G ) ) ).
% 0.32/0.47
% 0.32/0.47 % ext
% 0.32/0.47 thf(fact_48_shuffles_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.32/0.47 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.32/0.47 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.32/0.47 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.47 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 0.32/0.47 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % shuffles.induct
% 0.32/0.47 thf(fact_49_min__list_Oinduct,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.32/0.47 ( ! [X: A,Xs2: list @ A] :
% 0.32/0.47 ( ! [X213: A,X223: list @ A] :
% 0.32/0.47 ( ( Xs2
% 0.32/0.47 = ( cons @ A @ X213 @ X223 ) )
% 0.32/0.47 => ( P @ Xs2 ) )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.32/0.47 => ( ( P @ ( nil @ A ) )
% 0.32/0.47 => ( P @ A0 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % min_list.induct
% 0.32/0.47 thf(fact_50_know_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.32/0.47 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.32/0.47 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 0.32/0.47 | ( member2 @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % know.simps(2)
% 0.32/0.47 thf(fact_51_Expression2KSL_Osimps_I1_J,axiom,
% 0.32/0.47 ( ( secrec1371625429on2KSL @ ( nil @ secrecy_Expression ) )
% 0.32/0.47 = ( nil @ secrecy_KS ) ) ).
% 0.32/0.47
% 0.32/0.47 % Expression2KSL.simps(1)
% 0.32/0.47 thf(fact_52_insert__Nil,axiom,
% 0.32/0.47 ! [A: $tType,X3: A] :
% 0.32/0.47 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 0.32/0.47 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % insert_Nil
% 0.32/0.47 thf(fact_53_list__ex1__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,P: A > $o] :
% 0.32/0.47 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % list_ex1_simps(1)
% 0.32/0.47 thf(fact_54_eoutKnowsECorrect__def,axiom,
% 0.32/0.47 ( knowle1893229345orrect
% 0.32/0.47 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 0.32/0.47 ( ( eout @ C2 @ E2 )
% 0.32/0.47 = ( ? [K3: secrecy_Keys] :
% 0.32/0.47 ( ( E2
% 0.32/0.47 = ( secrecy_kE @ K3 ) )
% 0.32/0.47 & ( member2 @ secrecy_Keys @ K3 @ ( specKeys @ C2 ) ) )
% 0.32/0.47 | ? [S: secrecy_Secrets] :
% 0.32/0.47 ( ( E2
% 0.32/0.47 = ( secrecy_sE @ S ) )
% 0.32/0.47 & ( member2 @ secrecy_Secrets @ S @ ( specSecrets @ C2 ) ) )
% 0.32/0.47 | ( knowle2055185861_knows @ C2 @ ( cons @ secrecy_Expression @ E2 @ ( nil @ secrecy_Expression ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eoutKnowsECorrect_def
% 0.32/0.47 thf(fact_55_eoutKnowsECorrect__L1,axiom,
% 0.32/0.47 ! [C: secrecy_specID,E: secrecy_Expression] :
% 0.32/0.47 ( ( knowle1893229345orrect @ C @ E )
% 0.32/0.47 => ( ( eout @ C @ E )
% 0.32/0.47 => ( ? [K4: secrecy_Keys] :
% 0.32/0.47 ( ( E
% 0.32/0.47 = ( secrecy_kE @ K4 ) )
% 0.32/0.47 & ( member2 @ secrecy_Keys @ K4 @ ( specKeys @ C ) ) )
% 0.32/0.47 | ? [S2: secrecy_Secrets] :
% 0.32/0.47 ( ( E
% 0.32/0.47 = ( secrecy_sE @ S2 ) )
% 0.32/0.47 & ( member2 @ secrecy_Secrets @ S2 @ ( specSecrets @ C ) ) )
% 0.32/0.47 | ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ E @ ( nil @ secrecy_Expression ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eoutKnowsECorrect_L1
% 0.32/0.47 thf(fact_56_map__tailrec__rev_Oelims,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,X3: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 0.32/0.47 ( ( ( map_tailrec_rev @ A @ B @ X3 @ Xa @ Xb )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( ( Xa
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( Y != Xb ) )
% 0.32/0.47 => ~ ! [A3: A,As: list @ A] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( cons @ A @ A3 @ As ) )
% 0.32/0.47 => ( Y
% 0.32/0.47 != ( map_tailrec_rev @ A @ B @ X3 @ As @ ( cons @ B @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_tailrec_rev.elims
% 0.32/0.47 thf(fact_57_arg__min__list_Osimps_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( linorder @ B )
% 0.32/0.47 => ! [F3: A > B,X3: A] :
% 0.32/0.47 ( ( arg_min_list @ A @ B @ F3 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 = X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % arg_min_list.simps(1)
% 0.32/0.47 thf(fact_58_notSpecKeysSecretsExpr__L1,axiom,
% 0.32/0.47 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 0.32/0.47 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 0.32/0.47 => ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % notSpecKeysSecretsExpr_L1
% 0.32/0.47 thf(fact_59_Expression_Oinject_I2_J,axiom,
% 0.32/0.47 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 0.32/0.47 ( ( ( secrecy_sE @ X23 )
% 0.32/0.47 = ( secrecy_sE @ Y23 ) )
% 0.32/0.47 = ( X23 = Y23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % Expression.inject(2)
% 0.32/0.47 thf(fact_60_Expression_Odistinct_I1_J,axiom,
% 0.32/0.47 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 0.32/0.47 ( ( secrecy_kE @ X1 )
% 0.32/0.47 != ( secrecy_sE @ X23 ) ) ).
% 0.32/0.47
% 0.32/0.47 % Expression.distinct(1)
% 0.32/0.47 thf(fact_61_notSpecKeysSecretsExpr__L2,axiom,
% 0.32/0.47 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 0.32/0.47 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 0.32/0.47 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 0.32/0.47
% 0.32/0.47 % notSpecKeysSecretsExpr_L2
% 0.32/0.47 thf(fact_62_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,F3: A > B,A4: A,As2: list @ A,Bs2: list @ B] :
% 0.32/0.47 ( ( map_tailrec_rev @ A @ B @ F3 @ ( cons @ A @ A4 @ As2 ) @ Bs2 )
% 0.32/0.47 = ( map_tailrec_rev @ A @ B @ F3 @ As2 @ ( cons @ B @ ( F3 @ A4 ) @ Bs2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_tailrec_rev.simps(2)
% 0.32/0.47 thf(fact_63_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,F3: A > B,Bs2: list @ B] :
% 0.32/0.47 ( ( map_tailrec_rev @ A @ B @ F3 @ ( nil @ A ) @ Bs2 )
% 0.32/0.47 = Bs2 ) ).
% 0.32/0.47
% 0.32/0.47 % map_tailrec_rev.simps(1)
% 0.32/0.47 thf(fact_64_KS2Expression_Osimps_I2_J,axiom,
% 0.32/0.47 ! [M: secrecy_Secrets] :
% 0.32/0.47 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.32/0.47 = ( secrecy_sE @ M ) ) ).
% 0.32/0.47
% 0.32/0.47 % KS2Expression.simps(2)
% 0.32/0.47 thf(fact_65_eoutKnowCorrect__L1s,axiom,
% 0.32/0.47 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.32/0.47 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 0.32/0.47 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.32/0.47 => ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 0.32/0.47 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eoutKnowCorrect_L1s
% 0.32/0.47 thf(fact_66_eout__know__s,axiom,
% 0.32/0.47 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.32/0.47 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 0.32/0.47 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.32/0.47 = ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 0.32/0.47 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % eout_know_s
% 0.32/0.47 thf(fact_67_product__lists_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.32/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % product_lists.simps(1)
% 0.32/0.47 thf(fact_68_subseqs_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( subseqs @ A @ ( nil @ A ) )
% 0.32/0.47 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % subseqs.simps(1)
% 0.32/0.47 thf(fact_69_DecrEnc,axiom,
% 0.32/0.47 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list @ secrecy_Expression] :
% 0.32/0.47 ( ( encrDecrKeys @ K12 @ K22 )
% 0.32/0.47 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 0.32/0.47 = E3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % DecrEnc
% 0.32/0.47 thf(fact_70_ExtSign,axiom,
% 0.32/0.47 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list @ secrecy_Expression] :
% 0.32/0.47 ( ( encrDecrKeys @ K12 @ K22 )
% 0.32/0.47 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 0.32/0.47 = E3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % ExtSign
% 0.32/0.47 thf(fact_71_notSpecKeysSecretsExpr__def,axiom,
% 0.32/0.47 ( notSpe1586871396tsExpr
% 0.32/0.47 = ( ^ [P3: secrecy_specID,E2: list @ secrecy_Expression] :
% 0.32/0.47 ( ! [X4: secrecy_Keys] :
% 0.32/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X4 ) @ E2 )
% 0.32/0.47 => ~ ( member2 @ secrecy_KS @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 0.32/0.47 & ! [Y2: secrecy_Secrets] :
% 0.32/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y2 ) @ E2 )
% 0.32/0.47 => ~ ( member2 @ secrecy_KS @ ( secrecy_sKS @ Y2 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % notSpecKeysSecretsExpr_def
% 0.32/0.47 thf(fact_72_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A] :
% 0.32/0.47 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq_simps(3)
% 0.32/0.47 thf(fact_73_bind__simps_I1_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 0.32/0.47 ( ( bind @ B @ A @ ( nil @ B ) @ F3 )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % bind_simps(1)
% 0.32/0.47 thf(fact_74_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.32/0.47 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.32/0.47 = ( ( Less @ X3 @ Y )
% 0.32/0.47 | ( ~ ( Less @ Y @ X3 )
% 0.32/0.47 & ( lexordp_eq @ A @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq_simps(4)
% 0.32/0.47 thf(fact_75_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq_simps(1)
% 0.32/0.47 thf(fact_76_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.32/0.47 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq_simps(2)
% 0.32/0.47 thf(fact_77_ord_Olexordp__eq_Ocong,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( lexordp_eq @ A )
% 0.32/0.47 = ( lexordp_eq @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.cong
% 0.32/0.47 thf(fact_78_ord_Olexordp__eq__refl,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq_refl
% 0.32/0.47 thf(fact_79_ord_Olexordp__eq_OCons__eq,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ~ ( Less @ X3 @ Y )
% 0.32/0.47 => ( ~ ( Less @ Y @ X3 )
% 0.32/0.47 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys2 )
% 0.32/0.47 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.Cons_eq
% 0.32/0.47 thf(fact_80_ord_Olexordp__eq_OCons,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( Less @ X3 @ Y )
% 0.32/0.47 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.Cons
% 0.32/0.47 thf(fact_81_ord_Olexordp__eq_ONil,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.Nil
% 0.32/0.47 thf(fact_82_ord_Olexordp__eq_Oinducts,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.32/0.47 ( ( lexordp_eq @ A @ Less @ X1 @ X23 )
% 0.32/0.47 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.32/0.47 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ( Less @ X @ Y3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 0.32/0.47 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ~ ( Less @ X @ Y3 )
% 0.32/0.47 => ( ~ ( Less @ Y3 @ X )
% 0.32/0.47 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 )
% 0.32/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) )
% 0.32/0.47 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.inducts
% 0.32/0.47 thf(fact_83_ord_Olexordp__eq_Osimps,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( lexordp_eq @ A )
% 0.32/0.47 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.32/0.47 ( ? [Ys: list @ A] :
% 0.32/0.47 ( ( A12
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( A23 = Ys ) )
% 0.32/0.47 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 0.32/0.47 ( ( A12
% 0.32/0.47 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.47 & ( A23
% 0.32/0.47 = ( cons @ A @ Y2 @ Ys ) )
% 0.32/0.47 & ( Less2 @ X4 @ Y2 ) )
% 0.32/0.47 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 0.32/0.47 ( ( A12
% 0.32/0.47 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.47 & ( A23
% 0.32/0.47 = ( cons @ A @ Y2 @ Ys ) )
% 0.32/0.47 & ~ ( Less2 @ X4 @ Y2 )
% 0.32/0.47 & ~ ( Less2 @ Y2 @ X4 )
% 0.32/0.47 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.simps
% 0.32/0.47 thf(fact_84_ord_Olexordp__eq_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.32/0.47 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 0.32/0.47 => ( ( A1
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A] :
% 0.32/0.47 ( ? [Xs2: list @ A] :
% 0.32/0.47 ( A1
% 0.32/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.47 => ! [Y3: A] :
% 0.32/0.47 ( ? [Ys3: list @ A] :
% 0.32/0.47 ( A22
% 0.32/0.47 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.47 => ~ ( Less @ X @ Y3 ) ) )
% 0.32/0.47 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 0.32/0.47 ( ( A1
% 0.32/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.47 => ! [Ys3: list @ A] :
% 0.32/0.47 ( ( A22
% 0.32/0.47 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.47 => ( ~ ( Less @ X @ Y3 )
% 0.32/0.47 => ( ~ ( Less @ Y3 @ X )
% 0.32/0.47 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % ord.lexordp_eq.cases
% 0.32/0.47 thf(fact_85_mem_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A] :
% 0.32/0.47 ~ ( mem @ A @ X3 @ ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem.simps(1)
% 0.32/0.47 thf(fact_86_mem_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Y: A,L: list @ A] :
% 0.32/0.47 ( ( mem @ A @ X3 @ ( cons @ A @ Y @ L ) )
% 0.32/0.47 = ( ( X3 = Y )
% 0.32/0.47 | ( mem @ A @ X3 @ L ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem.simps(2)
% 0.32/0.47 thf(fact_87_listrelp_Oinducts,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X1: list @ A,X23: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.32/0.47 ( ( listrelp @ A @ B @ R @ X1 @ X23 )
% 0.32/0.47 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.32/0.47 => ( ! [X: A,Y3: B,Xs2: list @ A,Ys3: list @ B] :
% 0.32/0.47 ( ( R @ X @ Y3 )
% 0.32/0.47 => ( ( listrelp @ A @ B @ R @ Xs2 @ Ys3 )
% 0.32/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) ) )
% 0.32/0.47 => ( P @ X1 @ X23 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % listrelp.inducts
% 0.32/0.47 thf(fact_88_listrelp_Osimps,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( listrelp @ A @ B )
% 0.32/0.47 = ( ^ [R2: A > B > $o,A12: list @ A,A23: list @ B] :
% 0.32/0.47 ( ( ( A12
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( A23
% 0.32/0.47 = ( nil @ B ) ) )
% 0.32/0.47 | ? [X4: A,Y2: B,Xs3: list @ A,Ys: list @ B] :
% 0.32/0.47 ( ( A12
% 0.32/0.47 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.47 & ( A23
% 0.32/0.47 = ( cons @ B @ Y2 @ Ys ) )
% 0.32/0.47 & ( R2 @ X4 @ Y2 )
% 0.32/0.47 & ( listrelp @ A @ B @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % listrelp.simps
% 0.32/0.47 thf(fact_89_listrelp_Ocases,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,R: A > B > $o,A1: list @ A,A22: list @ B] :
% 0.32/0.47 ( ( listrelp @ A @ B @ R @ A1 @ A22 )
% 0.32/0.47 => ( ( ( A1
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( A22
% 0.32/0.47 != ( nil @ B ) ) )
% 0.32/0.47 => ~ ! [X: A,Y3: B,Xs2: list @ A] :
% 0.32/0.47 ( ( A1
% 0.32/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.47 => ! [Ys3: list @ B] :
% 0.32/0.47 ( ( A22
% 0.32/0.47 = ( cons @ B @ Y3 @ Ys3 ) )
% 0.32/0.47 => ( ( R @ X @ Y3 )
% 0.32/0.47 => ~ ( listrelp @ A @ B @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % listrelp.cases
% 0.32/0.47 thf(fact_90_lexordp__eq__simps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [X3: A,Xs: list @ A] :
% 0.32/0.47 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(3)
% 0.32/0.47 thf(fact_91_lexordp__eq__simps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [Xs: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(2)
% 0.32/0.47 thf(fact_92_lexordp__eq__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_simps(1)
% 0.32/0.47 thf(fact_93_lexordp__eq__antisym,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Ys2 @ Xs )
% 0.32/0.47 => ( Xs = Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_antisym
% 0.32/0.47 thf(fact_94_lexordp__eq__linear,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.32/0.47 | ( ord_lexordp_eq @ A @ Ys2 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_linear
% 0.32/0.47 thf(fact_95_lexordp__eq__trans,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( linorder @ A )
% 0.32/0.47 => ! [Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Ys2 @ Zs2 )
% 0.32/0.47 => ( ord_lexordp_eq @ A @ Xs @ Zs2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_trans
% 0.32/0.47 thf(fact_96_lexordp__eq__refl,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq_refl
% 0.32/0.47 thf(fact_97_lexordp__eq_ONil,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.Nil
% 0.32/0.47 thf(fact_98_listrelp_OCons,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y: B,Xs: list @ A,Ys2: list @ B] :
% 0.32/0.47 ( ( R @ X3 @ Y )
% 0.32/0.47 => ( ( listrelp @ A @ B @ R @ Xs @ Ys2 )
% 0.32/0.47 => ( listrelp @ A @ B @ R @ ( cons @ A @ X3 @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % listrelp.Cons
% 0.32/0.47 thf(fact_99_listrelp_ONil,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,R: A > B > $o] : ( listrelp @ A @ B @ R @ ( nil @ A ) @ ( nil @ B ) ) ).
% 0.32/0.47
% 0.32/0.47 % listrelp.Nil
% 0.32/0.47 thf(fact_100_mem__memS__eq,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( mem @ A )
% 0.32/0.47 = ( memS @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_memS_eq
% 0.32/0.47 thf(fact_101_mem__notdisjoint,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,L1: list @ A,L2: list @ A] :
% 0.32/0.47 ( ( mem @ A @ X3 @ L1 )
% 0.32/0.47 => ( ( mem @ A @ X3 @ L2 )
% 0.32/0.47 => ~ ( disjoint @ A @ L1 @ L2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % mem_notdisjoint
% 0.32/0.47 thf(fact_102_mem__notdisjoint2,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,Schedule: B > ( list @ A ),A2: B,B2: B,X3: A] :
% 0.32/0.47 ( ( disjoint @ A @ ( Schedule @ A2 ) @ ( Schedule @ B2 ) )
% 0.32/0.48 => ( ( mem @ A @ X3 @ ( Schedule @ A2 ) )
% 0.32/0.48 => ~ ( mem @ A @ X3 @ ( Schedule @ B2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % mem_notdisjoint2
% 0.32/0.48 thf(fact_103_lexordp__eq_Ocases,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [A1: list @ A,A22: list @ A] :
% 0.32/0.48 ( ( ord_lexordp_eq @ A @ A1 @ A22 )
% 0.32/0.48 => ( ( A1
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ! [X: A] :
% 0.32/0.48 ( ? [Xs2: list @ A] :
% 0.32/0.48 ( A1
% 0.32/0.48 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.48 => ! [Y3: A] :
% 0.32/0.48 ( ? [Ys3: list @ A] :
% 0.32/0.48 ( A22
% 0.32/0.48 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.48 => ~ ( ord_less @ A @ X @ Y3 ) ) )
% 0.32/0.48 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 0.32/0.48 ( ( A1
% 0.32/0.48 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.48 => ! [Ys3: list @ A] :
% 0.32/0.48 ( ( A22
% 0.32/0.48 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.48 => ( ~ ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( ~ ( ord_less @ A @ Y3 @ X )
% 0.32/0.48 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq.cases
% 0.32/0.48 thf(fact_104_lexordp__eq_Osimps,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ( ( ord_lexordp_eq @ A )
% 0.32/0.48 = ( ^ [A12: list @ A,A23: list @ A] :
% 0.32/0.48 ( ? [Ys: list @ A] :
% 0.32/0.48 ( ( A12
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( A23 = Ys ) )
% 0.32/0.48 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ( A12
% 0.32/0.48 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.48 & ( A23
% 0.32/0.48 = ( cons @ A @ Y2 @ Ys ) )
% 0.32/0.48 & ( ord_less @ A @ X4 @ Y2 ) )
% 0.32/0.48 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ( A12
% 0.32/0.48 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.48 & ( A23
% 0.32/0.48 = ( cons @ A @ Y2 @ Ys ) )
% 0.32/0.48 & ~ ( ord_less @ A @ X4 @ Y2 )
% 0.32/0.48 & ~ ( ord_less @ A @ Y2 @ X4 )
% 0.32/0.48 & ( ord_lexordp_eq @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq.simps
% 0.32/0.48 thf(fact_105_lexordp__eq__simps_I4_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.32/0.48 = ( ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 | ( ~ ( ord_less @ A @ Y @ X3 )
% 0.32/0.48 & ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq_simps(4)
% 0.32/0.48 thf(fact_106_lexordp__eq_OCons__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 => ( ~ ( ord_less @ A @ Y @ X3 )
% 0.32/0.48 => ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.32/0.48 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq.Cons_eq
% 0.32/0.48 thf(fact_107_lexordp__eq_OCons,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq.Cons
% 0.32/0.48 thf(fact_108_lexordp__eq_Oinducts,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.32/0.48 ( ( ord_lexordp_eq @ A @ X1 @ X23 )
% 0.32/0.48 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.32/0.48 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 0.32/0.48 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.48 ( ~ ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( ~ ( ord_less @ A @ Y3 @ X )
% 0.32/0.48 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys3 )
% 0.32/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.32/0.48 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) )
% 0.32/0.48 => ( P @ X1 @ X23 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq.inducts
% 0.32/0.48 thf(fact_109_lexordp_Ocases,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [A1: list @ A,A22: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ A1 @ A22 )
% 0.32/0.48 => ( ( ( A1
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ! [Y3: A,Ys3: list @ A] :
% 0.32/0.48 ( A22
% 0.32/0.48 != ( cons @ A @ Y3 @ Ys3 ) ) )
% 0.32/0.48 => ( ! [X: A] :
% 0.32/0.48 ( ? [Xs2: list @ A] :
% 0.32/0.48 ( A1
% 0.32/0.48 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.48 => ! [Y3: A] :
% 0.32/0.48 ( ? [Ys3: list @ A] :
% 0.32/0.48 ( A22
% 0.32/0.48 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.48 => ~ ( ord_less @ A @ X @ Y3 ) ) )
% 0.32/0.48 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 0.32/0.48 ( ( A1
% 0.32/0.48 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.48 => ! [Ys3: list @ A] :
% 0.32/0.48 ( ( A22
% 0.32/0.48 = ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.48 => ( ~ ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( ~ ( ord_less @ A @ Y3 @ X )
% 0.32/0.48 => ~ ( ord_lexordp @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp.cases
% 0.32/0.48 thf(fact_110_lexordp_Osimps,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ( ( ord_lexordp @ A )
% 0.32/0.48 = ( ^ [A12: list @ A,A23: list @ A] :
% 0.32/0.48 ( ? [Y2: A,Ys: list @ A] :
% 0.32/0.48 ( ( A12
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( A23
% 0.32/0.48 = ( cons @ A @ Y2 @ Ys ) ) )
% 0.32/0.48 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ( A12
% 0.32/0.48 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.48 & ( A23
% 0.32/0.48 = ( cons @ A @ Y2 @ Ys ) )
% 0.32/0.48 & ( ord_less @ A @ X4 @ Y2 ) )
% 0.32/0.48 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ( A12
% 0.32/0.48 = ( cons @ A @ X4 @ Xs3 ) )
% 0.32/0.48 & ( A23
% 0.32/0.48 = ( cons @ A @ Y2 @ Ys ) )
% 0.32/0.48 & ~ ( ord_less @ A @ X4 @ Y2 )
% 0.32/0.48 & ~ ( ord_less @ A @ Y2 @ X4 )
% 0.32/0.48 & ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp.simps
% 0.32/0.48 thf(fact_111_lexordp_Oinducts,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.32/0.48 ( ( ord_lexordp @ A @ X1 @ X23 )
% 0.32/0.48 => ( ! [Y3: A,Ys3: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.48 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 0.32/0.48 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.48 ( ~ ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( ~ ( ord_less @ A @ Y3 @ X )
% 0.32/0.48 => ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 0.32/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.32/0.48 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) )
% 0.32/0.48 => ( P @ X1 @ X23 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp.inducts
% 0.32/0.48 thf(fact_112_lexordp__cases,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 => ( ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ! [Y3: A,Ys4: list @ A] :
% 0.32/0.48 ( Ys2
% 0.32/0.48 != ( cons @ A @ Y3 @ Ys4 ) ) )
% 0.32/0.48 => ( ! [X: A] :
% 0.32/0.48 ( ? [Xs4: list @ A] :
% 0.32/0.48 ( Xs
% 0.32/0.48 = ( cons @ A @ X @ Xs4 ) )
% 0.32/0.48 => ! [Y3: A] :
% 0.32/0.48 ( ? [Ys4: list @ A] :
% 0.32/0.48 ( Ys2
% 0.32/0.48 = ( cons @ A @ Y3 @ Ys4 ) )
% 0.32/0.48 => ~ ( ord_less @ A @ X @ Y3 ) ) )
% 0.32/0.48 => ~ ! [X: A,Xs4: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 = ( cons @ A @ X @ Xs4 ) )
% 0.32/0.48 => ! [Ys4: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 = ( cons @ A @ X @ Ys4 ) )
% 0.32/0.48 => ~ ( ord_lexordp @ A @ Xs4 @ Ys4 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_cases
% 0.32/0.48 thf(fact_113_lexordp__induct,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [Xs: list @ A,Ys2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 => ( ! [Y3: A,Ys3: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys3 ) )
% 0.32/0.48 => ( ! [X: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ X @ Y3 )
% 0.32/0.48 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 0.32/0.48 => ( ! [X: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 0.32/0.48 => ( ( P @ Xs2 @ Ys3 )
% 0.32/0.48 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ X @ Ys3 ) ) ) )
% 0.32/0.48 => ( P @ Xs @ Ys2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_induct
% 0.32/0.48 thf(fact_114_lexordp__simps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Xs: list @ A] :
% 0.32/0.48 ~ ( ord_lexordp @ A @ Xs @ ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_simps(2)
% 0.32/0.48 thf(fact_115_lexordp__simps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ ( nil @ A ) @ Ys2 )
% 0.32/0.48 = ( Ys2
% 0.32/0.48 != ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_simps(1)
% 0.32/0.48 thf(fact_116_lexordp__simps_I3_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.32/0.48 = ( ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 | ( ~ ( ord_less @ A @ Y @ X3 )
% 0.32/0.48 & ( ord_lexordp @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_simps(3)
% 0.32/0.48 thf(fact_117_lexordp__irreflexive_H,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [Xs: list @ A] :
% 0.32/0.48 ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_irreflexive'
% 0.32/0.48 thf(fact_118_lexordp__linear,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 | ( Xs = Ys2 )
% 0.32/0.48 | ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_linear
% 0.32/0.48 thf(fact_119_lexordp__trans,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ! [Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 => ( ( ord_lexordp @ A @ Ys2 @ Zs2 )
% 0.32/0.48 => ( ord_lexordp @ A @ Xs @ Zs2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_trans
% 0.32/0.48 thf(fact_120_lexordp__antisym,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( order @ A )
% 0.32/0.48 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 => ~ ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_antisym
% 0.32/0.48 thf(fact_121_lexordp__irreflexive,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Xs: list @ A] :
% 0.32/0.48 ( ! [X: A] :
% 0.32/0.48 ~ ( ord_less @ A @ X @ X )
% 0.32/0.48 => ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_irreflexive
% 0.32/0.48 thf(fact_122_lexordp__conv__lexordp__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ( ( ord_lexordp @ A )
% 0.32/0.48 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ( ord_lexordp_eq @ A @ Xs3 @ Ys )
% 0.32/0.48 & ~ ( ord_lexordp_eq @ A @ Ys @ Xs3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_conv_lexordp_eq
% 0.32/0.48 thf(fact_123_lexordp__eq__conv__lexord,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ( ( ord_lexordp_eq @ A )
% 0.32/0.48 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ( Xs3 = Ys )
% 0.32/0.48 | ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq_conv_lexord
% 0.32/0.48 thf(fact_124_lexordp__into__lexordp__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 => ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_into_lexordp_eq
% 0.32/0.48 thf(fact_125_lexordp_OCons__eq,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ~ ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 => ( ~ ( ord_less @ A @ Y @ X3 )
% 0.32/0.48 => ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 0.32/0.48 => ( ord_lexordp @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp.Cons_eq
% 0.32/0.48 thf(fact_126_lexordp_OCons,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 => ( ord_lexordp @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp.Cons
% 0.32/0.48 thf(fact_127_lexordp_ONil,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Y: A,Ys2: list @ A] : ( ord_lexordp @ A @ ( nil @ A ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp.Nil
% 0.32/0.48 thf(fact_128_member__rec_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,Y: A] :
% 0.32/0.48 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 0.32/0.48
% 0.32/0.48 % member_rec(2)
% 0.32/0.48 thf(fact_129_member__rec_I1_J,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A,Y: A] :
% 0.32/0.48 ( ( member @ A @ ( cons @ A @ X3 @ Xs ) @ Y )
% 0.32/0.48 = ( ( X3 = Y )
% 0.32/0.48 | ( member @ A @ Xs @ Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % member_rec(1)
% 0.32/0.48 thf(fact_130_splice_Oelims,axiom,
% 0.32/0.48 ! [A: $tType,X3: list @ A,Xa: list @ A,Y: list @ A] :
% 0.32/0.48 ( ( ( splice @ A @ X3 @ Xa )
% 0.32/0.48 = Y )
% 0.32/0.48 => ( ( ( X3
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( Y != Xa ) )
% 0.32/0.48 => ~ ! [X: A,Xs2: list @ A] :
% 0.32/0.48 ( ( X3
% 0.32/0.48 = ( cons @ A @ X @ Xs2 ) )
% 0.32/0.48 => ( Y
% 0.32/0.48 != ( cons @ A @ X @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % splice.elims
% 0.32/0.48 thf(fact_131_lexordp__iff,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( linorder @ A )
% 0.32/0.48 => ( ( ord_lexordp @ A )
% 0.32/0.48 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 0.32/0.48 ( ? [X4: A,Vs: list @ A] :
% 0.32/0.48 ( Ys
% 0.32/0.48 = ( append @ A @ Xs3 @ ( cons @ A @ X4 @ Vs ) ) )
% 0.32/0.48 | ? [Us: list @ A,A5: A,B3: A,Vs: list @ A,Ws: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ A5 @ B3 )
% 0.32/0.48 & ( Xs3
% 0.32/0.48 = ( append @ A @ Us @ ( cons @ A @ A5 @ Vs ) ) )
% 0.32/0.48 & ( Ys
% 0.32/0.48 = ( append @ A @ Us @ ( cons @ A @ B3 @ Ws ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_iff
% 0.32/0.48 thf(fact_132_append_Oassoc,axiom,
% 0.32/0.48 ! [A: $tType,A4: list @ A,B4: list @ A,C3: list @ A] :
% 0.32/0.48 ( ( append @ A @ ( append @ A @ A4 @ B4 ) @ C3 )
% 0.32/0.48 = ( append @ A @ A4 @ ( append @ A @ B4 @ C3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append.assoc
% 0.32/0.48 thf(fact_133_append__assoc,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs2 )
% 0.32/0.48 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_assoc
% 0.32/0.48 thf(fact_134_append__same__eq,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Ys2 @ Xs )
% 0.32/0.48 = ( append @ A @ Zs2 @ Xs ) )
% 0.32/0.48 = ( Ys2 = Zs2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_same_eq
% 0.32/0.48 thf(fact_135_same__append__eq,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ Ys2 )
% 0.32/0.48 = ( append @ A @ Xs @ Zs2 ) )
% 0.32/0.48 = ( Ys2 = Zs2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % same_append_eq
% 0.32/0.48 thf(fact_136_append_Oright__neutral,axiom,
% 0.32/0.48 ! [A: $tType,A4: list @ A] :
% 0.32/0.48 ( ( append @ A @ A4 @ ( nil @ A ) )
% 0.32/0.48 = A4 ) ).
% 0.32/0.48
% 0.32/0.48 % append.right_neutral
% 0.32/0.48 thf(fact_137_append__is__Nil__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ Ys2 )
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_is_Nil_conv
% 0.32/0.48 thf(fact_138_Nil__is__append__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( nil @ A )
% 0.32/0.48 = ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Nil_is_append_conv
% 0.32/0.48 thf(fact_139_self__append__conv2,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 = ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % self_append_conv2
% 0.32/0.48 thf(fact_140_append__self__conv2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ Ys2 )
% 0.32/0.48 = Ys2 )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_self_conv2
% 0.32/0.48 thf(fact_141_self__append__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 = ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( Ys2
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % self_append_conv
% 0.32/0.48 thf(fact_142_append__self__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ Ys2 )
% 0.32/0.48 = Xs )
% 0.32/0.48 = ( Ys2
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_self_conv
% 0.32/0.48 thf(fact_143_append__Nil2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.32/0.48 = Xs ) ).
% 0.32/0.48
% 0.32/0.48 % append_Nil2
% 0.32/0.48 thf(fact_144_split__Nil__iff,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( splice @ A @ Xs @ Ys2 )
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % split_Nil_iff
% 0.32/0.48 thf(fact_145_splice__Nil2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 0.32/0.48 = Xs ) ).
% 0.32/0.48
% 0.32/0.48 % splice_Nil2
% 0.32/0.48 thf(fact_146_append1__eq__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A,Y: A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.48 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.32/0.48 = ( ( Xs = Ys2 )
% 0.32/0.48 & ( X3 = Y ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append1_eq_conv
% 0.32/0.48 thf(fact_147_bind__simps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,X3: B,Xs: list @ B,F3: B > ( list @ A )] :
% 0.32/0.48 ( ( bind @ B @ A @ ( cons @ B @ X3 @ Xs ) @ F3 )
% 0.32/0.48 = ( append @ A @ ( F3 @ X3 ) @ ( bind @ B @ A @ Xs @ F3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % bind_simps(2)
% 0.32/0.48 thf(fact_148_lexordp__append__leftI,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Us2: list @ A,Vs2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ Us2 @ Vs2 )
% 0.32/0.48 => ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_append_leftI
% 0.32/0.48 thf(fact_149_append__eq__appendI,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys2: list @ A,Us2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ Xs1 )
% 0.32/0.48 = Zs2 )
% 0.32/0.48 => ( ( Ys2
% 0.32/0.48 = ( append @ A @ Xs1 @ Us2 ) )
% 0.32/0.48 => ( ( append @ A @ Xs @ Ys2 )
% 0.32/0.48 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_eq_appendI
% 0.32/0.48 thf(fact_150_append__eq__append__conv2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ Ys2 )
% 0.32/0.48 = ( append @ A @ Zs2 @ Ts ) )
% 0.32/0.48 = ( ? [Us: list @ A] :
% 0.32/0.48 ( ( ( Xs
% 0.32/0.48 = ( append @ A @ Zs2 @ Us ) )
% 0.32/0.48 & ( ( append @ A @ Us @ Ys2 )
% 0.32/0.48 = Ts ) )
% 0.32/0.48 | ( ( ( append @ A @ Xs @ Us )
% 0.32/0.48 = Zs2 )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_eq_append_conv2
% 0.32/0.48 thf(fact_151_eq__Nil__appendI,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( Xs = Ys2 )
% 0.32/0.48 => ( Xs
% 0.32/0.48 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % eq_Nil_appendI
% 0.32/0.48 thf(fact_152_append__Nil,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A] :
% 0.32/0.48 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 0.32/0.48 = Ys2 ) ).
% 0.32/0.48
% 0.32/0.48 % append_Nil
% 0.32/0.48 thf(fact_153_append_Oleft__neutral,axiom,
% 0.32/0.48 ! [A: $tType,A4: list @ A] :
% 0.32/0.48 ( ( append @ A @ ( nil @ A ) @ A4 )
% 0.32/0.48 = A4 ) ).
% 0.32/0.48
% 0.32/0.48 % append.left_neutral
% 0.32/0.48 thf(fact_154_Cons__eq__appendI,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ( cons @ A @ X3 @ Xs1 )
% 0.32/0.48 = Ys2 )
% 0.32/0.48 => ( ( Xs
% 0.32/0.48 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.32/0.48 => ( ( cons @ A @ X3 @ Xs )
% 0.32/0.48 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Cons_eq_appendI
% 0.32/0.48 thf(fact_155_append__Cons,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( append @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 0.32/0.48 = ( cons @ A @ X3 @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_Cons
% 0.32/0.48 thf(fact_156_lexordp__eq__pref,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [U: list @ A,V: list @ A] : ( ord_lexordp_eq @ A @ U @ ( append @ A @ U @ V ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_eq_pref
% 0.32/0.48 thf(fact_157_ord_Olexordp__eq__pref,axiom,
% 0.32/0.48 ! [A: $tType,Less: A > A > $o,U: list @ A,V: list @ A] : ( lexordp_eq @ A @ Less @ U @ ( append @ A @ U @ V ) ) ).
% 0.32/0.48
% 0.32/0.48 % ord.lexordp_eq_pref
% 0.32/0.48 thf(fact_158_knows2b,axiom,
% 0.32/0.48 ! [A2: secrecy_specID,E: list @ secrecy_Expression,E1: list @ secrecy_Expression] :
% 0.32/0.48 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E @ E1 ) )
% 0.32/0.48 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.32/0.48
% 0.32/0.48 % knows2b
% 0.32/0.48 thf(fact_159_knows2a,axiom,
% 0.32/0.48 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E: list @ secrecy_Expression] :
% 0.32/0.48 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E ) )
% 0.32/0.48 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.32/0.48
% 0.32/0.48 % knows2a
% 0.32/0.48 thf(fact_160_knows3,axiom,
% 0.32/0.48 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E22: list @ secrecy_Expression] :
% 0.32/0.48 ( ( ( knowle2055185861_knows @ A2 @ E1 )
% 0.32/0.48 & ( knowle2055185861_knows @ A2 @ E22 ) )
% 0.32/0.48 => ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E22 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % knows3
% 0.32/0.48 thf(fact_161_splice_Osimps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( splice @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 0.32/0.48 = ( cons @ A @ X3 @ ( splice @ A @ Ys2 @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % splice.simps(2)
% 0.32/0.48 thf(fact_162_splice_Osimps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A] :
% 0.32/0.48 ( ( splice @ A @ ( nil @ A ) @ Ys2 )
% 0.32/0.48 = Ys2 ) ).
% 0.32/0.48
% 0.32/0.48 % splice.simps(1)
% 0.32/0.48 thf(fact_163_rev__nonempty__induct,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.48 => ( ! [X: A,Xs2: list @ A] :
% 0.32/0.48 ( ( Xs2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( P @ Xs2 )
% 0.32/0.48 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) )
% 0.32/0.48 => ( P @ Xs ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_nonempty_induct
% 0.32/0.48 thf(fact_164_append__eq__Cons__conv,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Zs2: list @ A,X3: A,Xs: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Ys2 @ Zs2 )
% 0.32/0.48 = ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( ( ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( Zs2
% 0.32/0.48 = ( cons @ A @ X3 @ Xs ) ) )
% 0.32/0.48 | ? [Ys5: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 = ( cons @ A @ X3 @ Ys5 ) )
% 0.32/0.48 & ( ( append @ A @ Ys5 @ Zs2 )
% 0.32/0.48 = Xs ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_eq_Cons_conv
% 0.32/0.48 thf(fact_165_Cons__eq__append__conv,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ( cons @ A @ X3 @ Xs )
% 0.32/0.48 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.32/0.48 = ( ( ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( ( cons @ A @ X3 @ Xs )
% 0.32/0.48 = Zs2 ) )
% 0.32/0.48 | ? [Ys5: list @ A] :
% 0.32/0.48 ( ( ( cons @ A @ X3 @ Ys5 )
% 0.32/0.48 = Ys2 )
% 0.32/0.48 & ( Xs
% 0.32/0.48 = ( append @ A @ Ys5 @ Zs2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Cons_eq_append_conv
% 0.32/0.48 thf(fact_166_rev__exhaust,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ~ ! [Ys3: list @ A,Y3: A] :
% 0.32/0.48 ( Xs
% 0.32/0.48 != ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_exhaust
% 0.32/0.48 thf(fact_167_rev__induct,axiom,
% 0.32/0.48 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.32/0.48 ( ( P @ ( nil @ A ) )
% 0.32/0.48 => ( ! [X: A,Xs2: list @ A] :
% 0.32/0.48 ( ( P @ Xs2 )
% 0.32/0.48 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) )
% 0.32/0.48 => ( P @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_induct
% 0.32/0.48 thf(fact_168_lexordp__append__leftD,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Xs: list @ A,Us2: list @ A,Vs2: list @ A] :
% 0.32/0.48 ( ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) )
% 0.32/0.48 => ( ! [A3: A] :
% 0.32/0.48 ~ ( ord_less @ A @ A3 @ A3 )
% 0.32/0.48 => ( ord_lexordp @ A @ Us2 @ Vs2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_append_leftD
% 0.32/0.48 thf(fact_169_lexordp__append__rightI,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [Ys2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ord_lexordp @ A @ Xs @ ( append @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_append_rightI
% 0.32/0.48 thf(fact_170_lexordp__append__left__rightI,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( ord @ A )
% 0.32/0.48 => ! [X3: A,Y: A,Us2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ord_less @ A @ X3 @ Y )
% 0.32/0.48 => ( ord_lexordp @ A @ ( append @ A @ Us2 @ ( cons @ A @ X3 @ Xs ) ) @ ( append @ A @ Us2 @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % lexordp_append_left_rightI
% 0.32/0.48 thf(fact_171_maps__simps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,F3: B > ( list @ A ),X3: B,Xs: list @ B] :
% 0.32/0.48 ( ( maps @ B @ A @ F3 @ ( cons @ B @ X3 @ Xs ) )
% 0.32/0.48 = ( append @ A @ ( F3 @ X3 ) @ ( maps @ B @ A @ F3 @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % maps_simps(1)
% 0.32/0.48 thf(fact_172_concat__eq__append__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ( concat @ A @ Xss2 )
% 0.32/0.48 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.32/0.48 = ( ( ( Xss2
% 0.32/0.48 = ( nil @ ( list @ A ) ) )
% 0.32/0.48 => ( ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( Zs2
% 0.32/0.48 = ( nil @ A ) ) ) )
% 0.32/0.48 & ( ( Xss2
% 0.32/0.48 != ( nil @ ( list @ A ) ) )
% 0.32/0.48 => ? [Xss1: list @ ( list @ A ),Xs3: list @ A,Xs5: list @ A,Xss22: list @ ( list @ A )] :
% 0.32/0.48 ( ( Xss2
% 0.32/0.48 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs3 @ Xs5 ) @ Xss22 ) ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs3 ) )
% 0.32/0.48 & ( Zs2
% 0.32/0.48 = ( append @ A @ Xs5 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % concat_eq_append_conv
% 0.32/0.48 thf(fact_173_rotate1_Osimps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.48 ( ( rotate1 @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rotate1.simps(2)
% 0.32/0.48 thf(fact_174_butlast__snoc,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.32/0.48 = Xs ) ).
% 0.32/0.48
% 0.32/0.48 % butlast_snoc
% 0.32/0.48 thf(fact_175_rotate1__is__Nil__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( ( rotate1 @ A @ Xs )
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rotate1_is_Nil_conv
% 0.32/0.48 thf(fact_176_concat__append,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 0.32/0.48 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys2 ) )
% 0.32/0.48 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % concat_append
% 0.32/0.48 thf(fact_177_butlast_Osimps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( butlast @ A @ ( nil @ A ) )
% 0.32/0.48 = ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % butlast.simps(1)
% 0.32/0.48 thf(fact_178_rotate1_Osimps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.32/0.48 = ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % rotate1.simps(1)
% 0.32/0.48 thf(fact_179_butlast_Osimps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( nil @ A ) ) )
% 0.32/0.48 & ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( cons @ A @ X3 @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % butlast.simps(2)
% 0.32/0.48 thf(fact_180_concat_Osimps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 0.32/0.48 = ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % concat.simps(1)
% 0.32/0.48 thf(fact_181_butlast__append,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( butlast @ A @ Xs ) ) )
% 0.32/0.48 & ( ( Ys2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( append @ A @ Xs @ ( butlast @ A @ Ys2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % butlast_append
% 0.32/0.48 thf(fact_182_concat_Osimps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,X3: list @ A,Xs: list @ ( list @ A )] :
% 0.32/0.48 ( ( concat @ A @ ( cons @ ( list @ A ) @ X3 @ Xs ) )
% 0.32/0.48 = ( append @ A @ X3 @ ( concat @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % concat.simps(2)
% 0.32/0.48 thf(fact_183_maps__simps_I2_J,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 0.32/0.48 ( ( maps @ B @ A @ F3 @ ( nil @ B ) )
% 0.32/0.48 = ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % maps_simps(2)
% 0.32/0.48 thf(fact_184_concat__eq__appendD,axiom,
% 0.32/0.48 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.48 ( ( ( concat @ A @ Xss2 )
% 0.32/0.48 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.32/0.48 => ( ( Xss2
% 0.32/0.48 != ( nil @ ( list @ A ) ) )
% 0.32/0.48 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs4: list @ A,Xss23: list @ ( list @ A )] :
% 0.32/0.48 ( ( Xss2
% 0.32/0.48 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs4 ) @ Xss23 ) ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 0.32/0.48 & ( Zs2
% 0.32/0.48 = ( append @ A @ Xs4 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % concat_eq_appendD
% 0.32/0.48 thf(fact_185_append__butlast__last__id,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.32/0.48 = Xs ) ) ).
% 0.32/0.48
% 0.32/0.48 % append_butlast_last_id
% 0.32/0.48 thf(fact_186_snoc__eq__iff__butlast,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.48 = Ys2 )
% 0.32/0.48 = ( ( Ys2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 & ( ( butlast @ A @ Ys2 )
% 0.32/0.48 = Xs )
% 0.32/0.48 & ( ( last @ A @ Ys2 )
% 0.32/0.48 = X3 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % snoc_eq_iff_butlast
% 0.32/0.48 thf(fact_187_last__snoc,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.32/0.48 = X3 ) ).
% 0.32/0.48
% 0.32/0.48 % last_snoc
% 0.32/0.48 thf(fact_188_last__appendR,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( last @ A @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_appendR
% 0.32/0.48 thf(fact_189_last__appendL,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_appendL
% 0.32/0.48 thf(fact_190_last__ConsR,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_ConsR
% 0.32/0.48 thf(fact_191_last__ConsL,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = X3 ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_ConsL
% 0.32/0.48 thf(fact_192_last_Osimps,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = X3 ) )
% 0.32/0.48 & ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( last @ A @ Xs ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last.simps
% 0.32/0.48 thf(fact_193_last__append,axiom,
% 0.32/0.48 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.48 ( ( ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( last @ A @ Xs ) ) )
% 0.32/0.48 & ( ( Ys2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( last @ A @ Ys2 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_append
% 0.32/0.48 thf(fact_194_longest__common__suffix,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ? [Ss: list @ A,Xs4: list @ A,Ys4: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 = ( append @ A @ Xs4 @ Ss ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( append @ A @ Ys4 @ Ss ) )
% 0.32/0.48 & ( ( Xs4
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( Ys4
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( ( last @ A @ Xs4 )
% 0.32/0.48 != ( last @ A @ Ys4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % longest_common_suffix
% 0.32/0.48 thf(fact_195_concat__conv__foldr,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( concat @ A )
% 0.32/0.48 = ( ^ [Xss3: list @ ( list @ A )] : ( foldr @ ( list @ A ) @ ( list @ A ) @ ( append @ A ) @ Xss3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % concat_conv_foldr
% 0.32/0.48 thf(fact_196_SuccD,axiom,
% 0.32/0.48 ! [A: $tType,K: A,Kl: set @ ( list @ A ),Kl2: list @ A] :
% 0.32/0.48 ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) )
% 0.32/0.48 => ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl ) ) ).
% 0.32/0.48
% 0.32/0.48 % SuccD
% 0.32/0.48 thf(fact_197_foldr__append,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,F3: B > A > A,Xs: list @ B,Ys2: list @ B,A4: A] :
% 0.32/0.48 ( ( foldr @ B @ A @ F3 @ ( append @ B @ Xs @ Ys2 ) @ A4 )
% 0.32/0.48 = ( foldr @ B @ A @ F3 @ Xs @ ( foldr @ B @ A @ F3 @ Ys2 @ A4 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % foldr_append
% 0.32/0.48 thf(fact_198_SuccI,axiom,
% 0.32/0.48 ! [A: $tType,Kl2: list @ A,K: A,Kl: set @ ( list @ A )] :
% 0.32/0.48 ( ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl )
% 0.32/0.48 => ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % SuccI
% 0.32/0.48 thf(fact_199_shift__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( bNF_Greatest_shift @ A @ B )
% 0.32/0.48 = ( ^ [Lab: ( list @ A ) > B,K3: A,Kl3: list @ A] : ( Lab @ ( cons @ A @ K3 @ Kl3 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % shift_def
% 0.32/0.48 thf(fact_200_empty__Shift,axiom,
% 0.32/0.48 ! [A: $tType,Kl: set @ ( list @ A ),K: A] :
% 0.32/0.48 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ Kl )
% 0.32/0.48 => ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ ( nil @ A ) ) )
% 0.32/0.48 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( bNF_Greatest_Shift @ A @ Kl @ K ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % empty_Shift
% 0.32/0.48 thf(fact_201_ShiftD,axiom,
% 0.32/0.48 ! [A: $tType,Kl2: list @ A,Kl: set @ ( list @ A ),K: A] :
% 0.32/0.48 ( ( member2 @ ( list @ A ) @ Kl2 @ ( bNF_Greatest_Shift @ A @ Kl @ K ) )
% 0.32/0.48 => ( member2 @ ( list @ A ) @ ( cons @ A @ K @ Kl2 ) @ Kl ) ) ).
% 0.32/0.48
% 0.32/0.48 % ShiftD
% 0.32/0.48 thf(fact_202_Succ__Shift,axiom,
% 0.32/0.48 ! [A: $tType,Kl: set @ ( list @ A ),K: A,Kl2: list @ A] :
% 0.32/0.48 ( ( bNF_Greatest_Succ @ A @ ( bNF_Greatest_Shift @ A @ Kl @ K ) @ Kl2 )
% 0.32/0.48 = ( bNF_Greatest_Succ @ A @ Kl @ ( cons @ A @ K @ Kl2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Succ_Shift
% 0.32/0.48 thf(fact_203_rev__eq__Cons__iff,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( rev @ A @ Xs )
% 0.32/0.48 = ( cons @ A @ Y @ Ys2 ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_eq_Cons_iff
% 0.32/0.48 thf(fact_204_append_Omonoid__axioms,axiom,
% 0.32/0.48 ! [A: $tType] : ( monoid @ ( list @ A ) @ ( append @ A ) @ ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % append.monoid_axioms
% 0.32/0.48 thf(fact_205_rev__is__rev__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( rev @ A @ Xs )
% 0.32/0.48 = ( rev @ A @ Ys2 ) )
% 0.32/0.48 = ( Xs = Ys2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_is_rev_conv
% 0.32/0.48 thf(fact_206_rev__rev__ident,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 0.32/0.48 = Xs ) ).
% 0.32/0.48
% 0.32/0.48 % rev_rev_ident
% 0.32/0.48 thf(fact_207_rev__is__Nil__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( ( rev @ A @ Xs )
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_is_Nil_conv
% 0.32/0.48 thf(fact_208_Nil__is__rev__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( ( nil @ A )
% 0.32/0.48 = ( rev @ A @ Xs ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( nil @ A ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Nil_is_rev_conv
% 0.32/0.48 thf(fact_209_rev__append,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( rev @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( rev @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_append
% 0.32/0.48 thf(fact_210_singleton__rev__conv,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.48 ( ( ( cons @ A @ X3 @ ( nil @ A ) )
% 0.32/0.48 = ( rev @ A @ Xs ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % singleton_rev_conv
% 0.32/0.48 thf(fact_211_rev__singleton__conv,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.48 ( ( ( rev @ A @ Xs )
% 0.32/0.48 = ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_singleton_conv
% 0.32/0.48 thf(fact_212_rev_Osimps_I1_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( rev @ A @ ( nil @ A ) )
% 0.32/0.48 = ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev.simps(1)
% 0.32/0.48 thf(fact_213_rev__swap,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( rev @ A @ Xs )
% 0.32/0.48 = Ys2 )
% 0.32/0.48 = ( Xs
% 0.32/0.48 = ( rev @ A @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev_swap
% 0.32/0.48 thf(fact_214_rev_Osimps_I2_J,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.48 ( ( rev @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rev.simps(2)
% 0.32/0.48 thf(fact_215_map__tailrec__def,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType] :
% 0.32/0.48 ( ( map_tailrec @ A @ B )
% 0.32/0.48 = ( ^ [F4: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F4 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % map_tailrec_def
% 0.32/0.48 thf(fact_216_hd__rev,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 0.32/0.48 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % hd_rev
% 0.32/0.48 thf(fact_217_hd__append2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( hd @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % hd_append2
% 0.32/0.48 thf(fact_218_hd__concat,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ ( list @ A )] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ ( list @ A ) ) )
% 0.32/0.48 => ( ( ( hd @ ( list @ A ) @ Xs )
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( hd @ A @ ( concat @ A @ Xs ) )
% 0.32/0.48 = ( hd @ A @ ( hd @ ( list @ A ) @ Xs ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % hd_concat
% 0.32/0.48 thf(fact_219_list_Osel_I1_J,axiom,
% 0.32/0.48 ! [A: $tType,X21: A,X22: list @ A] :
% 0.32/0.48 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.32/0.48 = X21 ) ).
% 0.32/0.48
% 0.32/0.48 % list.sel(1)
% 0.32/0.48 thf(fact_220_longest__common__prefix,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ? [Ps: list @ A,Xs4: list @ A,Ys4: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 = ( append @ A @ Ps @ Xs4 ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( append @ A @ Ps @ Ys4 ) )
% 0.32/0.48 & ( ( Xs4
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( Ys4
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( ( hd @ A @ Xs4 )
% 0.32/0.48 != ( hd @ A @ Ys4 ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % longest_common_prefix
% 0.32/0.48 thf(fact_221_hd__append,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( hd @ A @ Ys2 ) ) )
% 0.32/0.48 & ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( hd @ A @ Xs ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % hd_append
% 0.32/0.48 thf(fact_222_last__rev,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 0.32/0.48 = ( hd @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_rev
% 0.32/0.48 thf(fact_223_rotate1__hd__tl,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( rotate1 @ A @ Xs )
% 0.32/0.48 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % rotate1_hd_tl
% 0.32/0.48 thf(fact_224_distinct__adj__append__iff,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( ( distinct_adj @ A @ Xs )
% 0.32/0.48 & ( distinct_adj @ A @ Ys2 )
% 0.32/0.48 & ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( ( last @ A @ Xs )
% 0.32/0.48 != ( hd @ A @ Ys2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_append_iff
% 0.32/0.48 thf(fact_225_distinct__adj__Cons__Cons,axiom,
% 0.32/0.48 ! [B: $tType,X3: B,Y: B,Xs: list @ B] :
% 0.32/0.48 ( ( distinct_adj @ B @ ( cons @ B @ X3 @ ( cons @ B @ Y @ Xs ) ) )
% 0.32/0.48 = ( ( X3 != Y )
% 0.32/0.48 & ( distinct_adj @ B @ ( cons @ B @ Y @ Xs ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_Cons_Cons
% 0.32/0.48 thf(fact_226_distinct__adj__rev,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( distinct_adj @ A @ ( rev @ A @ Xs ) )
% 0.32/0.48 = ( distinct_adj @ A @ Xs ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_rev
% 0.32/0.48 thf(fact_227_tl__append2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( tl @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( append @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % tl_append2
% 0.32/0.48 thf(fact_228_butlast__rev,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( butlast @ A @ ( rev @ A @ Xs ) )
% 0.32/0.48 = ( rev @ A @ ( tl @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % butlast_rev
% 0.32/0.48 thf(fact_229_list_Ocollapse,axiom,
% 0.32/0.48 ! [A: $tType,List: list @ A] :
% 0.32/0.48 ( ( List
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.32/0.48 = List ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.collapse
% 0.32/0.48 thf(fact_230_hd__Cons__tl,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.32/0.48 = Xs ) ) ).
% 0.32/0.48
% 0.32/0.48 % hd_Cons_tl
% 0.32/0.48 thf(fact_231_list_Oexpand,axiom,
% 0.32/0.48 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.32/0.48 ( ( ( List
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 = ( List2
% 0.32/0.48 = ( nil @ A ) ) )
% 0.32/0.48 => ( ( ( List
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( List2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( ( ( hd @ A @ List )
% 0.32/0.48 = ( hd @ A @ List2 ) )
% 0.32/0.48 & ( ( tl @ A @ List )
% 0.32/0.48 = ( tl @ A @ List2 ) ) ) ) )
% 0.32/0.48 => ( List = List2 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.expand
% 0.32/0.48 thf(fact_232_distinct__adj__singleton,axiom,
% 0.32/0.48 ! [B: $tType,X3: B] : ( distinct_adj @ B @ ( cons @ B @ X3 @ ( nil @ B ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_singleton
% 0.32/0.48 thf(fact_233_tl__Nil,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( ( tl @ A @ Xs )
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ? [X4: A] :
% 0.32/0.48 ( Xs
% 0.32/0.48 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % tl_Nil
% 0.32/0.48 thf(fact_234_Nil__tl,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( ( nil @ A )
% 0.32/0.48 = ( tl @ A @ Xs ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ? [X4: A] :
% 0.32/0.48 ( Xs
% 0.32/0.48 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Nil_tl
% 0.32/0.48 thf(fact_235_distinct__adj__ConsD,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.48 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 => ( distinct_adj @ A @ Xs ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_ConsD
% 0.32/0.48 thf(fact_236_distinct__adj__Nil,axiom,
% 0.32/0.48 ! [A: $tType] : ( distinct_adj @ A @ ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_Nil
% 0.32/0.48 thf(fact_237_list_Osel_I3_J,axiom,
% 0.32/0.48 ! [A: $tType,X21: A,X22: list @ A] :
% 0.32/0.48 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 0.32/0.48 = X22 ) ).
% 0.32/0.48
% 0.32/0.48 % list.sel(3)
% 0.32/0.48 thf(fact_238_list_Osel_I2_J,axiom,
% 0.32/0.48 ! [A: $tType] :
% 0.32/0.48 ( ( tl @ A @ ( nil @ A ) )
% 0.32/0.48 = ( nil @ A ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.sel(2)
% 0.32/0.48 thf(fact_239_distinct__adj__appendD1,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 => ( distinct_adj @ A @ Xs ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_appendD1
% 0.32/0.48 thf(fact_240_distinct__adj__appendD2,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 => ( distinct_adj @ A @ Ys2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_appendD2
% 0.32/0.48 thf(fact_241_butlast__tl,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 0.32/0.48 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % butlast_tl
% 0.32/0.48 thf(fact_242_last__tl,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A] :
% 0.32/0.48 ( ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( ( tl @ A @ Xs )
% 0.32/0.48 != ( nil @ A ) ) )
% 0.32/0.48 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 0.32/0.48 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % last_tl
% 0.32/0.48 thf(fact_243_list_Oexhaust__sel,axiom,
% 0.32/0.48 ! [A: $tType,List: list @ A] :
% 0.32/0.48 ( ( List
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 => ( List
% 0.32/0.48 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.exhaust_sel
% 0.32/0.48 thf(fact_244_distinct__adj__Cons,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.48 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( ( X3
% 0.32/0.48 != ( hd @ A @ Xs ) )
% 0.32/0.48 & ( distinct_adj @ A @ Xs ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % distinct_adj_Cons
% 0.32/0.48 thf(fact_245_list_Osplit__sel,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 0.32/0.48 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 0.32/0.48 = ( ( ( List
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 => ( P @ F1 ) )
% 0.32/0.48 & ( ( List
% 0.32/0.48 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.32/0.48 => ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.split_sel
% 0.32/0.48 thf(fact_246_list_Osplit__sel__asm,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 0.32/0.48 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 0.32/0.48 = ( ~ ( ( ( List
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ~ ( P @ F1 ) )
% 0.32/0.48 | ( ( List
% 0.32/0.48 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.32/0.48 & ~ ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.split_sel_asm
% 0.32/0.48 thf(fact_247_list_Osimps_I5_J,axiom,
% 0.32/0.48 ! [B: $tType,A: $tType,F1: B,F2: A > ( list @ A ) > B,X21: A,X22: list @ A] :
% 0.32/0.48 ( ( case_list @ B @ A @ F1 @ F2 @ ( cons @ A @ X21 @ X22 ) )
% 0.32/0.48 = ( F2 @ X21 @ X22 ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.simps(5)
% 0.32/0.48 thf(fact_248_list_Osimps_I4_J,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType,F1: B,F2: A > ( list @ A ) > B] :
% 0.32/0.48 ( ( case_list @ B @ A @ F1 @ F2 @ ( nil @ A ) )
% 0.32/0.48 = F1 ) ).
% 0.32/0.48
% 0.32/0.48 % list.simps(4)
% 0.32/0.48 thf(fact_249_list_Ocase__eq__if,axiom,
% 0.32/0.48 ! [A: $tType,B: $tType] :
% 0.32/0.48 ( ( case_list @ B @ A )
% 0.32/0.48 = ( ^ [F12: B,F22: A > ( list @ A ) > B,List3: list @ A] :
% 0.32/0.48 ( if @ B
% 0.32/0.48 @ ( List3
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 @ F12
% 0.32/0.48 @ ( F22 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % list.case_eq_if
% 0.32/0.48 thf(fact_250_successively__append__iff,axiom,
% 0.32/0.48 ! [A: $tType,P: A > A > $o,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( successively @ A @ P @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( ( successively @ A @ P @ Xs )
% 0.32/0.48 & ( successively @ A @ P @ Ys2 )
% 0.32/0.48 & ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( Ys2
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 | ( P @ ( last @ A @ Xs ) @ ( hd @ A @ Ys2 ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % successively_append_iff
% 0.32/0.48 thf(fact_251_Cons__in__shuffles__iff,axiom,
% 0.32/0.48 ! [A: $tType,Z: A,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( ( ( Xs
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 & ( ( hd @ A @ Xs )
% 0.32/0.48 = Z )
% 0.32/0.48 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) )
% 0.32/0.48 | ( ( Ys2
% 0.32/0.48 != ( nil @ A ) )
% 0.32/0.48 & ( ( hd @ A @ Ys2 )
% 0.32/0.48 = Z )
% 0.32/0.48 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ ( tl @ A @ Ys2 ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Cons_in_shuffles_iff
% 0.32/0.48 thf(fact_252_Nil__in__shuffles,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.48 = ( ( Xs
% 0.32/0.48 = ( nil @ A ) )
% 0.32/0.48 & ( Ys2
% 0.32/0.48 = ( nil @ A ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % Nil_in_shuffles
% 0.32/0.48 thf(fact_253_splice__in__shuffles,axiom,
% 0.32/0.48 ! [A: $tType,Xs: list @ A,Ys2: list @ A] : ( member2 @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) @ ( shuffles @ A @ Xs @ Ys2 ) ) ).
% 0.32/0.48
% 0.32/0.48 % splice_in_shuffles
% 0.32/0.48 thf(fact_254_shufflesE,axiom,
% 0.32/0.48 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.48 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.48 => ( ( ( Zs2 = Xs )
% 0.32/0.48 => ( Ys2
% 0.32/0.48 != ( nil @ A ) ) )
% 0.32/0.48 => ( ( ( Zs2 = Ys2 )
% 0.32/0.48 => ( Xs
% 0.32/0.48 != ( nil @ A ) ) )
% 0.32/0.48 => ( ! [X: A,Xs4: list @ A] :
% 0.32/0.48 ( ( Xs
% 0.32/0.48 = ( cons @ A @ X @ Xs4 ) )
% 0.32/0.48 => ! [Z2: A,Zs3: list @ A] :
% 0.32/0.48 ( ( Zs2
% 0.32/0.48 = ( cons @ A @ Z2 @ Zs3 ) )
% 0.32/0.48 => ( ( X = Z2 )
% 0.32/0.48 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs4 @ Ys2 ) ) ) ) )
% 0.32/0.48 => ~ ! [Y3: A,Ys4: list @ A] :
% 0.32/0.48 ( ( Ys2
% 0.32/0.48 = ( cons @ A @ Y3 @ Ys4 ) )
% 0.32/0.48 => ! [Z2: A,Zs3: list @ A] :
% 0.32/0.48 ( ( Zs2
% 0.32/0.48 = ( cons @ A @ Z2 @ Zs3 ) )
% 0.32/0.48 => ( ( Y3 = Z2 )
% 0.32/0.48 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs @ Ys4 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.48
% 0.32/0.48 % shufflesE
% 0.32/0.48
% 0.32/0.48 % Type constructors (7)
% 0.32/0.48 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.32/0.48 ! [A6: $tType,A7: $tType] :
% 0.32/0.48 ( ( order @ A7 )
% 0.32/0.48 => ( order @ ( A6 > A7 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/0.48 ! [A6: $tType,A7: $tType] :
% 0.32/0.48 ( ( ord @ A7 )
% 0.32/0.48 => ( ord @ ( A6 > A7 ) ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 0.32/0.48 ! [A6: $tType] : ( order @ ( set @ A6 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 0.32/0.48 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.32/0.48 linorder @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 0.32/0.48 order @ $o ).
% 0.32/0.48
% 0.32/0.48 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 0.32/0.48 ord @ $o ).
% 0.32/0.48
% 0.32/0.48 % Helper facts (3)
% 0.32/0.48 thf(help_If_3_1_T,axiom,
% 0.32/0.48 ! [P: $o] :
% 0.32/0.48 ( ( P = $true )
% 0.32/0.48 | ( P = $false ) ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_2_1_T,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Y: A] :
% 0.32/0.48 ( ( if @ A @ $false @ X3 @ Y )
% 0.32/0.48 = Y ) ).
% 0.32/0.48
% 0.32/0.48 thf(help_If_1_1_T,axiom,
% 0.32/0.48 ! [A: $tType,X3: A,Y: A] :
% 0.32/0.48 ( ( if @ A @ $true @ X3 @ Y )
% 0.32/0.48 = X3 ) ).
% 0.32/0.48
% 0.32/0.48 % Conjectures (1)
% 0.32/0.48 thf(conj_0,conjecture,
% 0.32/0.48 knowle1437066798e_know @ a @ ( secrecy_kKS @ m ) ).
% 0.32/0.48
% 0.32/0.48 %------------------------------------------------------------------------------
% 0.32/0.48 ------------------------
% 2.95/1.56 ---- Embedded in THF ---
% 2.95/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.95/1.56 %%% Generated on Tue Feb 24 08:24:27 EST 2026
% 2.95/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.95/1.56 %%% Logic specification used:
% 2.95/1.56 %%% thf(spec, logic, $$dhol).
% 2.95/1.56
% 2.95/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2DTF7787.p
% 2.95/1.56 thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 2.95/1.56 thf(ty_t_Secrecy__types_OSecrets, type, secrecy_Secrets: $tType).
% 2.95/1.56 thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 2.95/1.56 thf(ty_t_Secrecy__types_OKeys, type, secrecy_Keys: $tType).
% 2.95/1.56 thf(ty_t_Secrecy__types_OKS, type, secrecy_KS: $tType).
% 2.95/1.56 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.95/1.56 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.95/1.56 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.95/1.56 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.95/1.56 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.95/1.56 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.95/1.56 thf(sy_c_BNF__Greatest__Fixpoint_OShift, type, bNF_Greatest_Shift: (!> [A:$tType]: (((set @ (list @ A)) > (A > (set @ (list @ A))))))).
% 2.95/1.56 thf(sy_c_BNF__Greatest__Fixpoint_OSucc, type, bNF_Greatest_Succ: (!> [A:$tType]: (((set @ (list @ A)) > ((list @ A) > (set @ A)))))).
% 2.95/1.56 thf(sy_c_BNF__Greatest__Fixpoint_Oshift, type, bNF_Greatest_shift: (!> [A:$tType,B:$tType]: ((((list @ A) > B) > (A > ((list @ A) > B)))))).
% 2.95/1.56 thf(sy_c_CompLocalSecrets_OLocalSecrets, type, localSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.95/1.56 thf(sy_c_Groups_Omonoid, type, monoid: (!> [A:$tType]: (((A > (A > A)) > (A > $o))))).
% 2.95/1.56 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.95/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect, type, knowle1667810483orrect: (secrecy_specID > (secrecy_KS > $o))).
% 2.95/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowsECorrect, type, knowle1893229345orrect: (secrecy_specID > (secrecy_Expression > $o))).
% 2.95/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow, type, knowle1437066798e_know: (secrecy_specID > (secrecy_KS > $o))).
% 2.95/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows, type, knowle2055185861_knows: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.95/1.56 thf(sy_c_ListExtras_Odisjoint, type, disjoint: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_ListExtras_Omem, type, mem: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_ListExtras_OmemS, type, memS: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.95/1.56 thf(sy_c_List_Oarg__min__list, type, arg_min_list: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > A))))).
% 2.95/1.56 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.95/1.56 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.95/1.56 thf(sy_c_List_Oconcat, type, concat: (!> [A:$tType]: (((list @ (list @ A)) > (list @ A))))).
% 2.95/1.56 thf(sy_c_List_Odistinct__adj, type, distinct_adj: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.95/1.56 thf(sy_c_List_Ofoldr, type, foldr: (!> [A:$tType,B:$tType]: (((A > (B > B)) > ((list @ A) > (B > B)))))).
% 2.95/1.56 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.95/1.56 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.95/1.56 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.95/1.56 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.95/1.56 thf(sy_c_List_Olist_Ocase__list, type, case_list: (!> [B:$tType,A:$tType]: ((B > ((A > ((list @ A) > B)) > ((list @ A) > B)))))).
% 2.95/1.56 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.95/1.56 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.95/1.56 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_List_Olistrelp, type, listrelp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((list @ A) > ((list @ B) > $o)))))).
% 2.95/1.56 thf(sy_c_List_Omap__tailrec, type, map_tailrec: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > (list @ B)))))).
% 2.95/1.56 thf(sy_c_List_Omap__tailrec__rev, type, map_tailrec_rev: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > ((list @ B) > (list @ B))))))).
% 2.95/1.56 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.95/1.56 thf(sy_c_List_Omember, type, member: (!> [A:$tType]: (((list @ A) > (A > $o))))).
% 2.95/1.56 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.95/1.56 thf(sy_c_List_Oord__class_Olexordp, type, ord_lexordp: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_List_Oord__class_Olexordp__eq, type, ord_lexordp_eq: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.95/1.56 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.95/1.56 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.95/1.56 thf(sy_c_List_Oshuffles, type, shuffles: (!> [A:$tType]: (((list @ A) > ((list @ A) > (set @ (list @ A))))))).
% 2.95/1.56 thf(sy_c_List_Osplice, type, splice: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.95/1.56 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.95/1.56 thf(sy_c_List_Osuccessively, type, successively: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > $o))))).
% 2.95/1.56 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.95/1.56 thf(sy_c_Secrecy_ODecr, type, decr: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.95/1.56 thf(sy_c_Secrecy_OEnc, type, enc: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.95/1.56 thf(sy_c_Secrecy_OEncrDecrKeys, type, encrDecrKeys: (secrecy_Keys > (secrecy_Keys > $o))).
% 2.95/1.56 thf(sy_c_Secrecy_OExt, type, ext: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.95/1.56 thf(sy_c_Secrecy_OSign, type, sign: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.95/1.56 thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 2.95/1.56 thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 2.95/1.56 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr, type, notSpe1586871396tsExpr: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.95/1.56 thf(sy_c_Secrecy_OspecKeys, type, specKeys: (secrecy_specID > (set @ secrecy_Keys))).
% 2.95/1.56 thf(sy_c_Secrecy_OspecKeysSecrets, type, specKeysSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.95/1.56 thf(sy_c_Secrecy_OspecSecrets, type, specSecrets: (secrecy_specID > (set @ secrecy_Secrets))).
% 2.95/1.56 thf(sy_c_Secrecy__types_OExpression2KSL, type, secrec1371625429on2KSL: ((list @ secrecy_Expression) > (list @ secrecy_KS))).
% 2.95/1.56 thf(sy_c_Secrecy__types_OExpression_OkE, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 2.95/1.56 thf(sy_c_Secrecy__types_OExpression_OsE, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 2.95/1.56 thf(sy_c_Secrecy__types_OKS2Expression, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 2.95/1.56 thf(sy_c_Secrecy__types_OKS_Ocase__KS, type, secrecy_case_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 2.95/1.56 thf(sy_c_Secrecy__types_OKS_OkKS, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 2.95/1.56 thf(sy_c_Secrecy__types_OKS_Orec__KS, type, secrecy_rec_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 2.95/1.56 thf(sy_c_Secrecy__types_OKS_OsKS, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 2.95/1.56 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.95/1.56 thf(sy_c_member, type, member2: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.95/1.56 thf(sy_v_A, type, a: secrecy_specID).
% 2.95/1.56 thf(sy_v_m, type, m: secrecy_Keys).
% 2.95/1.56 thf(fact_0_assms, axiom, ((knowle2055185861_knows @ a) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ m)) @ (nil @ secrecy_Expression)))).
% 2.95/1.56 thf(fact_1_KS_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kKS @ X1) = (secrecy_kKS @ Y1)) = (X1 = Y1))))).
% 2.95/1.56 thf(fact_2_knows4, axiom, (! [IncrDecrKeys:(secrecy_Keys > (secrecy_Keys > $o)),K1:secrecy_Keys,K2:secrecy_Keys,A2:secrecy_specID,E:(list @ secrecy_Expression)]: (((((IncrDecrKeys @ K1) @ K2) & (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K2)) & ((knowle2055185861_knows @ A2) @ ((enc @ K1) @ E)))) => ((knowle2055185861_knows @ A2) @ E))))).
% 2.95/1.56 thf(fact_3_knows5, axiom, (! [IncrDecrKeys:(secrecy_Keys > (secrecy_Keys > $o)),K1:secrecy_Keys,K2:secrecy_Keys,A2:secrecy_specID,E:(list @ secrecy_Expression)]: (((((IncrDecrKeys @ K1) @ K2) & (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K1)) & ((knowle2055185861_knows @ A2) @ ((sign @ K2) @ E)))) => ((knowle2055185861_knows @ A2) @ E))))).
% 2.95/1.56 thf(fact_4_knows6, axiom, (! [A2:secrecy_specID,K:secrecy_Keys,E1:(list @ secrecy_Expression)]: (((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K)) & ((knowle2055185861_knows @ A2) @ E1)) => ((knowle2055185861_knows @ A2) @ ((enc @ K) @ E1)))))).
% 2.95/1.56 thf(fact_5_knows7, axiom, (! [A2:secrecy_specID,K:secrecy_Keys,E1:(list @ secrecy_Expression)]: (((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K)) & ((knowle2055185861_knows @ A2) @ E1)) => ((knowle2055185861_knows @ A2) @ ((sign @ K) @ E1)))))).
% 2.95/1.56 thf(fact_6_know2knows__k, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: ((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)) => ((knowle2055185861_knows @ A2) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression))))))).
% 2.95/1.56 thf(fact_7_know1k, axiom, (! [C:secrecy_specID,M1:secrecy_Keys]: ((((knowle2055185861_knows @ C) @ (((cons @ secrecy_Expression) @ (secrec1016742679ession @ (secrecy_kKS @ M1))) @ (nil @ secrecy_Expression))) = ((knowle1437066798e_know @ C) @ (secrecy_kKS @ M1)))))).
% 2.95/1.56 thf(fact_8_KS_Osimps_I7_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 2.95/1.56 thf(fact_9_KS_Osimps_I5_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 2.95/1.56 thf(fact_10_eoutKnowCorrect__L1k, axiom, (! [C:secrecy_specID,M:secrecy_Keys]: ((((knowle1667810483orrect @ C) @ (secrecy_kKS @ M)) => (((eout @ C) @ (secrecy_kE @ M)) => ((((member2 @ secrecy_Keys) @ M) @ (specKeys @ C)) | ((knowle1437066798e_know @ C) @ (secrecy_kKS @ M)))))))).
% 2.95/1.56 thf(fact_11_eout__know__k, axiom, (! [C:secrecy_specID,M:secrecy_Keys]: ((((knowle1667810483orrect @ C) @ (secrecy_kKS @ M)) = (((eout @ C) @ (secrecy_kE @ M)) = ((((member2 @ secrecy_Keys) @ M) @ (specKeys @ C)) | ((knowle1437066798e_know @ C) @ (secrecy_kKS @ M)))))))).
% 2.95/1.56 thf(fact_12_know_Osimps_I1_J, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: ((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)) = (((ine @ A2) @ (secrecy_kE @ M)) | (((member2 @ secrecy_KS) @ (secrecy_kKS @ M)) @ (localSecrets @ A2))))))).
% 2.95/1.56 thf(fact_13_Expression_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kE @ X1) = (secrecy_kE @ Y1)) = (X1 = Y1))))).
% 2.95/1.56 thf(fact_14_knows__emptyexpression, axiom, (! [C:secrecy_specID]: (((knowle2055185861_knows @ C) @ (nil @ secrecy_Expression))))).
% 2.95/1.56 thf(fact_15_KS2Expression_Osimps_I1_J, axiom, (! [M:secrecy_Keys]: (((secrec1016742679ession @ (secrecy_kKS @ M)) = (secrecy_kE @ M))))).
% 2.95/1.56 thf(fact_16_list_Oinject, axiom, (! [A:$tType,X21:A,X22:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X22) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X22 = Y22)))))).
% 2.95/1.56 thf(fact_17_know1s, axiom, (! [C:secrecy_specID,M2:secrecy_Secrets]: ((((knowle2055185861_knows @ C) @ (((cons @ secrecy_Expression) @ (secrec1016742679ession @ (secrecy_sKS @ M2))) @ (nil @ secrecy_Expression))) = ((knowle1437066798e_know @ C) @ (secrecy_sKS @ M2)))))).
% 2.95/1.56 thf(fact_18_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X22))))).
% 2.95/1.56 thf(fact_19_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X22:(list @ A)]: (((List = (((cons @ A) @ X21) @ X22)) => (List != (nil @ A)))))).
% 2.95/1.56 thf(fact_20_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X222:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X222)))))))))).
% 2.95/1.56 thf(fact_21_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X12:A,X2:(list @ A)]: (((P @ X2) => (P @ (((cons @ A) @ X12) @ X2))))) => (P @ List)))))).
% 2.95/1.56 thf(fact_22_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y2:A,Ys:(list @ A)]: ((Xs = (((cons @ A) @ Y2) @ Ys)))))))).
% 2.95/1.56 thf(fact_23_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X) @ Xs2)) @ (nil @ B)))) => ((! [Y3:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y3) @ Ys3)))) => ((! [X:A,Xs2:(list @ A),Y3:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3))))) => ((P @ Xs) @ Ys2)))))))).
% 2.95/1.56 thf(fact_24_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.95/1.56 thf(fact_25_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y3:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y3) @ Zs)) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ Zs))))))) => (P @ Xs))))))).
% 2.95/1.56 thf(fact_26_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ Xs2)))) => (X3 = (nil @ A))))))))).
% 2.95/1.56 thf(fact_27_KS_Oinject_I2_J, axiom, (! [X23:secrecy_Secrets,Y23:secrecy_Secrets]: ((((secrecy_sKS @ X23) = (secrecy_sKS @ Y23)) = (X23 = Y23))))).
% 2.95/1.56 thf(fact_28_KS_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X23:secrecy_Secrets]: (((secrecy_kKS @ X1) != (secrecy_sKS @ X23))))).
% 2.95/1.56 thf(fact_29_KS_Oinduct, axiom, (! [P:(secrecy_KS > $o),KS:secrecy_KS]: (((! [X:secrecy_Keys]: ((P @ (secrecy_kKS @ X)))) => ((! [X:secrecy_Secrets]: ((P @ (secrecy_sKS @ X)))) => (P @ KS)))))).
% 2.95/1.56 thf(fact_30_KS_Oexhaust, axiom, (! [Y:secrecy_KS]: (((! [X12:secrecy_Keys]: ((Y != (secrecy_kKS @ X12)))) => (~ ((! [X2:secrecy_Secrets]: ((Y != (secrecy_sKS @ X2)))))))))).
% 2.95/1.56 thf(fact_31_KS_Osimps_I6_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X23:secrecy_Secrets]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X23)) = (F2 @ X23))))).
% 2.95/1.56 thf(fact_32_KS_Osimps_I8_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X23:secrecy_Secrets]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X23)) = (F2 @ X23))))).
% 2.95/1.56 thf(fact_33_not__Cons__self2, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((cons @ A) @ X3) @ Xs) != Xs)))).
% 2.95/1.56 thf(fact_34_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X) @ Ys3))))) => (P @ A0))))))))).
% 2.95/1.56 thf(fact_35_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:(list @ A)]: (((X3 != (nil @ A)) => (~ ((! [X:A,Ys3:(list @ A)]: ((X3 != (((cons @ A) @ X) @ Ys3))))))))))))).
% 2.95/1.56 thf(fact_36_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F:(A > B),X_1:(list @ B)]: ((((P @ F) @ (nil @ A)) @ X_1))) => ((! [F:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F) @ As) @ (((cons @ B) @ (F @ A3)) @ Bs)) => (((P @ F) @ (((cons @ A) @ A3) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.95/1.56 thf(fact_37_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X) @ Xs2)))))) => (P @ Xs))))))).
% 2.95/1.56 thf(fact_38_successively_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P2:(A > (A > $o))]: (((P @ P2) @ (nil @ A)))) => ((! [P2:(A > (A > $o)),X:A]: (((P @ P2) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [P2:(A > (A > $o)),X:A,Y3:A,Xs2:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ Y3) @ Xs2)) => ((P @ P2) @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.95/1.56 thf(fact_39_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F:(A > B),X:A]: (((P @ F) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [F:(A > B),X:A,Y3:A,Zs:(list @ A)]: ((((P @ F) @ (((cons @ A) @ Y3) @ Zs)) => ((P @ F) @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ Zs)))))) => ((! [A3:(A > B)]: (((P @ A3) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.95/1.56 thf(fact_40_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y3:A,Xs2:(list @ A)]: ((((X = Y3) => (P @ (((cons @ A) @ X) @ Xs2))) => (((X != Y3) => (P @ (((cons @ A) @ Y3) @ Xs2))) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ Xs2))))))) => (P @ A0))))))).
% 2.95/1.56 thf(fact_41_sorted__wrt_Oinduct, axiom, (! [A:$tType,P:((A > (A > $o)) > ((list @ A) > $o)),A0:(A > (A > $o)),A1:(list @ A)]: (((! [P2:(A > (A > $o))]: (((P @ P2) @ (nil @ A)))) => ((! [P2:(A > (A > $o)),X:A,Ys3:(list @ A)]: ((((P @ P2) @ Ys3) => ((P @ P2) @ (((cons @ A) @ X) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.95/1.56 thf(fact_42_remdups__adj_Ocases, axiom, (! [A:$tType,X3:(list @ A)]: (((X3 != (nil @ A)) => ((! [X:A]: ((X3 != (((cons @ A) @ X) @ (nil @ A))))) => (~ ((! [X:A,Y3:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ (((cons @ A) @ Y3) @ Xs2)))))))))))).
% 2.95/1.56 thf(fact_43_transpose_Ocases, axiom, (! [A:$tType,X3:(list @ (list @ A))]: (((X3 != (nil @ (list @ A))) => ((! [Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (nil @ A)) @ Xss)))) => (~ ((! [X:A,Xs2:(list @ A),Xss:(list @ (list @ A))]: ((X3 != (((cons @ (list @ A)) @ (((cons @ A) @ X) @ Xs2)) @ Xss))))))))))).
% 2.95/1.56 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member2 @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 2.95/1.56 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member2 @ A) @ X4) @ A2)))) = A2)))).
% 2.95/1.56 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) = (Q @ X)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.95/1.56 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G:(A > B)]: (((! [X:A]: (((F3 @ X) = (G @ X)))) => (F3 = G))))).
% 2.95/1.56 thf(fact_48_shuffles_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [Xs2:(list @ A)]: (((P @ Xs2) @ (nil @ A)))) => ((! [X:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y3) @ Ys3)) => (((P @ (((cons @ A) @ X) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.95/1.56 thf(fact_49_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: (((! [X213:A,X223:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X223)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.95/1.56 thf(fact_50_know_Osimps_I2_J, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: ((((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)) = (((ine @ A2) @ (secrecy_sE @ M)) | (((member2 @ secrecy_KS) @ (secrecy_sKS @ M)) @ (localSecrets @ A2))))))).
% 2.95/1.56 thf(fact_51_Expression2KSL_Osimps_I1_J, axiom, ((secrec1371625429on2KSL @ (nil @ secrecy_Expression)) = (nil @ secrecy_KS))).
% 2.95/1.56 thf(fact_52_insert__Nil, axiom, (! [A:$tType,X3:A]: (((((insert @ A) @ X3) @ (nil @ A)) = (((cons @ A) @ X3) @ (nil @ A)))))).
% 2.95/1.56 thf(fact_53_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_54_eoutKnowsECorrect__def, axiom, (knowle1893229345orrect = (^ [C2:secrecy_specID,E2:secrecy_Expression]: ((((eout @ C2) @ E2) = ((? [K3:secrecy_Keys]: (((E2 = (secrecy_kE @ K3)) & (((member2 @ secrecy_Keys) @ K3) @ (specKeys @ C2))))) | ((? [S:secrecy_Secrets]: (((E2 = (secrecy_sE @ S)) & (((member2 @ secrecy_Secrets) @ S) @ (specSecrets @ C2))))) | ((knowle2055185861_knows @ C2) @ (((cons @ secrecy_Expression) @ E2) @ (nil @ secrecy_Expression)))))))))).
% 2.95/1.56 thf(fact_55_eoutKnowsECorrect__L1, axiom, (! [C:secrecy_specID,E:secrecy_Expression]: ((((knowle1893229345orrect @ C) @ E) => (((eout @ C) @ E) => ((? [K4:secrecy_Keys]: (((E = (secrecy_kE @ K4)) & (((member2 @ secrecy_Keys) @ K4) @ (specKeys @ C))))) | ((? [S2:secrecy_Secrets]: (((E = (secrecy_sE @ S2)) & (((member2 @ secrecy_Secrets) @ S2) @ (specSecrets @ C))))) | ((knowle2055185861_knows @ C) @ (((cons @ secrecy_Expression) @ E) @ (nil @ secrecy_Expression)))))))))).
% 2.95/1.56 thf(fact_56_map__tailrec__rev_Oelims, axiom, (! [A:$tType,B:$tType,X3:(A > B),Xa:(list @ A),Xb:(list @ B),Y:(list @ B)]: ((((((((map_tailrec_rev @ A) @ B) @ X3) @ Xa) @ Xb) = Y) => (((Xa = (nil @ A)) => (Y != Xb)) => (~ ((! [A3:A,As:(list @ A)]: (((Xa = (((cons @ A) @ A3) @ As)) => (Y != (((((map_tailrec_rev @ A) @ B) @ X3) @ As) @ (((cons @ B) @ (X3 @ A3)) @ Xb))))))))))))).
% 2.95/1.56 thf(fact_57_arg__min__list_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [F3:(A > B),X3:A]: ((((((arg_min_list @ A) @ B) @ F3) @ (((cons @ A) @ X3) @ (nil @ A))) = X3))))))).
% 2.95/1.56 thf(fact_58_notSpecKeysSecretsExpr__L1, axiom, (! [P:secrecy_specID,A4:secrecy_Expression,L:(list @ secrecy_Expression)]: ((((notSpe1586871396tsExpr @ P) @ (((cons @ secrecy_Expression) @ A4) @ L)) => ((notSpe1586871396tsExpr @ P) @ (((cons @ secrecy_Expression) @ A4) @ (nil @ secrecy_Expression))))))).
% 2.95/1.56 thf(fact_59_Expression_Oinject_I2_J, axiom, (! [X23:secrecy_Secrets,Y23:secrecy_Secrets]: ((((secrecy_sE @ X23) = (secrecy_sE @ Y23)) = (X23 = Y23))))).
% 2.95/1.56 thf(fact_60_Expression_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X23:secrecy_Secrets]: (((secrecy_kE @ X1) != (secrecy_sE @ X23))))).
% 2.95/1.56 thf(fact_61_notSpecKeysSecretsExpr__L2, axiom, (! [P:secrecy_specID,A4:secrecy_Expression,L:(list @ secrecy_Expression)]: ((((notSpe1586871396tsExpr @ P) @ (((cons @ secrecy_Expression) @ A4) @ L)) => ((notSpe1586871396tsExpr @ P) @ L))))).
% 2.95/1.56 thf(fact_62_map__tailrec__rev_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,F3:(A > B),A4:A,As2:(list @ A),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F3) @ (((cons @ A) @ A4) @ As2)) @ Bs2) = (((((map_tailrec_rev @ A) @ B) @ F3) @ As2) @ (((cons @ B) @ (F3 @ A4)) @ Bs2)))))).
% 2.95/1.56 thf(fact_63_map__tailrec__rev_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,F3:(A > B),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F3) @ (nil @ A)) @ Bs2) = Bs2)))).
% 2.95/1.56 thf(fact_64_KS2Expression_Osimps_I2_J, axiom, (! [M:secrecy_Secrets]: (((secrec1016742679ession @ (secrecy_sKS @ M)) = (secrecy_sE @ M))))).
% 2.95/1.56 thf(fact_65_eoutKnowCorrect__L1s, axiom, (! [C:secrecy_specID,M:secrecy_Secrets]: ((((knowle1667810483orrect @ C) @ (secrecy_sKS @ M)) => (((eout @ C) @ (secrecy_sE @ M)) => ((((member2 @ secrecy_Secrets) @ M) @ (specSecrets @ C)) | ((knowle1437066798e_know @ C) @ (secrecy_sKS @ M)))))))).
% 2.95/1.56 thf(fact_66_eout__know__s, axiom, (! [C:secrecy_specID,M:secrecy_Secrets]: ((((knowle1667810483orrect @ C) @ (secrecy_sKS @ M)) = (((eout @ C) @ (secrecy_sE @ M)) = ((((member2 @ secrecy_Secrets) @ M) @ (specSecrets @ C)) | ((knowle1437066798e_know @ C) @ (secrecy_sKS @ M)))))))).
% 2.95/1.56 thf(fact_67_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.95/1.56 thf(fact_68_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.95/1.56 thf(fact_69_DecrEnc, axiom, (! [K12:secrecy_Keys,K22:secrecy_Keys,E3:(list @ secrecy_Expression)]: ((((encrDecrKeys @ K12) @ K22) => (((decr @ K22) @ ((enc @ K12) @ E3)) = E3))))).
% 2.95/1.56 thf(fact_70_ExtSign, axiom, (! [K12:secrecy_Keys,K22:secrecy_Keys,E3:(list @ secrecy_Expression)]: ((((encrDecrKeys @ K12) @ K22) => (((ext @ K12) @ ((sign @ K22) @ E3)) = E3))))).
% 2.95/1.56 thf(fact_71_notSpecKeysSecretsExpr__def, axiom, (notSpe1586871396tsExpr = (^ [P3:secrecy_specID,E2:(list @ secrecy_Expression)]: (((! [X4:secrecy_Keys]: (((((mem @ secrecy_Expression) @ (secrecy_kE @ X4)) @ E2) => (~ ((((member2 @ secrecy_KS) @ (secrecy_kKS @ X4)) @ (specKeysSecrets @ P3))))))) & (! [Y2:secrecy_Secrets]: (((((mem @ secrecy_Expression) @ (secrecy_sE @ Y2)) @ E2) => (~ ((((member2 @ secrecy_KS) @ (secrecy_sKS @ Y2)) @ (specKeysSecrets @ P3)))))))))))).
% 2.95/1.56 thf(fact_72_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_73_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F3:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F3) = (nil @ A))))).
% 2.95/1.56 thf(fact_74_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = (((Less @ X3) @ Y) | ((~ (((Less @ Y) @ X3))) & ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys2))))))).
% 2.95/1.56 thf(fact_75_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys2:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys2)))).
% 2.95/1.56 thf(fact_76_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.95/1.56 thf(fact_77_ord_Olexordp__eq_Ocong, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (lexordp_eq @ A))))).
% 2.95/1.56 thf(fact_78_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ Xs) @ Xs)))).
% 2.95/1.56 thf(fact_79_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X3) @ Y))) => ((~ (((Less @ Y) @ X3))) => (((((lexordp_eq @ A) @ Less) @ Xs) @ Ys2) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)))))))).
% 2.95/1.56 thf(fact_80_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: ((((Less @ X3) @ Y) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)))))).
% 2.95/1.56 thf(fact_81_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys2:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys2)))).
% 2.95/1.56 thf(fact_82_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X1:(list @ A),X23:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less) @ X1) @ X23) => ((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Y3:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((Less @ X) @ Y3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3))))) => ((! [X:A,Y3:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ (((Less @ X) @ Y3))) => ((~ (((Less @ Y3) @ X))) => (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))))) => ((P @ X1) @ X23)))))))).
% 2.95/1.56 thf(fact_83_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys)))) | ((? [X4:A,Y2:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys)) & ((Less2 @ X4) @ Y2))))) | (? [X4:A,Y2:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys)) & ((~ (((Less2 @ X4) @ Y2))) & ((~ (((Less2 @ Y2) @ X4))) & ((((lexordp_eq @ A) @ Less2) @ Xs3) @ Ys))))))))))))))).
% 2.95/1.56 thf(fact_84_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ A1) @ A22) => ((A1 != (nil @ A)) => ((! [X:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X) @ Xs2)))) => (! [Y3:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys3)))) => (~ (((Less @ X) @ Y3))))))))) => (~ ((! [X:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys3)) => ((~ (((Less @ X) @ Y3))) => ((~ (((Less @ Y3) @ X))) => (~ (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys3))))))))))))))))))).
% 2.95/1.56 thf(fact_85_mem_Osimps_I1_J, axiom, (! [A:$tType,X3:A]: ((~ ((((mem @ A) @ X3) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_86_mem_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Y:A,L:(list @ A)]: (((((mem @ A) @ X3) @ (((cons @ A) @ Y) @ L)) = ((X3 = Y) | (((mem @ A) @ X3) @ L)))))).
% 2.95/1.56 thf(fact_87_listrelp_Oinducts, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X1:(list @ A),X23:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((((((listrelp @ A) @ B) @ R) @ X1) @ X23) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Y3:B,Xs2:(list @ A),Ys3:(list @ B)]: ((((R @ X) @ Y3) => ((((((listrelp @ A) @ B) @ R) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y3) @ Ys3))))))) => ((P @ X1) @ X23))))))).
% 2.95/1.56 thf(fact_88_listrelp_Osimps, axiom, (! [B:$tType,A:$tType]: ((((listrelp @ A) @ B) = (^ [R2:(A > (B > $o)),A12:(list @ A),A23:(list @ B)]: ((((A12 = (nil @ A)) & (A23 = (nil @ B))) | (? [X4:A,Y2:B,Xs3:(list @ A),Ys:(list @ B)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ B) @ Y2) @ Ys)) & (((R2 @ X4) @ Y2) & (((((listrelp @ A) @ B) @ R2) @ Xs3) @ Ys))))))))))))).
% 2.95/1.56 thf(fact_89_listrelp_Ocases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A1:(list @ A),A22:(list @ B)]: (((((((listrelp @ A) @ B) @ R) @ A1) @ A22) => (((A1 = (nil @ A)) => (A22 != (nil @ B))) => (~ ((! [X:A,Y3:B,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys3:(list @ B)]: (((A22 = (((cons @ B) @ Y3) @ Ys3)) => (((R @ X) @ Y3) => (~ ((((((listrelp @ A) @ B) @ R) @ Xs2) @ Ys3))))))))))))))))).
% 2.95/1.56 thf(fact_90_lexordp__eq__simps_I3_J, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Xs:(list @ A)]: ((~ ((((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (nil @ A)))))))))).
% 2.95/1.56 thf(fact_91_lexordp__eq__simps_I2_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A))))))))).
% 2.95/1.56 thf(fact_92_lexordp__eq__simps_I1_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys2:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys2))))))).
% 2.95/1.56 thf(fact_93_lexordp__eq__antisym, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => ((((ord_lexordp_eq @ A) @ Ys2) @ Xs) => (Xs = Ys2))))))))).
% 2.95/1.56 thf(fact_94_lexordp__eq__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) | (((ord_lexordp_eq @ A) @ Ys2) @ Xs)))))))).
% 2.95/1.56 thf(fact_95_lexordp__eq__trans, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => ((((ord_lexordp_eq @ A) @ Ys2) @ Zs2) => (((ord_lexordp_eq @ A) @ Xs) @ Zs2))))))))).
% 2.95/1.56 thf(fact_96_lexordp__eq__refl, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: ((((ord_lexordp_eq @ A) @ Xs) @ Xs))))))).
% 2.95/1.56 thf(fact_97_lexordp__eq_ONil, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys2:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys2))))))).
% 2.95/1.56 thf(fact_98_listrelp_OCons, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X3:A,Y:B,Xs:(list @ A),Ys2:(list @ B)]: ((((R @ X3) @ Y) => ((((((listrelp @ A) @ B) @ R) @ Xs) @ Ys2) => (((((listrelp @ A) @ B) @ R) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ B) @ Y) @ Ys2))))))).
% 2.95/1.56 thf(fact_99_listrelp_ONil, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: ((((((listrelp @ A) @ B) @ R) @ (nil @ A)) @ (nil @ B))))).
% 2.95/1.56 thf(fact_100_mem__memS__eq, axiom, (! [A:$tType]: (((mem @ A) = (memS @ A))))).
% 2.95/1.56 thf(fact_101_mem__notdisjoint, axiom, (! [A:$tType,X3:A,L1:(list @ A),L2:(list @ A)]: (((((mem @ A) @ X3) @ L1) => ((((mem @ A) @ X3) @ L2) => (~ ((((disjoint @ A) @ L1) @ L2)))))))).
% 2.95/1.56 thf(fact_102_mem__notdisjoint2, axiom, (! [A:$tType,B:$tType,Schedule:(B > (list @ A)),A2:B,B2:B,X3:A]: (((((disjoint @ A) @ (Schedule @ A2)) @ (Schedule @ B2)) => ((((mem @ A) @ X3) @ (Schedule @ A2)) => (~ ((((mem @ A) @ X3) @ (Schedule @ B2))))))))).
% 2.95/1.56 thf(fact_103_lexordp__eq_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [A1:(list @ A),A22:(list @ A)]: (((((ord_lexordp_eq @ A) @ A1) @ A22) => ((A1 != (nil @ A)) => ((! [X:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X) @ Xs2)))) => (! [Y3:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys3)))) => (~ ((((ord_less @ A) @ X) @ Y3))))))))) => (~ ((! [X:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys3)) => ((~ ((((ord_less @ A) @ X) @ Y3))) => ((~ ((((ord_less @ A) @ Y3) @ X))) => (~ ((((ord_lexordp_eq @ A) @ Xs2) @ Ys3)))))))))))))))))))))).
% 2.95/1.56 thf(fact_104_lexordp__eq_Osimps, axiom, (! [A:$tType]: (((ord @ A) => ((ord_lexordp_eq @ A) = (^ [A12:(list @ A),A23:(list @ A)]: (((? [Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys)))) | ((? [X4:A,Y2:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys)) & (((ord_less @ A) @ X4) @ Y2))))) | (? [X4:A,Y2:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys)) & ((~ ((((ord_less @ A) @ X4) @ Y2))) & ((~ ((((ord_less @ A) @ Y2) @ X4))) & (((ord_lexordp_eq @ A) @ Xs3) @ Ys)))))))))))))))).
% 2.95/1.56 thf(fact_105_lexordp__eq__simps_I4_J, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = ((((ord_less @ A) @ X3) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X3))) & (((ord_lexordp_eq @ A) @ Xs) @ Ys2)))))))))).
% 2.95/1.56 thf(fact_106_lexordp__eq_OCons__eq, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X3))) => ((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))))).
% 2.95/1.56 thf(fact_107_lexordp__eq_OCons, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X3) @ Y) => (((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))).
% 2.95/1.56 thf(fact_108_lexordp__eq_Oinducts, axiom, (! [A:$tType]: (((ord @ A) => (! [X1:(list @ A),X23:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp_eq @ A) @ X1) @ X23) => ((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Y3:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_less @ A) @ X) @ Y3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3))))) => ((! [X:A,Y3:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y3))) => ((~ ((((ord_less @ A) @ Y3) @ X))) => ((((ord_lexordp_eq @ A) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))))) => ((P @ X1) @ X23))))))))))).
% 2.95/1.56 thf(fact_109_lexordp_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [A1:(list @ A),A22:(list @ A)]: (((((ord_lexordp @ A) @ A1) @ A22) => (((A1 = (nil @ A)) => (! [Y3:A,Ys3:(list @ A)]: ((A22 != (((cons @ A) @ Y3) @ Ys3))))) => ((! [X:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X) @ Xs2)))) => (! [Y3:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y3) @ Ys3)))) => (~ ((((ord_less @ A) @ X) @ Y3))))))))) => (~ ((! [X:A,Y3:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y3) @ Ys3)) => ((~ ((((ord_less @ A) @ X) @ Y3))) => ((~ ((((ord_less @ A) @ Y3) @ X))) => (~ ((((ord_lexordp @ A) @ Xs2) @ Ys3)))))))))))))))))))))).
% 2.95/1.56 thf(fact_110_lexordp_Osimps, axiom, (! [A:$tType]: (((ord @ A) => ((ord_lexordp @ A) = (^ [A12:(list @ A),A23:(list @ A)]: (((? [Y2:A,Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = (((cons @ A) @ Y2) @ Ys))))) | ((? [X4:A,Y2:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys)) & (((ord_less @ A) @ X4) @ Y2))))) | (? [X4:A,Y2:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y2) @ Ys)) & ((~ ((((ord_less @ A) @ X4) @ Y2))) & ((~ ((((ord_less @ A) @ Y2) @ X4))) & (((ord_lexordp @ A) @ Xs3) @ Ys)))))))))))))))).
% 2.95/1.56 thf(fact_111_lexordp_Oinducts, axiom, (! [A:$tType]: (((ord @ A) => (! [X1:(list @ A),X23:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp @ A) @ X1) @ X23) => ((! [Y3:A,Ys3:(list @ A)]: (((P @ (nil @ A)) @ (((cons @ A) @ Y3) @ Ys3)))) => ((! [X:A,Y3:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_less @ A) @ X) @ Y3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3))))) => ((! [X:A,Y3:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y3))) => ((~ ((((ord_less @ A) @ Y3) @ X))) => ((((ord_lexordp @ A) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3)))))))) => ((P @ X1) @ X23))))))))))).
% 2.95/1.56 thf(fact_112_lexordp__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => (((Xs = (nil @ A)) => (! [Y3:A,Ys4:(list @ A)]: ((Ys2 != (((cons @ A) @ Y3) @ Ys4))))) => ((! [X:A]: (((? [Xs4:(list @ A)]: ((Xs = (((cons @ A) @ X) @ Xs4)))) => (! [Y3:A]: (((? [Ys4:(list @ A)]: ((Ys2 = (((cons @ A) @ Y3) @ Ys4)))) => (~ ((((ord_less @ A) @ X) @ Y3))))))))) => (~ ((! [X:A,Xs4:(list @ A)]: (((Xs = (((cons @ A) @ X) @ Xs4)) => (! [Ys4:(list @ A)]: (((Ys2 = (((cons @ A) @ X) @ Ys4)) => (~ ((((ord_lexordp @ A) @ Xs4) @ Ys4)))))))))))))))))))).
% 2.95/1.56 thf(fact_113_lexordp__induct, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => ((! [Y3:A,Ys3:(list @ A)]: (((P @ (nil @ A)) @ (((cons @ A) @ Y3) @ Ys3)))) => ((! [X:A,Xs2:(list @ A),Y3:A,Ys3:(list @ A)]: (((((ord_less @ A) @ X) @ Y3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y3) @ Ys3))))) => ((! [X:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_lexordp @ A) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ X) @ Ys3)))))) => ((P @ Xs) @ Ys2))))))))))).
% 2.95/1.56 thf(fact_114_lexordp__simps_I2_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: ((~ ((((ord_lexordp @ A) @ Xs) @ (nil @ A)))))))))).
% 2.95/1.56 thf(fact_115_lexordp__simps_I1_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys2:(list @ A)]: (((((ord_lexordp @ A) @ (nil @ A)) @ Ys2) = (Ys2 != (nil @ A))))))))).
% 2.95/1.56 thf(fact_116_lexordp__simps_I3_J, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((ord_lexordp @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = ((((ord_less @ A) @ X3) @ Y) | ((~ ((((ord_less @ A) @ Y) @ X3))) & (((ord_lexordp @ A) @ Xs) @ Ys2)))))))))).
% 2.95/1.56 thf(fact_117_lexordp__irreflexive_H, axiom, (! [A:$tType]: (((order @ A) => (! [Xs:(list @ A)]: ((~ ((((ord_lexordp @ A) @ Xs) @ Xs))))))))).
% 2.95/1.56 thf(fact_118_lexordp__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) | ((Xs = Ys2) | (((ord_lexordp @ A) @ Ys2) @ Xs))))))))).
% 2.95/1.56 thf(fact_119_lexordp__trans, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => ((((ord_lexordp @ A) @ Ys2) @ Zs2) => (((ord_lexordp @ A) @ Xs) @ Zs2))))))))).
% 2.95/1.56 thf(fact_120_lexordp__antisym, axiom, (! [A:$tType]: (((order @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => (~ ((((ord_lexordp @ A) @ Ys2) @ Xs)))))))))).
% 2.95/1.56 thf(fact_121_lexordp__irreflexive, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: (((! [X:A]: ((~ ((((ord_less @ A) @ X) @ X))))) => (~ ((((ord_lexordp @ A) @ Xs) @ Xs)))))))))).
% 2.95/1.56 thf(fact_122_lexordp__conv__lexordp__eq, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_lexordp @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs3) @ Ys) & (~ ((((ord_lexordp_eq @ A) @ Ys) @ Xs3))))))))))).
% 2.95/1.56 thf(fact_123_lexordp__eq__conv__lexord, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_lexordp_eq @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: (((Xs3 = Ys) | (((ord_lexordp @ A) @ Xs3) @ Ys))))))))).
% 2.95/1.56 thf(fact_124_lexordp__into__lexordp__eq, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp @ A) @ Xs) @ Ys2) => (((ord_lexordp_eq @ A) @ Xs) @ Ys2)))))))).
% 2.95/1.56 thf(fact_125_lexordp_OCons__eq, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ ((((ord_less @ A) @ X3) @ Y))) => ((~ ((((ord_less @ A) @ Y) @ X3))) => ((((ord_lexordp @ A) @ Xs) @ Ys2) => (((ord_lexordp @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))))).
% 2.95/1.56 thf(fact_126_lexordp_OCons, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X3) @ Y) => (((ord_lexordp @ A) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2))))))))).
% 2.95/1.56 thf(fact_127_lexordp_ONil, axiom, (! [A:$tType]: (((ord @ A) => (! [Y:A,Ys2:(list @ A)]: ((((ord_lexordp @ A) @ (nil @ A)) @ (((cons @ A) @ Y) @ Ys2)))))))).
% 2.95/1.56 thf(fact_128_member__rec_I2_J, axiom, (! [A:$tType,Y:A]: ((~ ((((member @ A) @ (nil @ A)) @ Y)))))).
% 2.95/1.56 thf(fact_129_member__rec_I1_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Y:A]: (((((member @ A) @ (((cons @ A) @ X3) @ Xs)) @ Y) = ((X3 = Y) | (((member @ A) @ Xs) @ Y)))))).
% 2.95/1.56 thf(fact_130_splice_Oelims, axiom, (! [A:$tType,X3:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((splice @ A) @ X3) @ Xa) = Y) => (((X3 = (nil @ A)) => (Y != Xa)) => (~ ((! [X:A,Xs2:(list @ A)]: (((X3 = (((cons @ A) @ X) @ Xs2)) => (Y != (((cons @ A) @ X) @ (((splice @ A) @ Xa) @ Xs2))))))))))))).
% 2.95/1.56 thf(fact_131_lexordp__iff, axiom, (! [A:$tType]: (((linorder @ A) => ((ord_lexordp @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: (((? [X4:A,Vs:(list @ A)]: ((Ys = (((append @ A) @ Xs3) @ (((cons @ A) @ X4) @ Vs))))) | (? [Us:(list @ A),A5:A,B3:A,Vs:(list @ A),Ws:(list @ A)]: (((((ord_less @ A) @ A5) @ B3) & ((Xs3 = (((append @ A) @ Us) @ (((cons @ A) @ A5) @ Vs))) & (Ys = (((append @ A) @ Us) @ (((cons @ A) @ B3) @ Ws))))))))))))))).
% 2.95/1.56 thf(fact_132_append_Oassoc, axiom, (! [A:$tType,A4:(list @ A),B4:(list @ A),C3:(list @ A)]: (((((append @ A) @ (((append @ A) @ A4) @ B4)) @ C3) = (((append @ A) @ A4) @ (((append @ A) @ B4) @ C3)))))).
% 2.95/1.56 thf(fact_133_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys2)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys2) @ Zs2)))))).
% 2.95/1.56 thf(fact_134_append__same__eq, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys2) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys2 = Zs2))))).
% 2.95/1.56 thf(fact_135_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Xs) @ Zs2)) = (Ys2 = Zs2))))).
% 2.95/1.56 thf(fact_136_append_Oright__neutral, axiom, (! [A:$tType,A4:(list @ A)]: (((((append @ A) @ A4) @ (nil @ A)) = A4)))).
% 2.95/1.56 thf(fact_137_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.95/1.56 thf(fact_138_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.95/1.56 thf(fact_139_self__append__conv2, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (((append @ A) @ Xs) @ Ys2)) = (Xs = (nil @ A)))))).
% 2.95/1.56 thf(fact_140_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Ys2) = (Xs = (nil @ A)))))).
% 2.95/1.56 thf(fact_141_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys2)) = (Ys2 = (nil @ A)))))).
% 2.95/1.56 thf(fact_142_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Xs) = (Ys2 = (nil @ A)))))).
% 2.95/1.56 thf(fact_143_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.95/1.56 thf(fact_144_split__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((splice @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.95/1.56 thf(fact_145_splice__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((splice @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.95/1.56 thf(fact_146_append1__eq__conv, axiom, (! [A:$tType,Xs:(list @ A),X3:A,Ys2:(list @ A),Y:A]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A))) = (((append @ A) @ Ys2) @ (((cons @ A) @ Y) @ (nil @ A)))) = ((Xs = Ys2) & (X3 = Y)))))).
% 2.95/1.56 thf(fact_147_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X3:B,Xs:(list @ B),F3:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X3) @ Xs)) @ F3) = (((append @ A) @ (F3 @ X3)) @ ((((bind @ B) @ A) @ Xs) @ F3)))))).
% 2.95/1.56 thf(fact_148_lexordp__append__leftI, axiom, (! [A:$tType]: (((ord @ A) => (! [Us2:(list @ A),Vs2:(list @ A),Xs:(list @ A)]: (((((ord_lexordp @ A) @ Us2) @ Vs2) => (((ord_lexordp @ A) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Xs) @ Vs2))))))))).
% 2.95/1.56 thf(fact_149_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys2:(list @ A),Us2:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys2 = (((append @ A) @ Xs1) @ Us2)) => ((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs2) @ Us2))))))).
% 2.95/1.56 thf(fact_150_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs2) @ Ts)) = (? [Us:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us)) & ((((append @ A) @ Us) @ Ys2) = Ts)) | (((((append @ A) @ Xs) @ Us) = Zs2) & (Ys2 = (((append @ A) @ Us) @ Ts)))))))))).
% 2.95/1.56 thf(fact_151_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = Ys2) => (Xs = (((append @ A) @ (nil @ A)) @ Ys2)))))).
% 2.95/1.56 thf(fact_152_append__Nil, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.95/1.56 thf(fact_153_append_Oleft__neutral, axiom, (! [A:$tType,A4:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A4) = A4)))).
% 2.95/1.56 thf(fact_154_Cons__eq__appendI, axiom, (! [A:$tType,X3:A,Xs1:(list @ A),Ys2:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X3) @ Xs1) = Ys2) => ((Xs = (((append @ A) @ Xs1) @ Zs2)) => ((((cons @ A) @ X3) @ Xs) = (((append @ A) @ Ys2) @ Zs2))))))).
% 2.95/1.56 thf(fact_155_append__Cons, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys2:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X3) @ Xs)) @ Ys2) = (((cons @ A) @ X3) @ (((append @ A) @ Xs) @ Ys2)))))).
% 2.95/1.56 thf(fact_156_lexordp__eq__pref, axiom, (! [A:$tType]: (((ord @ A) => (! [U:(list @ A),V:(list @ A)]: ((((ord_lexordp_eq @ A) @ U) @ (((append @ A) @ U) @ V)))))))).
% 2.95/1.56 thf(fact_157_ord_Olexordp__eq__pref, axiom, (! [A:$tType,Less:(A > (A > $o)),U:(list @ A),V:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ U) @ (((append @ A) @ U) @ V))))).
% 2.95/1.56 thf(fact_158_knows2b, axiom, (! [A2:secrecy_specID,E:(list @ secrecy_Expression),E1:(list @ secrecy_Expression)]: ((((knowle2055185861_knows @ A2) @ (((append @ secrecy_Expression) @ E) @ E1)) => ((knowle2055185861_knows @ A2) @ E))))).
% 2.95/1.56 thf(fact_159_knows2a, axiom, (! [A2:secrecy_specID,E1:(list @ secrecy_Expression),E:(list @ secrecy_Expression)]: ((((knowle2055185861_knows @ A2) @ (((append @ secrecy_Expression) @ E1) @ E)) => ((knowle2055185861_knows @ A2) @ E))))).
% 2.95/1.56 thf(fact_160_knows3, axiom, (! [A2:secrecy_specID,E1:(list @ secrecy_Expression),E22:(list @ secrecy_Expression)]: (((((knowle2055185861_knows @ A2) @ E1) & ((knowle2055185861_knows @ A2) @ E22)) => ((knowle2055185861_knows @ A2) @ (((append @ secrecy_Expression) @ E1) @ E22)))))).
% 2.95/1.56 thf(fact_161_splice_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys2:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ X3) @ Xs)) @ Ys2) = (((cons @ A) @ X3) @ (((splice @ A) @ Ys2) @ Xs)))))).
% 2.95/1.56 thf(fact_162_splice_Osimps_I1_J, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((splice @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.95/1.56 thf(fact_163_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.95/1.56 thf(fact_164_append__eq__Cons__conv, axiom, (! [A:$tType,Ys2:(list @ A),Zs2:(list @ A),X3:A,Xs:(list @ A)]: ((((((append @ A) @ Ys2) @ Zs2) = (((cons @ A) @ X3) @ Xs)) = (((Ys2 = (nil @ A)) & (Zs2 = (((cons @ A) @ X3) @ Xs))) | (? [Ys5:(list @ A)]: (((Ys2 = (((cons @ A) @ X3) @ Ys5)) & ((((append @ A) @ Ys5) @ Zs2) = Xs))))))))).
% 2.95/1.56 thf(fact_165_Cons__eq__append__conv, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X3) @ Xs) = (((append @ A) @ Ys2) @ Zs2)) = (((Ys2 = (nil @ A)) & ((((cons @ A) @ X3) @ Xs) = Zs2)) | (? [Ys5:(list @ A)]: ((((((cons @ A) @ X3) @ Ys5) = Ys2) & (Xs = (((append @ A) @ Ys5) @ Zs2)))))))))).
% 2.95/1.56 thf(fact_166_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y3:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y3) @ (nil @ A)))))))))))).
% 2.95/1.56 thf(fact_167_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.95/1.56 thf(fact_168_lexordp__append__leftD, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A),Us2:(list @ A),Vs2:(list @ A)]: (((((ord_lexordp @ A) @ (((append @ A) @ Xs) @ Us2)) @ (((append @ A) @ Xs) @ Vs2)) => ((! [A3:A]: ((~ ((((ord_less @ A) @ A3) @ A3))))) => (((ord_lexordp @ A) @ Us2) @ Vs2))))))))).
% 2.95/1.56 thf(fact_169_lexordp__append__rightI, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 != (nil @ A)) => (((ord_lexordp @ A) @ Xs) @ (((append @ A) @ Xs) @ Ys2))))))))).
% 2.95/1.56 thf(fact_170_lexordp__append__left__rightI, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Y:A,Us2:(list @ A),Xs:(list @ A),Ys2:(list @ A)]: (((((ord_less @ A) @ X3) @ Y) => (((ord_lexordp @ A) @ (((append @ A) @ Us2) @ (((cons @ A) @ X3) @ Xs))) @ (((append @ A) @ Us2) @ (((cons @ A) @ Y) @ Ys2)))))))))).
% 2.95/1.56 thf(fact_171_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F3:(B > (list @ A)),X3:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F3) @ (((cons @ B) @ X3) @ Xs)) = (((append @ A) @ (F3 @ X3)) @ ((((maps @ B) @ A) @ F3) @ Xs)))))).
% 2.95/1.56 thf(fact_172_concat__eq__append__conv, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs2)) = (((Xss2 = (nil @ (list @ A))) => ((Ys2 = (nil @ A)) & (Zs2 = (nil @ A)))) & ((Xss2 != (nil @ (list @ A))) => (? [Xss1:(list @ (list @ A)),Xs3:(list @ A),Xs5:(list @ A),Xss22:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss1) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs3) @ Xs5)) @ Xss22))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss1)) @ Xs3)) & (Zs2 = (((append @ A) @ Xs5) @ ((concat @ A) @ Xss22))))))))))))).
% 2.95/1.56 thf(fact_173_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X3) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_174_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A)))) = Xs)))).
% 2.95/1.56 thf(fact_175_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.95/1.56 thf(fact_176_concat__append, axiom, (! [A:$tType,Xs:(list @ (list @ A)),Ys2:(list @ (list @ A))]: ((((concat @ A) @ (((append @ (list @ A)) @ Xs) @ Ys2)) = (((append @ A) @ ((concat @ A) @ Xs)) @ ((concat @ A) @ Ys2)))))).
% 2.95/1.56 thf(fact_177_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.95/1.56 thf(fact_178_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 2.95/1.56 thf(fact_179_butlast_Osimps_I2_J, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((Xs = (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X3) @ Xs)) = (nil @ A))) & ((Xs != (nil @ A)) => (((butlast @ A) @ (((cons @ A) @ X3) @ Xs)) = (((cons @ A) @ X3) @ ((butlast @ A) @ Xs)))))))).
% 2.95/1.56 thf(fact_180_concat_Osimps_I1_J, axiom, (! [A:$tType]: ((((concat @ A) @ (nil @ (list @ A))) = (nil @ A))))).
% 2.95/1.56 thf(fact_181_butlast__append, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: ((((Ys2 = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((butlast @ A) @ Xs))) & ((Ys2 != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys2)))))))).
% 2.95/1.56 thf(fact_182_concat_Osimps_I2_J, axiom, (! [A:$tType,X3:(list @ A),Xs:(list @ (list @ A))]: ((((concat @ A) @ (((cons @ (list @ A)) @ X3) @ Xs)) = (((append @ A) @ X3) @ ((concat @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_183_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F3:(B > (list @ A))]: ((((((maps @ B) @ A) @ F3) @ (nil @ B)) = (nil @ A))))).
% 2.95/1.56 thf(fact_184_concat__eq__appendD, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs2)) => ((Xss2 != (nil @ (list @ A))) => (? [Xss12:(list @ (list @ A)),Xs2:(list @ A),Xs4:(list @ A),Xss23:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss12) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs2) @ Xs4)) @ Xss23))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss12)) @ Xs2)) & (Zs2 = (((append @ A) @ Xs4) @ ((concat @ A) @ Xss23)))))))))))).
% 2.95/1.56 thf(fact_185_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 2.95/1.56 thf(fact_186_snoc__eq__iff__butlast, axiom, (! [A:$tType,Xs:(list @ A),X3:A,Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A))) = Ys2) = ((Ys2 != (nil @ A)) & ((((butlast @ A) @ Ys2) = Xs) & (((last @ A) @ Ys2) = X3))))))).
% 2.95/1.56 thf(fact_187_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A)))) = X3)))).
% 2.95/1.56 thf(fact_188_last__appendR, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Ys2)))))).
% 2.95/1.56 thf(fact_189_last__appendL, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_190_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_191_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = X3))))).
% 2.95/1.56 thf(fact_192_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = X3)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = ((last @ A) @ Xs))))))).
% 2.95/1.56 thf(fact_193_last__append, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: ((((Ys2 = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Xs))) & ((Ys2 != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Ys2))))))).
% 2.95/1.56 thf(fact_194_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((? [Ss:(list @ A),Xs4:(list @ A),Ys4:(list @ A)]: (((Xs = (((append @ A) @ Xs4) @ Ss)) & ((Ys2 = (((append @ A) @ Ys4) @ Ss)) & ((Xs4 = (nil @ A)) | ((Ys4 = (nil @ A)) | (((last @ A) @ Xs4) != ((last @ A) @ Ys4))))))))))).
% 2.95/1.56 thf(fact_195_concat__conv__foldr, axiom, (! [A:$tType]: (((concat @ A) = (^ [Xss3:(list @ (list @ A))]: ((((((foldr @ (list @ A)) @ (list @ A)) @ (append @ A)) @ Xss3) @ (nil @ A)))))))).
% 2.95/1.56 thf(fact_196_SuccD, axiom, (! [A:$tType,K:A,Kl:(set @ (list @ A)),Kl2:(list @ A)]: (((((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl) @ Kl2)) => (((member2 @ (list @ A)) @ (((append @ A) @ Kl2) @ (((cons @ A) @ K) @ (nil @ A)))) @ Kl))))).
% 2.95/1.56 thf(fact_197_foldr__append, axiom, (! [B:$tType,A:$tType,F3:(B > (A > A)),Xs:(list @ B),Ys2:(list @ B),A4:A]: (((((((foldr @ B) @ A) @ F3) @ (((append @ B) @ Xs) @ Ys2)) @ A4) = (((((foldr @ B) @ A) @ F3) @ Xs) @ (((((foldr @ B) @ A) @ F3) @ Ys2) @ A4)))))).
% 2.95/1.56 thf(fact_198_SuccI, axiom, (! [A:$tType,Kl2:(list @ A),K:A,Kl:(set @ (list @ A))]: (((((member2 @ (list @ A)) @ (((append @ A) @ Kl2) @ (((cons @ A) @ K) @ (nil @ A)))) @ Kl) => (((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl) @ Kl2)))))).
% 2.95/1.56 thf(fact_199_shift__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Greatest_shift @ A) @ B) = (^ [Lab:((list @ A) > B),K3:A,Kl3:(list @ A)]: ((Lab @ (((cons @ A) @ K3) @ Kl3)))))))).
% 2.95/1.56 thf(fact_200_empty__Shift, axiom, (! [A:$tType,Kl:(set @ (list @ A)),K:A]: (((((member2 @ (list @ A)) @ (nil @ A)) @ Kl) => ((((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl) @ (nil @ A))) => (((member2 @ (list @ A)) @ (nil @ A)) @ (((bNF_Greatest_Shift @ A) @ Kl) @ K))))))).
% 2.95/1.56 thf(fact_201_ShiftD, axiom, (! [A:$tType,Kl2:(list @ A),Kl:(set @ (list @ A)),K:A]: (((((member2 @ (list @ A)) @ Kl2) @ (((bNF_Greatest_Shift @ A) @ Kl) @ K)) => (((member2 @ (list @ A)) @ (((cons @ A) @ K) @ Kl2)) @ Kl))))).
% 2.95/1.56 thf(fact_202_Succ__Shift, axiom, (! [A:$tType,Kl:(set @ (list @ A)),K:A,Kl2:(list @ A)]: (((((bNF_Greatest_Succ @ A) @ (((bNF_Greatest_Shift @ A) @ Kl) @ K)) @ Kl2) = (((bNF_Greatest_Succ @ A) @ Kl) @ (((cons @ A) @ K) @ Kl2)))))).
% 2.95/1.56 thf(fact_203_rev__eq__Cons__iff, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((rev @ A) @ Xs) = (((cons @ A) @ Y) @ Ys2)) = (Xs = (((append @ A) @ ((rev @ A) @ Ys2)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.95/1.56 thf(fact_204_append_Omonoid__axioms, axiom, (! [A:$tType]: ((((monoid @ (list @ A)) @ (append @ A)) @ (nil @ A))))).
% 2.95/1.56 thf(fact_205_rev__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((rev @ A) @ Xs) = ((rev @ A) @ Ys2)) = (Xs = Ys2))))).
% 2.95/1.56 thf(fact_206_rev__rev__ident, axiom, (! [A:$tType,Xs:(list @ A)]: ((((rev @ A) @ ((rev @ A) @ Xs)) = Xs)))).
% 2.95/1.56 thf(fact_207_rev__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rev @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.95/1.56 thf(fact_208_Nil__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((rev @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.95/1.56 thf(fact_209_rev__append, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((rev @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((rev @ A) @ Ys2)) @ ((rev @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_210_singleton__rev__conv, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((((cons @ A) @ X3) @ (nil @ A)) = ((rev @ A) @ Xs)) = (Xs = (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_211_rev__singleton__conv, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: (((((rev @ A) @ Xs) = (((cons @ A) @ X3) @ (nil @ A))) = (Xs = (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_212_rev_Osimps_I1_J, axiom, (! [A:$tType]: ((((rev @ A) @ (nil @ A)) = (nil @ A))))).
% 2.95/1.56 thf(fact_213_rev__swap, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((rev @ A) @ Xs) = Ys2) = (Xs = ((rev @ A) @ Ys2)))))).
% 2.95/1.56 thf(fact_214_rev_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((rev @ A) @ (((cons @ A) @ X3) @ Xs)) = (((append @ A) @ ((rev @ A) @ Xs)) @ (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.95/1.56 thf(fact_215_map__tailrec__def, axiom, (! [B:$tType,A:$tType]: ((((map_tailrec @ A) @ B) = (^ [F4:(A > B),As3:(list @ A)]: (((rev @ B) @ (((((map_tailrec_rev @ A) @ B) @ F4) @ As3) @ (nil @ B))))))))).
% 2.95/1.56 thf(fact_216_hd__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ ((rev @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_217_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_218_hd__concat, axiom, (! [A:$tType,Xs:(list @ (list @ A))]: (((Xs != (nil @ (list @ A))) => ((((hd @ (list @ A)) @ Xs) != (nil @ A)) => (((hd @ A) @ ((concat @ A) @ Xs)) = ((hd @ A) @ ((hd @ (list @ A)) @ Xs)))))))).
% 2.95/1.56 thf(fact_219_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X22)) = X21)))).
% 2.95/1.56 thf(fact_220_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((? [Ps:(list @ A),Xs4:(list @ A),Ys4:(list @ A)]: (((Xs = (((append @ A) @ Ps) @ Xs4)) & ((Ys2 = (((append @ A) @ Ps) @ Ys4)) & ((Xs4 = (nil @ A)) | ((Ys4 = (nil @ A)) | (((hd @ A) @ Xs4) != ((hd @ A) @ Ys4))))))))))).
% 2.95/1.56 thf(fact_221_hd__append, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((Xs = (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Ys2))) & ((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Xs))))))).
% 2.95/1.56 thf(fact_222_last__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ ((rev @ A) @ Xs)) = ((hd @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_223_rotate1__hd__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((rotate1 @ A) @ Xs) = (((append @ A) @ ((tl @ A) @ Xs)) @ (((cons @ A) @ ((hd @ A) @ Xs)) @ (nil @ A)))))))).
% 2.95/1.56 thf(fact_224_distinct__adj__append__iff, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((distinct_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((distinct_adj @ A) @ Xs) & (((distinct_adj @ A) @ Ys2) & ((Xs = (nil @ A)) | ((Ys2 = (nil @ A)) | (((last @ A) @ Xs) != ((hd @ A) @ Ys2)))))))))).
% 2.95/1.56 thf(fact_225_distinct__adj__Cons__Cons, axiom, (! [B:$tType,X3:B,Y:B,Xs:(list @ B)]: ((((distinct_adj @ B) @ (((cons @ B) @ X3) @ (((cons @ B) @ Y) @ Xs))) = ((X3 != Y) & ((distinct_adj @ B) @ (((cons @ B) @ Y) @ Xs))))))).
% 2.95/1.56 thf(fact_226_distinct__adj__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((distinct_adj @ A) @ ((rev @ A) @ Xs)) = ((distinct_adj @ A) @ Xs))))).
% 2.95/1.56 thf(fact_227_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys2)))))).
% 2.95/1.56 thf(fact_228_butlast__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((rev @ A) @ Xs)) = ((rev @ A) @ ((tl @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_229_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.95/1.56 thf(fact_230_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.95/1.56 thf(fact_231_list_Oexpand, axiom, (! [A:$tType,List:(list @ A),List2:(list @ A)]: ((((List = (nil @ A)) = (List2 = (nil @ A))) => (((List != (nil @ A)) => ((List2 != (nil @ A)) => ((((hd @ A) @ List) = ((hd @ A) @ List2)) & (((tl @ A) @ List) = ((tl @ A) @ List2))))) => (List = List2)))))).
% 2.95/1.56 thf(fact_232_distinct__adj__singleton, axiom, (! [B:$tType,X3:B]: (((distinct_adj @ B) @ (((cons @ B) @ X3) @ (nil @ B)))))).
% 2.95/1.56 thf(fact_233_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X4:A]: ((Xs = (((cons @ A) @ X4) @ (nil @ A)))))))))).
% 2.95/1.56 thf(fact_234_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X4:A]: ((Xs = (((cons @ A) @ X4) @ (nil @ A)))))))))).
% 2.95/1.56 thf(fact_235_distinct__adj__ConsD, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((distinct_adj @ A) @ (((cons @ A) @ X3) @ Xs)) => ((distinct_adj @ A) @ Xs))))).
% 2.95/1.56 thf(fact_236_distinct__adj__Nil, axiom, (! [A:$tType]: (((distinct_adj @ A) @ (nil @ A))))).
% 2.95/1.56 thf(fact_237_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X22:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X22)) = X22)))).
% 2.95/1.56 thf(fact_238_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.95/1.56 thf(fact_239_distinct__adj__appendD1, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((distinct_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) => ((distinct_adj @ A) @ Xs))))).
% 2.95/1.56 thf(fact_240_distinct__adj__appendD2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((distinct_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) => ((distinct_adj @ A) @ Ys2))))).
% 2.95/1.56 thf(fact_241_butlast__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((tl @ A) @ Xs)) = ((tl @ A) @ ((butlast @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_242_last__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((Xs = (nil @ A)) | (((tl @ A) @ Xs) != (nil @ A))) => (((last @ A) @ ((tl @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.95/1.56 thf(fact_243_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.95/1.56 thf(fact_244_distinct__adj__Cons, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((distinct_adj @ A) @ (((cons @ A) @ X3) @ Xs)) = ((Xs = (nil @ A)) | ((X3 != ((hd @ A) @ Xs)) & ((distinct_adj @ A) @ Xs))))))).
% 2.95/1.56 thf(fact_245_list_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((list @ A) > B)),List:(list @ A)]: (((P @ (((((case_list @ B) @ A) @ F1) @ F2) @ List)) = (((List = (nil @ A)) => (P @ F1)) & ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) => (P @ ((F2 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))).
% 2.95/1.56 thf(fact_246_list_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((list @ A) > B)),List:(list @ A)]: (((P @ (((((case_list @ B) @ A) @ F1) @ F2) @ List)) = (~ ((((List = (nil @ A)) & (~ ((P @ F1)))) | ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) & (~ ((P @ ((F2 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))))))).
% 2.95/1.56 thf(fact_247_list_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:(A > ((list @ A) > B)),X21:A,X22:(list @ A)]: (((((((case_list @ B) @ A) @ F1) @ F2) @ (((cons @ A) @ X21) @ X22)) = ((F2 @ X21) @ X22))))).
% 2.95/1.56 thf(fact_248_list_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:(A > ((list @ A) > B))]: (((((((case_list @ B) @ A) @ F1) @ F2) @ (nil @ A)) = F1)))).
% 2.95/1.56 thf(fact_249_list_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_list @ B) @ A) = (^ [F12:B,F22:(A > ((list @ A) > B)),List3:(list @ A)]: (((((if @ B) @ (List3 = (nil @ A))) @ F12) @ ((F22 @ ((hd @ A) @ List3)) @ ((tl @ A) @ List3))))))))).
% 2.95/1.56 thf(fact_250_successively__append__iff, axiom, (! [A:$tType,P:(A > (A > $o)),Xs:(list @ A),Ys2:(list @ A)]: (((((successively @ A) @ P) @ (((append @ A) @ Xs) @ Ys2)) = ((((successively @ A) @ P) @ Xs) & ((((successively @ A) @ P) @ Ys2) & ((Xs = (nil @ A)) | ((Ys2 = (nil @ A)) | ((P @ ((last @ A) @ Xs)) @ ((hd @ A) @ Ys2)))))))))).
% 2.95/1.56 thf(fact_251_Cons__in__shuffles__iff, axiom, (! [A:$tType,Z:A,Zs2:(list @ A),Xs:(list @ A),Ys2:(list @ A)]: (((((member2 @ (list @ A)) @ (((cons @ A) @ Z) @ Zs2)) @ (((shuffles @ A) @ Xs) @ Ys2)) = (((Xs != (nil @ A)) & ((((hd @ A) @ Xs) = Z) & (((member2 @ (list @ A)) @ Zs2) @ (((shuffles @ A) @ ((tl @ A) @ Xs)) @ Ys2)))) | ((Ys2 != (nil @ A)) & ((((hd @ A) @ Ys2) = Z) & (((member2 @ (list @ A)) @ Zs2) @ (((shuffles @ A) @ Xs) @ ((tl @ A) @ Ys2)))))))))).
% 2.95/1.56 thf(fact_252_Nil__in__shuffles, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((member2 @ (list @ A)) @ (nil @ A)) @ (((shuffles @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.95/1.56 thf(fact_253_splice__in__shuffles, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((member2 @ (list @ A)) @ (((splice @ A) @ Xs) @ Ys2)) @ (((shuffles @ A) @ Xs) @ Ys2))))).
% 2.95/1.56 thf(fact_254_shufflesE, axiom, (! [A:$tType,Zs2:(list @ A),Xs:(list @ A),Ys2:(list @ A)]: (((((member2 @ (list @ A)) @ Zs2) @ (((shuffles @ A) @ Xs) @ Ys2)) => (((Zs2 = Xs) => (Ys2 != (nil @ A))) => (((Zs2 = Ys2) => (Xs != (nil @ A))) => ((! [X:A,Xs4:(list @ A)]: (((Xs = (((cons @ A) @ X) @ Xs4)) => (! [Z2:A,Zs3:(list @ A)]: (((Zs2 = (((cons @ A) @ Z2) @ Zs3)) => ((X = Z2) => (~ ((((member2 @ (list @ A)) @ Zs3) @ (((shuffles @ A) @ Xs4) @ Ys2))))))))))) => (~ ((! [Y3:A,Ys4:(list @ A)]: (((Ys2 = (((cons @ A) @ Y3) @ Ys4)) => (! [Z2:A,Zs3:(list @ A)]: (((Zs2 = (((cons @ A) @ Z2) @ Zs3)) => ((Y3 = Z2) => (~ ((((member2 @ (list @ A)) @ Zs3) @ (((shuffles @ A) @ Xs) @ Ys4)))))))))))))))))))).
% 2.95/1.56 thf(tcon_fun___Orderings_Oorder, axiom, (! [A6:$tType,A7:$tType]: (((order @ A7) => (order @ (A6 > A7)))))).
% 2.95/1.56 thf(tcon_fun___Orderings_Oord, axiom, (! [A6:$tType,A7:$tType]: (((ord @ A7) => (ord @ (A6 > A7)))))).
% 2.95/1.56 thf(tcon_Set_Oset___Orderings_Oorder_1, axiom, (! [A6:$tType]: ((order @ (set @ A6))))).
% 2.95/1.56 thf(tcon_Set_Oset___Orderings_Oord_2, axiom, (! [A6:$tType]: ((ord @ (set @ A6))))).
% 2.95/1.56 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.95/1.56 thf(tcon_HOL_Obool___Orderings_Oorder_3, axiom, (order @ $o)).
% 2.95/1.56 thf(tcon_HOL_Obool___Orderings_Oord_4, axiom, (ord @ $o)).
% 2.95/1.56 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.95/1.56 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 2.95/1.56 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 2.95/1.56 thf(conj_0, conjecture, ((knowle1437066798e_know @ a) @ (secrecy_kKS @ m))).
% 2.95/1.56 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2DTF7787.p
% 2.95/1.56 ------------------------
% 2.95/1.59 ---- Cleaned THF ---
% 2.95/1.60 thf(ty_t_Secrecy__types_OExpression,type,
% 2.95/1.60 secrecy_Expression: $tType ).
% 2.95/1.60
% 2.95/1.60 thf(ty_t_Secrecy__types_OSecrets,type,
% 2.95/1.60 secrecy_Secrets: $tType ).
% 2.95/1.60
% 2.95/1.60 thf(ty_t_Secrecy__types_OspecID,type,
% 2.95/1.60 secrecy_specID: $tType ).
% 2.95/1.60
% 2.95/1.60 thf(ty_t_Secrecy__types_OKeys,type,
% 2.95/1.60 secrecy_Keys: $tType ).
% 2.95/1.60
% 2.95/1.60 thf(ty_t_Secrecy__types_OKS,type,
% 2.95/1.60 secrecy_KS: $tType ).
% 2.95/1.60
% 2.95/1.60 thf(ty_t_List_Olist,type,
% 2.95/1.60 list: $tType > $tType ).
% 2.95/1.60
% 2.95/1.60 thf(ty_t_Set_Oset,type,
% 2.95/1.60 set: $tType > $tType ).
% 2.95/1.60
% 2.95/1.60 thf(sy_cl_HOL_Otype,type,
% 2.95/1.60 type:
% 2.95/1.60 !>[A: $tType] : $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_cl_Orderings_Oord,type,
% 2.95/1.60 ord:
% 2.95/1.60 !>[A: $tType] : $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_cl_Orderings_Oorder,type,
% 2.95/1.60 order:
% 2.95/1.60 !>[A: $tType] : $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_cl_Orderings_Olinorder,type,
% 2.95/1.60 linorder:
% 2.95/1.60 !>[A: $tType] : $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 2.95/1.60 bNF_Greatest_Shift:
% 2.95/1.60 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_BNF__Greatest__Fixpoint_OSucc,type,
% 2.95/1.60 bNF_Greatest_Succ:
% 2.95/1.60 !>[A: $tType] : ( ( set @ ( list @ A ) ) > ( list @ A ) > ( set @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 2.95/1.60 bNF_Greatest_shift:
% 2.95/1.60 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.95/1.60 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_Groups_Omonoid,type,
% 2.95/1.60 monoid:
% 2.95/1.60 !>[A: $tType] : ( ( A > A > A ) > A > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_If,type,
% 2.95/1.60 if:
% 2.95/1.60 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 2.95/1.60 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowsECorrect,type,
% 2.95/1.60 knowle1893229345orrect: secrecy_specID > secrecy_Expression > $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 2.95/1.60 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows,type,
% 2.95/1.60 knowle2055185861_knows: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_ListExtras_Odisjoint,type,
% 2.95/1.60 disjoint:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_ListExtras_Omem,type,
% 2.95/1.60 mem:
% 2.95/1.60 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_ListExtras_OmemS,type,
% 2.95/1.60 memS:
% 2.95/1.60 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Oappend,type,
% 2.95/1.60 append:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Oarg__min__list,type,
% 2.95/1.60 arg_min_list:
% 2.95/1.60 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > A ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Obind,type,
% 2.95/1.60 bind:
% 2.95/1.60 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Obutlast,type,
% 2.95/1.60 butlast:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Oconcat,type,
% 2.95/1.60 concat:
% 2.95/1.60 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Odistinct__adj,type,
% 2.95/1.60 distinct_adj:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Ofoldr,type,
% 2.95/1.60 foldr:
% 2.95/1.60 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Oinsert,type,
% 2.95/1.60 insert:
% 2.95/1.60 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olast,type,
% 2.95/1.60 last:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olist_OCons,type,
% 2.95/1.60 cons:
% 2.95/1.60 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olist_ONil,type,
% 2.95/1.60 nil:
% 2.95/1.60 !>[A: $tType] : ( list @ A ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olist_Ocase__list,type,
% 2.95/1.60 case_list:
% 2.95/1.60 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olist_Ohd,type,
% 2.95/1.60 hd:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olist_Otl,type,
% 2.95/1.60 tl:
% 2.95/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olist__ex1,type,
% 2.95/1.60 list_ex1:
% 2.95/1.60 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Olistrelp,type,
% 2.95/1.60 listrelp:
% 2.95/1.60 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 2.95/1.60
% 2.95/1.60 thf(sy_c_List_Omap__tailrec,type,
% 3.18/1.60 map_tailrec:
% 3.18/1.60 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Omap__tailrec__rev,type,
% 3.18/1.60 map_tailrec_rev:
% 3.18/1.60 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Omaps,type,
% 3.18/1.60 maps:
% 3.18/1.60 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Omember,type,
% 3.18/1.60 member:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Oord_Olexordp__eq,type,
% 3.18/1.60 lexordp_eq:
% 3.18/1.60 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Oord__class_Olexordp,type,
% 3.18/1.60 ord_lexordp:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 3.18/1.60 ord_lexordp_eq:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Oproduct__lists,type,
% 3.18/1.60 product_lists:
% 3.18/1.60 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Orev,type,
% 3.18/1.60 rev:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Orotate1,type,
% 3.18/1.60 rotate1:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Oshuffles,type,
% 3.18/1.60 shuffles:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( set @ ( list @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Osplice,type,
% 3.18/1.60 splice:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Osubseqs,type,
% 3.18/1.60 subseqs:
% 3.18/1.60 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_List_Osuccessively,type,
% 3.18/1.60 successively:
% 3.18/1.60 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Orderings_Oord__class_Oless,type,
% 3.18/1.60 ord_less:
% 3.18/1.60 !>[A: $tType] : ( A > A > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_ODecr,type,
% 3.18/1.60 decr: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OEnc,type,
% 3.18/1.60 enc: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 3.18/1.60 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OExt,type,
% 3.18/1.60 ext: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OSign,type,
% 3.18/1.60 sign: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_Oeout,type,
% 3.18/1.60 eout: secrecy_specID > secrecy_Expression > $o ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_Oine,type,
% 3.18/1.60 ine: secrecy_specID > secrecy_Expression > $o ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 3.18/1.60 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OspecKeys,type,
% 3.18/1.60 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 3.18/1.60 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy_OspecSecrets,type,
% 3.18/1.60 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 3.18/1.60 secrec1371625429on2KSL: ( list @ secrecy_Expression ) > ( list @ secrecy_KS ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 3.18/1.60 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 3.18/1.60 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 3.18/1.60 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 3.18/1.60 secrecy_case_KS:
% 3.18/1.60 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 3.18/1.60 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 3.18/1.60 secrecy_rec_KS:
% 3.18/1.60 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 3.18/1.60 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_Set_OCollect,type,
% 3.18/1.60 collect:
% 3.18/1.60 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_c_member,type,
% 3.18/1.60 member2:
% 3.18/1.60 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.18/1.60
% 3.18/1.60 thf(sy_v_A,type,
% 3.18/1.60 a: secrecy_specID ).
% 3.18/1.60
% 3.18/1.60 thf(sy_v_m,type,
% 3.18/1.60 m: secrecy_Keys ).
% 3.18/1.60
% 3.18/1.60 thf(fact_0_assms,axiom,
% 3.18/1.60 knowle2055185861_knows @ a @ ( cons @ secrecy_Expression @ ( secrecy_kE @ m ) @ ( nil @ secrecy_Expression ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_1_KS_Oinject_I1_J,axiom,
% 3.18/1.60 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.18/1.60 ( ( ( secrecy_kKS @ X1 )
% 3.18/1.60 = ( secrecy_kKS @ Y1 ) )
% 3.18/1.60 = ( X1 = Y1 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_2_knows4,axiom,
% 3.18/1.60 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 3.18/1.60 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 3.18/1.60 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K2 ) )
% 3.18/1.60 & ( knowle2055185861_knows @ A2 @ ( enc @ K1 @ E ) ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_3_knows5,axiom,
% 3.18/1.60 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 3.18/1.60 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 3.18/1.60 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K1 ) )
% 3.18/1.60 & ( knowle2055185861_knows @ A2 @ ( sign @ K2 @ E ) ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_4_knows6,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 3.18/1.60 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 3.18/1.60 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ ( enc @ K @ E1 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_5_knows7,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 3.18/1.60 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 3.18/1.60 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ ( sign @ K @ E1 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_6_know2knows__k,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 3.18/1.60 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_7_know1k,axiom,
% 3.18/1.60 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 3.18/1.60 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ ( nil @ secrecy_Expression ) ) )
% 3.18/1.60 = ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_8_KS_Osimps_I7_J,axiom,
% 3.18/1.60 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 3.18/1.60 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 3.18/1.60 = ( F1 @ X1 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_9_KS_Osimps_I5_J,axiom,
% 3.18/1.60 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 3.18/1.60 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 3.18/1.60 = ( F1 @ X1 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_10_eoutKnowCorrect__L1k,axiom,
% 3.18/1.60 ! [C: secrecy_specID,M: secrecy_Keys] :
% 3.18/1.60 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 3.18/1.60 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 3.18/1.60 => ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 3.18/1.60 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_11_eout__know__k,axiom,
% 3.18/1.60 ! [C: secrecy_specID,M: secrecy_Keys] :
% 3.18/1.60 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 3.18/1.60 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 3.18/1.60 = ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 3.18/1.60 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_12_know_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 3.18/1.60 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.18/1.60 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 3.18/1.60 | ( member2 @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_13_Expression_Oinject_I1_J,axiom,
% 3.18/1.60 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.18/1.60 ( ( ( secrecy_kE @ X1 )
% 3.18/1.60 = ( secrecy_kE @ Y1 ) )
% 3.18/1.60 = ( X1 = Y1 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_14_knows__emptyexpression,axiom,
% 3.18/1.60 ! [C: secrecy_specID] : ( knowle2055185861_knows @ C @ ( nil @ secrecy_Expression ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_15_KS2Expression_Osimps_I1_J,axiom,
% 3.18/1.60 ! [M: secrecy_Keys] :
% 3.18/1.60 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 3.18/1.60 = ( secrecy_kE @ M ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_16_list_Oinject,axiom,
% 3.18/1.60 ! [A: $tType,X21: A,X22: list @ A,Y21: A,Y22: list @ A] :
% 3.18/1.60 ( ( ( cons @ A @ X21 @ X22 )
% 3.18/1.60 = ( cons @ A @ Y21 @ Y22 ) )
% 3.18/1.60 = ( ( X21 = Y21 )
% 3.18/1.60 & ( X22 = Y22 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_17_know1s,axiom,
% 3.18/1.60 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 3.18/1.60 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ ( nil @ secrecy_Expression ) ) )
% 3.18/1.60 = ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_18_list_Odistinct_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,X21: A,X22: list @ A] :
% 3.18/1.60 ( ( nil @ A )
% 3.18/1.60 != ( cons @ A @ X21 @ X22 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_19_list_OdiscI,axiom,
% 3.18/1.60 ! [A: $tType,List: list @ A,X21: A,X22: list @ A] :
% 3.18/1.60 ( ( List
% 3.18/1.60 = ( cons @ A @ X21 @ X22 ) )
% 3.18/1.60 => ( List
% 3.18/1.60 != ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_20_list_Oexhaust,axiom,
% 3.18/1.60 ! [A: $tType,Y: list @ A] :
% 3.18/1.60 ( ( Y
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ~ ! [X212: A,X222: list @ A] :
% 3.18/1.60 ( Y
% 3.18/1.60 != ( cons @ A @ X212 @ X222 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_21_list_Oinducts,axiom,
% 3.18/1.60 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 3.18/1.60 ( ( P @ ( nil @ A ) )
% 3.18/1.60 => ( ! [X12: A,X2: list @ A] :
% 3.18/1.60 ( ( P @ X2 )
% 3.18/1.60 => ( P @ ( cons @ A @ X12 @ X2 ) ) )
% 3.18/1.60 => ( P @ List ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_22_neq__Nil__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 = ( ? [Y2: A,Ys: list @ A] :
% 3.18/1.60 ( Xs
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_23_list__induct2_H,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 3.18/1.60 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 3.18/1.60 => ( ! [Y3: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A,Y3: B,Ys3: list @ B] :
% 3.18/1.60 ( ( P @ Xs2 @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) )
% 3.18/1.60 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_24_splice_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.18/1.60 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ( P @ Ys3 @ Xs2 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 ) )
% 3.18/1.60 => ( P @ A0 @ A1 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_25_induct__list012,axiom,
% 3.18/1.60 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 3.18/1.60 ( ( P @ ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ( ! [X: A,Y3: A,Zs: list @ A] :
% 3.18/1.60 ( ( P @ Zs )
% 3.18/1.60 => ( ( P @ ( cons @ A @ Y3 @ Zs ) )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Zs ) ) ) ) )
% 3.18/1.60 => ( P @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_26_min__list_Ocases,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: list @ A] :
% 3.18/1.60 ( ! [X: A,Xs2: list @ A] :
% 3.18/1.60 ( X3
% 3.18/1.60 != ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ( X3
% 3.18/1.60 = ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_27_KS_Oinject_I2_J,axiom,
% 3.18/1.60 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 3.18/1.60 ( ( ( secrecy_sKS @ X23 )
% 3.18/1.60 = ( secrecy_sKS @ Y23 ) )
% 3.18/1.60 = ( X23 = Y23 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_28_KS_Odistinct_I1_J,axiom,
% 3.18/1.60 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 3.18/1.60 ( ( secrecy_kKS @ X1 )
% 3.18/1.60 != ( secrecy_sKS @ X23 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_29_KS_Oinduct,axiom,
% 3.18/1.60 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 3.18/1.60 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 3.18/1.60 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 3.18/1.60 => ( P @ KS ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_30_KS_Oexhaust,axiom,
% 3.18/1.60 ! [Y: secrecy_KS] :
% 3.18/1.60 ( ! [X12: secrecy_Keys] :
% 3.18/1.60 ( Y
% 3.18/1.60 != ( secrecy_kKS @ X12 ) )
% 3.18/1.60 => ~ ! [X2: secrecy_Secrets] :
% 3.18/1.60 ( Y
% 3.18/1.60 != ( secrecy_sKS @ X2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_31_KS_Osimps_I6_J,axiom,
% 3.18/1.60 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X23: secrecy_Secrets] :
% 3.18/1.60 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X23 ) )
% 3.18/1.60 = ( F2 @ X23 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_32_KS_Osimps_I8_J,axiom,
% 3.18/1.60 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X23: secrecy_Secrets] :
% 3.18/1.60 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X23 ) )
% 3.18/1.60 = ( F2 @ X23 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_33_not__Cons__self2,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( cons @ A @ X3 @ Xs )
% 3.18/1.60 != Xs ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_34_strict__sorted_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 3.18/1.60 ( ( P @ ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A,Ys3: list @ A] :
% 3.18/1.60 ( ( P @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Ys3 ) ) )
% 3.18/1.60 => ( P @ A0 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_35_strict__sorted_Ocases,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [X3: list @ A] :
% 3.18/1.60 ( ( X3
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ~ ! [X: A,Ys3: list @ A] :
% 3.18/1.60 ( X3
% 3.18/1.60 != ( cons @ A @ X @ Ys3 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_36_map__tailrec__rev_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 3.18/1.60 ( ! [F: A > B,X_1: list @ B] : ( P @ F @ ( nil @ A ) @ X_1 )
% 3.18/1.60 => ( ! [F: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 3.18/1.60 ( ( P @ F @ As @ ( cons @ B @ ( F @ A3 ) @ Bs ) )
% 3.18/1.60 => ( P @ F @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 3.18/1.60 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_37_list__nonempty__induct,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A] :
% 3.18/1.60 ( ( Xs2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( P @ Xs2 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 3.18/1.60 => ( P @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_38_successively_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.18/1.60 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 3.18/1.60 => ( ! [P2: A > A > $o,X: A] : ( P @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ( ! [P2: A > A > $o,X: A,Y3: A,Xs2: list @ A] :
% 3.18/1.60 ( ( P @ P2 @ ( cons @ A @ Y3 @ Xs2 ) )
% 3.18/1.60 => ( P @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs2 ) ) ) )
% 3.18/1.60 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_39_arg__min__list_Oinduct,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType] :
% 3.18/1.60 ( ( linorder @ B )
% 3.18/1.60 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 3.18/1.60 ( ! [F: A > B,X: A] : ( P @ F @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ( ! [F: A > B,X: A,Y3: A,Zs: list @ A] :
% 3.18/1.60 ( ( P @ F @ ( cons @ A @ Y3 @ Zs ) )
% 3.18/1.60 => ( P @ F @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Zs ) ) ) )
% 3.18/1.60 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 3.18/1.60 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_40_remdups__adj_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 3.18/1.60 ( ( P @ ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A] :
% 3.18/1.60 ( ( ( X = Y3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 3.18/1.60 => ( ( ( X != Y3 )
% 3.18/1.60 => ( P @ ( cons @ A @ Y3 @ Xs2 ) ) )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) )
% 3.18/1.60 => ( P @ A0 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_41_sorted__wrt_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 3.18/1.60 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 3.18/1.60 => ( ! [P2: A > A > $o,X: A,Ys3: list @ A] :
% 3.18/1.60 ( ( P @ P2 @ Ys3 )
% 3.18/1.60 => ( P @ P2 @ ( cons @ A @ X @ Ys3 ) ) )
% 3.18/1.60 => ( P @ A0 @ A1 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_42_remdups__adj_Ocases,axiom,
% 3.18/1.60 ! [A: $tType,X3: list @ A] :
% 3.18/1.60 ( ( X3
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] :
% 3.18/1.60 ( X3
% 3.18/1.60 != ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 3.18/1.60 ( X3
% 3.18/1.60 != ( cons @ A @ X @ ( cons @ A @ Y3 @ Xs2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_43_transpose_Ocases,axiom,
% 3.18/1.60 ! [A: $tType,X3: list @ ( list @ A )] :
% 3.18/1.60 ( ( X3
% 3.18/1.60 != ( nil @ ( list @ A ) ) )
% 3.18/1.60 => ( ! [Xss: list @ ( list @ A )] :
% 3.18/1.60 ( X3
% 3.18/1.60 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 3.18/1.60 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 3.18/1.60 ( X3
% 3.18/1.60 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_44_mem__Collect__eq,axiom,
% 3.18/1.60 ! [A: $tType,A4: A,P: A > $o] :
% 3.18/1.60 ( ( member2 @ A @ A4 @ ( collect @ A @ P ) )
% 3.18/1.60 = ( P @ A4 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_45_Collect__mem__eq,axiom,
% 3.18/1.60 ! [A: $tType,A2: set @ A] :
% 3.18/1.60 ( ( collect @ A
% 3.18/1.60 @ ^ [X4: A] : ( member2 @ A @ X4 @ A2 ) )
% 3.18/1.60 = A2 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_46_Collect__cong,axiom,
% 3.18/1.60 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.18/1.60 ( ! [X: A] :
% 3.18/1.60 ( ( P @ X )
% 3.18/1.60 = ( Q @ X ) )
% 3.18/1.60 => ( ( collect @ A @ P )
% 3.18/1.60 = ( collect @ A @ Q ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_47_ext,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 3.18/1.60 ( ! [X: A] :
% 3.18/1.60 ( ( F3 @ X )
% 3.18/1.60 = ( G @ X ) )
% 3.18/1.60 => ( F3 = G ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_48_shuffles_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 3.18/1.60 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.18/1.60 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 3.18/1.60 ( ( P @ Xs2 @ ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) )
% 3.18/1.60 => ( P @ A0 @ A1 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_49_min__list_Oinduct,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 3.18/1.60 ( ! [X: A,Xs2: list @ A] :
% 3.18/1.60 ( ! [X213: A,X223: list @ A] :
% 3.18/1.60 ( ( Xs2
% 3.18/1.60 = ( cons @ A @ X213 @ X223 ) )
% 3.18/1.60 => ( P @ Xs2 ) )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 3.18/1.60 => ( ( P @ ( nil @ A ) )
% 3.18/1.60 => ( P @ A0 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_50_know_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 3.18/1.60 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.18/1.60 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 3.18/1.60 | ( member2 @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_51_Expression2KSL_Osimps_I1_J,axiom,
% 3.18/1.60 ( ( secrec1371625429on2KSL @ ( nil @ secrecy_Expression ) )
% 3.18/1.60 = ( nil @ secrecy_KS ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_52_insert__Nil,axiom,
% 3.18/1.60 ! [A: $tType,X3: A] :
% 3.18/1.60 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 3.18/1.60 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_53_list__ex1__simps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,P: A > $o] :
% 3.18/1.60 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_54_eoutKnowsECorrect__def,axiom,
% 3.18/1.60 ( knowle1893229345orrect
% 3.18/1.60 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 3.18/1.60 ( ( eout @ C2 @ E2 )
% 3.18/1.60 = ( ? [K3: secrecy_Keys] :
% 3.18/1.60 ( ( E2
% 3.18/1.60 = ( secrecy_kE @ K3 ) )
% 3.18/1.60 & ( member2 @ secrecy_Keys @ K3 @ ( specKeys @ C2 ) ) )
% 3.18/1.60 | ? [S: secrecy_Secrets] :
% 3.18/1.60 ( ( E2
% 3.18/1.60 = ( secrecy_sE @ S ) )
% 3.18/1.60 & ( member2 @ secrecy_Secrets @ S @ ( specSecrets @ C2 ) ) )
% 3.18/1.60 | ( knowle2055185861_knows @ C2 @ ( cons @ secrecy_Expression @ E2 @ ( nil @ secrecy_Expression ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_55_eoutKnowsECorrect__L1,axiom,
% 3.18/1.60 ! [C: secrecy_specID,E: secrecy_Expression] :
% 3.18/1.60 ( ( knowle1893229345orrect @ C @ E )
% 3.18/1.60 => ( ( eout @ C @ E )
% 3.18/1.60 => ( ? [K4: secrecy_Keys] :
% 3.18/1.60 ( ( E
% 3.18/1.60 = ( secrecy_kE @ K4 ) )
% 3.18/1.60 & ( member2 @ secrecy_Keys @ K4 @ ( specKeys @ C ) ) )
% 3.18/1.60 | ? [S2: secrecy_Secrets] :
% 3.18/1.60 ( ( E
% 3.18/1.60 = ( secrecy_sE @ S2 ) )
% 3.18/1.60 & ( member2 @ secrecy_Secrets @ S2 @ ( specSecrets @ C ) ) )
% 3.18/1.60 | ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ E @ ( nil @ secrecy_Expression ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_56_map__tailrec__rev_Oelims,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,X3: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 3.18/1.60 ( ( ( map_tailrec_rev @ A @ B @ X3 @ Xa @ Xb )
% 3.18/1.60 = Y )
% 3.18/1.60 => ( ( ( Xa
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( Y != Xb ) )
% 3.18/1.60 => ~ ! [A3: A,As: list @ A] :
% 3.18/1.60 ( ( Xa
% 3.18/1.60 = ( cons @ A @ A3 @ As ) )
% 3.18/1.60 => ( Y
% 3.18/1.60 != ( map_tailrec_rev @ A @ B @ X3 @ As @ ( cons @ B @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_57_arg__min__list_Osimps_I1_J,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType] :
% 3.18/1.60 ( ( linorder @ B )
% 3.18/1.60 => ! [F3: A > B,X3: A] :
% 3.18/1.60 ( ( arg_min_list @ A @ B @ F3 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 3.18/1.60 = X3 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_58_notSpecKeysSecretsExpr__L1,axiom,
% 3.18/1.60 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 3.18/1.60 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 3.18/1.60 => ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ ( nil @ secrecy_Expression ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_59_Expression_Oinject_I2_J,axiom,
% 3.18/1.60 ! [X23: secrecy_Secrets,Y23: secrecy_Secrets] :
% 3.18/1.60 ( ( ( secrecy_sE @ X23 )
% 3.18/1.60 = ( secrecy_sE @ Y23 ) )
% 3.18/1.60 = ( X23 = Y23 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_60_Expression_Odistinct_I1_J,axiom,
% 3.18/1.60 ! [X1: secrecy_Keys,X23: secrecy_Secrets] :
% 3.18/1.60 ( ( secrecy_kE @ X1 )
% 3.18/1.60 != ( secrecy_sE @ X23 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_61_notSpecKeysSecretsExpr__L2,axiom,
% 3.18/1.60 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 3.18/1.60 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 3.18/1.60 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_62_map__tailrec__rev_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,F3: A > B,A4: A,As2: list @ A,Bs2: list @ B] :
% 3.18/1.60 ( ( map_tailrec_rev @ A @ B @ F3 @ ( cons @ A @ A4 @ As2 ) @ Bs2 )
% 3.18/1.60 = ( map_tailrec_rev @ A @ B @ F3 @ As2 @ ( cons @ B @ ( F3 @ A4 ) @ Bs2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_63_map__tailrec__rev_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,F3: A > B,Bs2: list @ B] :
% 3.18/1.60 ( ( map_tailrec_rev @ A @ B @ F3 @ ( nil @ A ) @ Bs2 )
% 3.18/1.60 = Bs2 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_64_KS2Expression_Osimps_I2_J,axiom,
% 3.18/1.60 ! [M: secrecy_Secrets] :
% 3.18/1.60 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 3.18/1.60 = ( secrecy_sE @ M ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_65_eoutKnowCorrect__L1s,axiom,
% 3.18/1.60 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 3.18/1.60 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 3.18/1.60 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 3.18/1.60 => ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 3.18/1.60 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_66_eout__know__s,axiom,
% 3.18/1.60 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 3.18/1.60 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 3.18/1.60 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 3.18/1.60 = ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 3.18/1.60 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_67_product__lists_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 3.18/1.60 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_68_subseqs_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( subseqs @ A @ ( nil @ A ) )
% 3.18/1.60 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_69_DecrEnc,axiom,
% 3.18/1.60 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list @ secrecy_Expression] :
% 3.18/1.60 ( ( encrDecrKeys @ K12 @ K22 )
% 3.18/1.60 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 3.18/1.60 = E3 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_70_ExtSign,axiom,
% 3.18/1.60 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list @ secrecy_Expression] :
% 3.18/1.60 ( ( encrDecrKeys @ K12 @ K22 )
% 3.18/1.60 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 3.18/1.60 = E3 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_71_notSpecKeysSecretsExpr__def,axiom,
% 3.18/1.60 ( notSpe1586871396tsExpr
% 3.18/1.60 = ( ^ [P3: secrecy_specID,E2: list @ secrecy_Expression] :
% 3.18/1.60 ( ! [X4: secrecy_Keys] :
% 3.18/1.60 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X4 ) @ E2 )
% 3.18/1.60 => ~ ( member2 @ secrecy_KS @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 3.18/1.60 & ! [Y2: secrecy_Secrets] :
% 3.18/1.60 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y2 ) @ E2 )
% 3.18/1.60 => ~ ( member2 @ secrecy_KS @ ( secrecy_sKS @ Y2 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_72_ord_Olexordp__eq__simps_I3_J,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A] :
% 3.18/1.60 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_73_bind__simps_I1_J,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 3.18/1.60 ( ( bind @ B @ A @ ( nil @ B ) @ F3 )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_74_ord_Olexordp__eq__simps_I4_J,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 3.18/1.60 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 3.18/1.60 = ( ( Less @ X3 @ Y )
% 3.18/1.60 | ( ~ ( Less @ Y @ X3 )
% 3.18/1.60 & ( lexordp_eq @ A @ Less @ Xs @ Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_75_ord_Olexordp__eq__simps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_76_ord_Olexordp__eq__simps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 3.18/1.60 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_77_ord_Olexordp__eq_Ocong,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( lexordp_eq @ A )
% 3.18/1.60 = ( lexordp_eq @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_78_ord_Olexordp__eq__refl,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_79_ord_Olexordp__eq_OCons__eq,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ~ ( Less @ X3 @ Y )
% 3.18/1.60 => ( ~ ( Less @ Y @ X3 )
% 3.18/1.60 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys2 )
% 3.18/1.60 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_80_ord_Olexordp__eq_OCons,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( Less @ X3 @ Y )
% 3.18/1.60 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_81_ord_Olexordp__eq_ONil,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_82_ord_Olexordp__eq_Oinducts,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 3.18/1.60 ( ( lexordp_eq @ A @ Less @ X1 @ X23 )
% 3.18/1.60 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ( Less @ X @ Y3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ~ ( Less @ X @ Y3 )
% 3.18/1.60 => ( ~ ( Less @ Y3 @ X )
% 3.18/1.60 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 )
% 3.18/1.60 => ( ( P @ Xs2 @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) )
% 3.18/1.60 => ( P @ X1 @ X23 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_83_ord_Olexordp__eq_Osimps,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( lexordp_eq @ A )
% 3.18/1.60 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 3.18/1.60 ( ? [Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( A23 = Ys ) )
% 3.18/1.60 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) )
% 3.18/1.60 & ( Less2 @ X4 @ Y2 ) )
% 3.18/1.60 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) )
% 3.18/1.60 & ~ ( Less2 @ X4 @ Y2 )
% 3.18/1.60 & ~ ( Less2 @ Y2 @ X4 )
% 3.18/1.60 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_84_ord_Olexordp__eq_Ocases,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 3.18/1.60 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 3.18/1.60 => ( ( A1
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] :
% 3.18/1.60 ( ? [Xs2: list @ A] :
% 3.18/1.60 ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Y3: A] :
% 3.18/1.60 ( ? [Ys3: list @ A] :
% 3.18/1.60 ( A22
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ~ ( Less @ X @ Y3 ) ) )
% 3.18/1.60 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 3.18/1.60 ( ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Ys3: list @ A] :
% 3.18/1.60 ( ( A22
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ~ ( Less @ X @ Y3 )
% 3.18/1.60 => ( ~ ( Less @ Y3 @ X )
% 3.18/1.60 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_85_mem_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: A] :
% 3.18/1.60 ~ ( mem @ A @ X3 @ ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_86_mem_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Y: A,L: list @ A] :
% 3.18/1.60 ( ( mem @ A @ X3 @ ( cons @ A @ Y @ L ) )
% 3.18/1.60 = ( ( X3 = Y )
% 3.18/1.60 | ( mem @ A @ X3 @ L ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_87_listrelp_Oinducts,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,R: A > B > $o,X1: list @ A,X23: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 3.18/1.60 ( ( listrelp @ A @ B @ R @ X1 @ X23 )
% 3.18/1.60 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 3.18/1.60 => ( ! [X: A,Y3: B,Xs2: list @ A,Ys3: list @ B] :
% 3.18/1.60 ( ( R @ X @ Y3 )
% 3.18/1.60 => ( ( listrelp @ A @ B @ R @ Xs2 @ Ys3 )
% 3.18/1.60 => ( ( P @ Xs2 @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y3 @ Ys3 ) ) ) ) )
% 3.18/1.60 => ( P @ X1 @ X23 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_88_listrelp_Osimps,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType] :
% 3.18/1.60 ( ( listrelp @ A @ B )
% 3.18/1.60 = ( ^ [R2: A > B > $o,A12: list @ A,A23: list @ B] :
% 3.18/1.60 ( ( ( A12
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( nil @ B ) ) )
% 3.18/1.60 | ? [X4: A,Y2: B,Xs3: list @ A,Ys: list @ B] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ B @ Y2 @ Ys ) )
% 3.18/1.60 & ( R2 @ X4 @ Y2 )
% 3.18/1.60 & ( listrelp @ A @ B @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_89_listrelp_Ocases,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,R: A > B > $o,A1: list @ A,A22: list @ B] :
% 3.18/1.60 ( ( listrelp @ A @ B @ R @ A1 @ A22 )
% 3.18/1.60 => ( ( ( A1
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( A22
% 3.18/1.60 != ( nil @ B ) ) )
% 3.18/1.60 => ~ ! [X: A,Y3: B,Xs2: list @ A] :
% 3.18/1.60 ( ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Ys3: list @ B] :
% 3.18/1.60 ( ( A22
% 3.18/1.60 = ( cons @ B @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ( R @ X @ Y3 )
% 3.18/1.60 => ~ ( listrelp @ A @ B @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_90_lexordp__eq__simps_I3_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Xs: list @ A] :
% 3.18/1.60 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_91_lexordp__eq__simps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Xs: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_92_lexordp__eq__simps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_93_lexordp__eq__antisym,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ( ord_lexordp_eq @ A @ Ys2 @ Xs )
% 3.18/1.60 => ( Xs = Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_94_lexordp__eq__linear,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 3.18/1.60 | ( ord_lexordp_eq @ A @ Ys2 @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_95_lexordp__eq__trans,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ( ord_lexordp_eq @ A @ Ys2 @ Zs2 )
% 3.18/1.60 => ( ord_lexordp_eq @ A @ Xs @ Zs2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_96_lexordp__eq__refl,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_97_lexordp__eq_ONil,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_98_listrelp_OCons,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y: B,Xs: list @ A,Ys2: list @ B] :
% 3.18/1.60 ( ( R @ X3 @ Y )
% 3.18/1.60 => ( ( listrelp @ A @ B @ R @ Xs @ Ys2 )
% 3.18/1.60 => ( listrelp @ A @ B @ R @ ( cons @ A @ X3 @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_99_listrelp_ONil,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,R: A > B > $o] : ( listrelp @ A @ B @ R @ ( nil @ A ) @ ( nil @ B ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_100_mem__memS__eq,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( mem @ A )
% 3.18/1.60 = ( memS @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_101_mem__notdisjoint,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,L1: list @ A,L2: list @ A] :
% 3.18/1.60 ( ( mem @ A @ X3 @ L1 )
% 3.18/1.60 => ( ( mem @ A @ X3 @ L2 )
% 3.18/1.60 => ~ ( disjoint @ A @ L1 @ L2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_102_mem__notdisjoint2,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,Schedule: B > ( list @ A ),A2: B,B2: B,X3: A] :
% 3.18/1.60 ( ( disjoint @ A @ ( Schedule @ A2 ) @ ( Schedule @ B2 ) )
% 3.18/1.60 => ( ( mem @ A @ X3 @ ( Schedule @ A2 ) )
% 3.18/1.60 => ~ ( mem @ A @ X3 @ ( Schedule @ B2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_103_lexordp__eq_Ocases,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [A1: list @ A,A22: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ A1 @ A22 )
% 3.18/1.60 => ( ( A1
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] :
% 3.18/1.60 ( ? [Xs2: list @ A] :
% 3.18/1.60 ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Y3: A] :
% 3.18/1.60 ( ? [Ys3: list @ A] :
% 3.18/1.60 ( A22
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ~ ( ord_less @ A @ X @ Y3 ) ) )
% 3.18/1.60 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 3.18/1.60 ( ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Ys3: list @ A] :
% 3.18/1.60 ( ( A22
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ~ ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( ~ ( ord_less @ A @ Y3 @ X )
% 3.18/1.60 => ~ ( ord_lexordp_eq @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_104_lexordp__eq_Osimps,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ( ( ord_lexordp_eq @ A )
% 3.18/1.60 = ( ^ [A12: list @ A,A23: list @ A] :
% 3.18/1.60 ( ? [Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( A23 = Ys ) )
% 3.18/1.60 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) )
% 3.18/1.60 & ( ord_less @ A @ X4 @ Y2 ) )
% 3.18/1.60 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) )
% 3.18/1.60 & ~ ( ord_less @ A @ X4 @ Y2 )
% 3.18/1.60 & ~ ( ord_less @ A @ Y2 @ X4 )
% 3.18/1.60 & ( ord_lexordp_eq @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_105_lexordp__eq__simps_I4_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 3.18/1.60 = ( ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 | ( ~ ( ord_less @ A @ Y @ X3 )
% 3.18/1.60 & ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_106_lexordp__eq_OCons__eq,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 => ( ~ ( ord_less @ A @ Y @ X3 )
% 3.18/1.60 => ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_107_lexordp__eq_OCons,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 => ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_108_lexordp__eq_Oinducts,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ X1 @ X23 )
% 3.18/1.60 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ~ ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( ~ ( ord_less @ A @ Y3 @ X )
% 3.18/1.60 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys3 )
% 3.18/1.60 => ( ( P @ Xs2 @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) )
% 3.18/1.60 => ( P @ X1 @ X23 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_109_lexordp_Ocases,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [A1: list @ A,A22: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ A1 @ A22 )
% 3.18/1.60 => ( ( ( A1
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ! [Y3: A,Ys3: list @ A] :
% 3.18/1.60 ( A22
% 3.18/1.60 != ( cons @ A @ Y3 @ Ys3 ) ) )
% 3.18/1.60 => ( ! [X: A] :
% 3.18/1.60 ( ? [Xs2: list @ A] :
% 3.18/1.60 ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Y3: A] :
% 3.18/1.60 ( ? [Ys3: list @ A] :
% 3.18/1.60 ( A22
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ~ ( ord_less @ A @ X @ Y3 ) ) )
% 3.18/1.60 => ~ ! [X: A,Y3: A,Xs2: list @ A] :
% 3.18/1.60 ( ( A1
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ! [Ys3: list @ A] :
% 3.18/1.60 ( ( A22
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ~ ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( ~ ( ord_less @ A @ Y3 @ X )
% 3.18/1.60 => ~ ( ord_lexordp @ A @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_110_lexordp_Osimps,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ( ( ord_lexordp @ A )
% 3.18/1.60 = ( ^ [A12: list @ A,A23: list @ A] :
% 3.18/1.60 ( ? [Y2: A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) ) )
% 3.18/1.60 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) )
% 3.18/1.60 & ( ord_less @ A @ X4 @ Y2 ) )
% 3.18/1.60 | ? [X4: A,Y2: A,Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( A12
% 3.18/1.60 = ( cons @ A @ X4 @ Xs3 ) )
% 3.18/1.60 & ( A23
% 3.18/1.60 = ( cons @ A @ Y2 @ Ys ) )
% 3.18/1.60 & ~ ( ord_less @ A @ X4 @ Y2 )
% 3.18/1.60 & ~ ( ord_less @ A @ Y2 @ X4 )
% 3.18/1.60 & ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_111_lexordp_Oinducts,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X1: list @ A,X23: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 3.18/1.60 ( ( ord_lexordp @ A @ X1 @ X23 )
% 3.18/1.60 => ( ! [Y3: A,Ys3: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 3.18/1.60 => ( ! [X: A,Y3: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ~ ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( ~ ( ord_less @ A @ Y3 @ X )
% 3.18/1.60 => ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 3.18/1.60 => ( ( P @ Xs2 @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) ) ) ) )
% 3.18/1.60 => ( P @ X1 @ X23 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_112_lexordp__cases,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ! [Y3: A,Ys4: list @ A] :
% 3.18/1.60 ( Ys2
% 3.18/1.60 != ( cons @ A @ Y3 @ Ys4 ) ) )
% 3.18/1.60 => ( ! [X: A] :
% 3.18/1.60 ( ? [Xs4: list @ A] :
% 3.18/1.60 ( Xs
% 3.18/1.60 = ( cons @ A @ X @ Xs4 ) )
% 3.18/1.60 => ! [Y3: A] :
% 3.18/1.60 ( ? [Ys4: list @ A] :
% 3.18/1.60 ( Ys2
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys4 ) )
% 3.18/1.60 => ~ ( ord_less @ A @ X @ Y3 ) ) )
% 3.18/1.60 => ~ ! [X: A,Xs4: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 = ( cons @ A @ X @ Xs4 ) )
% 3.18/1.60 => ! [Ys4: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 = ( cons @ A @ X @ Ys4 ) )
% 3.18/1.60 => ~ ( ord_lexordp @ A @ Xs4 @ Ys4 ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_113_lexordp__induct,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ! [Y3: A,Ys3: list @ A] : ( P @ ( nil @ A ) @ ( cons @ A @ Y3 @ Ys3 ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A,Y3: A,Ys3: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ X @ Y3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y3 @ Ys3 ) ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A,Ys3: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs2 @ Ys3 )
% 3.18/1.60 => ( ( P @ Xs2 @ Ys3 )
% 3.18/1.60 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ X @ Ys3 ) ) ) )
% 3.18/1.60 => ( P @ Xs @ Ys2 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_114_lexordp__simps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Xs: list @ A] :
% 3.18/1.60 ~ ( ord_lexordp @ A @ Xs @ ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_115_lexordp__simps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ ( nil @ A ) @ Ys2 )
% 3.18/1.60 = ( Ys2
% 3.18/1.60 != ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_116_lexordp__simps_I3_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 3.18/1.60 = ( ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 | ( ~ ( ord_less @ A @ Y @ X3 )
% 3.18/1.60 & ( ord_lexordp @ A @ Xs @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_117_lexordp__irreflexive_H,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( order @ A )
% 3.18/1.60 => ! [Xs: list @ A] :
% 3.18/1.60 ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_118_lexordp__linear,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 | ( Xs = Ys2 )
% 3.18/1.60 | ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_119_lexordp__trans,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ( ord_lexordp @ A @ Ys2 @ Zs2 )
% 3.18/1.60 => ( ord_lexordp @ A @ Xs @ Zs2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_120_lexordp__antisym,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( order @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 => ~ ( ord_lexordp @ A @ Ys2 @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_121_lexordp__irreflexive,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Xs: list @ A] :
% 3.18/1.60 ( ! [X: A] :
% 3.18/1.60 ~ ( ord_less @ A @ X @ X )
% 3.18/1.60 => ~ ( ord_lexordp @ A @ Xs @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_122_lexordp__conv__lexordp__eq,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ( ( ord_lexordp @ A )
% 3.18/1.60 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( ord_lexordp_eq @ A @ Xs3 @ Ys )
% 3.18/1.60 & ~ ( ord_lexordp_eq @ A @ Ys @ Xs3 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_123_lexordp__eq__conv__lexord,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ( ( ord_lexordp_eq @ A )
% 3.18/1.60 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ( Xs3 = Ys )
% 3.18/1.60 | ( ord_lexordp @ A @ Xs3 @ Ys ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_124_lexordp__into__lexordp__eq,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ord_lexordp_eq @ A @ Xs @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_125_lexordp_OCons__eq,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ~ ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 => ( ~ ( ord_less @ A @ Y @ X3 )
% 3.18/1.60 => ( ( ord_lexordp @ A @ Xs @ Ys2 )
% 3.18/1.60 => ( ord_lexordp @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_126_lexordp_OCons,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 => ( ord_lexordp @ A @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_127_lexordp_ONil,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Y: A,Ys2: list @ A] : ( ord_lexordp @ A @ ( nil @ A ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_128_member__rec_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,Y: A] :
% 3.18/1.60 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_129_member__rec_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A,Y: A] :
% 3.18/1.60 ( ( member @ A @ ( cons @ A @ X3 @ Xs ) @ Y )
% 3.18/1.60 = ( ( X3 = Y )
% 3.18/1.60 | ( member @ A @ Xs @ Y ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_130_splice_Oelims,axiom,
% 3.18/1.60 ! [A: $tType,X3: list @ A,Xa: list @ A,Y: list @ A] :
% 3.18/1.60 ( ( ( splice @ A @ X3 @ Xa )
% 3.18/1.60 = Y )
% 3.18/1.60 => ( ( ( X3
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( Y != Xa ) )
% 3.18/1.60 => ~ ! [X: A,Xs2: list @ A] :
% 3.18/1.60 ( ( X3
% 3.18/1.60 = ( cons @ A @ X @ Xs2 ) )
% 3.18/1.60 => ( Y
% 3.18/1.60 != ( cons @ A @ X @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_131_lexordp__iff,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( linorder @ A )
% 3.18/1.60 => ( ( ord_lexordp @ A )
% 3.18/1.60 = ( ^ [Xs3: list @ A,Ys: list @ A] :
% 3.18/1.60 ( ? [X4: A,Vs: list @ A] :
% 3.18/1.60 ( Ys
% 3.18/1.60 = ( append @ A @ Xs3 @ ( cons @ A @ X4 @ Vs ) ) )
% 3.18/1.60 | ? [Us: list @ A,A5: A,B3: A,Vs: list @ A,Ws: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ A5 @ B3 )
% 3.18/1.60 & ( Xs3
% 3.18/1.60 = ( append @ A @ Us @ ( cons @ A @ A5 @ Vs ) ) )
% 3.18/1.60 & ( Ys
% 3.18/1.60 = ( append @ A @ Us @ ( cons @ A @ B3 @ Ws ) ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_132_append_Oassoc,axiom,
% 3.18/1.60 ! [A: $tType,A4: list @ A,B4: list @ A,C3: list @ A] :
% 3.18/1.60 ( ( append @ A @ ( append @ A @ A4 @ B4 ) @ C3 )
% 3.18/1.60 = ( append @ A @ A4 @ ( append @ A @ B4 @ C3 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_133_append__assoc,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs2 )
% 3.18/1.60 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_134_append__same__eq,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Ys2 @ Xs )
% 3.18/1.60 = ( append @ A @ Zs2 @ Xs ) )
% 3.18/1.60 = ( Ys2 = Zs2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_135_same__append__eq,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ Ys2 )
% 3.18/1.60 = ( append @ A @ Xs @ Zs2 ) )
% 3.18/1.60 = ( Ys2 = Zs2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_136_append_Oright__neutral,axiom,
% 3.18/1.60 ! [A: $tType,A4: list @ A] :
% 3.18/1.60 ( ( append @ A @ A4 @ ( nil @ A ) )
% 3.18/1.60 = A4 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_137_append__is__Nil__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ Ys2 )
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_138_Nil__is__append__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( nil @ A )
% 3.18/1.60 = ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_139_self__append__conv2,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 = ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_140_append__self__conv2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ Ys2 )
% 3.18/1.60 = Ys2 )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_141_self__append__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 = ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( Ys2
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_142_append__self__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ Ys2 )
% 3.18/1.60 = Xs )
% 3.18/1.60 = ( Ys2
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_143_append__Nil2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( append @ A @ Xs @ ( nil @ A ) )
% 3.18/1.60 = Xs ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_144_split__Nil__iff,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( splice @ A @ Xs @ Ys2 )
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_145_splice__Nil2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 3.18/1.60 = Xs ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_146_append1__eq__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A,Y: A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 3.18/1.60 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 3.18/1.60 = ( ( Xs = Ys2 )
% 3.18/1.60 & ( X3 = Y ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_147_bind__simps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,X3: B,Xs: list @ B,F3: B > ( list @ A )] :
% 3.18/1.60 ( ( bind @ B @ A @ ( cons @ B @ X3 @ Xs ) @ F3 )
% 3.18/1.60 = ( append @ A @ ( F3 @ X3 ) @ ( bind @ B @ A @ Xs @ F3 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_148_lexordp__append__leftI,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Us2: list @ A,Vs2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ Us2 @ Vs2 )
% 3.18/1.60 => ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_149_append__eq__appendI,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys2: list @ A,Us2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ Xs1 )
% 3.18/1.60 = Zs2 )
% 3.18/1.60 => ( ( Ys2
% 3.18/1.60 = ( append @ A @ Xs1 @ Us2 ) )
% 3.18/1.60 => ( ( append @ A @ Xs @ Ys2 )
% 3.18/1.60 = ( append @ A @ Zs2 @ Us2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_150_append__eq__append__conv2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A,Ts: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ Ys2 )
% 3.18/1.60 = ( append @ A @ Zs2 @ Ts ) )
% 3.18/1.60 = ( ? [Us: list @ A] :
% 3.18/1.60 ( ( ( Xs
% 3.18/1.60 = ( append @ A @ Zs2 @ Us ) )
% 3.18/1.60 & ( ( append @ A @ Us @ Ys2 )
% 3.18/1.60 = Ts ) )
% 3.18/1.60 | ( ( ( append @ A @ Xs @ Us )
% 3.18/1.60 = Zs2 )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( append @ A @ Us @ Ts ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_151_eq__Nil__appendI,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( Xs = Ys2 )
% 3.18/1.60 => ( Xs
% 3.18/1.60 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_152_append__Nil,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A] :
% 3.18/1.60 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 3.18/1.60 = Ys2 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_153_append_Oleft__neutral,axiom,
% 3.18/1.60 ! [A: $tType,A4: list @ A] :
% 3.18/1.60 ( ( append @ A @ ( nil @ A ) @ A4 )
% 3.18/1.60 = A4 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_154_Cons__eq__appendI,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ( cons @ A @ X3 @ Xs1 )
% 3.18/1.60 = Ys2 )
% 3.18/1.60 => ( ( Xs
% 3.18/1.60 = ( append @ A @ Xs1 @ Zs2 ) )
% 3.18/1.60 => ( ( cons @ A @ X3 @ Xs )
% 3.18/1.60 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_155_append__Cons,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( append @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 3.18/1.60 = ( cons @ A @ X3 @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_156_lexordp__eq__pref,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [U: list @ A,V: list @ A] : ( ord_lexordp_eq @ A @ U @ ( append @ A @ U @ V ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_157_ord_Olexordp__eq__pref,axiom,
% 3.18/1.60 ! [A: $tType,Less: A > A > $o,U: list @ A,V: list @ A] : ( lexordp_eq @ A @ Less @ U @ ( append @ A @ U @ V ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_158_knows2b,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,E: list @ secrecy_Expression,E1: list @ secrecy_Expression] :
% 3.18/1.60 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E @ E1 ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_159_knows2a,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E: list @ secrecy_Expression] :
% 3.18/1.60 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_160_knows3,axiom,
% 3.18/1.60 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E22: list @ secrecy_Expression] :
% 3.18/1.60 ( ( ( knowle2055185861_knows @ A2 @ E1 )
% 3.18/1.60 & ( knowle2055185861_knows @ A2 @ E22 ) )
% 3.18/1.60 => ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E22 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_161_splice_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( splice @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 3.18/1.60 = ( cons @ A @ X3 @ ( splice @ A @ Ys2 @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_162_splice_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A] :
% 3.18/1.60 ( ( splice @ A @ ( nil @ A ) @ Ys2 )
% 3.18/1.60 = Ys2 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_163_rev__nonempty__induct,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A] :
% 3.18/1.60 ( ( Xs2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( P @ Xs2 )
% 3.18/1.60 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) )
% 3.18/1.60 => ( P @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_164_append__eq__Cons__conv,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Zs2: list @ A,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Ys2 @ Zs2 )
% 3.18/1.60 = ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( ( ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( Zs2
% 3.18/1.60 = ( cons @ A @ X3 @ Xs ) ) )
% 3.18/1.60 | ? [Ys5: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 = ( cons @ A @ X3 @ Ys5 ) )
% 3.18/1.60 & ( ( append @ A @ Ys5 @ Zs2 )
% 3.18/1.60 = Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_165_Cons__eq__append__conv,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ( cons @ A @ X3 @ Xs )
% 3.18/1.60 = ( append @ A @ Ys2 @ Zs2 ) )
% 3.18/1.60 = ( ( ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( ( cons @ A @ X3 @ Xs )
% 3.18/1.60 = Zs2 ) )
% 3.18/1.60 | ? [Ys5: list @ A] :
% 3.18/1.60 ( ( ( cons @ A @ X3 @ Ys5 )
% 3.18/1.60 = Ys2 )
% 3.18/1.60 & ( Xs
% 3.18/1.60 = ( append @ A @ Ys5 @ Zs2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_166_rev__exhaust,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ~ ! [Ys3: list @ A,Y3: A] :
% 3.18/1.60 ( Xs
% 3.18/1.60 != ( append @ A @ Ys3 @ ( cons @ A @ Y3 @ ( nil @ A ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_167_rev__induct,axiom,
% 3.18/1.60 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 3.18/1.60 ( ( P @ ( nil @ A ) )
% 3.18/1.60 => ( ! [X: A,Xs2: list @ A] :
% 3.18/1.60 ( ( P @ Xs2 )
% 3.18/1.60 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) )
% 3.18/1.60 => ( P @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_168_lexordp__append__leftD,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Xs: list @ A,Us2: list @ A,Vs2: list @ A] :
% 3.18/1.60 ( ( ord_lexordp @ A @ ( append @ A @ Xs @ Us2 ) @ ( append @ A @ Xs @ Vs2 ) )
% 3.18/1.60 => ( ! [A3: A] :
% 3.18/1.60 ~ ( ord_less @ A @ A3 @ A3 )
% 3.18/1.60 => ( ord_lexordp @ A @ Us2 @ Vs2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_169_lexordp__append__rightI,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [Ys2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ord_lexordp @ A @ Xs @ ( append @ A @ Xs @ Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_170_lexordp__append__left__rightI,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( ord @ A )
% 3.18/1.60 => ! [X3: A,Y: A,Us2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ord_less @ A @ X3 @ Y )
% 3.18/1.60 => ( ord_lexordp @ A @ ( append @ A @ Us2 @ ( cons @ A @ X3 @ Xs ) ) @ ( append @ A @ Us2 @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_171_maps__simps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,F3: B > ( list @ A ),X3: B,Xs: list @ B] :
% 3.18/1.60 ( ( maps @ B @ A @ F3 @ ( cons @ B @ X3 @ Xs ) )
% 3.18/1.60 = ( append @ A @ ( F3 @ X3 ) @ ( maps @ B @ A @ F3 @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_172_concat__eq__append__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ( concat @ A @ Xss2 )
% 3.18/1.60 = ( append @ A @ Ys2 @ Zs2 ) )
% 3.18/1.60 = ( ( ( Xss2
% 3.18/1.60 = ( nil @ ( list @ A ) ) )
% 3.18/1.60 => ( ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( Zs2
% 3.18/1.60 = ( nil @ A ) ) ) )
% 3.18/1.60 & ( ( Xss2
% 3.18/1.60 != ( nil @ ( list @ A ) ) )
% 3.18/1.60 => ? [Xss1: list @ ( list @ A ),Xs3: list @ A,Xs5: list @ A,Xss22: list @ ( list @ A )] :
% 3.18/1.60 ( ( Xss2
% 3.18/1.60 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs3 @ Xs5 ) @ Xss22 ) ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs3 ) )
% 3.18/1.60 & ( Zs2
% 3.18/1.60 = ( append @ A @ Xs5 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_173_rotate1_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( rotate1 @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_174_butlast__snoc,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 3.18/1.60 = Xs ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_175_rotate1__is__Nil__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( ( rotate1 @ A @ Xs )
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_176_concat__append,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 3.18/1.60 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys2 ) )
% 3.18/1.60 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_177_butlast_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( butlast @ A @ ( nil @ A ) )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_178_rotate1_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( rotate1 @ A @ ( nil @ A ) )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_179_butlast_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( nil @ A ) ) )
% 3.18/1.60 & ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( cons @ A @ X3 @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_180_concat_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_181_butlast__append,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( butlast @ A @ Xs ) ) )
% 3.18/1.60 & ( ( Ys2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( append @ A @ Xs @ ( butlast @ A @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_182_concat_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: list @ A,Xs: list @ ( list @ A )] :
% 3.18/1.60 ( ( concat @ A @ ( cons @ ( list @ A ) @ X3 @ Xs ) )
% 3.18/1.60 = ( append @ A @ X3 @ ( concat @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_183_maps__simps_I2_J,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 3.18/1.60 ( ( maps @ B @ A @ F3 @ ( nil @ B ) )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_184_concat__eq__appendD,axiom,
% 3.18/1.60 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 3.18/1.60 ( ( ( concat @ A @ Xss2 )
% 3.18/1.60 = ( append @ A @ Ys2 @ Zs2 ) )
% 3.18/1.60 => ( ( Xss2
% 3.18/1.60 != ( nil @ ( list @ A ) ) )
% 3.18/1.60 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs4: list @ A,Xss23: list @ ( list @ A )] :
% 3.18/1.60 ( ( Xss2
% 3.18/1.60 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs4 ) @ Xss23 ) ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 3.18/1.60 & ( Zs2
% 3.18/1.60 = ( append @ A @ Xs4 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_185_append__butlast__last__id,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 3.18/1.60 = Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_186_snoc__eq__iff__butlast,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 3.18/1.60 = Ys2 )
% 3.18/1.60 = ( ( Ys2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 & ( ( butlast @ A @ Ys2 )
% 3.18/1.60 = Xs )
% 3.18/1.60 & ( ( last @ A @ Ys2 )
% 3.18/1.60 = X3 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_187_last__snoc,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 3.18/1.60 = X3 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_188_last__appendR,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( last @ A @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_189_last__appendL,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( last @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_190_last__ConsR,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( last @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_191_last__ConsL,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = X3 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_192_last_Osimps,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = X3 ) )
% 3.18/1.60 & ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( last @ A @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_193_last__append,axiom,
% 3.18/1.60 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 3.18/1.60 ( ( ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( last @ A @ Xs ) ) )
% 3.18/1.60 & ( ( Ys2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( last @ A @ Ys2 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_194_longest__common__suffix,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ? [Ss: list @ A,Xs4: list @ A,Ys4: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 = ( append @ A @ Xs4 @ Ss ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( append @ A @ Ys4 @ Ss ) )
% 3.18/1.60 & ( ( Xs4
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( Ys4
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( ( last @ A @ Xs4 )
% 3.18/1.60 != ( last @ A @ Ys4 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_195_concat__conv__foldr,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( concat @ A )
% 3.18/1.60 = ( ^ [Xss3: list @ ( list @ A )] : ( foldr @ ( list @ A ) @ ( list @ A ) @ ( append @ A ) @ Xss3 @ ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_196_SuccD,axiom,
% 3.18/1.60 ! [A: $tType,K: A,Kl: set @ ( list @ A ),Kl2: list @ A] :
% 3.18/1.60 ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) )
% 3.18/1.60 => ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_197_foldr__append,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,F3: B > A > A,Xs: list @ B,Ys2: list @ B,A4: A] :
% 3.18/1.60 ( ( foldr @ B @ A @ F3 @ ( append @ B @ Xs @ Ys2 ) @ A4 )
% 3.18/1.60 = ( foldr @ B @ A @ F3 @ Xs @ ( foldr @ B @ A @ F3 @ Ys2 @ A4 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_198_SuccI,axiom,
% 3.18/1.60 ! [A: $tType,Kl2: list @ A,K: A,Kl: set @ ( list @ A )] :
% 3.18/1.60 ( ( member2 @ ( list @ A ) @ ( append @ A @ Kl2 @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl )
% 3.18/1.60 => ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ Kl2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_199_shift__def,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType] :
% 3.18/1.60 ( ( bNF_Greatest_shift @ A @ B )
% 3.18/1.60 = ( ^ [Lab: ( list @ A ) > B,K3: A,Kl3: list @ A] : ( Lab @ ( cons @ A @ K3 @ Kl3 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_200_empty__Shift,axiom,
% 3.18/1.60 ! [A: $tType,Kl: set @ ( list @ A ),K: A] :
% 3.18/1.60 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ Kl )
% 3.18/1.60 => ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl @ ( nil @ A ) ) )
% 3.18/1.60 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( bNF_Greatest_Shift @ A @ Kl @ K ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_201_ShiftD,axiom,
% 3.18/1.60 ! [A: $tType,Kl2: list @ A,Kl: set @ ( list @ A ),K: A] :
% 3.18/1.60 ( ( member2 @ ( list @ A ) @ Kl2 @ ( bNF_Greatest_Shift @ A @ Kl @ K ) )
% 3.18/1.60 => ( member2 @ ( list @ A ) @ ( cons @ A @ K @ Kl2 ) @ Kl ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_202_Succ__Shift,axiom,
% 3.18/1.60 ! [A: $tType,Kl: set @ ( list @ A ),K: A,Kl2: list @ A] :
% 3.18/1.60 ( ( bNF_Greatest_Succ @ A @ ( bNF_Greatest_Shift @ A @ Kl @ K ) @ Kl2 )
% 3.18/1.60 = ( bNF_Greatest_Succ @ A @ Kl @ ( cons @ A @ K @ Kl2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_203_rev__eq__Cons__iff,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( rev @ A @ Xs )
% 3.18/1.60 = ( cons @ A @ Y @ Ys2 ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_204_append_Omonoid__axioms,axiom,
% 3.18/1.60 ! [A: $tType] : ( monoid @ ( list @ A ) @ ( append @ A ) @ ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_205_rev__is__rev__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( rev @ A @ Xs )
% 3.18/1.60 = ( rev @ A @ Ys2 ) )
% 3.18/1.60 = ( Xs = Ys2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_206_rev__rev__ident,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 3.18/1.60 = Xs ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_207_rev__is__Nil__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( ( rev @ A @ Xs )
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_208_Nil__is__rev__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( ( nil @ A )
% 3.18/1.60 = ( rev @ A @ Xs ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( nil @ A ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_209_rev__append,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( rev @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( rev @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_210_singleton__rev__conv,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( ( cons @ A @ X3 @ ( nil @ A ) )
% 3.18/1.60 = ( rev @ A @ Xs ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_211_rev__singleton__conv,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,X3: A] :
% 3.18/1.60 ( ( ( rev @ A @ Xs )
% 3.18/1.60 = ( cons @ A @ X3 @ ( nil @ A ) ) )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_212_rev_Osimps_I1_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( rev @ A @ ( nil @ A ) )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_213_rev__swap,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( rev @ A @ Xs )
% 3.18/1.60 = Ys2 )
% 3.18/1.60 = ( Xs
% 3.18/1.60 = ( rev @ A @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_214_rev_Osimps_I2_J,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( rev @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_215_map__tailrec__def,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType] :
% 3.18/1.60 ( ( map_tailrec @ A @ B )
% 3.18/1.60 = ( ^ [F4: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F4 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_216_hd__rev,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 3.18/1.60 = ( last @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_217_hd__append2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( hd @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_218_hd__concat,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ ( list @ A )] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ ( list @ A ) ) )
% 3.18/1.60 => ( ( ( hd @ ( list @ A ) @ Xs )
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( hd @ A @ ( concat @ A @ Xs ) )
% 3.18/1.60 = ( hd @ A @ ( hd @ ( list @ A ) @ Xs ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_219_list_Osel_I1_J,axiom,
% 3.18/1.60 ! [A: $tType,X21: A,X22: list @ A] :
% 3.18/1.60 ( ( hd @ A @ ( cons @ A @ X21 @ X22 ) )
% 3.18/1.60 = X21 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_220_longest__common__prefix,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ? [Ps: list @ A,Xs4: list @ A,Ys4: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 = ( append @ A @ Ps @ Xs4 ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( append @ A @ Ps @ Ys4 ) )
% 3.18/1.60 & ( ( Xs4
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( Ys4
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( ( hd @ A @ Xs4 )
% 3.18/1.60 != ( hd @ A @ Ys4 ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_221_hd__append,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( hd @ A @ Ys2 ) ) )
% 3.18/1.60 & ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( hd @ A @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_222_last__rev,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 3.18/1.60 = ( hd @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_223_rotate1__hd__tl,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( rotate1 @ A @ Xs )
% 3.18/1.60 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_224_distinct__adj__append__iff,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( ( distinct_adj @ A @ Xs )
% 3.18/1.60 & ( distinct_adj @ A @ Ys2 )
% 3.18/1.60 & ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( ( last @ A @ Xs )
% 3.18/1.60 != ( hd @ A @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_225_distinct__adj__Cons__Cons,axiom,
% 3.18/1.60 ! [B: $tType,X3: B,Y: B,Xs: list @ B] :
% 3.18/1.60 ( ( distinct_adj @ B @ ( cons @ B @ X3 @ ( cons @ B @ Y @ Xs ) ) )
% 3.18/1.60 = ( ( X3 != Y )
% 3.18/1.60 & ( distinct_adj @ B @ ( cons @ B @ Y @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_226_distinct__adj__rev,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( distinct_adj @ A @ ( rev @ A @ Xs ) )
% 3.18/1.60 = ( distinct_adj @ A @ Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_227_tl__append2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( tl @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( append @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_228_butlast__rev,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( butlast @ A @ ( rev @ A @ Xs ) )
% 3.18/1.60 = ( rev @ A @ ( tl @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_229_list_Ocollapse,axiom,
% 3.18/1.60 ! [A: $tType,List: list @ A] :
% 3.18/1.60 ( ( List
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 3.18/1.60 = List ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_230_hd__Cons__tl,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 3.18/1.60 = Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_231_list_Oexpand,axiom,
% 3.18/1.60 ! [A: $tType,List: list @ A,List2: list @ A] :
% 3.18/1.60 ( ( ( List
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 = ( List2
% 3.18/1.60 = ( nil @ A ) ) )
% 3.18/1.60 => ( ( ( List
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( List2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( ( ( hd @ A @ List )
% 3.18/1.60 = ( hd @ A @ List2 ) )
% 3.18/1.60 & ( ( tl @ A @ List )
% 3.18/1.60 = ( tl @ A @ List2 ) ) ) ) )
% 3.18/1.60 => ( List = List2 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_232_distinct__adj__singleton,axiom,
% 3.18/1.60 ! [B: $tType,X3: B] : ( distinct_adj @ B @ ( cons @ B @ X3 @ ( nil @ B ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_233_tl__Nil,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( ( tl @ A @ Xs )
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ? [X4: A] :
% 3.18/1.60 ( Xs
% 3.18/1.60 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_234_Nil__tl,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( ( nil @ A )
% 3.18/1.60 = ( tl @ A @ Xs ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ? [X4: A] :
% 3.18/1.60 ( Xs
% 3.18/1.60 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_235_distinct__adj__ConsD,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 => ( distinct_adj @ A @ Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_236_distinct__adj__Nil,axiom,
% 3.18/1.60 ! [A: $tType] : ( distinct_adj @ A @ ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_237_list_Osel_I3_J,axiom,
% 3.18/1.60 ! [A: $tType,X21: A,X22: list @ A] :
% 3.18/1.60 ( ( tl @ A @ ( cons @ A @ X21 @ X22 ) )
% 3.18/1.60 = X22 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_238_list_Osel_I2_J,axiom,
% 3.18/1.60 ! [A: $tType] :
% 3.18/1.60 ( ( tl @ A @ ( nil @ A ) )
% 3.18/1.60 = ( nil @ A ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_239_distinct__adj__appendD1,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 => ( distinct_adj @ A @ Xs ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_240_distinct__adj__appendD2,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 => ( distinct_adj @ A @ Ys2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_241_butlast__tl,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 3.18/1.60 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_242_last__tl,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A] :
% 3.18/1.60 ( ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( ( tl @ A @ Xs )
% 3.18/1.60 != ( nil @ A ) ) )
% 3.18/1.60 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 3.18/1.60 = ( last @ A @ Xs ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_243_list_Oexhaust__sel,axiom,
% 3.18/1.60 ! [A: $tType,List: list @ A] :
% 3.18/1.60 ( ( List
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 => ( List
% 3.18/1.60 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_244_distinct__adj__Cons,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Xs: list @ A] :
% 3.18/1.60 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( ( X3
% 3.18/1.60 != ( hd @ A @ Xs ) )
% 3.18/1.60 & ( distinct_adj @ A @ Xs ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_245_list_Osplit__sel,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 3.18/1.60 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 3.18/1.60 = ( ( ( List
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 => ( P @ F1 ) )
% 3.18/1.60 & ( ( List
% 3.18/1.60 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 3.18/1.60 => ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_246_list_Osplit__sel__asm,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 3.18/1.60 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 3.18/1.60 = ( ~ ( ( ( List
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ~ ( P @ F1 ) )
% 3.18/1.60 | ( ( List
% 3.18/1.60 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 3.18/1.60 & ~ ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_247_list_Osimps_I5_J,axiom,
% 3.18/1.60 ! [B: $tType,A: $tType,F1: B,F2: A > ( list @ A ) > B,X21: A,X22: list @ A] :
% 3.18/1.60 ( ( case_list @ B @ A @ F1 @ F2 @ ( cons @ A @ X21 @ X22 ) )
% 3.18/1.60 = ( F2 @ X21 @ X22 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_248_list_Osimps_I4_J,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType,F1: B,F2: A > ( list @ A ) > B] :
% 3.18/1.60 ( ( case_list @ B @ A @ F1 @ F2 @ ( nil @ A ) )
% 3.18/1.60 = F1 ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_249_list_Ocase__eq__if,axiom,
% 3.18/1.60 ! [A: $tType,B: $tType] :
% 3.18/1.60 ( ( case_list @ B @ A )
% 3.18/1.60 = ( ^ [F12: B,F22: A > ( list @ A ) > B,List3: list @ A] :
% 3.18/1.60 ( if @ B
% 3.18/1.60 @ ( List3
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 @ F12
% 3.18/1.60 @ ( F22 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_250_successively__append__iff,axiom,
% 3.18/1.60 ! [A: $tType,P: A > A > $o,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( successively @ A @ P @ ( append @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( ( successively @ A @ P @ Xs )
% 3.18/1.60 & ( successively @ A @ P @ Ys2 )
% 3.18/1.60 & ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( Ys2
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 | ( P @ ( last @ A @ Xs ) @ ( hd @ A @ Ys2 ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_251_Cons__in__shuffles__iff,axiom,
% 3.18/1.60 ! [A: $tType,Z: A,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( ( ( Xs
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 & ( ( hd @ A @ Xs )
% 3.18/1.60 = Z )
% 3.18/1.60 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) )
% 3.18/1.60 | ( ( Ys2
% 3.18/1.60 != ( nil @ A ) )
% 3.18/1.60 & ( ( hd @ A @ Ys2 )
% 3.18/1.60 = Z )
% 3.18/1.60 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ ( tl @ A @ Ys2 ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_252_Nil__in__shuffles,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 3.18/1.60 = ( ( Xs
% 3.18/1.60 = ( nil @ A ) )
% 3.18/1.60 & ( Ys2
% 3.18/1.60 = ( nil @ A ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_253_splice__in__shuffles,axiom,
% 3.18/1.60 ! [A: $tType,Xs: list @ A,Ys2: list @ A] : ( member2 @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) @ ( shuffles @ A @ Xs @ Ys2 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(fact_254_shufflesE,axiom,
% 3.18/1.60 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 3.18/1.60 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 3.18/1.60 => ( ( ( Zs2 = Xs )
% 3.18/1.60 => ( Ys2
% 3.18/1.60 != ( nil @ A ) ) )
% 3.18/1.60 => ( ( ( Zs2 = Ys2 )
% 3.18/1.60 => ( Xs
% 3.18/1.60 != ( nil @ A ) ) )
% 3.18/1.60 => ( ! [X: A,Xs4: list @ A] :
% 3.18/1.60 ( ( Xs
% 3.18/1.60 = ( cons @ A @ X @ Xs4 ) )
% 3.18/1.60 => ! [Z2: A,Zs3: list @ A] :
% 3.18/1.60 ( ( Zs2
% 3.18/1.60 = ( cons @ A @ Z2 @ Zs3 ) )
% 3.18/1.60 => ( ( X = Z2 )
% 3.18/1.60 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs4 @ Ys2 ) ) ) ) )
% 3.18/1.60 => ~ ! [Y3: A,Ys4: list @ A] :
% 3.18/1.60 ( ( Ys2
% 3.18/1.60 = ( cons @ A @ Y3 @ Ys4 ) )
% 3.18/1.60 => ! [Z2: A,Zs3: list @ A] :
% 3.18/1.60 ( ( Zs2
% 3.18/1.60 = ( cons @ A @ Z2 @ Zs3 ) )
% 3.18/1.60 => ( ( Y3 = Z2 )
% 3.18/1.60 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs @ Ys4 ) ) ) ) ) ) ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.18/1.60 ! [A6: $tType,A7: $tType] :
% 3.18/1.60 ( ( order @ A7 )
% 3.18/1.60 => ( order @ ( A6 > A7 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_fun___Orderings_Oord,axiom,
% 3.18/1.60 ! [A6: $tType,A7: $tType] :
% 3.18/1.60 ( ( ord @ A7 )
% 3.18/1.60 => ( ord @ ( A6 > A7 ) ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_Set_Oset___Orderings_Oorder_1,axiom,
% 3.18/1.60 ! [A6: $tType] : ( order @ ( set @ A6 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_Set_Oset___Orderings_Oord_2,axiom,
% 3.18/1.60 ! [A6: $tType] : ( ord @ ( set @ A6 ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 3.18/1.60 linorder @ $o ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_HOL_Obool___Orderings_Oorder_3,axiom,
% 3.18/1.60 order @ $o ).
% 3.18/1.60
% 3.18/1.60 thf(tcon_HOL_Obool___Orderings_Oord_4,axiom,
% 3.18/1.60 ord @ $o ).
% 3.18/1.60
% 3.18/1.60 thf(help_If_3_1_T,axiom,
% 3.18/1.60 ! [P: $o] :
% 3.18/1.60 ( ( P = $true )
% 3.18/1.60 | ( P = $false ) ) ).
% 3.18/1.60
% 3.18/1.60 thf(help_If_2_1_T,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Y: A] :
% 3.18/1.60 ( ( if @ A @ $false @ X3 @ Y )
% 3.18/1.60 = Y ) ).
% 3.18/1.60
% 3.18/1.60 thf(help_If_1_1_T,axiom,
% 3.18/1.60 ! [A: $tType,X3: A,Y: A] :
% 3.18/1.60 ( ( if @ A @ $true @ X3 @ Y )
% 3.18/1.60 = X3 ) ).
% 3.18/1.60
% 3.18/1.60 thf(conj_0,conjecture,
% 3.18/1.60 knowle1437066798e_know @ a @ ( secrecy_kKS @ m ) ).
% 3.18/1.60 ------------------------
% 3.18/1.63 % (7979)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/183Mi)
% 3.18/1.63 % (7981)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_7787 for (2999ds/27Mi)
% 3.18/1.63 % (7980)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_7787 for (2999ds/4Mi)
% 3.18/1.63 % (7985)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/18Mi)
% 3.18/1.63 % (7980)Instruction limit reached!
% 3.18/1.63 % (7980)------------------------------
% 3.18/1.63 % (7980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.63 % (7980)Termination reason: Unknown
% 3.18/1.63 % (7980)Termination phase: shuffling
% 3.18/1.63
% 3.18/1.63 % (7980)Memory used [KB]: 1407
% 3.18/1.63 % (7980)Time elapsed: 0.003 s
% 3.18/1.63 % (7980)Instructions burned: 5 (million)
% 3.18/1.63 % (7980)------------------------------
% 3.18/1.63 % (7980)------------------------------
% 3.18/1.63 % (7983)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_7787 for (2999ds/2Mi)
% 3.18/1.63 % (7984)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_7787 for (2999ds/275Mi)
% 3.18/1.63 % (7982)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/2Mi)
% 3.18/1.64 % (7983)Instruction limit reached!
% 3.18/1.64 % (7983)------------------------------
% 3.18/1.64 % (7983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64 % (7983)Termination reason: Unknown
% 3.18/1.64 % (7983)Termination phase: shuffling
% 3.18/1.64
% 3.18/1.64 % (7983)Memory used [KB]: 1407
% 3.18/1.64 % (7983)Time elapsed: 0.003 s
% 3.18/1.64 % (7983)Instructions burned: 3 (million)
% 3.18/1.64 % (7983)------------------------------
% 3.18/1.64 % (7983)------------------------------
% 3.18/1.64 % (7985)Instruction limit reached!
% 3.18/1.64 % (7985)------------------------------
% 3.18/1.64 % (7985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64 % (7985)Termination reason: Unknown
% 3.18/1.64 % (7985)Termination phase: shuffling
% 3.18/1.64
% 3.18/1.64 % (7985)Memory used [KB]: 1791
% 3.18/1.64 % (7985)Time elapsed: 0.008 s
% 3.18/1.64 % (7985)Instructions burned: 19 (million)
% 3.18/1.64 % (7985)------------------------------
% 3.18/1.64 % (7985)------------------------------
% 3.18/1.64 % (7982)Instruction limit reached!
% 3.18/1.64 % (7982)------------------------------
% 3.18/1.64 % (7982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64 % (7982)Termination reason: Unknown
% 3.18/1.64 % (7982)Termination phase: shuffling
% 3.18/1.64
% 3.18/1.64 % (7982)Memory used [KB]: 1407
% 3.18/1.64 % (7982)Time elapsed: 0.004 s
% 3.18/1.64 % (7982)Instructions burned: 3 (million)
% 3.18/1.64 % (7982)------------------------------
% 3.18/1.64 % (7982)------------------------------
% 3.18/1.64 % (7981)Instruction limit reached!
% 3.18/1.64 % (7981)------------------------------
% 3.18/1.64 % (7981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64 % (7981)Termination reason: Unknown
% 3.18/1.64 % (7981)Termination phase: Property scanning
% 3.18/1.64
% 3.18/1.64 % (7981)Memory used [KB]: 1918
% 3.18/1.64 % (7981)Time elapsed: 0.011 s
% 3.18/1.64 % (7981)Instructions burned: 29 (million)
% 3.18/1.64 % (7981)------------------------------
% 3.18/1.64 % (7981)------------------------------
% 3.18/1.64 % (7986)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/3Mi)
% 3.18/1.64 % (7986)Instruction limit reached!
% 3.18/1.64 % (7986)------------------------------
% 3.18/1.64 % (7986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.64 % (7986)Termination reason: Unknown
% 3.18/1.64 % (7986)Termination phase: shuffling
% 3.18/1.64
% 3.18/1.64 % (7986)Memory used [KB]: 1407
% 3.18/1.64 % (7986)Time elapsed: 0.003 s
% 3.18/1.64 % (7986)Instructions burned: 4 (million)
% 3.18/1.64 % (7986)------------------------------
% 3.18/1.64 % (7986)------------------------------
% 3.18/1.65 % (7988)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_7787 for (2999ds/15Mi)
% 3.18/1.65 % (7987)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_7787 for (2999ds/37Mi)
% 3.18/1.65 % (7990)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_7787 for (2999ds/1041Mi)
% 3.18/1.65 % (7991)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/7Mi)
% 3.18/1.65 % (7988)Instruction limit reached!
% 3.18/1.65 % (7988)------------------------------
% 3.18/1.65 % (7988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.65 % (7988)Termination reason: Unknown
% 3.18/1.65 % (7988)Termination phase: shuffling
% 3.18/1.65
% 3.18/1.65 % (7988)Memory used [KB]: 1791
% 3.18/1.65 % (7988)Time elapsed: 0.007 s
% 3.18/1.65 % (7988)Instructions burned: 17 (million)
% 3.18/1.65 % (7988)------------------------------
% 3.18/1.65 % (7988)------------------------------
% 3.18/1.65 % (7989)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_7787 for (2999ds/3Mi)
% 3.18/1.65 % (7991)Instruction limit reached!
% 3.18/1.65 % (7991)------------------------------
% 3.18/1.65 % (7991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.65 % (7991)Termination reason: Unknown
% 3.18/1.65 % (7991)Termination phase: shuffling
% 3.18/1.65
% 3.18/1.65 % (7991)Memory used [KB]: 1535
% 3.18/1.65 % (7991)Time elapsed: 0.004 s
% 3.18/1.65 % (7991)Instructions burned: 7 (million)
% 3.18/1.65 % (7991)------------------------------
% 3.18/1.65 % (7991)------------------------------
% 3.18/1.66 % (7989)Instruction limit reached!
% 3.18/1.66 % (7989)------------------------------
% 3.18/1.66 % (7989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.66 % (7989)Termination reason: Unknown
% 3.18/1.66 % (7989)Termination phase: shuffling
% 3.18/1.66
% 3.18/1.66 % (7989)Memory used [KB]: 1407
% 3.18/1.66 % (7989)Time elapsed: 0.004 s
% 3.18/1.66 % (7989)Instructions burned: 3 (million)
% 3.18/1.66 % (7989)------------------------------
% 3.18/1.66 % (7989)------------------------------
% 3.18/1.66 % (7987)Instruction limit reached!
% 3.18/1.66 % (7987)------------------------------
% 3.18/1.66 % (7987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.66 % (7987)Termination reason: Unknown
% 3.18/1.66 % (7987)Termination phase: shuffling
% 3.18/1.66
% 3.18/1.66 % (7987)Memory used [KB]: 2174
% 3.18/1.66 % (7987)Time elapsed: 0.014 s
% 3.18/1.66 % (7987)Instructions burned: 39 (million)
% 3.18/1.66 % (7987)------------------------------
% 3.18/1.66 % (7987)------------------------------
% 3.18/1.66 % (7992)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/16Mi)
% 3.18/1.66 % (7984)Refutation not found, incomplete strategy
% 3.18/1.66 % (7984)------------------------------
% 3.18/1.66 % (7984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.66 % (7984)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.66
% 3.18/1.66
% 3.18/1.66 % (7984)Memory used [KB]: 6652
% 3.18/1.66 % (7984)Time elapsed: 0.030 s
% 3.18/1.66 % (7984)Instructions burned: 53 (million)
% 3.18/1.66 % (7984)------------------------------
% 3.18/1.66 % (7984)------------------------------
% 3.18/1.66 % (7993)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_7787 for (2999ds/3Mi)
% 3.18/1.67 % (7993)Instruction limit reached!
% 3.18/1.67 % (7993)------------------------------
% 3.18/1.67 % (7993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.67 % (7993)Termination reason: Unknown
% 3.18/1.67 % (7993)Termination phase: shuffling
% 3.18/1.67
% 3.18/1.67 % (7993)Memory used [KB]: 1407
% 3.18/1.67 % (7993)Time elapsed: 0.003 s
% 3.18/1.67 % (7993)Instructions burned: 5 (million)
% 3.18/1.67 % (7993)------------------------------
% 3.18/1.67 % (7993)------------------------------
% 3.18/1.67 % (7992)Instruction limit reached!
% 3.18/1.67 % (7992)------------------------------
% 3.18/1.67 % (7992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.67 % (7992)Termination reason: Unknown
% 3.18/1.67 % (7992)Termination phase: shuffling
% 3.18/1.67
% 3.18/1.67 % (7992)Memory used [KB]: 1791
% 3.18/1.67 % (7992)Time elapsed: 0.008 s
% 3.18/1.67 % (7992)Instructions burned: 18 (million)
% 3.18/1.67 % (7992)------------------------------
% 3.18/1.67 % (7992)------------------------------
% 3.18/1.67 % (7995)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/7Mi)
% 3.18/1.67 % (7994)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_7787 for (2999ds/3Mi)
% 3.18/1.67 % (7995)Instruction limit reached!
% 3.18/1.67 % (7995)------------------------------
% 3.18/1.67 % (7995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.67 % (7995)Termination reason: Unknown
% 3.18/1.67 % (7995)Termination phase: shuffling
% 3.18/1.67
% 3.18/1.67 % (7995)Memory used [KB]: 1535
% 3.18/1.67 % (7995)Time elapsed: 0.004 s
% 3.18/1.67 % (7995)Instructions burned: 7 (million)
% 3.18/1.67 % (7995)------------------------------
% 3.18/1.67 % (7995)------------------------------
% 3.18/1.67 % (7996)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/3Mi)
% 3.18/1.67 % (7997)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/4Mi)
% 3.18/1.68 % (7994)Instruction limit reached!
% 3.18/1.68 % (7994)------------------------------
% 3.18/1.68 % (7994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.68 % (7994)Termination reason: Unknown
% 3.18/1.68 % (7994)Termination phase: shuffling
% 3.18/1.68
% 3.18/1.68 % (7994)Memory used [KB]: 1407
% 3.18/1.68 % (7994)Time elapsed: 0.004 s
% 3.18/1.68 % (7994)Instructions burned: 3 (million)
% 3.18/1.68 % (7994)------------------------------
% 3.18/1.68 % (7994)------------------------------
% 3.18/1.68 % (7996)Instruction limit reached!
% 3.18/1.68 % (7996)------------------------------
% 3.18/1.68 % (7996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.68 % (7996)Termination reason: Unknown
% 3.18/1.68 % (7996)Termination phase: shuffling
% 3.18/1.68
% 3.18/1.68 % (7996)Memory used [KB]: 1407
% 3.18/1.68 % (7996)Time elapsed: 0.003 s
% 3.18/1.68 % (7996)Instructions burned: 4 (million)
% 3.18/1.68 % (7996)------------------------------
% 3.18/1.68 % (7996)------------------------------
% 3.18/1.68 % (7997)Instruction limit reached!
% 3.18/1.68 % (7997)------------------------------
% 3.18/1.68 % (7997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.68 % (7997)Termination reason: Unknown
% 3.18/1.68 % (7997)Termination phase: shuffling
% 3.18/1.68
% 3.18/1.68 % (7997)Memory used [KB]: 1535
% 3.18/1.68 % (7997)Time elapsed: 0.003 s
% 3.18/1.68 % (7997)Instructions burned: 6 (million)
% 3.18/1.68 % (7997)------------------------------
% 3.18/1.68 % (7997)------------------------------
% 3.18/1.68 % (7998)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/18Mi)
% 3.18/1.68 % (7979)Instruction limit reached!
% 3.18/1.68 % (7979)------------------------------
% 3.18/1.68 % (7979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.68 % (7979)Termination reason: Unknown
% 3.18/1.68 % (7979)Termination phase: Saturation
% 3.18/1.68
% 3.18/1.68 % (7979)Memory used [KB]: 7419
% 3.18/1.68 % (7979)Time elapsed: 0.058 s
% 3.18/1.68 % (7979)Instructions burned: 186 (million)
% 3.18/1.68 % (7979)------------------------------
% 3.18/1.68 % (7979)------------------------------
% 3.18/1.68 % (7999)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/710Mi)
% 3.18/1.68 % (7998)Instruction limit reached!
% 3.18/1.68 % (7998)------------------------------
% 3.18/1.68 % (7998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.68 % (7998)Termination reason: Unknown
% 3.18/1.68 % (7998)Termination phase: shuffling
% 3.18/1.68
% 3.18/1.68 % (7998)Memory used [KB]: 1791
% 3.18/1.68 % (7998)Time elapsed: 0.008 s
% 3.18/1.68 % (7998)Instructions burned: 18 (million)
% 3.18/1.68 % (7998)------------------------------
% 3.18/1.68 % (7998)------------------------------
% 3.18/1.69 % (8002)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_7787 for (2999ds/21Mi)
% 3.18/1.69 % (8001)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_7787 for (2999ds/902Mi)
% 3.18/1.69 % (8000)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/6Mi)
% 3.18/1.69 % (8005)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/5Mi)
% 3.18/1.69 % (8002)Instruction limit reached!
% 3.18/1.69 % (8002)------------------------------
% 3.18/1.69 % (8002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.69 % (8002)Termination reason: Unknown
% 3.18/1.69 % (8002)Termination phase: shuffling
% 3.18/1.69
% 3.18/1.69 % (8002)Memory used [KB]: 1791
% 3.18/1.69 % (8002)Time elapsed: 0.008 s
% 3.18/1.69 % (8002)Instructions burned: 22 (million)
% 3.18/1.69 % (8002)------------------------------
% 3.18/1.69 % (8002)------------------------------
% 3.18/1.69 % (8000)Instruction limit reached!
% 3.18/1.69 % (8000)------------------------------
% 3.18/1.69 % (8000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.69 % (8000)Termination reason: Unknown
% 3.18/1.69 % (8000)Termination phase: shuffling
% 3.18/1.69
% 3.18/1.69 % (8000)Memory used [KB]: 1535
% 3.18/1.69 % (8000)Time elapsed: 0.004 s
% 3.18/1.69 % (8000)Instructions burned: 7 (million)
% 3.18/1.69 % (8000)------------------------------
% 3.18/1.69 % (8000)------------------------------
% 3.18/1.69 % (8005)Instruction limit reached!
% 3.18/1.69 % (8005)------------------------------
% 3.18/1.69 % (8005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.69 % (8005)Termination reason: Unknown
% 3.18/1.69 % (8005)Termination phase: shuffling
% 3.18/1.69
% 3.18/1.69 % (8005)Memory used [KB]: 1535
% 3.18/1.69 % (8005)Time elapsed: 0.003 s
% 3.18/1.69 % (8005)Instructions burned: 7 (million)
% 3.18/1.69 % (8005)------------------------------
% 3.18/1.69 % (8005)------------------------------
% 3.18/1.70 % (8007)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_7787 for (2999ds/6Mi)
% 3.18/1.70 % (8007)Instruction limit reached!
% 3.18/1.70 % (8007)------------------------------
% 3.18/1.70 % (8007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.70 % (8007)Termination reason: Unknown
% 3.18/1.70 % (8007)Termination phase: shuffling
% 3.18/1.70
% 3.18/1.70 % (8007)Memory used [KB]: 1535
% 3.18/1.70 % (8007)Time elapsed: 0.004 s
% 3.18/1.70 % (8007)Instructions burned: 7 (million)
% 3.18/1.70 % (8007)------------------------------
% 3.18/1.70 % (8007)------------------------------
% 3.18/1.70 % (8010)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/377Mi)
% 3.18/1.70 % (8012)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_7787 for (2999ds/19Mi)
% 3.18/1.70 % (8011)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_7787 for (2999ds/779Mi)
% 3.18/1.71 % (8013)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/879Mi)
% 3.18/1.71 % (8012)Instruction limit reached!
% 3.18/1.71 % (8012)------------------------------
% 3.18/1.71 % (8012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.71 % (8012)Termination reason: Unknown
% 3.18/1.71 % (8012)Termination phase: shuffling
% 3.18/1.71
% 3.18/1.71 % (8012)Memory used [KB]: 1663
% 3.18/1.71 % (8012)Time elapsed: 0.006 s
% 3.18/1.71 % (8012)Instructions burned: 19 (million)
% 3.18/1.71 % (8012)------------------------------
% 3.18/1.71 % (8012)------------------------------
% 3.18/1.72 % (8014)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_7787 for (2999ds/17Mi)
% 3.18/1.72 % (8014)Instruction limit reached!
% 3.18/1.72 % (8014)------------------------------
% 3.18/1.72 % (8014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.72 % (8014)Termination reason: Unknown
% 3.18/1.72 % (8014)Termination phase: shuffling
% 3.18/1.72
% 3.18/1.72 % (8014)Memory used [KB]: 1791
% 3.18/1.72 % (8014)Time elapsed: 0.007 s
% 3.18/1.72 % (8014)Instructions burned: 19 (million)
% 3.18/1.72 % (8014)------------------------------
% 3.18/1.72 % (8014)------------------------------
% 3.18/1.74 % (8001)Refutation not found, incomplete strategy
% 3.18/1.74 % (8001)------------------------------
% 3.18/1.74 % (8001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.74 % (8001)Termination reason: Refutation not found, incomplete strategy
% 3.18/1.74
% 3.18/1.74
% 3.18/1.74 % (8001)Memory used [KB]: 7675
% 3.18/1.74 % (8001)Time elapsed: 0.050 s
% 3.18/1.74 % (8001)Instructions burned: 166 (million)
% 3.18/1.74 % (8001)------------------------------
% 3.18/1.74 % (8001)------------------------------
% 3.18/1.74 % (8016)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_7787 for (2998ds/3Mi)
% 3.18/1.75 % (8016)Instruction limit reached!
% 3.18/1.75 % (8016)------------------------------
% 3.18/1.75 % (8016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.75 % (8016)Termination reason: Unknown
% 3.18/1.75 % (8016)Termination phase: shuffling
% 3.18/1.75
% 3.18/1.75 % (8016)Memory used [KB]: 1407
% 3.18/1.75 % (8016)Time elapsed: 0.006 s
% 3.18/1.75 % (8016)Instructions burned: 3 (million)
% 3.18/1.75 % (8016)------------------------------
% 3.18/1.75 % (8016)------------------------------
% 3.18/1.75 % (8018)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_7787 for (2998ds/30Mi)
% 3.18/1.76 % (8018)Instruction limit reached!
% 3.18/1.76 % (8018)------------------------------
% 3.18/1.76 % (8018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.76 % (8018)Termination reason: Unknown
% 3.18/1.76 % (8018)Termination phase: Property scanning
% 3.18/1.76
% 3.18/1.76 % (8018)Memory used [KB]: 2046
% 3.18/1.76 % (8018)Time elapsed: 0.017 s
% 3.18/1.76 % (8018)Instructions burned: 31 (million)
% 3.18/1.76 % (8018)------------------------------
% 3.18/1.76 % (8018)------------------------------
% 3.18/1.77 % (8026)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_7787 for (2998ds/127Mi)
% 3.18/1.78 % (8030)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_7787 for (2998ds/100Mi)
% 3.18/1.82 % (8026)Instruction limit reached!
% 3.18/1.82 % (8026)------------------------------
% 3.18/1.82 % (8026)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.82 % (8026)Termination reason: Unknown
% 3.18/1.82 % (8026)Termination phase: Saturation
% 3.18/1.82
% 3.18/1.82 % (8026)Memory used [KB]: 7036
% 3.18/1.82 % (8026)Time elapsed: 0.050 s
% 3.18/1.82 % (8026)Instructions burned: 127 (million)
% 3.18/1.82 % (8026)------------------------------
% 3.18/1.82 % (8026)------------------------------
% 3.18/1.83 % (8030)Instruction limit reached!
% 3.18/1.83 % (8030)------------------------------
% 3.18/1.83 % (8030)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.83 % (8030)Termination reason: Unknown
% 3.18/1.83 % (8030)Termination phase: Property scanning
% 3.18/1.83
% 3.18/1.83 % (8030)Memory used [KB]: 2430
% 3.18/1.83 % (8030)Time elapsed: 0.047 s
% 3.18/1.83 % (8030)Instructions burned: 102 (million)
% 3.18/1.83 % (8030)------------------------------
% 3.18/1.83 % (8030)------------------------------
% 3.18/1.84 % (8045)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_7787 for (2997ds/3Mi)
% 3.18/1.84 % (8045)Instruction limit reached!
% 3.18/1.84 % (8045)------------------------------
% 3.18/1.84 % (8045)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.84 % (8045)Termination reason: Unknown
% 3.18/1.84 % (8045)Termination phase: shuffling
% 3.18/1.84
% 3.18/1.84 % (8045)Memory used [KB]: 1407
% 3.18/1.84 % (8045)Time elapsed: 0.003 s
% 3.18/1.84 % (8045)Instructions burned: 3 (million)
% 3.18/1.84 % (8045)------------------------------
% 3.18/1.84 % (8045)------------------------------
% 3.18/1.84 % (8047)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_7787 for (2997ds/20Mi)
% 3.18/1.85 % (8047)Instruction limit reached!
% 3.18/1.85 % (8047)------------------------------
% 3.18/1.85 % (8047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.85 % (8047)Termination reason: Unknown
% 3.18/1.85 % (8047)Termination phase: shuffling
% 3.18/1.85
% 3.18/1.85 % (8047)Memory used [KB]: 1918
% 3.18/1.85 % (8047)Time elapsed: 0.008 s
% 3.18/1.85 % (8047)Instructions burned: 21 (million)
% 3.18/1.85 % (8047)------------------------------
% 3.18/1.85 % (8047)------------------------------
% 3.18/1.86 % (8051)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_7787 for (2997ds/86Mi)
% 3.18/1.86 % (8010)Instruction limit reached!
% 3.18/1.86 % (8010)------------------------------
% 3.18/1.86 % (8010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.86 % (8010)Termination reason: Unknown
% 3.18/1.86 % (8010)Termination phase: Saturation
% 3.18/1.86
% 3.18/1.86 % (8010)Memory used [KB]: 8187
% 3.18/1.86 % (8010)Time elapsed: 0.156 s
% 3.18/1.86 % (8010)Instructions burned: 378 (million)
% 3.18/1.86 % (8010)------------------------------
% 3.18/1.86 % (8010)------------------------------
% 3.18/1.86 % (8053)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_7787 for (2997ds/107Mi)
% 3.18/1.87 % (8055)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_7787 for (2997ds/39Mi)
% 3.18/1.88 % (8055)Instruction limit reached!
% 3.18/1.88 % (8055)------------------------------
% 3.18/1.88 % (8055)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.88 % (8055)Termination reason: Unknown
% 3.18/1.88 % (8055)Termination phase: shuffling
% 3.18/1.88
% 3.18/1.88 % (8055)Memory used [KB]: 2174
% 3.18/1.88 % (8055)Time elapsed: 0.013 s
% 3.18/1.88 % (8055)Instructions burned: 39 (million)
% 3.18/1.88 % (8055)------------------------------
% 3.18/1.88 % (8055)------------------------------
% 3.18/1.89 % (8057)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_7787 for (2997ds/448Mi)
% 3.18/1.90 % (8051)Instruction limit reached!
% 3.18/1.90 % (8051)------------------------------
% 3.18/1.90 % (8051)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.90 % (8051)Termination reason: Unknown
% 3.18/1.90 % (8051)Termination phase: Property scanning
% 3.18/1.90
% 3.18/1.90 % (8051)Memory used [KB]: 2558
% 3.18/1.90 % (8051)Time elapsed: 0.043 s
% 3.18/1.90 % (8051)Instructions burned: 87 (million)
% 3.18/1.90 % (8051)------------------------------
% 3.18/1.90 % (8051)------------------------------
% 3.18/1.91 % (8060)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_7787 for (2997ds/46Mi)
% 3.18/1.91 % (8053)Instruction limit reached!
% 3.18/1.91 % (8053)------------------------------
% 3.18/1.91 % (8053)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.91 % (8053)Termination reason: Unknown
% 3.18/1.91 % (8053)Termination phase: Saturation
% 3.18/1.91
% 3.18/1.91 % (8053)Memory used [KB]: 6908
% 3.18/1.91 % (8053)Time elapsed: 0.052 s
% 3.18/1.91 % (8053)Instructions burned: 108 (million)
% 3.18/1.91 % (8053)------------------------------
% 3.18/1.91 % (8053)------------------------------
% 3.18/1.93 % (8062)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_7787 for (2997ds/98Mi)
% 3.18/1.94 % (8060)Instruction limit reached!
% 3.18/1.94 % (8060)------------------------------
% 3.18/1.94 % (8060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.94 % (8060)Termination reason: Unknown
% 3.18/1.94 % (8060)Termination phase: Preprocessing 1
% 3.18/1.94
% 3.18/1.94 % (8060)Memory used [KB]: 1918
% 3.18/1.94 % (8060)Time elapsed: 0.024 s
% 3.18/1.94 % (8060)Instructions burned: 47 (million)
% 3.18/1.94 % (8060)------------------------------
% 3.18/1.94 % (8060)------------------------------
% 3.18/1.95 % (8064)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_7787 for (2996ds/507Mi)
% 3.18/1.97 % (8062)Instruction limit reached!
% 3.18/1.97 % (8062)------------------------------
% 3.18/1.97 % (8062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.97 % (8062)Termination reason: Unknown
% 3.18/1.97 % (8062)Termination phase: Property scanning
% 3.18/1.97
% 3.18/1.97 % (8062)Memory used [KB]: 2430
% 3.18/1.97 % (8062)Time elapsed: 0.046 s
% 3.18/1.97 % (8062)Instructions burned: 99 (million)
% 3.18/1.97 % (8062)------------------------------
% 3.18/1.97 % (8062)------------------------------
% 3.18/1.99 % (7999)Instruction limit reached!
% 3.18/1.99 % (7999)------------------------------
% 3.18/1.99 % (7999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/1.99 % (7999)Termination reason: Unknown
% 3.18/1.99 % (7999)Termination phase: Saturation
% 3.18/1.99
% 3.18/1.99 % (7999)Memory used [KB]: 8059
% 3.18/1.99 % (7999)Time elapsed: 0.305 s
% 3.18/1.99 % (7999)Instructions burned: 710 (million)
% 3.18/1.99 % (7999)------------------------------
% 3.18/1.99 % (7999)------------------------------
% 3.18/1.99 % (8065)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_7787 for (2996ds/149Mi)
% 3.18/2.00 % (8069)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_7787 for (2996ds/39Mi)
% 3.18/2.01 % (8069)Instruction limit reached!
% 3.18/2.01 % (8069)------------------------------
% 3.18/2.01 % (8069)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.01 % (8069)Termination reason: Unknown
% 3.18/2.01 % (8069)Termination phase: Preprocessing 1
% 3.18/2.01
% 3.18/2.01 % (8069)Memory used [KB]: 1918
% 3.18/2.01 % (8069)Time elapsed: 0.013 s
% 3.18/2.01 % (8069)Instructions burned: 39 (million)
% 3.18/2.01 % (8069)------------------------------
% 3.18/2.01 % (8069)------------------------------
% 3.18/2.02 % (8072)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/6Mi)
% 3.18/2.02 % (8072)Instruction limit reached!
% 3.18/2.02 % (8072)------------------------------
% 3.18/2.02 % (8072)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.18/2.02 % (8072)Termination reason: Unknown
% 3.18/2.02 % (8072)Termination phase: shuffling
% 3.18/2.02
% 3.18/2.02 % (8072)Memory used [KB]: 1407
% 3.18/2.02 % (8072)Time elapsed: 0.003 s
% 3.18/2.02 % (8072)Instructions burned: 6 (million)
% 3.18/2.02 % (8072)------------------------------
% 3.18/2.02 % (8072)------------------------------
% 5.97/2.03 % (8073)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/1087Mi)
% 5.97/2.05 % (8057)Instruction limit reached!
% 5.97/2.05 % (8057)------------------------------
% 5.97/2.05 % (8057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.05 % (8057)Termination reason: Unknown
% 5.97/2.06 % (8057)Termination phase: Saturation
% 5.97/2.06
% 5.97/2.06 % (8057)Memory used [KB]: 7803
% 5.97/2.06 % (8057)Time elapsed: 0.185 s
% 5.97/2.06 % (8057)Instructions burned: 448 (million)
% 5.97/2.06 % (8057)------------------------------
% 5.97/2.06 % (8057)------------------------------
% 5.97/2.06 % (8065)Instruction limit reached!
% 5.97/2.06 % (8065)------------------------------
% 5.97/2.06 % (8065)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.06 % (8065)Termination reason: Unknown
% 5.97/2.06 % (8065)Termination phase: Saturation
% 5.97/2.06
% 5.97/2.06 % (8065)Memory used [KB]: 7036
% 5.97/2.06 % (8065)Time elapsed: 0.069 s
% 5.97/2.06 % (8065)Instructions burned: 149 (million)
% 5.97/2.06 % (8065)------------------------------
% 5.97/2.06 % (8065)------------------------------
% 5.97/2.06 % (8011)Instruction limit reached!
% 5.97/2.06 % (8011)------------------------------
% 5.97/2.06 % (8011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.06 % (8011)Termination reason: Unknown
% 5.97/2.06 % (8011)Termination phase: Saturation
% 5.97/2.06
% 5.97/2.06 % (8011)Memory used [KB]: 7803
% 5.97/2.06 % (8011)Time elapsed: 0.361 s
% 5.97/2.06 % (8011)Instructions burned: 780 (million)
% 5.97/2.06 % (8011)------------------------------
% 5.97/2.06 % (8011)------------------------------
% 5.97/2.07 % (8077)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/47Mi)
% 5.97/2.07 % (8078)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/44Mi)
% 5.97/2.07 % (8079)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/432Mi)
% 5.97/2.09 % (7990)Instruction limit reached!
% 5.97/2.09 % (7990)------------------------------
% 5.97/2.09 % (7990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.09 % (7990)Termination reason: Unknown
% 5.97/2.09 % (7990)Termination phase: Saturation
% 5.97/2.09
% 5.97/2.09 % (7990)Memory used [KB]: 9850
% 5.97/2.09 % (7990)Time elapsed: 0.443 s
% 5.97/2.09 % (7990)Instructions burned: 1041 (million)
% 5.97/2.09 % (7990)------------------------------
% 5.97/2.09 % (7990)------------------------------
% 5.97/2.09 % (8078)Instruction limit reached!
% 5.97/2.09 % (8078)------------------------------
% 5.97/2.09 % (8078)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.09 % (8078)Termination reason: Unknown
% 5.97/2.09 % (8078)Termination phase: shuffling
% 5.97/2.09
% 5.97/2.09 % (8078)Memory used [KB]: 2302
% 5.97/2.09 % (8078)Time elapsed: 0.022 s
% 5.97/2.09 % (8078)Instructions burned: 45 (million)
% 5.97/2.09 % (8078)------------------------------
% 5.97/2.09 % (8078)------------------------------
% 5.97/2.09 % (8077)Instruction limit reached!
% 5.97/2.09 % (8077)------------------------------
% 5.97/2.09 % (8077)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.09 % (8077)Termination reason: Unknown
% 5.97/2.09 % (8077)Termination phase: Preprocessing 3
% 5.97/2.09
% 5.97/2.09 % (8077)Memory used [KB]: 2174
% 5.97/2.09 % (8077)Time elapsed: 0.025 s
% 5.97/2.09 % (8077)Instructions burned: 48 (million)
% 5.97/2.09 % (8077)------------------------------
% 5.97/2.09 % (8077)------------------------------
% 5.97/2.10 % (8013)Instruction limit reached!
% 5.97/2.10 % (8013)------------------------------
% 5.97/2.10 % (8013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.10 % (8013)Termination reason: Unknown
% 5.97/2.10 % (8013)Termination phase: Saturation
% 5.97/2.10
% 5.97/2.10 % (8013)Memory used [KB]: 8443
% 5.97/2.10 % (8013)Time elapsed: 0.398 s
% 5.97/2.10 % (8013)Instructions burned: 880 (million)
% 5.97/2.10 % (8013)------------------------------
% 5.97/2.10 % (8013)------------------------------
% 5.97/2.11 % (8081)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/62Mi)
% 5.97/2.11 % (8082)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/31Mi)
% 5.97/2.11 % (8083)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_7787 for (2995ds/96Mi)
% 5.97/2.12 % (8085)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/453Mi)
% 5.97/2.13 % (8082)Instruction limit reached!
% 5.97/2.13 % (8082)------------------------------
% 5.97/2.13 % (8082)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.97/2.13 % (8082)Termination reason: Unknown
% 5.97/2.13 % (8082)Termination phase: Property scanning
% 5.97/2.13
% 5.97/2.13 % (8082)Memory used [KB]: 1918
% 5.97/2.13 % (8082)Time elapsed: 0.017 s
% 5.97/2.13 % (8082)Instructions burned: 32 (million)
% 5.97/2.13 % (8082)------------------------------
% 5.97/2.13 % (8082)------------------------------
% 6.47/2.13 % (8081)Instruction limit reached!
% 6.47/2.13 % (8081)------------------------------
% 6.47/2.13 % (8081)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.13 % (8081)Termination reason: Unknown
% 6.47/2.13 % (8081)Termination phase: Property scanning
% 6.47/2.13
% 6.47/2.13 % (8081)Memory used [KB]: 2302
% 6.47/2.13 % (8081)Time elapsed: 0.030 s
% 6.47/2.13 % (8081)Instructions burned: 62 (million)
% 6.47/2.13 % (8081)------------------------------
% 6.47/2.13 % (8081)------------------------------
% 6.47/2.14 % (8086)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/71Mi)
% 6.47/2.15 % (8087)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/83Mi)
% 6.47/2.16 % (8083)Instruction limit reached!
% 6.47/2.16 % (8083)------------------------------
% 6.47/2.16 % (8083)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.16 % (8083)Termination reason: Unknown
% 6.47/2.16 % (8083)Termination phase: Property scanning
% 6.47/2.16
% 6.47/2.16 % (8083)Memory used [KB]: 2558
% 6.47/2.16 % (8083)Time elapsed: 0.047 s
% 6.47/2.16 % (8083)Instructions burned: 97 (million)
% 6.47/2.16 % (8083)------------------------------
% 6.47/2.16 % (8083)------------------------------
% 6.47/2.16 % (8086)Instruction limit reached!
% 6.47/2.16 % (8086)------------------------------
% 6.47/2.16 % (8086)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.16 % (8086)Termination reason: Unknown
% 6.47/2.16 % (8086)Termination phase: Property scanning
% 6.47/2.16
% 6.47/2.16 % (8086)Memory used [KB]: 2558
% 6.47/2.16 % (8086)Time elapsed: 0.023 s
% 6.47/2.16 % (8086)Instructions burned: 73 (million)
% 6.47/2.16 % (8086)------------------------------
% 6.47/2.16 % (8086)------------------------------
% 6.47/2.17 % (8090)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/41Mi)
% 6.47/2.17 % (8089)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/11Mi)
% 6.47/2.18 % (8089)Instruction limit reached!
% 6.47/2.18 % (8089)------------------------------
% 6.47/2.18 % (8089)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.18 % (8089)Termination reason: Unknown
% 6.47/2.18 % (8089)Termination phase: shuffling
% 6.47/2.18
% 6.47/2.18 % (8089)Memory used [KB]: 1663
% 6.47/2.18 % (8089)Time elapsed: 0.004 s
% 6.47/2.18 % (8089)Instructions burned: 11 (million)
% 6.47/2.18 % (8089)------------------------------
% 6.47/2.18 % (8089)------------------------------
% 6.47/2.19 % (8093)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/6Mi)
% 6.47/2.19 % (8093)Instruction limit reached!
% 6.47/2.19 % (8093)------------------------------
% 6.47/2.19 % (8093)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.19 % (8093)Termination reason: Unknown
% 6.47/2.19 % (8093)Termination phase: shuffling
% 6.47/2.19
% 6.47/2.19 % (8093)Memory used [KB]: 1535
% 6.47/2.19 % (8093)Time elapsed: 0.004 s
% 6.47/2.19 % (8093)Instructions burned: 7 (million)
% 6.47/2.19 % (8093)------------------------------
% 6.47/2.19 % (8093)------------------------------
% 6.47/2.19 % (8090)Instruction limit reached!
% 6.47/2.19 % (8090)------------------------------
% 6.47/2.19 % (8090)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.19 % (8090)Termination reason: Unknown
% 6.47/2.19 % (8090)Termination phase: shuffling
% 6.47/2.19
% 6.47/2.19 % (8090)Memory used [KB]: 2174
% 6.47/2.19 % (8090)Time elapsed: 0.020 s
% 6.47/2.19 % (8090)Instructions burned: 42 (million)
% 6.47/2.19 % (8090)------------------------------
% 6.47/2.19 % (8090)------------------------------
% 6.47/2.19 % (8087)Instruction limit reached!
% 6.47/2.19 % (8087)------------------------------
% 6.47/2.19 % (8087)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.19 % (8087)Termination reason: Unknown
% 6.47/2.19 % (8087)Termination phase: Saturation
% 6.47/2.19
% 6.47/2.19 % (8087)Memory used [KB]: 6652
% 6.47/2.19 % (8087)Time elapsed: 0.042 s
% 6.47/2.19 % (8087)Instructions burned: 83 (million)
% 6.47/2.19 % (8087)------------------------------
% 6.47/2.19 % (8087)------------------------------
% 6.47/2.19 % (8064)Instruction limit reached!
% 6.47/2.19 % (8064)------------------------------
% 6.47/2.19 % (8064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.47/2.19 % (8064)Termination reason: Unknown
% 6.47/2.19 % (8064)Termination phase: Saturation
% 6.47/2.19
% 6.47/2.19 % (8064)Memory used [KB]: 8827
% 6.47/2.19 % (8064)Time elapsed: 0.264 s
% 6.47/2.19 % (8064)Instructions burned: 508 (million)
% 6.47/2.19 % (8064)------------------------------
% 6.47/2.19 % (8064)------------------------------
% 6.80/2.20 % (8097)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/343Mi)
% 6.80/2.21 % (8096)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/150Mi)
% 6.80/2.21 % (8098)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/109Mi)
% 6.80/2.21 % (8099)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_7787 for (2994ds/253Mi)
% 6.80/2.24 % (8079)Instruction limit reached!
% 6.80/2.24 % (8079)------------------------------
% 6.80/2.24 % (8079)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.80/2.24 % (8079)Termination reason: Unknown
% 6.80/2.24 % (8079)Termination phase: Saturation
% 6.80/2.24
% 6.80/2.24 % (8079)Memory used [KB]: 3837
% 6.80/2.24 % (8079)Time elapsed: 0.167 s
% 6.80/2.24 % (8079)Instructions burned: 434 (million)
% 6.80/2.24 % (8079)------------------------------
% 6.80/2.24 % (8079)------------------------------
% 6.80/2.25 % (8099)Refutation not found, incomplete strategy
% 6.80/2.25 % (8099)------------------------------
% 6.80/2.25 % (8099)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.80/2.25 % (8099)Termination reason: Refutation not found, incomplete strategy
% 6.80/2.25
% 6.80/2.25
% 6.80/2.25 % (8099)Memory used [KB]: 6908
% 6.80/2.25 % (8099)Time elapsed: 0.042 s
% 6.80/2.25 % (8099)Instructions burned: 82 (million)
% 6.80/2.25 % (8099)------------------------------
% 6.80/2.25 % (8099)------------------------------
% 6.80/2.25 % (8105)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_7787 for (2993ds/140Mi)
% 6.80/2.26 % (8098)Instruction limit reached!
% 6.80/2.26 % (8098)------------------------------
% 6.80/2.26 % (8098)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.80/2.26 % (8098)Termination reason: Unknown
% 6.80/2.26 % (8098)Termination phase: Property scanning
% 6.80/2.26
% 6.80/2.26 % (8098)Memory used [KB]: 2430
% 6.80/2.26 % (8098)Time elapsed: 0.052 s
% 6.80/2.26 % (8098)Instructions burned: 110 (million)
% 6.80/2.26 % (8098)------------------------------
% 6.80/2.26 % (8098)------------------------------
% 6.80/2.27 % (8107)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_7787 for (2993ds/614Mi)
% 6.80/2.27 % (8108)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_7787 for (2993ds/202Mi)
% 6.80/2.28 % (8096)Instruction limit reached!
% 6.80/2.28 % (8096)------------------------------
% 6.80/2.28 % (8096)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.80/2.28 % (8096)Termination reason: Unknown
% 6.80/2.28 % (8096)Termination phase: Saturation
% 6.80/2.28
% 6.80/2.28 % (8096)Memory used [KB]: 7164
% 6.80/2.28 % (8096)Time elapsed: 0.072 s
% 6.80/2.28 % (8096)Instructions burned: 150 (million)
% 6.80/2.28 % (8096)------------------------------
% 6.80/2.28 % (8096)------------------------------
% 6.80/2.30 % (8108)Refutation not found, incomplete strategy
% 6.80/2.30 % (8108)------------------------------
% 6.80/2.30 % (8108)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.80/2.30 % (8108)Termination reason: Refutation not found, incomplete strategy
% 6.80/2.30
% 6.80/2.30
% 6.80/2.30 % (8108)Memory used [KB]: 6780
% 6.80/2.30 % (8108)Time elapsed: 0.023 s
% 6.80/2.30 % (8108)Instructions burned: 64 (million)
% 6.80/2.30 % (8108)------------------------------
% 6.80/2.30 % (8108)------------------------------
% 7.24/2.30 % (8111)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_7787 for (2993ds/339Mi)
% 7.24/2.30 % (8105)Instruction limit reached!
% 7.24/2.30 % (8105)------------------------------
% 7.24/2.30 % (8105)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.30 % (8105)Termination reason: Unknown
% 7.24/2.30 % (8105)Termination phase: Saturation
% 7.24/2.30
% 7.24/2.30 % (8105)Memory used [KB]: 7164
% 7.24/2.30 % (8105)Time elapsed: 0.051 s
% 7.24/2.30 % (8105)Instructions burned: 141 (million)
% 7.24/2.30 % (8105)------------------------------
% 7.24/2.30 % (8105)------------------------------
% 7.24/2.31 % (8114)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=283:si=on:rtra=on_0 on DTF2THF_7787 for (2993ds/283Mi)
% 7.24/2.32 % (8116)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_7787 for (2993ds/134Mi)
% 7.24/2.33 % (8085)Instruction limit reached!
% 7.24/2.33 % (8085)------------------------------
% 7.24/2.33 % (8085)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.33 % (8085)Termination reason: Unknown
% 7.24/2.33 % (8085)Termination phase: Saturation
% 7.24/2.33
% 7.24/2.33 % (8085)Memory used [KB]: 7931
% 7.24/2.33 % (8085)Time elapsed: 0.210 s
% 7.24/2.33 % (8085)Instructions burned: 454 (million)
% 7.24/2.33 % (8085)------------------------------
% 7.24/2.33 % (8085)------------------------------
% 7.24/2.35 % (8120)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_7787 for (2992ds/298Mi)
% 7.24/2.36 % (8116)Instruction limit reached!
% 7.24/2.36 % (8116)------------------------------
% 7.24/2.36 % (8116)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.36 % (8116)Termination reason: Unknown
% 7.24/2.36 % (8116)Termination phase: Saturation
% 7.24/2.36
% 7.24/2.36 % (8116)Memory used [KB]: 7164
% 7.24/2.36 % (8116)Time elapsed: 0.040 s
% 7.24/2.36 % (8116)Instructions burned: 136 (million)
% 7.24/2.36 % (8116)------------------------------
% 7.24/2.36 % (8116)------------------------------
% 7.24/2.36 % (8097)Instruction limit reached!
% 7.24/2.36 % (8097)------------------------------
% 7.24/2.36 % (8097)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.24/2.36 % (8097)Termination reason: Unknown
% 7.24/2.36 % (8097)Termination phase: Saturation
% 7.24/2.36
% 7.24/2.36 % (8097)Memory used [KB]: 7291
% 7.24/2.36 % (8097)Time elapsed: 0.164 s
% 7.24/2.36 % (8097)Instructions burned: 345 (million)
% 7.24/2.36 % (8097)------------------------------
% 7.24/2.36 % (8097)------------------------------
% 7.24/2.37 % (8121)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_7787 for (2992ds/192Mi)
% 7.24/2.38 % (8122)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_7787 for (2992ds/258Mi)
% 7.75/2.43 % (8111)Instruction limit reached!
% 7.75/2.43 % (8111)------------------------------
% 7.75/2.43 % (8111)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.43 % (8111)Termination reason: Unknown
% 7.75/2.43 % (8111)Termination phase: Saturation
% 7.75/2.43
% 7.75/2.43 % (8111)Memory used [KB]: 7675
% 7.75/2.43 % (8111)Time elapsed: 0.132 s
% 7.75/2.43 % (8111)Instructions burned: 339 (million)
% 7.75/2.43 % (8111)------------------------------
% 7.75/2.43 % (8111)------------------------------
% 7.75/2.43 % (8114)Instruction limit reached!
% 7.75/2.43 % (8114)------------------------------
% 7.75/2.43 % (8114)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.43 % (8114)Termination reason: Unknown
% 7.75/2.43 % (8114)Termination phase: Saturation
% 7.75/2.43
% 7.75/2.43 % (8114)Memory used [KB]: 7547
% 7.75/2.43 % (8114)Time elapsed: 0.128 s
% 7.75/2.43 % (8114)Instructions burned: 283 (million)
% 7.75/2.43 % (8114)------------------------------
% 7.75/2.43 % (8114)------------------------------
% 7.75/2.44 % (8121)Instruction limit reached!
% 7.75/2.44 % (8121)------------------------------
% 7.75/2.44 % (8121)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.44 % (8121)Termination reason: Unknown
% 7.75/2.44 % (8121)Termination phase: Saturation
% 7.75/2.44
% 7.75/2.44 % (8121)Memory used [KB]: 3582
% 7.75/2.44 % (8121)Time elapsed: 0.073 s
% 7.75/2.44 % (8121)Instructions burned: 193 (million)
% 7.75/2.44 % (8121)------------------------------
% 7.75/2.44 % (8121)------------------------------
% 7.75/2.45 % (8127)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/231Mi)
% 7.75/2.45 % (8126)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/90Mi)
% 7.75/2.46 % (8128)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/458Mi)
% 7.75/2.46 % (8122)Refutation not found, incomplete strategy
% 7.75/2.46 % (8122)------------------------------
% 7.75/2.46 % (8122)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.46 % (8122)Termination reason: Refutation not found, incomplete strategy
% 7.75/2.46
% 7.75/2.46
% 7.75/2.46 % (8122)Memory used [KB]: 7291
% 7.75/2.46 % (8122)Time elapsed: 0.079 s
% 7.75/2.46 % (8122)Instructions burned: 164 (million)
% 7.75/2.46 % (8122)------------------------------
% 7.75/2.46 % (8122)------------------------------
% 7.75/2.47 % (8131)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/31Mi)
% 7.75/2.48 % (8120)Instruction limit reached!
% 7.75/2.48 % (8120)------------------------------
% 7.75/2.48 % (8120)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.48 % (8120)Termination reason: Unknown
% 7.75/2.48 % (8120)Termination phase: Saturation
% 7.75/2.48
% 7.75/2.48 % (8120)Memory used [KB]: 7675
% 7.75/2.48 % (8120)Time elapsed: 0.136 s
% 7.75/2.48 % (8120)Instructions burned: 299 (million)
% 7.75/2.48 % (8120)------------------------------
% 7.75/2.48 % (8120)------------------------------
% 7.75/2.49 % (8073)Instruction limit reached!
% 7.75/2.49 % (8073)------------------------------
% 7.75/2.49 % (8073)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.49 % (8073)Termination reason: Unknown
% 7.75/2.49 % (8073)Termination phase: Saturation
% 7.75/2.49
% 7.75/2.49 % (8073)Memory used [KB]: 8699
% 7.75/2.49 % (8073)Time elapsed: 0.459 s
% 7.75/2.49 % (8073)Instructions burned: 1089 (million)
% 7.75/2.49 % (8073)------------------------------
% 7.75/2.49 % (8073)------------------------------
% 7.75/2.49 % (8131)Instruction limit reached!
% 7.75/2.49 % (8131)------------------------------
% 7.75/2.49 % (8131)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.49 % (8131)Termination reason: Unknown
% 7.75/2.49 % (8131)Termination phase: Property scanning
% 7.75/2.49
% 7.75/2.49 % (8131)Memory used [KB]: 1918
% 7.75/2.49 % (8131)Time elapsed: 0.017 s
% 7.75/2.49 % (8131)Instructions burned: 32 (million)
% 7.75/2.49 % (8131)------------------------------
% 7.75/2.49 % (8131)------------------------------
% 7.75/2.49 % (8126)Instruction limit reached!
% 7.75/2.49 % (8126)------------------------------
% 7.75/2.49 % (8126)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.75/2.49 % (8126)Termination reason: Unknown
% 7.75/2.49 % (8126)Termination phase: Property scanning
% 7.75/2.49
% 7.75/2.49 % (8126)Memory used [KB]: 2430
% 7.75/2.49 % (8126)Time elapsed: 0.044 s
% 7.75/2.49 % (8126)Instructions burned: 90 (million)
% 7.75/2.49 % (8126)------------------------------
% 7.75/2.49 % (8126)------------------------------
% 8.91/2.50 % (8135)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/297Mi)
% 8.91/2.50 % (8136)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/987Mi)
% 8.91/2.51 % (8137)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/182Mi)
% 8.91/2.51 % (8138)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_7787 for (2991ds/182Mi)
% 8.91/2.55 % (8107)Instruction limit reached!
% 8.91/2.55 % (8107)------------------------------
% 8.91/2.55 % (8107)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.55 % (8107)Termination reason: Unknown
% 8.91/2.55 % (8107)Termination phase: Saturation
% 8.91/2.55
% 8.91/2.55 % (8107)Memory used [KB]: 8315
% 8.91/2.55 % (8107)Time elapsed: 0.283 s
% 8.91/2.55 % (8107)Instructions burned: 614 (million)
% 8.91/2.55 % (8107)------------------------------
% 8.91/2.55 % (8107)------------------------------
% 8.91/2.55 % (8127)Instruction limit reached!
% 8.91/2.55 % (8127)------------------------------
% 8.91/2.55 % (8127)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.55 % (8127)Termination reason: Unknown
% 8.91/2.55 % (8127)Termination phase: Saturation
% 8.91/2.55
% 8.91/2.55 % (8127)Memory used [KB]: 7164
% 8.91/2.55 % (8127)Time elapsed: 0.105 s
% 8.91/2.55 % (8127)Instructions burned: 232 (million)
% 8.91/2.55 % (8127)------------------------------
% 8.91/2.55 % (8127)------------------------------
% 8.91/2.56 % (8139)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_7787 for (2990ds/154Mi)
% 8.91/2.58 % (8140)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_7787 for (2990ds/79Mi)
% 8.91/2.58 % (8138)Instruction limit reached!
% 8.91/2.58 % (8138)------------------------------
% 8.91/2.58 % (8138)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.58 % (8138)Termination reason: Unknown
% 8.91/2.58 % (8138)Termination phase: Saturation
% 8.91/2.58
% 8.91/2.58 % (8138)Memory used [KB]: 7419
% 8.91/2.58 % (8138)Time elapsed: 0.076 s
% 8.91/2.58 % (8138)Instructions burned: 183 (million)
% 8.91/2.58 % (8138)------------------------------
% 8.91/2.58 % (8138)------------------------------
% 8.91/2.58 % (8137)Instruction limit reached!
% 8.91/2.58 % (8137)------------------------------
% 8.91/2.58 % (8137)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.91/2.59 % (8137)Termination reason: Unknown
% 8.91/2.59 % (8137)Termination phase: Saturation
% 8.91/2.59
% 8.91/2.59 % (8137)Memory used [KB]: 7164
% 8.91/2.59 % (8137)Time elapsed: 0.080 s
% 8.91/2.59 % (8137)Instructions burned: 184 (million)
% 8.91/2.59 % (8137)------------------------------
% 8.91/2.59 % (8137)------------------------------
% 8.91/2.59 % (8144)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_7787 for (2990ds/216Mi)
% 8.91/2.59 % (8145)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_7787 for (2990ds/114Mi)
% 9.51/2.60 % (8135)Instruction limit reached!
% 9.51/2.60 % (8135)------------------------------
% 9.51/2.60 % (8135)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.60 % (8135)Termination reason: Unknown
% 9.51/2.60 % (8135)Termination phase: Saturation
% 9.51/2.60
% 9.51/2.60 % (8135)Memory used [KB]: 7419
% 9.51/2.60 % (8135)Time elapsed: 0.124 s
% 9.51/2.60 % (8135)Instructions burned: 298 (million)
% 9.51/2.60 % (8135)------------------------------
% 9.51/2.60 % (8135)------------------------------
% 9.51/2.62 % (8147)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_7787 for (2990ds/922Mi)
% 9.51/2.62 % (8140)Instruction limit reached!
% 9.51/2.62 % (8140)------------------------------
% 9.51/2.62 % (8140)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.62 % (8140)Termination reason: Unknown
% 9.51/2.62 % (8140)Termination phase: Property scanning
% 9.51/2.62
% 9.51/2.62 % (8140)Memory used [KB]: 2430
% 9.51/2.62 % (8140)Time elapsed: 0.039 s
% 9.51/2.62 % (8140)Instructions burned: 80 (million)
% 9.51/2.62 % (8140)------------------------------
% 9.51/2.62 % (8140)------------------------------
% 9.51/2.63 % (8139)Instruction limit reached!
% 9.51/2.63 % (8139)------------------------------
% 9.51/2.63 % (8139)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.63 % (8139)Termination reason: Unknown
% 9.51/2.63 % (8139)Termination phase: Property scanning
% 9.51/2.63
% 9.51/2.63 % (8139)Memory used [KB]: 2430
% 9.51/2.63 % (8139)Time elapsed: 0.071 s
% 9.51/2.63 % (8139)Instructions burned: 156 (million)
% 9.51/2.63 % (8139)------------------------------
% 9.51/2.63 % (8139)------------------------------
% 9.51/2.63 % (8148)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_7787 for (2989ds/182Mi)
% 9.51/2.65 % (8145)Instruction limit reached!
% 9.51/2.65 % (8145)------------------------------
% 9.51/2.65 % (8145)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.65 % (8145)Termination reason: Unknown
% 9.51/2.65 % (8145)Termination phase: Saturation
% 9.51/2.65
% 9.51/2.65 % (8145)Memory used [KB]: 7036
% 9.51/2.65 % (8145)Time elapsed: 0.053 s
% 9.51/2.65 % (8145)Instructions burned: 115 (million)
% 9.51/2.65 % (8145)------------------------------
% 9.51/2.65 % (8145)------------------------------
% 9.51/2.65 % (8151)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_7787 for (2989ds/164Mi)
% 9.51/2.66 % (8152)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_7787 for (2989ds/50Mi)
% 9.51/2.67 % (8144)Instruction limit reached!
% 9.51/2.67 % (8144)------------------------------
% 9.51/2.67 % (8144)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.67 % (8144)Termination reason: Unknown
% 9.51/2.67 % (8144)Termination phase: Saturation
% 9.51/2.67
% 9.51/2.67 % (8144)Memory used [KB]: 7291
% 9.51/2.67 % (8144)Time elapsed: 0.106 s
% 9.51/2.67 % (8144)Instructions burned: 216 (million)
% 9.51/2.67 % (8144)------------------------------
% 9.51/2.67 % (8144)------------------------------
% 9.51/2.68 % (8128)Instruction limit reached!
% 9.51/2.68 % (8128)------------------------------
% 9.51/2.68 % (8128)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.68 % (8128)Termination reason: Unknown
% 9.51/2.68 % (8128)Termination phase: Saturation
% 9.51/2.68
% 9.51/2.68 % (8128)Memory used [KB]: 8315
% 9.51/2.68 % (8128)Time elapsed: 0.226 s
% 9.51/2.68 % (8128)Instructions burned: 459 (million)
% 9.51/2.68 % (8128)------------------------------
% 9.51/2.68 % (8128)------------------------------
% 9.51/2.68 % (8155)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_7787 for (2989ds/368Mi)
% 9.51/2.69 % (8152)Instruction limit reached!
% 9.51/2.69 % (8152)------------------------------
% 9.51/2.69 % (8152)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.51/2.69 % (8152)Termination reason: Unknown
% 9.51/2.69 % (8152)Termination phase: Property scanning
% 9.51/2.69
% 9.51/2.69 % (8152)Memory used [KB]: 2302
% 9.51/2.69 % (8152)Time elapsed: 0.025 s
% 9.51/2.69 % (8152)Instructions burned: 50 (million)
% 9.51/2.69 % (8152)------------------------------
% 9.51/2.69 % (8152)------------------------------
% 10.19/2.70 % (8156)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_7787 for (2989ds/1021Mi)
% 10.19/2.71 % (8159)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_7787 for (2989ds/267Mi)
% 10.19/2.71 % (8148)Instruction limit reached!
% 10.19/2.71 % (8148)------------------------------
% 10.19/2.71 % (8148)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.19/2.71 % (8148)Termination reason: Unknown
% 10.19/2.71 % (8148)Termination phase: Saturation
% 10.19/2.71
% 10.19/2.71 % (8148)Memory used [KB]: 6908
% 10.19/2.71 % (8148)Time elapsed: 0.082 s
% 10.19/2.71 % (8148)Instructions burned: 182 (million)
% 10.19/2.71 % (8148)------------------------------
% 10.19/2.71 % (8148)------------------------------
% 10.19/2.73 % (8151)Instruction limit reached!
% 10.19/2.73 % (8151)------------------------------
% 10.19/2.73 % (8151)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.19/2.73 % (8151)Termination reason: Unknown
% 10.19/2.73 % (8151)Termination phase: Saturation
% 10.19/2.73
% 10.19/2.73 % (8151)Memory used [KB]: 2814
% 10.19/2.73 % (8151)Time elapsed: 0.077 s
% 10.19/2.73 % (8151)Instructions burned: 164 (million)
% 10.19/2.73 % (8151)------------------------------
% 10.19/2.73 % (8151)------------------------------
% 10.19/2.73 % (8161)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_7787 for (2988ds/204Mi)
% 10.19/2.74 % (8162)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_7787 for (2988ds/26Mi)
% 10.19/2.75 % (8162)Instruction limit reached!
% 10.19/2.75 % (8162)------------------------------
% 10.19/2.75 % (8162)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.19/2.75 % (8162)Termination reason: Unknown
% 10.19/2.75 % (8162)Termination phase: shuffling
% 10.19/2.75
% 10.19/2.75 % (8162)Memory used [KB]: 2046
% 10.19/2.75 % (8162)Time elapsed: 0.014 s
% 10.19/2.75 % (8162)Instructions burned: 27 (million)
% 10.19/2.75 % (8162)------------------------------
% 10.19/2.75 % (8162)------------------------------
% 10.19/2.78 % (8166)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_7787 for (2988ds/53Mi)
% 10.19/2.79 % (8155)Instruction limit reached!
% 10.19/2.79 % (8155)------------------------------
% 10.19/2.79 % (8155)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.19/2.79 % (8155)Termination reason: Unknown
% 10.19/2.79 % (8155)Termination phase: Saturation
% 10.19/2.79
% 10.19/2.79 % (8155)Memory used [KB]: 8059
% 10.19/2.79 % (8155)Time elapsed: 0.112 s
% 10.19/2.79 % (8155)Instructions burned: 369 (million)
% 10.19/2.79 % (8155)------------------------------
% 10.19/2.79 % (8155)------------------------------
% 10.53/2.80 % (8166)Instruction limit reached!
% 10.53/2.80 % (8166)------------------------------
% 10.53/2.80 % (8166)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.80 % (8166)Termination reason: Unknown
% 10.53/2.80 % (8166)Termination phase: Property scanning
% 10.53/2.80
% 10.53/2.80 % (8166)Memory used [KB]: 2302
% 10.53/2.80 % (8166)Time elapsed: 0.027 s
% 10.53/2.80 % (8166)Instructions burned: 54 (million)
% 10.53/2.80 % (8166)------------------------------
% 10.53/2.80 % (8166)------------------------------
% 10.53/2.81 % (8169)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_7787 for (2988ds/4436Mi)
% 10.53/2.82 % (8171)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_7787 for (2988ds/1539Mi)
% 10.53/2.83 % (8161)Instruction limit reached!
% 10.53/2.83 % (8161)------------------------------
% 10.53/2.83 % (8161)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.83 % (8161)Termination reason: Unknown
% 10.53/2.83 % (8161)Termination phase: Saturation
% 10.53/2.83
% 10.53/2.83 % (8161)Memory used [KB]: 7291
% 10.53/2.83 % (8161)Time elapsed: 0.098 s
% 10.53/2.83 % (8161)Instructions burned: 204 (million)
% 10.53/2.83 % (8161)------------------------------
% 10.53/2.83 % (8161)------------------------------
% 10.53/2.84 % (8159)Instruction limit reached!
% 10.53/2.84 % (8159)------------------------------
% 10.53/2.84 % (8159)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.53/2.84 % (8159)Termination reason: Unknown
% 10.53/2.84 % (8159)Termination phase: Saturation
% 10.53/2.84
% 10.53/2.84 % (8159)Memory used [KB]: 7547
% 10.53/2.84 % (8159)Time elapsed: 0.127 s
% 10.53/2.84 % (8159)Instructions burned: 268 (million)
% 10.53/2.84 % (8159)------------------------------
% 10.53/2.84 % (8159)------------------------------
% 10.53/2.85 % (8173)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_7787 for (2987ds/408Mi)
% 10.53/2.86 % (8174)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_7787 for (2987ds/5205Mi)
% 10.83/2.94 % (8136)Instruction limit reached!
% 10.83/2.94 % (8136)------------------------------
% 10.83/2.94 % (8136)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.83/2.94 % (8136)Termination reason: Unknown
% 10.83/2.94 % (8136)Termination phase: Saturation
% 10.83/2.94
% 10.83/2.94 % (8136)Memory used [KB]: 9594
% 10.83/2.94 % (8136)Time elapsed: 0.438 s
% 10.83/2.94 % (8136)Instructions burned: 987 (million)
% 10.83/2.94 % (8136)------------------------------
% 10.83/2.94 % (8136)------------------------------
% 10.83/2.96 % (8181)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_7787 for (2986ds/1913Mi)
% 12.68/3.04 % (8173)Instruction limit reached!
% 12.68/3.04 % (8173)------------------------------
% 12.68/3.04 % (8173)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.04 % (8173)Termination reason: Unknown
% 12.68/3.04 % (8173)Termination phase: Saturation
% 12.68/3.04
% 12.68/3.04 % (8173)Memory used [KB]: 8571
% 12.68/3.04 % (8173)Time elapsed: 0.201 s
% 12.68/3.04 % (8173)Instructions burned: 408 (million)
% 12.68/3.04 % (8173)------------------------------
% 12.68/3.04 % (8173)------------------------------
% 12.68/3.06 % (8185)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_7787 for (2985ds/4350Mi)
% 12.68/3.07 % (8147)Instruction limit reached!
% 12.68/3.07 % (8147)------------------------------
% 12.68/3.07 % (8147)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.68/3.07 % (8147)Termination reason: Unknown
% 12.68/3.07 % (8147)Termination phase: Saturation
% 12.68/3.07
% 12.68/3.07 % (8147)Memory used [KB]: 8059
% 12.68/3.07 % (8147)Time elapsed: 0.450 s
% 12.68/3.07 % (8147)Instructions burned: 922 (million)
% 12.68/3.07 % (8147)------------------------------
% 12.68/3.07 % (8147)------------------------------
% 12.68/3.08 % (8186)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_7787 for (2985ds/68Mi)
% 13.28/3.12 % (8186)Instruction limit reached!
% 13.28/3.12 % (8186)------------------------------
% 13.28/3.12 % (8186)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.28/3.12 % (8186)Termination reason: Unknown
% 13.28/3.12 % (8186)Termination phase: Property scanning
% 13.28/3.12
% 13.28/3.12 % (8186)Memory used [KB]: 2430
% 13.28/3.12 % (8186)Time elapsed: 0.035 s
% 13.28/3.12 % (8186)Instructions burned: 69 (million)
% 13.28/3.12 % (8186)------------------------------
% 13.28/3.12 % (8186)------------------------------
% 13.28/3.13 % (8156)Instruction limit reached!
% 13.28/3.13 % (8156)------------------------------
% 13.28/3.13 % (8156)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.28/3.13 % (8156)Termination reason: Unknown
% 13.28/3.13 % (8156)Termination phase: Saturation
% 13.28/3.13
% 13.28/3.13 % (8156)Memory used [KB]: 9466
% 13.28/3.13 % (8156)Time elapsed: 0.432 s
% 13.28/3.13 % (8156)Instructions burned: 1022 (million)
% 13.28/3.13 % (8156)------------------------------
% 13.28/3.13 % (8156)------------------------------
% 13.28/3.13 % (8187)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_7787 for (2984ds/358Mi)
% 13.28/3.15 % (8189)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_7787 for (2984ds/31Mi)
% 13.28/3.16 % (8189)Instruction limit reached!
% 13.28/3.16 % (8189)------------------------------
% 13.28/3.16 % (8189)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.28/3.16 % (8189)Termination reason: Unknown
% 13.28/3.16 % (8189)Termination phase: Property scanning
% 13.28/3.16
% 13.28/3.16 % (8189)Memory used [KB]: 1918
% 13.28/3.16 % (8189)Time elapsed: 0.011 s
% 13.28/3.16 % (8189)Instructions burned: 32 (million)
% 13.28/3.16 % (8189)------------------------------
% 13.28/3.16 % (8189)------------------------------
% 13.28/3.17 % (8190)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_7787 for (2984ds/279Mi)
% 13.68/3.20 % (8190)Refutation not found, incomplete strategy
% 13.68/3.20 % (8190)------------------------------
% 13.68/3.20 % (8190)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.68/3.20 % (8190)Termination reason: Refutation not found, incomplete strategy
% 13.68/3.20
% 13.68/3.20
% 13.68/3.20 % (8190)Memory used [KB]: 6908
% 13.68/3.20 % (8190)Time elapsed: 0.032 s
% 13.68/3.20 % (8190)Instructions burned: 107 (million)
% 13.68/3.20 % (8190)------------------------------
% 13.68/3.20 % (8190)------------------------------
% 13.68/3.22 % (8192)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_7787 for (2984ds/258Mi)
% 14.13/3.30 % (8187)Instruction limit reached!
% 14.13/3.30 % (8187)------------------------------
% 14.13/3.30 % (8187)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.13/3.30 % (8187)Termination reason: Unknown
% 14.13/3.30 % (8187)Termination phase: Saturation
% 14.13/3.30
% 14.13/3.30 % (8187)Memory used [KB]: 7547
% 14.13/3.30 % (8187)Time elapsed: 0.167 s
% 14.13/3.30 % (8187)Instructions burned: 358 (million)
% 14.13/3.30 % (8187)------------------------------
% 14.13/3.30 % (8187)------------------------------
% 14.13/3.31 % (8196)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_7787 for (2983ds/26Mi)
% 14.13/3.32 % (8192)Instruction limit reached!
% 14.13/3.32 % (8192)------------------------------
% 14.13/3.32 % (8192)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.13/3.32 % (8192)Termination reason: Unknown
% 14.13/3.32 % (8192)Termination phase: Saturation
% 14.13/3.32
% 14.13/3.32 % (8192)Memory used [KB]: 7675
% 14.13/3.32 % (8192)Time elapsed: 0.106 s
% 14.13/3.32 % (8192)Instructions burned: 259 (million)
% 14.13/3.32 % (8192)------------------------------
% 14.13/3.32 % (8192)------------------------------
% 14.13/3.33 % (8196)Instruction limit reached!
% 14.13/3.33 % (8196)------------------------------
% 14.13/3.33 % (8196)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.13/3.33 % (8196)Termination reason: Unknown
% 14.13/3.33 % (8196)Termination phase: shuffling
% 14.13/3.33
% 14.13/3.33 % (8196)Memory used [KB]: 1918
% 14.13/3.33 % (8196)Time elapsed: 0.014 s
% 14.13/3.33 % (8196)Instructions burned: 27 (million)
% 14.13/3.33 % (8196)------------------------------
% 14.13/3.33 % (8196)------------------------------
% 14.13/3.34 % (8198)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_7787 for (2982ds/995Mi)
% 14.13/3.34 % (8199)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_7787 for (2982ds/373Mi)
% 14.86/3.42 % (8171)Instruction limit reached!
% 14.86/3.42 % (8171)------------------------------
% 14.86/3.42 % (8171)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.42 % (8171)Termination reason: Unknown
% 14.86/3.42 % (8171)Termination phase: Saturation
% 14.86/3.42
% 14.86/3.42 % (8171)Memory used [KB]: 12792
% 14.86/3.42 % (8171)Time elapsed: 0.600 s
% 14.86/3.42 % (8171)Instructions burned: 1542 (million)
% 14.86/3.42 % (8171)------------------------------
% 14.86/3.42 % (8171)------------------------------
% 14.86/3.43 % (8201)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_7787 for (2981ds/253Mi)
% 14.86/3.49 % (8199)Instruction limit reached!
% 14.86/3.49 % (8199)------------------------------
% 14.86/3.49 % (8199)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.86/3.49 % (8199)Termination reason: Unknown
% 14.86/3.49 % (8199)Termination phase: Saturation
% 14.86/3.49
% 14.86/3.49 % (8199)Memory used [KB]: 8187
% 14.86/3.49 % (8199)Time elapsed: 0.148 s
% 14.86/3.49 % (8199)Instructions burned: 374 (million)
% 14.86/3.49 % (8199)------------------------------
% 14.86/3.49 % (8199)------------------------------
% 15.36/3.50 % (8204)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_7787 for (2981ds/832Mi)
% 15.36/3.53 % (8201)Instruction limit reached!
% 15.36/3.53 % (8201)------------------------------
% 15.36/3.53 % (8201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.36/3.53 % (8201)Termination reason: Unknown
% 15.36/3.53 % (8201)Termination phase: Saturation
% 15.36/3.53
% 15.36/3.53 % (8201)Memory used [KB]: 7547
% 15.36/3.53 % (8201)Time elapsed: 0.103 s
% 15.36/3.53 % (8201)Instructions burned: 253 (million)
% 15.36/3.53 % (8201)------------------------------
% 15.36/3.53 % (8201)------------------------------
% 15.36/3.53 % (8181)Instruction limit reached!
% 15.36/3.53 % (8181)------------------------------
% 15.36/3.53 % (8181)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.36/3.53 % (8181)Termination reason: Unknown
% 15.36/3.53 % (8181)Termination phase: Saturation
% 15.36/3.53
% 15.36/3.53 % (8181)Memory used [KB]: 2814
% 15.36/3.53 % (8181)Time elapsed: 0.574 s
% 15.36/3.53 % (8181)Instructions burned: 1915 (million)
% 15.36/3.53 % (8181)------------------------------
% 15.36/3.53 % (8181)------------------------------
% 15.36/3.55 % (8207)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=40:si=on:rtra=on_0 on DTF2THF_7787 for (2980ds/40Mi)
% 15.36/3.55 % (8206)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_7787 for (2980ds/668Mi)
% 15.36/3.56 % (8204)Refutation not found, incomplete strategy
% 15.36/3.56 % (8204)------------------------------
% 15.36/3.56 % (8204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.36/3.56 % (8204)Termination reason: Refutation not found, incomplete strategy
% 15.36/3.56
% 15.36/3.56
% 15.36/3.56 % (8204)Memory used [KB]: 8059
% 15.36/3.56 % (8204)Time elapsed: 0.058 s
% 15.36/3.56 % (8204)Instructions burned: 188 (million)
% 15.36/3.56 % (8204)------------------------------
% 15.36/3.56 % (8204)------------------------------
% 15.36/3.56 % (8207)Instruction limit reached!
% 15.36/3.56 % (8207)------------------------------
% 15.36/3.56 % (8207)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.36/3.56 % (8207)Termination reason: Unknown
% 15.36/3.56 % (8207)Termination phase: shuffling
% 15.36/3.56
% 15.36/3.56 % (8207)Memory used [KB]: 2174
% 15.36/3.56 % (8207)Time elapsed: 0.020 s
% 15.36/3.56 % (8207)Instructions burned: 40 (million)
% 15.36/3.56 % (8207)------------------------------
% 15.36/3.56 % (8207)------------------------------
% 15.36/3.57 % (8208)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_7787 for (2980ds/294Mi)
% 15.36/3.58 % (8209)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_7787 for (2980ds/187Mi)
% 15.36/3.59 % (8208)Refutation not found, incomplete strategy
% 15.36/3.59 % (8208)------------------------------
% 15.36/3.59 % (8208)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.36/3.59 % (8208)Termination reason: Refutation not found, incomplete strategy
% 15.36/3.59
% 15.36/3.59
% 15.36/3.59 % (8208)Memory used [KB]: 6908
% 15.36/3.59 % (8208)Time elapsed: 0.028 s
% 15.36/3.59 % (8208)Instructions burned: 101 (million)
% 15.36/3.59 % (8208)------------------------------
% 15.36/3.59 % (8208)------------------------------
% 15.86/3.60 % (8210)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_7787 for (2980ds/371Mi)
% 15.86/3.67 % (8209)Instruction limit reached!
% 15.86/3.67 % (8209)------------------------------
% 15.86/3.67 % (8209)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.86/3.67 % (8209)Termination reason: Unknown
% 15.86/3.67 % (8209)Termination phase: Saturation
% 15.86/3.67
% 15.86/3.67 % (8209)Memory used [KB]: 7419
% 15.86/3.67 % (8209)Time elapsed: 0.090 s
% 15.86/3.67 % (8209)Instructions burned: 187 (million)
% 15.86/3.67 % (8209)------------------------------
% 15.86/3.67 % (8209)------------------------------
% 15.86/3.69 % (8211)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_7787 for (2979ds/1827Mi)
% 16.16/3.73 % (8210)Instruction limit reached!
% 16.16/3.73 % (8210)------------------------------
% 16.16/3.73 % (8210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/3.73 % (8210)Termination reason: Unknown
% 16.16/3.73 % (8210)Termination phase: Saturation
% 16.16/3.73
% 16.16/3.73 % (8210)Memory used [KB]: 7164
% 16.16/3.73 % (8210)Time elapsed: 0.126 s
% 16.16/3.73 % (8210)Instructions burned: 371 (million)
% 16.16/3.73 % (8210)------------------------------
% 16.16/3.73 % (8210)------------------------------
% 16.16/3.74 % (8214)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_7787 for (2978ds/70Mi)
% 16.16/3.76 % (8214)Instruction limit reached!
% 16.16/3.76 % (8214)------------------------------
% 16.16/3.76 % (8214)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.16/3.76 % (8214)Termination reason: Unknown
% 16.16/3.76 % (8214)Termination phase: Property scanning
% 16.16/3.76
% 16.16/3.76 % (8214)Memory used [KB]: 2302
% 16.16/3.76 % (8214)Time elapsed: 0.020 s
% 16.16/3.76 % (8214)Instructions burned: 70 (million)
% 16.16/3.76 % (8214)------------------------------
% 16.16/3.76 % (8214)------------------------------
% 16.16/3.77 % (8215)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_7787 for (2978ds/316Mi)
% 16.52/3.81 % (8198)Instruction limit reached!
% 16.52/3.81 % (8198)------------------------------
% 16.52/3.81 % (8198)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/3.81 % (8198)Termination reason: Unknown
% 16.52/3.81 % (8198)Termination phase: Saturation
% 16.52/3.81
% 16.52/3.81 % (8198)Memory used [KB]: 9210
% 16.52/3.81 % (8198)Time elapsed: 0.469 s
% 16.52/3.81 % (8198)Instructions burned: 996 (million)
% 16.52/3.81 % (8198)------------------------------
% 16.52/3.81 % (8198)------------------------------
% 16.52/3.82 % (8218)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_7787 for (2978ds/932Mi)
% 16.52/3.83 % (8215)Refutation not found, incomplete strategy
% 16.52/3.83 % (8215)------------------------------
% 16.52/3.83 % (8215)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/3.83 % (8215)Termination reason: Refutation not found, incomplete strategy
% 16.52/3.83
% 16.52/3.83
% 16.52/3.83 % (8215)Memory used [KB]: 7547
% 16.52/3.83 % (8215)Time elapsed: 0.065 s
% 16.52/3.83 % (8215)Instructions burned: 235 (million)
% 16.52/3.83 % (8215)------------------------------
% 16.52/3.83 % (8215)------------------------------
% 16.52/3.84 % (8174)First to succeed.
% 16.52/3.84 % (8220)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_7787 for (2977ds/4714Mi)
% 16.52/3.84 % (8174)Refutation found. Thanks to Tanya!
% 16.52/3.84 % SZS status Theorem for DTF2THF_7787
% 16.52/3.84 % SZS output start Proof for DTF2THF_7787
% 16.52/3.84 thf(type_def_5, type, list: ($tType) > $tType).
% 16.52/3.84 thf(type_def_6, type, set: ($tType) > $tType).
% 16.52/3.84 thf(type_def_8, type, secrecy_specID: $tType).
% 16.52/3.84 thf(type_def_9, type, secrecy_KS: $tType).
% 16.52/3.84 thf(type_def_10, type, secrecy_Expression: $tType).
% 16.52/3.84 thf(type_def_11, type, secrecy_Keys: $tType).
% 16.52/3.84 thf(type_def_12, type, secrecy_Secrets: $tType).
% 16.52/3.84 thf(func_def_0, type, secrecy_Expression: $tType).
% 16.52/3.84 thf(func_def_1, type, secrecy_Secrets: $tType).
% 16.52/3.84 thf(func_def_2, type, secrecy_specID: $tType).
% 16.52/3.84 thf(func_def_3, type, secrecy_Keys: $tType).
% 16.52/3.84 thf(func_def_4, type, secrecy_KS: $tType).
% 16.52/3.84 thf(func_def_5, type, list: ($tType) > $tType).
% 16.52/3.84 thf(func_def_6, type, set: ($tType) > $tType).
% 16.52/3.84 thf(func_def_7, type, type: !>[X0: $tType]:($o)).
% 16.52/3.84 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 16.52/3.84 thf(func_def_9, type, order: !>[X0: $tType]:($o)).
% 16.52/3.84 thf(func_def_10, type, linorder: !>[X0: $tType]:($o)).
% 16.52/3.84 thf(func_def_11, type, bNF_Greatest_Shift: !>[X0: $tType]:(set @ list @ X0 > X0 > set @ list @ X0)).
% 16.52/3.84 thf(func_def_12, type, bNF_Greatest_Succ: !>[X0: $tType]:(set @ list @ X0 > list @ X0 > set @ X0)).
% 16.52/3.84 thf(func_def_13, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > X0 > list @ X0 > X1)).
% 16.52/3.84 thf(func_def_14, type, localSecrets: secrecy_specID > set @ secrecy_KS).
% 16.52/3.84 thf(func_def_15, type, monoid: !>[X0: $tType]:((X0 > X0 > X0) > X0 > $o)).
% 16.52/3.84 thf(func_def_16, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 16.52/3.84 thf(func_def_17, type, knowle1667810483orrect: secrecy_specID > secrecy_KS > $o).
% 16.52/3.84 thf(func_def_18, type, knowle1893229345orrect: secrecy_specID > secrecy_Expression > $o).
% 16.52/3.84 thf(func_def_19, type, knowle1437066798e_know: secrecy_specID > secrecy_KS > $o).
% 16.52/3.84 thf(func_def_20, type, knowle2055185861_knows: secrecy_specID > list @ secrecy_Expression > $o).
% 16.52/3.84 thf(func_def_21, type, disjoint: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_22, type, mem: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_23, type, memS: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_24, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_25, type, arg_min_list: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > X0)).
% 16.52/3.84 thf(func_def_26, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 16.52/3.84 thf(func_def_27, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_28, type, concat: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_29, type, distinct_adj: !>[X0: $tType]:(list @ X0 > $o)).
% 16.52/3.84 thf(func_def_30, type, foldr: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > list @ X0 > X1 > X1)).
% 16.52/3.84 thf(func_def_31, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_32, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 16.52/3.84 thf(func_def_33, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_34, type, nil: !>[X0: $tType]:(list @ X0)).
% 16.52/3.84 thf(func_def_35, type, case_list: !>[X0: $tType, X1: $tType]:(X0 > (X1 > list @ X1 > X0) > list @ X1 > X0)).
% 16.52/3.84 thf(func_def_36, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 16.52/3.84 thf(func_def_37, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_38, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_39, type, listrelp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > list @ X0 > list @ X1 > $o)).
% 16.52/3.84 thf(func_def_40, type, map_tailrec: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 16.52/3.84 thf(func_def_41, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1 > list @ X1)).
% 16.52/3.84 thf(func_def_42, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 16.52/3.84 thf(func_def_43, type, member: !>[X0: $tType]:(list @ X0 > X0 > $o)).
% 16.52/3.84 thf(func_def_44, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_45, type, ord_lexordp: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_46, type, ord_lexordp_eq: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_47, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 16.52/3.84 thf(func_def_48, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_49, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_50, type, shuffles: !>[X0: $tType]:(list @ X0 > list @ X0 > set @ list @ X0)).
% 16.52/3.84 thf(func_def_51, type, splice: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 16.52/3.84 thf(func_def_52, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 16.52/3.84 thf(func_def_53, type, successively: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > $o)).
% 16.52/3.84 thf(func_def_54, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 16.52/3.84 thf(func_def_55, type, decr: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 16.52/3.84 thf(func_def_56, type, enc: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 16.52/3.84 thf(func_def_57, type, encrDecrKeys: secrecy_Keys > secrecy_Keys > $o).
% 16.52/3.84 thf(func_def_58, type, ext: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 16.52/3.84 thf(func_def_59, type, sign: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 16.52/3.84 thf(func_def_60, type, eout: secrecy_specID > secrecy_Expression > $o).
% 16.52/3.84 thf(func_def_61, type, ine: secrecy_specID > secrecy_Expression > $o).
% 16.52/3.84 thf(func_def_62, type, notSpe1586871396tsExpr: secrecy_specID > list @ secrecy_Expression > $o).
% 16.52/3.84 thf(func_def_63, type, specKeys: secrecy_specID > set @ secrecy_Keys).
% 16.52/3.84 thf(func_def_64, type, specKeysSecrets: secrecy_specID > set @ secrecy_KS).
% 16.52/3.84 thf(func_def_65, type, specSecrets: secrecy_specID > set @ secrecy_Secrets).
% 16.52/3.84 thf(func_def_66, type, secrec1371625429on2KSL: list @ secrecy_Expression > list @ secrecy_KS).
% 16.52/3.84 thf(func_def_67, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 16.52/3.84 thf(func_def_68, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 16.52/3.84 thf(func_def_69, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 16.52/3.84 thf(func_def_70, type, secrecy_case_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 16.52/3.84 thf(func_def_71, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 16.52/3.84 thf(func_def_72, type, secrecy_rec_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 16.52/3.84 thf(func_def_73, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 16.52/3.84 thf(func_def_74, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 16.52/3.84 thf(func_def_75, type, member2: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 16.52/3.84 thf(func_def_76, type, a: secrecy_specID).
% 16.52/3.84 thf(func_def_77, type, m: secrecy_Keys).
% 16.52/3.84 thf(func_def_98, type, ph1: !>[X0: $tType]:(X0)).
% 16.52/3.84 thf(f3942,plain,(
% 16.52/3.84 $false),
% 16.52/3.84 inference(trivial_inequality_removal,[status(thm)],[f3938])).
% 16.52/3.84 thf(f3938,plain,(
% 16.52/3.84 ($false = $true)),
% 16.52/3.84 inference(equality_proxy_clausification,[status(thm)],[f3932])).
% 16.52/3.84 thf(f3932,plain,(
% 16.52/3.84 (($true = $false) = $true)),
% 16.52/3.84 inference(forward_demodulation,[status(thm)],[f3931,f1361])).
% 16.52/3.84 thf(f1361,plain,(
% 16.52/3.84 ((knowle1437066798e_know @ a @ (secrecy_kKS @ m)) = $false)),
% 16.52/3.84 inference(not_proxy_clausification,[status(thm)],[f1321])).
% 16.52/3.84 thf(f1321,plain,(
% 16.52/3.84 ((~ (knowle1437066798e_know @ a @ (secrecy_kKS @ m))) = $true)),
% 16.52/3.84 inference(cnf_transformation,[status(thm)],[f566])).
% 16.52/3.84 thf(f566,plain,(
% 16.52/3.84 ((~ (knowle1437066798e_know @ a @ (secrecy_kKS @ m))) = $true)),
% 16.52/3.84 inference(fool_elimination,[status(thm)],[f565])).
% 16.52/3.84 thf(f565,plain,(
% 16.52/3.84 ~(knowle1437066798e_know @ a @ (secrecy_kKS @ m))),
% 16.52/3.84 inference(rectify,[status(thm)],[f267])).
% 16.52/3.84 thf(f267,negated_conjecture,(
% 16.52/3.84 ~(knowle1437066798e_know @ a @ (secrecy_kKS @ m))),
% 16.52/3.84 inference(negated_conjecture,[status(cth)],[f266])).
% 16.52/3.84 thf(f266,conjecture,(
% 16.52/3.84 (knowle1437066798e_know @ a @ (secrecy_kKS @ m))),
% 16.52/3.84 file('/export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2THF_7787.p',conj_0)).
% 16.52/3.84 thf(f3931,plain,(
% 16.52/3.84 (($true = (knowle1437066798e_know @ a @ (secrecy_kKS @ m))) = $true)),
% 16.52/3.84 inference(superposition,[status(thm)],[f3928,f1957])).
% 16.52/3.84 thf(f1957,plain,(
% 16.52/3.84 ((knowle2055185861_knows @ a @ (insert @ secrecy_Expression @ (secrecy_kE @ m) @ nil @ secrecy_Expression)) = $true)),
% 16.52/3.84 inference(backward_demodulation,[status(thm)],[f1310,f1953])).
% 16.52/3.84 thf(f1953,plain,(
% 16.52/3.84 ( ! [X0 : $tType,X1 : X0] : (((cons @ X0 @ X1 @ nil @ X0) = (insert @ X0 @ X1 @ nil @ X0))) )),
% 16.52/3.84 inference(equality_proxy_clausification,[status(thm)],[f1946])).
% 16.52/3.84 thf(f1946,plain,(
% 16.52/3.84 ( ! [X0 : $tType,X1 : X0] : (($true = ((cons @ X0 @ X1 @ nil @ X0) = (insert @ X0 @ X1 @ nil @ X0)))) )),
% 16.52/3.84 inference(beta_eta_normalization,[status(thm)],[f1945])).
% 16.52/3.84 thf(f1945,plain,(
% 16.52/3.84 ( ! [X0 : $tType,X1 : X0] : ((((^[Y0 : X0]: ((cons @ X0 @ Y0 @ nil @ X0) = (insert @ X0 @ Y0 @ nil @ X0))) @ X1) = $true)) )),
% 16.52/3.84 inference(pi_clausification,[status(thm)],[f1089])).
% 16.52/3.84 thf(f1089,plain,(
% 16.52/3.84 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: ((cons @ X0 @ Y0 @ nil @ X0) = (insert @ X0 @ Y0 @ nil @ X0)))) = $true)) )),
% 16.52/3.84 inference(cnf_transformation,[status(thm)],[f972])).
% 16.52/3.84 thf(f972,plain,(
% 16.52/3.84 ! [X0 : $tType] : ((!! @ X0 @ (^[Y0 : X0]: ((cons @ X0 @ Y0 @ nil @ X0) = (insert @ X0 @ Y0 @ nil @ X0)))) = $true)),
% 16.52/3.84 inference(closure,[status(thm)],[f660])).
% 16.52/3.84 thf(f660,plain,(
% 16.52/3.84 ( ! [X0 : $tType] : (((!! @ X0 @ (^[Y0 : X0]: ((cons @ X0 @ Y0 @ nil @ X0) = (insert @ X0 @ Y0 @ nil @ X0)))) = $true)) )),
% 16.52/3.84 inference(fool_elimination,[status(thm)],[f659])).
% 16.52/3.84 thf(f659,plain,(
% 16.52/3.84 ! [X0 : $tType,X1 : X0] : ((cons @ X0 @ X1 @ nil @ X0) = (insert @ X0 @ X1 @ nil @ X0))),
% 16.52/3.84 inference(rectify,[status(thm)],[f53])).
% 16.52/3.84 thf(f53,axiom,(
% 16.52/3.84 ! [X0 : $tType,X40 : X0] : ((insert @ X0 @ X40 @ nil @ X0) = (cons @ X0 @ X40 @ nil @ X0))),
% 16.52/3.84 file('/export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2THF_7787.p',fact_52_insert__Nil)).
% 16.52/3.84 thf(f1310,plain,(
% 16.52/3.84 ((knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_kE @ m) @ nil @ secrecy_Expression)) = $true)),
% 16.52/3.84 inference(cnf_transformation,[status(thm)],[f621])).
% 16.52/3.84 thf(f621,plain,(
% 16.52/3.84 ((knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_kE @ m) @ nil @ secrecy_Expression)) = $true)),
% 16.52/3.84 inference(fool_elimination,[status(thm)],[f620])).
% 16.52/3.84 thf(f620,plain,(
% 16.52/3.84 (knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_kE @ m) @ nil @ secrecy_Expression))),
% 16.52/3.84 inference(rectify,[status(thm)],[f1])).
% 16.52/3.84 thf(f1,axiom,(
% 16.52/3.84 (knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_kE @ m) @ nil @ secrecy_Expression))),
% 16.52/3.84 file('/export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2THF_7787.p',fact_0_assms)).
% 16.52/3.84 thf(f3928,plain,(
% 16.52/3.84 ( ! [X2 : secrecy_specID,X1 : secrecy_Keys] : ((((knowle2055185861_knows @ X2 @ (insert @ secrecy_Expression @ (secrecy_kE @ X1) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X2 @ (secrecy_kKS @ X1))) = $true)) )),
% 16.52/3.84 inference(forward_demodulation,[status(thm)],[f3927,f1534])).
% 16.52/3.84 thf(f1534,plain,(
% 16.52/3.84 ( ! [X1 : secrecy_Keys] : (((secrecy_kE @ X1) = (secrec1016742679ession @ (secrecy_kKS @ X1)))) )),
% 16.52/3.84 inference(equality_proxy_clausification,[status(thm)],[f1529])).
% 16.52/3.84 thf(f1529,plain,(
% 16.52/3.84 ( ! [X1 : secrecy_Keys] : ((((secrec1016742679ession @ (secrecy_kKS @ X1)) = (secrecy_kE @ X1)) = $true)) )),
% 16.52/3.84 inference(beta_eta_normalization,[status(thm)],[f1528])).
% 16.52/3.84 thf(f1528,plain,(
% 16.52/3.84 ( ! [X1 : secrecy_Keys] : ((((^[Y0 : secrecy_Keys]: ((secrec1016742679ession @ (secrecy_kKS @ Y0)) = (secrecy_kE @ Y0))) @ X1) = $true)) )),
% 16.52/3.84 inference(pi_clausification,[status(thm)],[f1185])).
% 16.52/3.84 thf(f1185,plain,(
% 16.52/3.84 ($true = (!! @ secrecy_Keys @ (^[Y0 : secrecy_Keys]: ((secrec1016742679ession @ (secrecy_kKS @ Y0)) = (secrecy_kE @ Y0)))))),
% 16.52/3.84 inference(cnf_transformation,[status(thm)],[f681])).
% 16.52/3.84 thf(f681,plain,(
% 16.52/3.84 ($true = (!! @ secrecy_Keys @ (^[Y0 : secrecy_Keys]: ((secrec1016742679ession @ (secrecy_kKS @ Y0)) = (secrecy_kE @ Y0)))))),
% 16.52/3.84 inference(fool_elimination,[status(thm)],[f680])).
% 16.52/3.84 thf(f680,plain,(
% 16.52/3.84 ! [X0 : secrecy_Keys] : ((secrec1016742679ession @ (secrecy_kKS @ X0)) = (secrecy_kE @ X0))),
% 16.52/3.84 inference(rectify,[status(thm)],[f16])).
% 16.52/3.84 thf(f16,axiom,(
% 16.52/3.84 ! [X11 : secrecy_Keys] : ((secrecy_kE @ X11) = (secrec1016742679ession @ (secrecy_kKS @ X11)))),
% 16.52/3.84 file('/export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2THF_7787.p',fact_15_KS2Expression_Osimps_I1_J)).
% 16.52/3.84 thf(f3927,plain,(
% 16.52/3.84 ( ! [X2 : secrecy_specID,X1 : secrecy_Keys] : (($true = ((knowle2055185861_knows @ X2 @ (insert @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X2 @ (secrecy_kKS @ X1))))) )),
% 16.52/3.84 inference(forward_demodulation,[status(thm)],[f3926,f1953])).
% 16.52/3.84 thf(f3926,plain,(
% 16.52/3.84 ( ! [X2 : secrecy_specID,X1 : secrecy_Keys] : ((((knowle2055185861_knows @ X2 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X2 @ (secrecy_kKS @ X1))) = $true)) )),
% 16.52/3.84 inference(beta_eta_normalization,[status(thm)],[f3925])).
% 16.52/3.84 thf(f3925,plain,(
% 16.52/3.84 ( ! [X2 : secrecy_specID,X1 : secrecy_Keys] : (($true = ((^[Y0 : secrecy_specID]: ((knowle2055185861_knows @ Y0 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ Y0 @ (secrecy_kKS @ X1)))) @ X2))) )),
% 16.52/3.84 inference(pi_clausification,[status(thm)],[f3924])).
% 16.52/3.84 thf(f3924,plain,(
% 16.52/3.84 ( ! [X1 : secrecy_Keys] : (((!! @ secrecy_specID @ (^[Y0 : secrecy_specID]: ((knowle2055185861_knows @ Y0 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ Y0 @ (secrecy_kKS @ X1))))) = $true)) )),
% 16.52/3.84 inference(beta_eta_normalization,[status(thm)],[f3923])).
% 16.52/3.84 thf(f3923,plain,(
% 16.52/3.84 ( ! [X1 : secrecy_Keys] : ((((^[Y0 : secrecy_Keys]: (!! @ secrecy_specID @ (^[Y1 : secrecy_specID]: ((knowle2055185861_knows @ Y1 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ Y0)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ Y1 @ (secrecy_kKS @ Y0)))))) @ X1) = $true)) )),
% 16.52/3.84 inference(pi_clausification,[status(thm)],[f1271])).
% 16.52/3.84 thf(f1271,plain,(
% 16.52/3.84 ((!! @ secrecy_Keys @ (^[Y0 : secrecy_Keys]: (!! @ secrecy_specID @ (^[Y1 : secrecy_specID]: ((knowle2055185861_knows @ Y1 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ Y0)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ Y1 @ (secrecy_kKS @ Y0))))))) = $true)),
% 16.52/3.84 inference(cnf_transformation,[status(thm)],[f502])).
% 16.52/3.84 thf(f502,plain,(
% 16.52/3.84 ((!! @ secrecy_Keys @ (^[Y0 : secrecy_Keys]: (!! @ secrecy_specID @ (^[Y1 : secrecy_specID]: ((knowle2055185861_knows @ Y1 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ Y0)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ Y1 @ (secrecy_kKS @ Y0))))))) = $true)),
% 16.52/3.84 inference(fool_elimination,[status(thm)],[f501])).
% 16.52/3.84 thf(f501,plain,(
% 16.52/3.84 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((knowle2055185861_knows @ X0 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))),
% 16.52/3.84 inference(rectify,[status(thm)],[f8])).
% 16.52/3.84 thf(f8,axiom,(
% 16.52/3.84 ! [X12 : secrecy_specID,X13 : secrecy_Keys] : ((knowle2055185861_knows @ X12 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_kKS @ X13)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X12 @ (secrecy_kKS @ X13)))),
% 16.52/3.84 file('/export/starexec/sandbox/tmp/tmp.KIvIGEgyuq/DTF2THF_7787.p',fact_7_know1k)).
% 16.52/3.84 % SZS output end Proof for DTF2THF_7787
% 16.52/3.84 % (8174)------------------------------
% 16.52/3.84 % (8174)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.52/3.84 % (8174)Termination reason: Refutation
% 16.52/3.84
% 16.52/3.84 % (8174)Memory used [KB]: 12792
% 16.52/3.84 % (8174)Time elapsed: 0.993 s
% 16.52/3.84 % (8174)Instructions burned: 2304 (million)
% 16.52/3.84 % (8174)------------------------------
% 16.52/3.84 % (8174)------------------------------
% 16.52/3.84 % (7978)Success in time 2.22 s
%------------------------------------------------------------------------------