%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP085^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n015.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 08:55:26 AM UTC 2026
% Result : Theorem 6.28s 2.12s
% Output : Refutation 6.28s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP085^2 : TPTP v9.2.1. Released v7.5.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n015.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 08:26:01 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : ITP085^2 : TPTP v9.2.1. Released v7.5.0.
% 0.20/0.46 % Domain : Interactive Theorem Proving
% 0.20/0.46 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_155__3292644_1
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.20/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Des21]
% 0.20/0.46 % Names : KnowledgeKeysSecrets/prob_155__3292644_1 [Des21]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.33 v8.1.0, 0.25 v7.5.0
% 0.20/0.46 % Syntax : Number of formulae : 337 ( 152 unt; 74 typ; 0 def)
% 0.20/0.46 % Number of atoms : 663 ( 436 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 13 ( 2 avg)
% 0.20/0.46 % Number of connectives : 3820 ( 123 ~; 42 |; 74 &;3316 @)
% 0.20/0.46 % ( 0 <=>; 265 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 23 ( 7 avg)
% 0.20/0.46 % Number of types : 6 ( 5 usr)
% 0.20/0.46 % Number of type conns : 285 ( 285 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 72 ( 69 usr; 4 con; 0-5 aty)
% 0.20/0.46 % Number of variables : 1037 ( 23 ^; 921 !; 41 ?;1037 :)
% 0.20/0.46 % ( 52 !>; 0 ?*; 0 @-; 0 @+)
% 0.20/0.46 % SPC : TH1_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:19:04.419
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % Could-be-implicit typings (7)
% 0.20/0.46 thf(ty_t_Secrecy__types_OExpression,type,
% 0.20/0.46 secrecy_Expression: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Secrecy__types_OSecrets,type,
% 0.20/0.46 secrecy_Secrets: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Secrecy__types_OspecID,type,
% 0.20/0.46 secrecy_specID: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Secrecy__types_OKeys,type,
% 0.20/0.46 secrecy_Keys: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Secrecy__types_OKS,type,
% 0.20/0.46 secrecy_KS: $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_List_Olist,type,
% 0.20/0.46 list: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 thf(ty_t_Set_Oset,type,
% 0.20/0.46 set: $tType > $tType ).
% 0.20/0.46
% 0.20/0.46 % Explicit typings (67)
% 0.20/0.46 thf(sy_cl_HOL_Otype,type,
% 0.20/0.46 type:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.20/0.46 ord:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.20/0.46 linorder:
% 0.20/0.46 !>[A: $tType] : $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 0.20/0.46 bNF_Greatest_Shift:
% 0.20/0.46 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Greatest__Fixpoint_OSucc,type,
% 0.20/0.46 bNF_Greatest_Succ:
% 0.20/0.46 !>[A: $tType] : ( ( set @ ( list @ A ) ) > ( list @ A ) > ( set @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 0.20/0.46 bNF_Greatest_shift:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.20/0.46 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_If,type,
% 0.20/0.46 if:
% 0.20/0.46 !>[A: $tType] : ( $o > A > A > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 0.20/0.46 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowsECorrect,type,
% 0.20/0.46 knowle1893229345orrect: secrecy_specID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 0.20/0.46 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows,type,
% 0.20/0.46 knowle2055185861_knows: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_ListExtras_Omem,type,
% 0.20/0.46 mem:
% 0.20/0.46 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oappend,type,
% 0.20/0.46 append:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oarg__min__list,type,
% 0.20/0.46 arg_min_list:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Obind,type,
% 0.20/0.46 bind:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Obutlast,type,
% 0.20/0.46 butlast:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oconcat,type,
% 0.20/0.46 concat:
% 0.20/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Odistinct__adj,type,
% 0.20/0.46 distinct_adj:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Ofoldr,type,
% 0.20/0.46 foldr:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oinsert,type,
% 0.20/0.46 insert:
% 0.20/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olast,type,
% 0.20/0.46 last:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_OCons,type,
% 0.20/0.46 cons:
% 0.20/0.46 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_ONil,type,
% 0.20/0.46 nil:
% 0.20/0.46 !>[A: $tType] : ( list @ A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_Ocase__list,type,
% 0.20/0.46 case_list:
% 0.20/0.46 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_Ohd,type,
% 0.20/0.46 hd:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist_Otl,type,
% 0.20/0.46 tl:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olist__ex1,type,
% 0.20/0.46 list_ex1:
% 0.20/0.46 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Olistrelp,type,
% 0.20/0.46 listrelp:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Omap__tailrec,type,
% 0.20/0.46 map_tailrec:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Omap__tailrec__rev,type,
% 0.20/0.46 map_tailrec_rev:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Omaps,type,
% 0.20/0.46 maps:
% 0.20/0.46 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Omember,type,
% 0.20/0.46 member:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oord_Olexordp__eq,type,
% 0.20/0.46 lexordp_eq:
% 0.20/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 0.20/0.46 ord_lexordp_eq:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oproduct__lists,type,
% 0.20/0.46 product_lists:
% 0.20/0.46 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oremdups__adj,type,
% 0.20/0.46 remdups_adj:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Orev,type,
% 0.20/0.46 rev:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Orotate1,type,
% 0.20/0.46 rotate1:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Oshuffles,type,
% 0.20/0.46 shuffles:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( set @ ( list @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Osplice,type,
% 0.20/0.46 splice:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Osubseqs,type,
% 0.20/0.46 subseqs:
% 0.20/0.46 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_List_Osuccessively,type,
% 0.20/0.46 successively:
% 0.20/0.46 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Orderings_Oord__class_Oless,type,
% 0.20/0.46 ord_less:
% 0.20/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_ODecr,type,
% 0.20/0.46 decr: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OEnc,type,
% 0.20/0.46 enc: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.20/0.46 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OExt,type,
% 0.20/0.46 ext: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OSign,type,
% 0.20/0.46 sign: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.20/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.20/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.20/0.46 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.20/0.46 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.20/0.46 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.20/0.46 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 0.20/0.46 secrec1371625429on2KSL: ( list @ secrecy_Expression ) > ( list @ secrecy_KS ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.20/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.20/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.20/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 0.20/0.46 secrecy_case_KS:
% 0.20/0.46 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.20/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 0.20/0.46 secrecy_rec_KS:
% 0.20/0.46 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.20/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_Set_OCollect,type,
% 0.20/0.46 collect:
% 0.20/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_c_member,type,
% 0.20/0.46 member2:
% 0.20/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_A,type,
% 0.20/0.46 a: secrecy_specID ).
% 0.20/0.46
% 0.20/0.46 thf(sy_v_m,type,
% 0.20/0.46 m: secrecy_Secrets ).
% 0.20/0.46
% 0.20/0.46 % Relevant facts (255)
% 0.20/0.46 thf(fact_0_assms,axiom,
% 0.20/0.46 knowle2055185861_knows @ a @ ( cons @ secrecy_Expression @ ( secrecy_sE @ m ) @ ( nil @ secrecy_Expression ) ) ).
% 0.20/0.46
% 0.20/0.46 % assms
% 0.20/0.46 thf(fact_1_KS_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.20/0.46 ( ( ( secrecy_sKS @ X2 )
% 0.20/0.46 = ( secrecy_sKS @ Y2 ) )
% 0.20/0.46 = ( X2 = Y2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.inject(2)
% 0.20/0.46 thf(fact_2_know2knows__s,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.20/0.46 => ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_sE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know2knows_s
% 0.20/0.46 thf(fact_3_know1s,axiom,
% 0.20/0.46 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ ( nil @ secrecy_Expression ) ) )
% 0.20/0.46 = ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know1s
% 0.20/0.46 thf(fact_4_KS_Osimps_I8_J,axiom,
% 0.20/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 0.20/0.46 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 0.20/0.46 = ( F2 @ X2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.simps(8)
% 0.20/0.46 thf(fact_5_KS_Osimps_I6_J,axiom,
% 0.20/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 0.20/0.46 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 0.20/0.46 = ( F2 @ X2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.simps(6)
% 0.20/0.46 thf(fact_6_eoutKnowCorrect__L1s,axiom,
% 0.20/0.46 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 0.20/0.46 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.20/0.46 => ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 0.20/0.46 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutKnowCorrect_L1s
% 0.20/0.46 thf(fact_7_eout__know__s,axiom,
% 0.20/0.46 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 0.20/0.46 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.20/0.46 = ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 0.20/0.46 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_know_s
% 0.20/0.46 thf(fact_8_know_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.20/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.20/0.46 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 0.20/0.46 | ( member2 @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know.simps(2)
% 0.20/0.46 thf(fact_9_KS2Expression_Osimps_I2_J,axiom,
% 0.20/0.46 ! [M: secrecy_Secrets] :
% 0.20/0.46 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.20/0.46 = ( secrecy_sE @ M ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS2Expression.simps(2)
% 0.20/0.46 thf(fact_10_knows4,axiom,
% 0.20/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 0.20/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.20/0.46 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K2 ) )
% 0.20/0.46 & ( knowle2055185861_knows @ A2 @ ( enc @ K1 @ E ) ) )
% 0.20/0.46 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows4
% 0.20/0.46 thf(fact_11_knows5,axiom,
% 0.20/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 0.20/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.20/0.46 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K1 ) )
% 0.20/0.46 & ( knowle2055185861_knows @ A2 @ ( sign @ K2 @ E ) ) )
% 0.20/0.46 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows5
% 0.20/0.46 thf(fact_12_knows6,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 0.20/0.46 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 0.20/0.46 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 0.20/0.46 => ( knowle2055185861_knows @ A2 @ ( enc @ K @ E1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows6
% 0.20/0.46 thf(fact_13_KS_Oinject_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.20/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.20/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.20/0.46 = ( X1 = Y1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.inject(1)
% 0.20/0.46 thf(fact_14_Expression_Oinject_I2_J,axiom,
% 0.20/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.20/0.46 ( ( ( secrecy_sE @ X2 )
% 0.20/0.46 = ( secrecy_sE @ Y2 ) )
% 0.20/0.46 = ( X2 = Y2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression.inject(2)
% 0.20/0.46 thf(fact_15_KS_Osimps_I7_J,axiom,
% 0.20/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.20/0.46 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.20/0.46 = ( F1 @ X1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.simps(7)
% 0.20/0.46 thf(fact_16_KS_Osimps_I5_J,axiom,
% 0.20/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.20/0.46 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.20/0.46 = ( F1 @ X1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.simps(5)
% 0.20/0.46 thf(fact_17_know1k,axiom,
% 0.20/0.46 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 0.20/0.46 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ ( nil @ secrecy_Expression ) ) )
% 0.20/0.46 = ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know1k
% 0.20/0.46 thf(fact_18_knows__emptyexpression,axiom,
% 0.20/0.46 ! [C: secrecy_specID] : ( knowle2055185861_knows @ C @ ( nil @ secrecy_Expression ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows_emptyexpression
% 0.20/0.46 thf(fact_19_KS_Oexhaust,axiom,
% 0.20/0.46 ! [Y: secrecy_KS] :
% 0.20/0.46 ( ! [X12: secrecy_Keys] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( secrecy_kKS @ X12 ) )
% 0.20/0.46 => ~ ! [X22: secrecy_Secrets] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.exhaust
% 0.20/0.46 thf(fact_20_KS_Oinduct,axiom,
% 0.20/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.20/0.46 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.20/0.46 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.20/0.46 => ( P @ KS ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.induct
% 0.20/0.46 thf(fact_21_KS_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.20/0.46 ( ( secrecy_kKS @ X1 )
% 0.20/0.46 != ( secrecy_sKS @ X2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS.distinct(1)
% 0.20/0.46 thf(fact_22_knows7,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 0.20/0.46 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 0.20/0.46 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 0.20/0.46 => ( knowle2055185861_knows @ A2 @ ( sign @ K @ E1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows7
% 0.20/0.46 thf(fact_23_list_Oinject,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 0.20/0.46 ( ( ( cons @ A @ X21 @ X222 )
% 0.20/0.46 = ( cons @ A @ Y21 @ Y22 ) )
% 0.20/0.46 = ( ( X21 = Y21 )
% 0.20/0.46 & ( X222 = Y22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.inject
% 0.20/0.46 thf(fact_24_list_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,X21: A,X222: list @ A] :
% 0.20/0.46 ( ( nil @ A )
% 0.20/0.46 != ( cons @ A @ X21 @ X222 ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.distinct(1)
% 0.20/0.46 thf(fact_25_list_OdiscI,axiom,
% 0.20/0.46 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 0.20/0.46 ( ( List
% 0.20/0.46 = ( cons @ A @ X21 @ X222 ) )
% 0.20/0.46 => ( List
% 0.20/0.46 != ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.discI
% 0.20/0.46 thf(fact_26_list_Oexhaust,axiom,
% 0.20/0.46 ! [A: $tType,Y: list @ A] :
% 0.20/0.46 ( ( Y
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ~ ! [X212: A,X223: list @ A] :
% 0.20/0.46 ( Y
% 0.20/0.46 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.exhaust
% 0.20/0.46 thf(fact_27_list_Oinducts,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X12: A,X22: list @ A] :
% 0.20/0.46 ( ( P @ X22 )
% 0.20/0.46 => ( P @ ( cons @ A @ X12 @ X22 ) ) )
% 0.20/0.46 => ( P @ List ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list.inducts
% 0.20/0.46 thf(fact_28_neq__Nil__conv,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 = ( ? [Y3: A,Ys: list @ A] :
% 0.20/0.46 ( Xs
% 0.20/0.46 = ( cons @ A @ Y3 @ Ys ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % neq_Nil_conv
% 0.20/0.46 thf(fact_29_list__induct2_H,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 0.20/0.46 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [Y4: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys3 ) )
% 0.20/0.46 => ( ! [X: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 0.20/0.46 ( ( P @ Xs2 @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) )
% 0.20/0.46 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_induct2'
% 0.20/0.46 thf(fact_30_splice_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.20/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [X: A,Xs2: list @ A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ Ys3 @ Xs2 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % splice.induct
% 0.20/0.46 thf(fact_31_induct__list012,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X: A,Y4: A,Zs: list @ A] :
% 0.20/0.46 ( ( P @ Zs )
% 0.20/0.46 => ( ( P @ ( cons @ A @ Y4 @ Zs ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs ) ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % induct_list012
% 0.20/0.46 thf(fact_32_min__list_Ocases,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [X3: list @ A] :
% 0.20/0.46 ( ! [X: A,Xs2: list @ A] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( cons @ A @ X @ Xs2 ) )
% 0.20/0.46 => ( X3
% 0.20/0.46 = ( nil @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % min_list.cases
% 0.20/0.46 thf(fact_33_min__list_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( ord @ A )
% 0.20/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.20/0.46 ( ! [X: A,Xs2: list @ A] :
% 0.20/0.46 ( ! [X213: A,X224: list @ A] :
% 0.20/0.46 ( ( Xs2
% 0.20/0.46 = ( cons @ A @ X213 @ X224 ) )
% 0.20/0.46 => ( P @ Xs2 ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.20/0.46 => ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % min_list.induct
% 0.20/0.46 thf(fact_34_not__Cons__self2,axiom,
% 0.20/0.46 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.20/0.46 ( ( cons @ A @ X3 @ Xs )
% 0.20/0.46 != Xs ) ).
% 0.20/0.46
% 0.20/0.46 % not_Cons_self2
% 0.20/0.46 thf(fact_35_strict__sorted_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A )
% 0.20/0.46 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Ys3 ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % strict_sorted.induct
% 0.20/0.46 thf(fact_36_strict__sorted_Ocases,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( linorder @ A )
% 0.20/0.46 => ! [X3: list @ A] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ~ ! [X: A,Ys3: list @ A] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( cons @ A @ X @ Ys3 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % strict_sorted.cases
% 0.20/0.46 thf(fact_37_map__tailrec__rev_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 0.20/0.46 ( ! [F: A > B,X_1: list @ B] : ( P @ F @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [F: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 0.20/0.46 ( ( P @ F @ As @ ( cons @ B @ ( F @ A3 ) @ Bs ) )
% 0.20/0.46 => ( P @ F @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 0.20/0.46 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % map_tailrec_rev.induct
% 0.20/0.46 thf(fact_38_list__nonempty__induct,axiom,
% 0.20/0.46 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.20/0.46 ( ( Xs
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X: A,Xs2: list @ A] :
% 0.20/0.46 ( ( Xs2
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ( P @ Xs2 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 0.20/0.46 => ( P @ Xs ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_nonempty_induct
% 0.20/0.46 thf(fact_39_successively_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.20/0.46 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [P2: A > A > $o,X: A] : ( P @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [P2: A > A > $o,X: A,Y4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( P @ P2 @ ( cons @ A @ Y4 @ Xs2 ) )
% 0.20/0.46 => ( P @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % successively.induct
% 0.20/0.46 thf(fact_40_arg__min__list_Oinduct,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType] :
% 0.20/0.46 ( ( linorder @ B )
% 0.20/0.46 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 0.20/0.46 ( ! [F: A > B,X: A] : ( P @ F @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [F: A > B,X: A,Y4: A,Zs: list @ A] :
% 0.20/0.46 ( ( P @ F @ ( cons @ A @ Y4 @ Zs ) )
% 0.20/0.46 => ( P @ F @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs ) ) ) )
% 0.20/0.46 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % arg_min_list.induct
% 0.20/0.46 thf(fact_41_remdups__adj_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 0.20/0.46 ( ( P @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 => ( ! [X: A,Y4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( ( X = Y4 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 0.20/0.46 => ( ( ( X != Y4 )
% 0.20/0.46 => ( P @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 0.20/0.46 => ( P @ A0 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % remdups_adj.induct
% 0.20/0.46 thf(fact_42_sorted__wrt_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 0.20/0.46 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [P2: A > A > $o,X: A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ P2 @ Ys3 )
% 0.20/0.46 => ( P @ P2 @ ( cons @ A @ X @ Ys3 ) ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % sorted_wrt.induct
% 0.20/0.46 thf(fact_43_remdups__adj_Ocases,axiom,
% 0.20/0.46 ! [A: $tType,X3: list @ A] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.46 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % remdups_adj.cases
% 0.20/0.46 thf(fact_44_mem__Collect__eq,axiom,
% 0.20/0.46 ! [A: $tType,A4: A,P: A > $o] :
% 0.20/0.46 ( ( member2 @ A @ A4 @ ( collect @ A @ P ) )
% 0.20/0.46 = ( P @ A4 ) ) ).
% 0.20/0.46
% 0.20/0.46 % mem_Collect_eq
% 0.20/0.46 thf(fact_45_Collect__mem__eq,axiom,
% 0.20/0.46 ! [A: $tType,A2: set @ A] :
% 0.20/0.46 ( ( collect @ A
% 0.20/0.46 @ ^ [X4: A] : ( member2 @ A @ X4 @ A2 ) )
% 0.20/0.46 = A2 ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_mem_eq
% 0.20/0.46 thf(fact_46_Collect__cong,axiom,
% 0.20/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.20/0.46 ( ! [X: A] :
% 0.20/0.46 ( ( P @ X )
% 0.20/0.46 = ( Q @ X ) )
% 0.20/0.46 => ( ( collect @ A @ P )
% 0.20/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % Collect_cong
% 0.20/0.46 thf(fact_47_ext,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 0.20/0.46 ( ! [X: A] :
% 0.20/0.46 ( ( F3 @ X )
% 0.20/0.46 = ( G @ X ) )
% 0.20/0.46 => ( F3 = G ) ) ).
% 0.20/0.46
% 0.20/0.46 % ext
% 0.20/0.46 thf(fact_48_transpose_Ocases,axiom,
% 0.20/0.46 ! [A: $tType,X3: list @ ( list @ A )] :
% 0.20/0.46 ( ( X3
% 0.20/0.46 != ( nil @ ( list @ A ) ) )
% 0.20/0.46 => ( ! [Xss: list @ ( list @ A )] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 0.20/0.46 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 0.20/0.46 ( X3
% 0.20/0.46 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % transpose.cases
% 0.20/0.46 thf(fact_49_shuffles_Oinduct,axiom,
% 0.20/0.46 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 0.20/0.46 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.46 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 0.20/0.46 ( ( P @ Xs2 @ ( cons @ A @ Y4 @ Ys3 ) )
% 0.20/0.46 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) )
% 0.20/0.46 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % shuffles.induct
% 0.20/0.46 thf(fact_50_knows1k,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.20/0.46 = ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows1k
% 0.20/0.46 thf(fact_51_know2knows__k,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.20/0.46 => ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know2knows_k
% 0.20/0.46 thf(fact_52_knows2know__k,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 0.20/0.46 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows2know_k
% 0.20/0.46 thf(fact_53_know2knowsPQ__k,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 0.20/0.46 ( ( ( knowle1437066798e_know @ P @ ( secrecy_kKS @ M ) )
% 0.20/0.46 | ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ M ) ) )
% 0.20/0.46 => ( ( knowle2055185861_knows @ P @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 0.20/0.46 | ( knowle2055185861_knows @ Q @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know2knowsPQ_k
% 0.20/0.46 thf(fact_54_knows2knowPQ__k,axiom,
% 0.20/0.46 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 0.20/0.46 ( ( ( knowle2055185861_knows @ P @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 0.20/0.46 | ( knowle2055185861_knows @ Q @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) )
% 0.20/0.46 => ( ( knowle1437066798e_know @ P @ ( secrecy_kKS @ M ) )
% 0.20/0.46 | ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ M ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows2knowPQ_k
% 0.20/0.46 thf(fact_55_know2knows__neg__k,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.20/0.46 => ~ ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know2knows_neg_k
% 0.20/0.46 thf(fact_56_knows2know__neg__k,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ~ ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 0.20/0.46 => ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % knows2know_neg_k
% 0.20/0.46 thf(fact_57_know_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.20/0.46 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 0.20/0.46 | ( member2 @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % know.simps(1)
% 0.20/0.46 thf(fact_58_insert__Nil,axiom,
% 0.20/0.46 ! [A: $tType,X3: A] :
% 0.20/0.46 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 0.20/0.46 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % insert_Nil
% 0.20/0.46 thf(fact_59_Expression_Oinject_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.20/0.46 ( ( ( secrecy_kE @ X1 )
% 0.20/0.46 = ( secrecy_kE @ Y1 ) )
% 0.20/0.46 = ( X1 = Y1 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression.inject(1)
% 0.20/0.46 thf(fact_60_Expression_Odistinct_I1_J,axiom,
% 0.20/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.20/0.46 ( ( secrecy_kE @ X1 )
% 0.20/0.46 != ( secrecy_sE @ X2 ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression.distinct(1)
% 0.20/0.46 thf(fact_61_KS2Expression_Osimps_I1_J,axiom,
% 0.20/0.46 ! [M: secrecy_Keys] :
% 0.20/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.20/0.46 = ( secrecy_kE @ M ) ) ).
% 0.20/0.46
% 0.20/0.46 % KS2Expression.simps(1)
% 0.20/0.46 thf(fact_62_eoutKnowCorrect__L1k,axiom,
% 0.20/0.46 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 0.20/0.46 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.20/0.46 => ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.20/0.46 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutKnowCorrect_L1k
% 0.20/0.46 thf(fact_63_eout__know__k,axiom,
% 0.20/0.46 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.20/0.46 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 0.20/0.46 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.20/0.46 = ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.20/0.46 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eout_know_k
% 0.20/0.46 thf(fact_64_eoutKnowsECorrect__L1,axiom,
% 0.20/0.46 ! [C: secrecy_specID,E: secrecy_Expression] :
% 0.20/0.46 ( ( knowle1893229345orrect @ C @ E )
% 0.20/0.46 => ( ( eout @ C @ E )
% 0.20/0.46 => ( ? [K3: secrecy_Keys] :
% 0.20/0.46 ( ( E
% 0.20/0.46 = ( secrecy_kE @ K3 ) )
% 0.20/0.46 & ( member2 @ secrecy_Keys @ K3 @ ( specKeys @ C ) ) )
% 0.20/0.46 | ? [S: secrecy_Secrets] :
% 0.20/0.46 ( ( E
% 0.20/0.46 = ( secrecy_sE @ S ) )
% 0.20/0.46 & ( member2 @ secrecy_Secrets @ S @ ( specSecrets @ C ) ) )
% 0.20/0.46 | ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ E @ ( nil @ secrecy_Expression ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutKnowsECorrect_L1
% 0.20/0.46 thf(fact_65_eoutKnowsECorrect__def,axiom,
% 0.20/0.46 ( knowle1893229345orrect
% 0.20/0.46 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 0.20/0.46 ( ( eout @ C2 @ E2 )
% 0.20/0.46 = ( ? [K4: secrecy_Keys] :
% 0.20/0.46 ( ( E2
% 0.20/0.46 = ( secrecy_kE @ K4 ) )
% 0.20/0.46 & ( member2 @ secrecy_Keys @ K4 @ ( specKeys @ C2 ) ) )
% 0.20/0.46 | ? [S2: secrecy_Secrets] :
% 0.20/0.46 ( ( E2
% 0.20/0.46 = ( secrecy_sE @ S2 ) )
% 0.20/0.46 & ( member2 @ secrecy_Secrets @ S2 @ ( specSecrets @ C2 ) ) )
% 0.20/0.46 | ( knowle2055185861_knows @ C2 @ ( cons @ secrecy_Expression @ E2 @ ( nil @ secrecy_Expression ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % eoutKnowsECorrect_def
% 0.20/0.46 thf(fact_66_product__lists_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 0.20/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % product_lists.simps(1)
% 0.20/0.46 thf(fact_67_subseqs_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( subseqs @ A @ ( nil @ A ) )
% 0.20/0.46 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % subseqs.simps(1)
% 0.20/0.46 thf(fact_68_Expression2KSL_Osimps_I1_J,axiom,
% 0.20/0.46 ( ( secrec1371625429on2KSL @ ( nil @ secrecy_Expression ) )
% 0.20/0.46 = ( nil @ secrecy_KS ) ) ).
% 0.20/0.46
% 0.20/0.46 % Expression2KSL.simps(1)
% 0.20/0.46 thf(fact_69_list__ex1__simps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,P: A > $o] :
% 0.20/0.46 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % list_ex1_simps(1)
% 0.20/0.46 thf(fact_70_map__tailrec__rev_Oelims,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,X3: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 0.20/0.46 ( ( ( map_tailrec_rev @ A @ B @ X3 @ Xa @ Xb )
% 0.20/0.46 = Y )
% 0.20/0.46 => ( ( ( Xa
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 => ( Y != Xb ) )
% 0.20/0.46 => ~ ! [A3: A,As: list @ A] :
% 0.20/0.46 ( ( Xa
% 0.20/0.46 = ( cons @ A @ A3 @ As ) )
% 0.20/0.46 => ( Y
% 0.20/0.46 != ( map_tailrec_rev @ A @ B @ X3 @ As @ ( cons @ B @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % map_tailrec_rev.elims
% 0.20/0.46 thf(fact_71_arg__min__list_Osimps_I1_J,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType] :
% 0.20/0.46 ( ( linorder @ B )
% 0.20/0.46 => ! [F3: A > B,X3: A] :
% 0.20/0.46 ( ( arg_min_list @ A @ B @ F3 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.20/0.46 = X3 ) ) ).
% 0.20/0.46
% 0.20/0.46 % arg_min_list.simps(1)
% 0.20/0.46 thf(fact_72_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A] :
% 0.20/0.46 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq_simps(3)
% 0.20/0.46 thf(fact_73_bind__simps_I1_J,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 0.20/0.46 ( ( bind @ B @ A @ ( nil @ B ) @ F3 )
% 0.20/0.46 = ( nil @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % bind_simps(1)
% 0.20/0.46 thf(fact_74_listrelp_Oinducts,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,R: A > B > $o,X1: list @ A,X2: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 0.20/0.46 ( ( listrelp @ A @ B @ R @ X1 @ X2 )
% 0.20/0.46 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 0.20/0.46 => ( ! [X: A,Y4: B,Xs2: list @ A,Ys3: list @ B] :
% 0.20/0.46 ( ( R @ X @ Y4 )
% 0.20/0.46 => ( ( listrelp @ A @ B @ R @ Xs2 @ Ys3 )
% 0.20/0.46 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.46 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) ) )
% 0.20/0.46 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % listrelp.inducts
% 0.20/0.46 thf(fact_75_listrelp_Osimps,axiom,
% 0.20/0.46 ! [B: $tType,A: $tType] :
% 0.20/0.46 ( ( listrelp @ A @ B )
% 0.20/0.46 = ( ^ [R2: A > B > $o,A12: list @ A,A23: list @ B] :
% 0.20/0.46 ( ( ( A12
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( A23
% 0.20/0.46 = ( nil @ B ) ) )
% 0.20/0.46 | ? [X4: A,Y3: B,Xs3: list @ A,Ys: list @ B] :
% 0.20/0.46 ( ( A12
% 0.20/0.46 = ( cons @ A @ X4 @ Xs3 ) )
% 0.20/0.46 & ( A23
% 0.20/0.46 = ( cons @ B @ Y3 @ Ys ) )
% 0.20/0.46 & ( R2 @ X4 @ Y3 )
% 0.20/0.46 & ( listrelp @ A @ B @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % listrelp.simps
% 0.20/0.46 thf(fact_76_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.20/0.46 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 0.20/0.46 = ( ( Less @ X3 @ Y )
% 0.20/0.46 | ( ~ ( Less @ Y @ X3 )
% 0.20/0.46 & ( lexordp_eq @ A @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq_simps(4)
% 0.20/0.46 thf(fact_77_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 0.20/0.46 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 0.20/0.46 = ( Xs
% 0.20/0.46 = ( nil @ A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq_simps(2)
% 0.20/0.46 thf(fact_78_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq_simps(1)
% 0.20/0.46 thf(fact_79_ord_Olexordp__eq__refl,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq_refl
% 0.20/0.46 thf(fact_80_ord_Olexordp__eq_Ocong,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lexordp_eq @ A )
% 0.20/0.46 = ( lexordp_eq @ A ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq.cong
% 0.20/0.46 thf(fact_81_ord_Olexordp__eq_OCons,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.46 ( ( Less @ X3 @ Y )
% 0.20/0.46 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq.Cons
% 0.20/0.46 thf(fact_82_ord_Olexordp__eq_OCons__eq,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.46 ( ~ ( Less @ X3 @ Y )
% 0.20/0.46 => ( ~ ( Less @ Y @ X3 )
% 0.20/0.46 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys2 )
% 0.20/0.46 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq.Cons_eq
% 0.20/0.46 thf(fact_83_ord_Olexordp__eq_ONil,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq.Nil
% 0.20/0.46 thf(fact_84_listrelp_OCons,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y: B,Xs: list @ A,Ys2: list @ B] :
% 0.20/0.46 ( ( R @ X3 @ Y )
% 0.20/0.46 => ( ( listrelp @ A @ B @ R @ Xs @ Ys2 )
% 0.20/0.46 => ( listrelp @ A @ B @ R @ ( cons @ A @ X3 @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % listrelp.Cons
% 0.20/0.46 thf(fact_85_listrelp_ONil,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,R: A > B > $o] : ( listrelp @ A @ B @ R @ ( nil @ A ) @ ( nil @ B ) ) ).
% 0.20/0.46
% 0.20/0.46 % listrelp.Nil
% 0.20/0.46 thf(fact_86_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,F3: A > B,A4: A,As2: list @ A,Bs2: list @ B] :
% 0.20/0.46 ( ( map_tailrec_rev @ A @ B @ F3 @ ( cons @ A @ A4 @ As2 ) @ Bs2 )
% 0.20/0.46 = ( map_tailrec_rev @ A @ B @ F3 @ As2 @ ( cons @ B @ ( F3 @ A4 ) @ Bs2 ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % map_tailrec_rev.simps(2)
% 0.20/0.46 thf(fact_87_map__tailrec__rev_Osimps_I1_J,axiom,
% 0.20/0.46 ! [A: $tType,B: $tType,F3: A > B,Bs2: list @ B] :
% 0.20/0.46 ( ( map_tailrec_rev @ A @ B @ F3 @ ( nil @ A ) @ Bs2 )
% 0.20/0.46 = Bs2 ) ).
% 0.20/0.46
% 0.20/0.46 % map_tailrec_rev.simps(1)
% 0.20/0.46 thf(fact_88_ord_Olexordp__eq_Ocases,axiom,
% 0.20/0.46 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 0.20/0.46 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 0.20/0.46 => ( ( A1
% 0.20/0.46 != ( nil @ A ) )
% 0.20/0.46 => ( ! [X: A] :
% 0.20/0.46 ( ? [Xs2: list @ A] :
% 0.20/0.46 ( A1
% 0.20/0.46 = ( cons @ A @ X @ Xs2 ) )
% 0.20/0.46 => ! [Y4: A] :
% 0.20/0.46 ( ? [Ys3: list @ A] :
% 0.20/0.46 ( A22
% 0.20/0.46 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.20/0.46 => ~ ( Less @ X @ Y4 ) ) )
% 0.20/0.46 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.20/0.46 ( ( A1
% 0.20/0.46 = ( cons @ A @ X @ Xs2 ) )
% 0.20/0.46 => ! [Ys3: list @ A] :
% 0.20/0.46 ( ( A22
% 0.20/0.46 = ( cons @ A @ Y4 @ Ys3 ) )
% 0.20/0.46 => ( ~ ( Less @ X @ Y4 )
% 0.20/0.46 => ( ~ ( Less @ Y4 @ X )
% 0.20/0.46 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 % ord.lexordp_eq.cases
% 0.20/0.46 thf(fact_89_ord_Olexordp__eq_Osimps,axiom,
% 0.20/0.46 ! [A: $tType] :
% 0.20/0.46 ( ( lexordp_eq @ A )
% 0.20/0.46 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 0.20/0.46 ( ? [Ys: list @ A] :
% 0.20/0.46 ( ( A12
% 0.20/0.46 = ( nil @ A ) )
% 0.20/0.46 & ( A23 = Ys ) )
% 0.20/0.46 | ? [X4: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.20/0.46 ( ( A12
% 0.20/0.46 = ( cons @ A @ X4 @ Xs3 ) )
% 0.20/0.47 & ( A23
% 0.20/0.47 = ( cons @ A @ Y3 @ Ys ) )
% 0.20/0.47 & ( Less2 @ X4 @ Y3 ) )
% 0.20/0.47 | ? [X4: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 0.20/0.47 ( ( A12
% 0.20/0.47 = ( cons @ A @ X4 @ Xs3 ) )
% 0.20/0.47 & ( A23
% 0.20/0.47 = ( cons @ A @ Y3 @ Ys ) )
% 0.20/0.47 & ~ ( Less2 @ X4 @ Y3 )
% 0.20/0.47 & ~ ( Less2 @ Y3 @ X4 )
% 0.20/0.47 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord.lexordp_eq.simps
% 0.20/0.47 thf(fact_90_ord_Olexordp__eq_Oinducts,axiom,
% 0.20/0.47 ! [A: $tType,Less: A > A > $o,X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.20/0.47 ( ( lexordp_eq @ A @ Less @ X1 @ X2 )
% 0.20/0.47 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.20/0.47 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.20/0.47 ( ( Less @ X @ Y4 )
% 0.20/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.20/0.47 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.20/0.47 ( ~ ( Less @ X @ Y4 )
% 0.20/0.47 => ( ~ ( Less @ Y4 @ X )
% 0.20/0.47 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 )
% 0.20/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.20/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 0.20/0.47 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord.lexordp_eq.inducts
% 0.20/0.47 thf(fact_91_listrelp_Ocases,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,R: A > B > $o,A1: list @ A,A22: list @ B] :
% 0.20/0.47 ( ( listrelp @ A @ B @ R @ A1 @ A22 )
% 0.20/0.47 => ( ( ( A1
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 => ( A22
% 0.20/0.47 != ( nil @ B ) ) )
% 0.20/0.47 => ~ ! [X: A,Y4: B,Xs2: list @ A] :
% 0.20/0.47 ( ( A1
% 0.20/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.20/0.47 => ! [Ys3: list @ B] :
% 0.20/0.47 ( ( A22
% 0.20/0.47 = ( cons @ B @ Y4 @ Ys3 ) )
% 0.20/0.47 => ( ( R @ X @ Y4 )
% 0.20/0.47 => ~ ( listrelp @ A @ B @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % listrelp.cases
% 0.20/0.47 thf(fact_92_lexordp__eq__simps_I3_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A )
% 0.20/0.47 => ! [X3: A,Xs: list @ A] :
% 0.20/0.47 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_simps(3)
% 0.20/0.47 thf(fact_93_notSpecKeysSecretsExpr__L1,axiom,
% 0.20/0.47 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 0.20/0.47 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 0.20/0.47 => ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ ( nil @ secrecy_Expression ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % notSpecKeysSecretsExpr_L1
% 0.20/0.47 thf(fact_94_member__rec_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,Y: A] :
% 0.20/0.47 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 0.20/0.47
% 0.20/0.47 % member_rec(2)
% 0.20/0.47 thf(fact_95_member__rec_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,X3: A,Xs: list @ A,Y: A] :
% 0.20/0.47 ( ( member @ A @ ( cons @ A @ X3 @ Xs ) @ Y )
% 0.20/0.47 = ( ( X3 = Y )
% 0.20/0.47 | ( member @ A @ Xs @ Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % member_rec(1)
% 0.20/0.47 thf(fact_96_splice_Oelims,axiom,
% 0.20/0.47 ! [A: $tType,X3: list @ A,Xa: list @ A,Y: list @ A] :
% 0.20/0.47 ( ( ( splice @ A @ X3 @ Xa )
% 0.20/0.47 = Y )
% 0.20/0.47 => ( ( ( X3
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 => ( Y != Xa ) )
% 0.20/0.47 => ~ ! [X: A,Xs2: list @ A] :
% 0.20/0.47 ( ( X3
% 0.20/0.47 = ( cons @ A @ X @ Xs2 ) )
% 0.20/0.47 => ( Y
% 0.20/0.47 != ( cons @ A @ X @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splice.elims
% 0.20/0.47 thf(fact_97_bind__simps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,B: $tType,X3: B,Xs: list @ B,F3: B > ( list @ A )] :
% 0.20/0.47 ( ( bind @ B @ A @ ( cons @ B @ X3 @ Xs ) @ F3 )
% 0.20/0.47 = ( append @ A @ ( F3 @ X3 ) @ ( bind @ B @ A @ Xs @ F3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % bind_simps(2)
% 0.20/0.47 thf(fact_98_append_Oassoc,axiom,
% 0.20/0.47 ! [A: $tType,A4: list @ A,B2: list @ A,C3: list @ A] :
% 0.20/0.47 ( ( append @ A @ ( append @ A @ A4 @ B2 ) @ C3 )
% 0.20/0.47 = ( append @ A @ A4 @ ( append @ A @ B2 @ C3 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append.assoc
% 0.20/0.47 thf(fact_99_append__assoc,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.20/0.47 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs2 )
% 0.20/0.47 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_assoc
% 0.20/0.47 thf(fact_100_append__same__eq,axiom,
% 0.20/0.47 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Ys2 @ Xs )
% 0.20/0.47 = ( append @ A @ Zs2 @ Xs ) )
% 0.20/0.47 = ( Ys2 = Zs2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_same_eq
% 0.20/0.47 thf(fact_101_same__append__eq,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ Ys2 )
% 0.20/0.47 = ( append @ A @ Xs @ Zs2 ) )
% 0.20/0.47 = ( Ys2 = Zs2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % same_append_eq
% 0.20/0.47 thf(fact_102_append_Oright__neutral,axiom,
% 0.20/0.47 ! [A: $tType,A4: list @ A] :
% 0.20/0.47 ( ( append @ A @ A4 @ ( nil @ A ) )
% 0.20/0.47 = A4 ) ).
% 0.20/0.47
% 0.20/0.47 % append.right_neutral
% 0.20/0.47 thf(fact_103_append__is__Nil__conv,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ Ys2 )
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 = ( ( Xs
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 & ( Ys2
% 0.20/0.47 = ( nil @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_is_Nil_conv
% 0.20/0.47 thf(fact_104_Nil__is__append__conv,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ( nil @ A )
% 0.20/0.47 = ( append @ A @ Xs @ Ys2 ) )
% 0.20/0.47 = ( ( Xs
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 & ( Ys2
% 0.20/0.47 = ( nil @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Nil_is_append_conv
% 0.20/0.47 thf(fact_105_self__append__conv2,axiom,
% 0.20/0.47 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.20/0.47 ( ( Ys2
% 0.20/0.47 = ( append @ A @ Xs @ Ys2 ) )
% 0.20/0.47 = ( Xs
% 0.20/0.47 = ( nil @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % self_append_conv2
% 0.20/0.47 thf(fact_106_append__self__conv2,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ Ys2 )
% 0.20/0.47 = Ys2 )
% 0.20/0.47 = ( Xs
% 0.20/0.47 = ( nil @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_self_conv2
% 0.20/0.47 thf(fact_107_self__append__conv,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( Xs
% 0.20/0.47 = ( append @ A @ Xs @ Ys2 ) )
% 0.20/0.47 = ( Ys2
% 0.20/0.47 = ( nil @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % self_append_conv
% 0.20/0.47 thf(fact_108_append__self__conv,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ Ys2 )
% 0.20/0.47 = Xs )
% 0.20/0.47 = ( Ys2
% 0.20/0.47 = ( nil @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_self_conv
% 0.20/0.47 thf(fact_109_append__Nil2,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A] :
% 0.20/0.47 ( ( append @ A @ Xs @ ( nil @ A ) )
% 0.20/0.47 = Xs ) ).
% 0.20/0.47
% 0.20/0.47 % append_Nil2
% 0.20/0.47 thf(fact_110_lexordp__eq__simps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A )
% 0.20/0.47 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_simps(1)
% 0.20/0.47 thf(fact_111_lexordp__eq__simps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A )
% 0.20/0.47 => ! [Xs: list @ A] :
% 0.20/0.47 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 0.20/0.47 = ( Xs
% 0.20/0.47 = ( nil @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_simps(2)
% 0.20/0.47 thf(fact_112_split__Nil__iff,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ( splice @ A @ Xs @ Ys2 )
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 = ( ( Xs
% 0.20/0.47 = ( nil @ A ) )
% 0.20/0.47 & ( Ys2
% 0.20/0.47 = ( nil @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % split_Nil_iff
% 0.20/0.47 thf(fact_113_splice__Nil2,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A] :
% 0.20/0.47 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 0.20/0.47 = Xs ) ).
% 0.20/0.47
% 0.20/0.47 % splice_Nil2
% 0.20/0.47 thf(fact_114_append1__eq__conv,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A,Y: A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.20/0.47 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 0.20/0.47 = ( ( Xs = Ys2 )
% 0.20/0.47 & ( X3 = Y ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append1_eq_conv
% 0.20/0.47 thf(fact_115_append__eq__appendI,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys2: list @ A,Us: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ Xs1 )
% 0.20/0.47 = Zs2 )
% 0.20/0.47 => ( ( Ys2
% 0.20/0.47 = ( append @ A @ Xs1 @ Us ) )
% 0.20/0.47 => ( ( append @ A @ Xs @ Ys2 )
% 0.20/0.47 = ( append @ A @ Zs2 @ Us ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_eq_appendI
% 0.20/0.47 thf(fact_116_append__eq__append__conv2,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A,Ts: list @ A] :
% 0.20/0.47 ( ( ( append @ A @ Xs @ Ys2 )
% 0.20/0.47 = ( append @ A @ Zs2 @ Ts ) )
% 0.20/0.47 = ( ? [Us2: list @ A] :
% 0.20/0.47 ( ( ( Xs
% 0.20/0.47 = ( append @ A @ Zs2 @ Us2 ) )
% 0.20/0.47 & ( ( append @ A @ Us2 @ Ys2 )
% 0.20/0.47 = Ts ) )
% 0.20/0.47 | ( ( ( append @ A @ Xs @ Us2 )
% 0.20/0.47 = Zs2 )
% 0.20/0.47 & ( Ys2
% 0.20/0.47 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_eq_append_conv2
% 0.20/0.47 thf(fact_117_lexordp__eq__pref,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A )
% 0.20/0.47 => ! [U: list @ A,V: list @ A] : ( ord_lexordp_eq @ A @ U @ ( append @ A @ U @ V ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_pref
% 0.20/0.47 thf(fact_118_lexordp__eq__refl,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A )
% 0.20/0.47 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_refl
% 0.20/0.47 thf(fact_119_lexordp__eq__trans,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A )
% 0.20/0.47 => ! [Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.20/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.20/0.47 => ( ( ord_lexordp_eq @ A @ Ys2 @ Zs2 )
% 0.20/0.47 => ( ord_lexordp_eq @ A @ Xs @ Zs2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_trans
% 0.20/0.47 thf(fact_120_lexordp__eq__linear,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A )
% 0.20/0.47 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.20/0.47 | ( ord_lexordp_eq @ A @ Ys2 @ Xs ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_linear
% 0.20/0.47 thf(fact_121_lexordp__eq__antisym,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( linorder @ A )
% 0.20/0.47 => ! [Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 0.20/0.47 => ( ( ord_lexordp_eq @ A @ Ys2 @ Xs )
% 0.20/0.47 => ( Xs = Ys2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq_antisym
% 0.20/0.47 thf(fact_122_append__Cons,axiom,
% 0.20/0.47 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( append @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 0.20/0.47 = ( cons @ A @ X3 @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % append_Cons
% 0.20/0.47 thf(fact_123_Cons__eq__appendI,axiom,
% 0.20/0.47 ! [A: $tType,X3: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 0.20/0.47 ( ( ( cons @ A @ X3 @ Xs1 )
% 0.20/0.47 = Ys2 )
% 0.20/0.47 => ( ( Xs
% 0.20/0.47 = ( append @ A @ Xs1 @ Zs2 ) )
% 0.20/0.47 => ( ( cons @ A @ X3 @ Xs )
% 0.20/0.47 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % Cons_eq_appendI
% 0.20/0.47 thf(fact_124_append_Oleft__neutral,axiom,
% 0.20/0.47 ! [A: $tType,A4: list @ A] :
% 0.20/0.47 ( ( append @ A @ ( nil @ A ) @ A4 )
% 0.20/0.47 = A4 ) ).
% 0.20/0.47
% 0.20/0.47 % append.left_neutral
% 0.20/0.47 thf(fact_125_append__Nil,axiom,
% 0.20/0.47 ! [A: $tType,Ys2: list @ A] :
% 0.20/0.47 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 0.20/0.47 = Ys2 ) ).
% 0.20/0.47
% 0.20/0.47 % append_Nil
% 0.20/0.47 thf(fact_126_eq__Nil__appendI,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( Xs = Ys2 )
% 0.20/0.47 => ( Xs
% 0.20/0.47 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % eq_Nil_appendI
% 0.20/0.47 thf(fact_127_knows2b,axiom,
% 0.20/0.47 ! [A2: secrecy_specID,E: list @ secrecy_Expression,E1: list @ secrecy_Expression] :
% 0.20/0.47 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E @ E1 ) )
% 0.20/0.47 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.20/0.47
% 0.20/0.47 % knows2b
% 0.20/0.47 thf(fact_128_knows2a,axiom,
% 0.20/0.47 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E: list @ secrecy_Expression] :
% 0.20/0.47 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E ) )
% 0.20/0.47 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.20/0.47
% 0.20/0.47 % knows2a
% 0.20/0.47 thf(fact_129_knows3,axiom,
% 0.20/0.47 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E22: list @ secrecy_Expression] :
% 0.20/0.47 ( ( ( knowle2055185861_knows @ A2 @ E1 )
% 0.20/0.47 & ( knowle2055185861_knows @ A2 @ E22 ) )
% 0.20/0.47 => ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E22 ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % knows3
% 0.20/0.47 thf(fact_130_ord_Olexordp__eq__pref,axiom,
% 0.20/0.47 ! [A: $tType,Less: A > A > $o,U: list @ A,V: list @ A] : ( lexordp_eq @ A @ Less @ U @ ( append @ A @ U @ V ) ) ).
% 0.20/0.47
% 0.20/0.47 % ord.lexordp_eq_pref
% 0.20/0.47 thf(fact_131_lexordp__eq_ONil,axiom,
% 0.20/0.47 ! [A: $tType] :
% 0.20/0.47 ( ( ord @ A )
% 0.20/0.47 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 0.20/0.47
% 0.20/0.47 % lexordp_eq.Nil
% 0.20/0.47 thf(fact_132_notSpecKeysSecretsExpr__L2,axiom,
% 0.20/0.47 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 0.20/0.47 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 0.20/0.47 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 0.20/0.47
% 0.20/0.47 % notSpecKeysSecretsExpr_L2
% 0.20/0.47 thf(fact_133_splice_Osimps_I2_J,axiom,
% 0.20/0.47 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 0.20/0.47 ( ( splice @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 0.20/0.47 = ( cons @ A @ X3 @ ( splice @ A @ Ys2 @ Xs ) ) ) ).
% 0.20/0.47
% 0.20/0.47 % splice.simps(2)
% 0.20/0.47 thf(fact_134_splice_Osimps_I1_J,axiom,
% 0.20/0.47 ! [A: $tType,Ys2: list @ A] :
% 0.20/0.47 ( ( splice @ A @ ( nil @ A ) @ Ys2 )
% 0.20/0.47 = Ys2 ) ).
% 0.20/0.47
% 0.20/0.47 % splice.simps(1)
% 0.20/0.47 thf(fact_135_rev__nonempty__induct,axiom,
% 0.20/0.47 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 0.20/0.47 ( ( Xs
% 0.20/0.47 != ( nil @ A ) )
% 0.20/0.47 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 0.20/0.47 => ( ! [X: A,Xs2: list @ A] :
% 0.20/0.47 ( ( Xs2
% 0.20/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( P @ Xs2 )
% 0.32/0.47 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) )
% 0.32/0.47 => ( P @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_nonempty_induct
% 0.32/0.47 thf(fact_136_append__eq__Cons__conv,axiom,
% 0.32/0.47 ! [A: $tType,Ys2: list @ A,Zs2: list @ A,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( ( append @ A @ Ys2 @ Zs2 )
% 0.32/0.47 = ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( Zs2
% 0.32/0.47 = ( cons @ A @ X3 @ Xs ) ) )
% 0.32/0.47 | ? [Ys4: list @ A] :
% 0.32/0.47 ( ( Ys2
% 0.32/0.47 = ( cons @ A @ X3 @ Ys4 ) )
% 0.32/0.47 & ( ( append @ A @ Ys4 @ Zs2 )
% 0.32/0.47 = Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % append_eq_Cons_conv
% 0.32/0.47 thf(fact_137_Cons__eq__append__conv,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.47 ( ( ( cons @ A @ X3 @ Xs )
% 0.32/0.47 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.32/0.47 = ( ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( ( cons @ A @ X3 @ Xs )
% 0.32/0.47 = Zs2 ) )
% 0.32/0.47 | ? [Ys4: list @ A] :
% 0.32/0.47 ( ( ( cons @ A @ X3 @ Ys4 )
% 0.32/0.47 = Ys2 )
% 0.32/0.47 & ( Xs
% 0.32/0.47 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Cons_eq_append_conv
% 0.32/0.47 thf(fact_138_rev__exhaust,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 => ~ ! [Ys3: list @ A,Y4: A] :
% 0.32/0.47 ( Xs
% 0.32/0.47 != ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_exhaust
% 0.32/0.47 thf(fact_139_rev__induct,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,Xs2: list @ A] :
% 0.32/0.47 ( ( P @ Xs2 )
% 0.32/0.47 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) )
% 0.32/0.47 => ( P @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_induct
% 0.32/0.47 thf(fact_140_maps__simps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,F3: B > ( list @ A ),X3: B,Xs: list @ B] :
% 0.32/0.47 ( ( maps @ B @ A @ F3 @ ( cons @ B @ X3 @ Xs ) )
% 0.32/0.47 = ( append @ A @ ( F3 @ X3 ) @ ( maps @ B @ A @ F3 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % maps_simps(1)
% 0.32/0.47 thf(fact_141_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_142_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_143_concat__eq__append__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.47 ( ( ( concat @ A @ Xss2 )
% 0.32/0.47 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.32/0.47 = ( ( ( Xss2
% 0.32/0.47 = ( nil @ ( list @ A ) ) )
% 0.32/0.47 => ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( Zs2
% 0.32/0.47 = ( nil @ A ) ) ) )
% 0.32/0.47 & ( ( Xss2
% 0.32/0.47 != ( nil @ ( list @ A ) ) )
% 0.32/0.47 => ? [Xss1: list @ ( list @ A ),Xs3: list @ A,Xs4: list @ A,Xss22: list @ ( list @ A )] :
% 0.32/0.47 ( ( Xss2
% 0.32/0.47 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.32/0.47 & ( Ys2
% 0.32/0.47 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs3 ) )
% 0.32/0.47 & ( Zs2
% 0.32/0.47 = ( append @ A @ Xs4 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % concat_eq_append_conv
% 0.32/0.47 thf(fact_144_rotate1_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( rotate1 @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rotate1.simps(2)
% 0.32/0.47 thf(fact_145_rotate1__is__Nil__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( rotate1 @ A @ Xs )
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rotate1_is_Nil_conv
% 0.32/0.47 thf(fact_146_concat__append,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 0.32/0.47 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys2 ) )
% 0.32/0.47 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % concat_append
% 0.32/0.47 thf(fact_147_rotate1_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( rotate1 @ A @ ( nil @ A ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % rotate1.simps(1)
% 0.32/0.47 thf(fact_148_concat_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % concat.simps(1)
% 0.32/0.47 thf(fact_149_concat_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: list @ A,Xs: list @ ( list @ A )] :
% 0.32/0.47 ( ( concat @ A @ ( cons @ ( list @ A ) @ X3 @ Xs ) )
% 0.32/0.47 = ( append @ A @ X3 @ ( concat @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % concat.simps(2)
% 0.32/0.47 thf(fact_150_maps__simps_I2_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 0.32/0.47 ( ( maps @ B @ A @ F3 @ ( nil @ B ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % maps_simps(2)
% 0.32/0.47 thf(fact_151_concat__eq__appendD,axiom,
% 0.32/0.47 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 0.32/0.47 ( ( ( concat @ A @ Xss2 )
% 0.32/0.47 = ( append @ A @ Ys2 @ Zs2 ) )
% 0.32/0.47 => ( ( Xss2
% 0.32/0.47 != ( nil @ ( list @ A ) ) )
% 0.32/0.47 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs5: list @ A,Xss23: list @ ( list @ A )] :
% 0.32/0.47 ( ( Xss2
% 0.32/0.47 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.32/0.47 & ( Ys2
% 0.32/0.47 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 0.32/0.47 & ( Zs2
% 0.32/0.47 = ( append @ A @ Xs5 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % concat_eq_appendD
% 0.32/0.47 thf(fact_152_butlast__snoc,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.32/0.47 = Xs ) ).
% 0.32/0.47
% 0.32/0.47 % butlast_snoc
% 0.32/0.47 thf(fact_153_last__snoc,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 0.32/0.47 = X3 ) ).
% 0.32/0.47
% 0.32/0.47 % last_snoc
% 0.32/0.47 thf(fact_154_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 & ! [Y3: secrecy_Secrets] :
% 0.32/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y3 ) @ E2 )
% 0.32/0.47 => ~ ( member2 @ secrecy_KS @ ( secrecy_sKS @ Y3 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % notSpecKeysSecretsExpr_def
% 0.32/0.47 thf(fact_155_last__appendR,axiom,
% 0.32/0.47 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.47 ( ( Ys2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( last @ A @ Ys2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_appendR
% 0.32/0.47 thf(fact_156_last__appendL,axiom,
% 0.32/0.47 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.47 ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_appendL
% 0.32/0.47 thf(fact_157_append__butlast__last__id,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 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 0.32/0.47 = Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % append_butlast_last_id
% 0.32/0.47 thf(fact_158_butlast_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( butlast @ A @ ( nil @ A ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % butlast.simps(1)
% 0.32/0.47 thf(fact_159_snoc__eq__iff__butlast,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 = Ys2 )
% 0.32/0.47 = ( ( Ys2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 & ( ( butlast @ A @ Ys2 )
% 0.32/0.47 = Xs )
% 0.32/0.47 & ( ( last @ A @ Ys2 )
% 0.32/0.47 = X3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % snoc_eq_iff_butlast
% 0.32/0.47 thf(fact_160_last__ConsR,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_ConsR
% 0.32/0.47 thf(fact_161_last__ConsL,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = X3 ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_ConsL
% 0.32/0.47 thf(fact_162_last_Osimps,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = X3 ) )
% 0.32/0.47 & ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last.simps
% 0.32/0.47 thf(fact_163_longest__common__suffix,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ? [Ss: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 = ( append @ A @ Xs5 @ Ss ) )
% 0.32/0.47 & ( Ys2
% 0.32/0.47 = ( append @ A @ Ys5 @ Ss ) )
% 0.32/0.47 & ( ( Xs5
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( Ys5
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( ( last @ A @ Xs5 )
% 0.32/0.47 != ( last @ A @ Ys5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % longest_common_suffix
% 0.32/0.47 thf(fact_164_last__append,axiom,
% 0.32/0.47 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.47 ( ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) )
% 0.32/0.47 & ( ( Ys2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( last @ A @ Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_append
% 0.32/0.47 thf(fact_165_butlast_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( nil @ A ) ) )
% 0.32/0.47 & ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( cons @ A @ X3 @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % butlast.simps(2)
% 0.32/0.47 thf(fact_166_butlast__append,axiom,
% 0.32/0.47 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 0.32/0.47 ( ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( butlast @ A @ Xs ) ) )
% 0.32/0.47 & ( ( Ys2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( append @ A @ Xs @ ( butlast @ A @ Ys2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % butlast_append
% 0.32/0.47 thf(fact_167_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_168_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_169_concat__conv__foldr,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( concat @ A )
% 0.32/0.47 = ( ^ [Xss3: list @ ( list @ A )] : ( foldr @ ( list @ A ) @ ( list @ A ) @ ( append @ A ) @ Xss3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % concat_conv_foldr
% 0.32/0.47 thf(fact_170_foldr__append,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,F3: B > A > A,Xs: list @ B,Ys2: list @ B,A4: A] :
% 0.32/0.47 ( ( foldr @ B @ A @ F3 @ ( append @ B @ Xs @ Ys2 ) @ A4 )
% 0.32/0.47 = ( foldr @ B @ A @ F3 @ Xs @ ( foldr @ B @ A @ F3 @ Ys2 @ A4 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % foldr_append
% 0.32/0.47 thf(fact_171_SuccI,axiom,
% 0.32/0.47 ! [A: $tType,Kl: list @ A,K: A,Kl2: set @ ( list @ A )] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ ( append @ A @ Kl @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl2 )
% 0.32/0.47 => ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl2 @ Kl ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % SuccI
% 0.32/0.47 thf(fact_172_SuccD,axiom,
% 0.32/0.47 ! [A: $tType,K: A,Kl2: set @ ( list @ A ),Kl: list @ A] :
% 0.32/0.47 ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl2 @ Kl ) )
% 0.32/0.47 => ( member2 @ ( list @ A ) @ ( append @ A @ Kl @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % SuccD
% 0.32/0.47 thf(fact_173_rev__eq__Cons__iff,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( rev @ A @ Xs )
% 0.32/0.47 = ( cons @ A @ Y @ Ys2 ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_eq_Cons_iff
% 0.32/0.47 thf(fact_174_rev__rev__ident,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 0.32/0.47 = Xs ) ).
% 0.32/0.47
% 0.32/0.47 % rev_rev_ident
% 0.32/0.47 thf(fact_175_rev__is__rev__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( rev @ A @ Xs )
% 0.32/0.47 = ( rev @ A @ Ys2 ) )
% 0.32/0.47 = ( Xs = Ys2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_is_rev_conv
% 0.32/0.47 thf(fact_176_Nil__is__rev__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( nil @ A )
% 0.32/0.47 = ( rev @ A @ Xs ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Nil_is_rev_conv
% 0.32/0.47 thf(fact_177_rev__is__Nil__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( rev @ A @ Xs )
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_is_Nil_conv
% 0.32/0.47 thf(fact_178_rev__append,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( rev @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( rev @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_append
% 0.32/0.47 thf(fact_179_singleton__rev__conv,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( ( cons @ A @ X3 @ ( nil @ A ) )
% 0.32/0.47 = ( rev @ A @ Xs ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % singleton_rev_conv
% 0.32/0.47 thf(fact_180_rev__singleton__conv,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A] :
% 0.32/0.47 ( ( ( rev @ A @ Xs )
% 0.32/0.47 = ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_singleton_conv
% 0.32/0.47 thf(fact_181_rev__swap,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( rev @ A @ Xs )
% 0.32/0.47 = Ys2 )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( rev @ A @ Ys2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev_swap
% 0.32/0.47 thf(fact_182_rev_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( rev @ A @ ( nil @ A ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev.simps(1)
% 0.32/0.47 thf(fact_183_rev_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( rev @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rev.simps(2)
% 0.32/0.47 thf(fact_184_map__tailrec__def,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( map_tailrec @ A @ B )
% 0.32/0.47 = ( ^ [F4: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F4 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % map_tailrec_def
% 0.32/0.47 thf(fact_185_shift__def,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType] :
% 0.32/0.47 ( ( bNF_Greatest_shift @ A @ B )
% 0.32/0.47 = ( ^ [Lab: ( list @ A ) > B,K4: A,Kl3: list @ A] : ( Lab @ ( cons @ A @ K4 @ Kl3 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % shift_def
% 0.32/0.47 thf(fact_186_empty__Shift,axiom,
% 0.32/0.47 ! [A: $tType,Kl2: set @ ( list @ A ),K: A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ Kl2 )
% 0.32/0.47 => ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl2 @ ( nil @ A ) ) )
% 0.32/0.47 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( bNF_Greatest_Shift @ A @ Kl2 @ K ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % empty_Shift
% 0.32/0.47 thf(fact_187_ShiftD,axiom,
% 0.32/0.47 ! [A: $tType,Kl: list @ A,Kl2: set @ ( list @ A ),K: A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ Kl @ ( bNF_Greatest_Shift @ A @ Kl2 @ K ) )
% 0.32/0.47 => ( member2 @ ( list @ A ) @ ( cons @ A @ K @ Kl ) @ Kl2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % ShiftD
% 0.32/0.47 thf(fact_188_Succ__Shift,axiom,
% 0.32/0.47 ! [A: $tType,Kl2: set @ ( list @ A ),K: A,Kl: list @ A] :
% 0.32/0.47 ( ( bNF_Greatest_Succ @ A @ ( bNF_Greatest_Shift @ A @ Kl2 @ K ) @ Kl )
% 0.32/0.47 = ( bNF_Greatest_Succ @ A @ Kl2 @ ( cons @ A @ K @ Kl ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Succ_Shift
% 0.32/0.47 thf(fact_189_last__rev,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 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 0.32/0.47 = ( hd @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_rev
% 0.32/0.47 thf(fact_190_hd__rev,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 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % hd_rev
% 0.32/0.47 thf(fact_191_hd__append2,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( hd @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % hd_append2
% 0.32/0.47 thf(fact_192_hd__append,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( hd @ A @ Ys2 ) ) )
% 0.32/0.47 & ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( hd @ A @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % hd_append
% 0.32/0.47 thf(fact_193_longest__common__prefix,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ? [Ps: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 = ( append @ A @ Ps @ Xs5 ) )
% 0.32/0.47 & ( Ys2
% 0.32/0.47 = ( append @ A @ Ps @ Ys5 ) )
% 0.32/0.47 & ( ( Xs5
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( Ys5
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( ( hd @ A @ Xs5 )
% 0.32/0.47 != ( hd @ A @ Ys5 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % longest_common_prefix
% 0.32/0.47 thf(fact_194_hd__concat,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ ( list @ A )] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ ( list @ A ) ) )
% 0.32/0.47 => ( ( ( hd @ ( list @ A ) @ Xs )
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( hd @ A @ ( concat @ A @ Xs ) )
% 0.32/0.47 = ( hd @ A @ ( hd @ ( list @ A ) @ Xs ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % hd_concat
% 0.32/0.47 thf(fact_195_list_Osel_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X21: A,X222: list @ A] :
% 0.32/0.47 ( ( hd @ A @ ( cons @ A @ X21 @ X222 ) )
% 0.32/0.47 = X21 ) ).
% 0.32/0.47
% 0.32/0.47 % list.sel(1)
% 0.32/0.47 thf(fact_196_rotate1__hd__tl,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 => ( ( rotate1 @ A @ Xs )
% 0.32/0.47 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % rotate1_hd_tl
% 0.32/0.47 thf(fact_197_distinct__adj__append__iff,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( ( distinct_adj @ A @ Xs )
% 0.32/0.47 & ( distinct_adj @ A @ Ys2 )
% 0.32/0.47 & ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( ( last @ A @ Xs )
% 0.32/0.47 != ( hd @ A @ Ys2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_append_iff
% 0.32/0.47 thf(fact_198_distinct__adj__Cons__Cons,axiom,
% 0.32/0.47 ! [B: $tType,X3: B,Y: B,Xs: list @ B] :
% 0.32/0.47 ( ( distinct_adj @ B @ ( cons @ B @ X3 @ ( cons @ B @ Y @ Xs ) ) )
% 0.32/0.47 = ( ( X3 != Y )
% 0.32/0.47 & ( distinct_adj @ B @ ( cons @ B @ Y @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_Cons_Cons
% 0.32/0.47 thf(fact_199_distinct__adj__rev,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( distinct_adj @ A @ ( rev @ A @ Xs ) )
% 0.32/0.47 = ( distinct_adj @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_rev
% 0.32/0.47 thf(fact_200_tl__append2,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( tl @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( append @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tl_append2
% 0.32/0.47 thf(fact_201_butlast__rev,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( butlast @ A @ ( rev @ A @ Xs ) )
% 0.32/0.47 = ( rev @ A @ ( tl @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % butlast_rev
% 0.32/0.47 thf(fact_202_list_Ocollapse,axiom,
% 0.32/0.47 ! [A: $tType,List: list @ A] :
% 0.32/0.47 ( ( List
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 0.32/0.47 = List ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.collapse
% 0.32/0.47 thf(fact_203_hd__Cons__tl,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 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 0.32/0.47 = Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % hd_Cons_tl
% 0.32/0.47 thf(fact_204_list_Oexpand,axiom,
% 0.32/0.47 ! [A: $tType,List: list @ A,List2: list @ A] :
% 0.32/0.47 ( ( ( List
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 = ( List2
% 0.32/0.47 = ( nil @ A ) ) )
% 0.32/0.47 => ( ( ( List
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( List2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ( ( hd @ A @ List )
% 0.32/0.47 = ( hd @ A @ List2 ) )
% 0.32/0.47 & ( ( tl @ A @ List )
% 0.32/0.47 = ( tl @ A @ List2 ) ) ) ) )
% 0.32/0.47 => ( List = List2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.expand
% 0.32/0.47 thf(fact_205_butlast__tl,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 0.32/0.47 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % butlast_tl
% 0.32/0.47 thf(fact_206_distinct__adj__appendD1,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 => ( distinct_adj @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_appendD1
% 0.32/0.47 thf(fact_207_distinct__adj__appendD2,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 => ( distinct_adj @ A @ Ys2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_appendD2
% 0.32/0.47 thf(fact_208_distinct__adj__Nil,axiom,
% 0.32/0.47 ! [A: $tType] : ( distinct_adj @ A @ ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_Nil
% 0.32/0.47 thf(fact_209_distinct__adj__ConsD,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 => ( distinct_adj @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_ConsD
% 0.32/0.47 thf(fact_210_list_Osel_I2_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( tl @ A @ ( nil @ A ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.sel(2)
% 0.32/0.47 thf(fact_211_list_Osel_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,X21: A,X222: list @ A] :
% 0.32/0.47 ( ( tl @ A @ ( cons @ A @ X21 @ X222 ) )
% 0.32/0.47 = X222 ) ).
% 0.32/0.47
% 0.32/0.47 % list.sel(3)
% 0.32/0.47 thf(fact_212_tl__Nil,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( tl @ A @ Xs )
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 = ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ? [X4: A] :
% 0.32/0.47 ( Xs
% 0.32/0.47 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % tl_Nil
% 0.32/0.47 thf(fact_213_Nil__tl,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( nil @ A )
% 0.32/0.47 = ( tl @ A @ Xs ) )
% 0.32/0.47 = ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ? [X4: A] :
% 0.32/0.47 ( Xs
% 0.32/0.47 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Nil_tl
% 0.32/0.47 thf(fact_214_last__tl,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 | ( ( tl @ A @ Xs )
% 0.32/0.47 != ( nil @ A ) ) )
% 0.32/0.47 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_tl
% 0.32/0.47 thf(fact_215_distinct__adj__singleton,axiom,
% 0.32/0.47 ! [B: $tType,X3: B] : ( distinct_adj @ B @ ( cons @ B @ X3 @ ( nil @ B ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_singleton
% 0.32/0.47 thf(fact_216_list_Oexhaust__sel,axiom,
% 0.32/0.47 ! [A: $tType,List: list @ A] :
% 0.32/0.47 ( ( List
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( List
% 0.32/0.47 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.exhaust_sel
% 0.32/0.47 thf(fact_217_distinct__adj__Cons,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( ( X3
% 0.32/0.47 != ( hd @ A @ Xs ) )
% 0.32/0.47 & ( distinct_adj @ A @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_Cons
% 0.32/0.47 thf(fact_218_list_Osplit__sel__asm,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 0.32/0.47 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 0.32/0.47 = ( ~ ( ( ( List
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ~ ( P @ F1 ) )
% 0.32/0.47 | ( ( List
% 0.32/0.47 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.32/0.47 & ~ ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.split_sel_asm
% 0.32/0.47 thf(fact_219_list_Osplit__sel,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 0.32/0.47 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 0.32/0.47 = ( ( ( List
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( P @ F1 ) )
% 0.32/0.47 & ( ( List
% 0.32/0.47 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 0.32/0.47 => ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.split_sel
% 0.32/0.47 thf(fact_220_list_Osimps_I4_J,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType,F1: B,F2: A > ( list @ A ) > B] :
% 0.32/0.47 ( ( case_list @ B @ A @ F1 @ F2 @ ( nil @ A ) )
% 0.32/0.47 = F1 ) ).
% 0.32/0.47
% 0.32/0.47 % list.simps(4)
% 0.32/0.47 thf(fact_221_list_Osimps_I5_J,axiom,
% 0.32/0.47 ! [B: $tType,A: $tType,F1: B,F2: A > ( list @ A ) > B,X21: A,X222: list @ A] :
% 0.32/0.47 ( ( case_list @ B @ A @ F1 @ F2 @ ( cons @ A @ X21 @ X222 ) )
% 0.32/0.47 = ( F2 @ X21 @ X222 ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.simps(5)
% 0.32/0.47 thf(fact_222_list_Ocase__eq__if,axiom,
% 0.32/0.47 ! [A: $tType,B: $tType] :
% 0.32/0.47 ( ( case_list @ B @ A )
% 0.32/0.47 = ( ^ [F12: B,F22: A > ( list @ A ) > B,List3: list @ A] :
% 0.32/0.47 ( if @ B
% 0.32/0.47 @ ( List3
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 @ F12
% 0.32/0.47 @ ( F22 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % list.case_eq_if
% 0.32/0.47 thf(fact_223_successively__append__iff,axiom,
% 0.32/0.47 ! [A: $tType,P: A > A > $o,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( successively @ A @ P @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( ( successively @ A @ P @ Xs )
% 0.32/0.47 & ( successively @ A @ P @ Ys2 )
% 0.32/0.47 & ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( P @ ( last @ A @ Xs ) @ ( hd @ A @ Ys2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively_append_iff
% 0.32/0.47 thf(fact_224_Cons__in__shuffles__iff,axiom,
% 0.32/0.47 ! [A: $tType,Z: A,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( ( ( Xs
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 & ( ( hd @ A @ Xs )
% 0.32/0.47 = Z )
% 0.32/0.47 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) )
% 0.32/0.47 | ( ( Ys2
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 & ( ( hd @ A @ Ys2 )
% 0.32/0.47 = Z )
% 0.32/0.47 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ ( tl @ A @ Ys2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Cons_in_shuffles_iff
% 0.32/0.47 thf(fact_225_Nil__in__shuffles,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 & ( Ys2
% 0.32/0.47 = ( nil @ A ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Nil_in_shuffles
% 0.32/0.47 thf(fact_226_splice__in__shuffles,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] : ( member2 @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) @ ( shuffles @ A @ Xs @ Ys2 ) ) ).
% 0.32/0.47
% 0.32/0.47 % splice_in_shuffles
% 0.32/0.47 thf(fact_227_shufflesE,axiom,
% 0.32/0.47 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.47 => ( ( ( Zs2 = Xs )
% 0.32/0.47 => ( Ys2
% 0.32/0.47 != ( nil @ A ) ) )
% 0.32/0.47 => ( ( ( Zs2 = Ys2 )
% 0.32/0.47 => ( Xs
% 0.32/0.47 != ( nil @ A ) ) )
% 0.32/0.47 => ( ! [X: A,Xs5: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 = ( cons @ A @ X @ Xs5 ) )
% 0.32/0.47 => ! [Z2: A,Zs3: list @ A] :
% 0.32/0.47 ( ( Zs2
% 0.32/0.47 = ( cons @ A @ Z2 @ Zs3 ) )
% 0.32/0.47 => ( ( X = Z2 )
% 0.32/0.47 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs5 @ Ys2 ) ) ) ) )
% 0.32/0.47 => ~ ! [Y4: A,Ys5: list @ A] :
% 0.32/0.47 ( ( Ys2
% 0.32/0.47 = ( cons @ A @ Y4 @ Ys5 ) )
% 0.32/0.47 => ! [Z2: A,Zs3: list @ A] :
% 0.32/0.47 ( ( Zs2
% 0.32/0.47 = ( cons @ A @ Z2 @ Zs3 ) )
% 0.32/0.47 => ( ( Y4 = Z2 )
% 0.32/0.47 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % shufflesE
% 0.32/0.47 thf(fact_228_successively_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,P: A > A > $o,X3: A] : ( successively @ A @ P @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.simps(2)
% 0.32/0.47 thf(fact_229_successively_Oelims_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A > A > $o,Xa: list @ A,Y: $o] :
% 0.32/0.47 ( ( ( successively @ A @ X3 @ Xa )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( ( Xa
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ~ Y )
% 0.32/0.47 => ( ( ? [X: A] :
% 0.32/0.47 ( Xa
% 0.32/0.47 = ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ~ Y )
% 0.32/0.47 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.32/0.47 => ( Y
% 0.32/0.47 = ( ~ ( ( X3 @ X @ Y4 )
% 0.32/0.47 & ( successively @ A @ X3 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.elims(1)
% 0.32/0.47 thf(fact_230_successively_Oelims_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A > A > $o,Xa: list @ A] :
% 0.32/0.47 ( ( successively @ A @ X3 @ Xa )
% 0.32/0.47 => ( ( Xa
% 0.32/0.47 != ( nil @ A ) )
% 0.32/0.47 => ( ! [X: A] :
% 0.32/0.47 ( Xa
% 0.32/0.47 != ( cons @ A @ X @ ( nil @ A ) ) )
% 0.32/0.47 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.32/0.47 => ~ ( ( X3 @ X @ Y4 )
% 0.32/0.47 & ( successively @ A @ X3 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.elims(2)
% 0.32/0.47 thf(fact_231_shuffles__commutes,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( shuffles @ A )
% 0.32/0.47 = ( ^ [Xs3: list @ A,Ys: list @ A] : ( shuffles @ A @ Ys @ Xs3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % shuffles_commutes
% 0.32/0.47 thf(fact_232_successively_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType,P: A > A > $o] : ( successively @ A @ P @ ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.simps(1)
% 0.32/0.47 thf(fact_233_successively_Osimps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,P: A > A > $o,X3: A,Y: A,Xs: list @ A] :
% 0.32/0.47 ( ( successively @ A @ P @ ( cons @ A @ X3 @ ( cons @ A @ Y @ Xs ) ) )
% 0.32/0.47 = ( ( P @ X3 @ Y )
% 0.32/0.47 & ( successively @ A @ P @ ( cons @ A @ Y @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.simps(3)
% 0.32/0.47 thf(fact_234_successively_Oelims_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A > A > $o,Xa: list @ A] :
% 0.32/0.47 ( ~ ( successively @ A @ X3 @ Xa )
% 0.32/0.47 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.32/0.47 ( ( Xa
% 0.32/0.47 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.32/0.47 => ( ( X3 @ X @ Y4 )
% 0.32/0.47 & ( successively @ A @ X3 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively.elims(3)
% 0.32/0.47 thf(fact_235_Nil__in__shufflesI,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( shuffles @ A @ Xs @ Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Nil_in_shufflesI
% 0.32/0.47 thf(fact_236_Cons__in__shuffles__rightI,axiom,
% 0.32/0.47 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A,Z: A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.47 => ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ Xs @ ( cons @ A @ Z @ Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Cons_in_shuffles_rightI
% 0.32/0.47 thf(fact_237_Cons__in__shuffles__leftI,axiom,
% 0.32/0.47 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A,Z: A] :
% 0.32/0.47 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 0.32/0.47 => ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ ( cons @ A @ Z @ Xs ) @ Ys2 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % Cons_in_shuffles_leftI
% 0.32/0.47 thf(fact_238_successively__Cons,axiom,
% 0.32/0.47 ! [A: $tType,P: A > A > $o,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( successively @ A @ P @ ( cons @ A @ X3 @ Xs ) )
% 0.32/0.47 = ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( ( P @ X3 @ ( hd @ A @ Xs ) )
% 0.32/0.47 & ( successively @ A @ P @ Xs ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively_Cons
% 0.32/0.47 thf(fact_239_remdups__adj__append_H,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 0.32/0.47 ( ( ( Xs
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( Ys2
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 | ( ( last @ A @ Xs )
% 0.32/0.47 != ( hd @ A @ Ys2 ) ) )
% 0.32/0.47 => ( ( remdups_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 0.32/0.47 = ( append @ A @ ( remdups_adj @ A @ Xs ) @ ( remdups_adj @ A @ Ys2 ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj_append'
% 0.32/0.47 thf(fact_240_remdups__adj__append,axiom,
% 0.32/0.47 ! [A: $tType,Xs_1: list @ A,X3: A,Xs_2: list @ A] :
% 0.32/0.47 ( ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X3 @ Xs_2 ) ) )
% 0.32/0.47 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs_2 ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj_append
% 0.32/0.47 thf(fact_241_remdups__adj__Nil__iff,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( ( remdups_adj @ A @ Xs )
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 = ( Xs
% 0.32/0.47 = ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj_Nil_iff
% 0.32/0.47 thf(fact_242_remdups__adj__rev,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( remdups_adj @ A @ ( rev @ A @ Xs ) )
% 0.32/0.47 = ( rev @ A @ ( remdups_adj @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj_rev
% 0.32/0.47 thf(fact_243_hd__remdups__adj,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( hd @ A @ ( remdups_adj @ A @ Xs ) )
% 0.32/0.47 = ( hd @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % hd_remdups_adj
% 0.32/0.47 thf(fact_244_last__remdups__adj,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] :
% 0.32/0.47 ( ( last @ A @ ( remdups_adj @ A @ Xs ) )
% 0.32/0.47 = ( last @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % last_remdups_adj
% 0.32/0.47 thf(fact_245_remdups__adj__Cons__alt,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Xs: list @ A] :
% 0.32/0.47 ( ( cons @ A @ X3 @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs ) ) ) )
% 0.32/0.47 = ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj_Cons_alt
% 0.32/0.47 thf(fact_246_successively__remdups__adjI,axiom,
% 0.32/0.47 ! [A: $tType,P: A > A > $o,Xs: list @ A] :
% 0.32/0.47 ( ( successively @ A @ P @ Xs )
% 0.32/0.47 => ( successively @ A @ P @ ( remdups_adj @ A @ Xs ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % successively_remdups_adjI
% 0.32/0.47 thf(fact_247_distinct__adj__remdups__adj,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A] : ( distinct_adj @ A @ ( remdups_adj @ A @ Xs ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_remdups_adj
% 0.32/0.47 thf(fact_248_distinct__adj__altdef,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( distinct_adj @ A )
% 0.32/0.47 = ( ^ [Xs3: list @ A] :
% 0.32/0.47 ( ( remdups_adj @ A @ Xs3 )
% 0.32/0.47 = Xs3 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % distinct_adj_altdef
% 0.32/0.47 thf(fact_249_remdups__adj_Osimps_I2_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A] :
% 0.32/0.47 ( ( remdups_adj @ A @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 0.32/0.47 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.simps(2)
% 0.32/0.47 thf(fact_250_remdups__adj_Oelims,axiom,
% 0.32/0.47 ! [A: $tType,X3: list @ A,Y: list @ A] :
% 0.32/0.47 ( ( ( remdups_adj @ A @ X3 )
% 0.32/0.47 = Y )
% 0.32/0.47 => ( ( ( X3
% 0.32/0.47 = ( nil @ A ) )
% 0.32/0.47 => ( Y
% 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 => ( Y
% 0.32/0.47 != ( cons @ A @ X @ ( nil @ A ) ) ) )
% 0.32/0.47 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 0.32/0.47 ( ( X3
% 0.32/0.47 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 0.32/0.47 => ~ ( ( ( X = Y4 )
% 0.32/0.47 => ( Y
% 0.32/0.47 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs2 ) ) ) )
% 0.32/0.47 & ( ( X != Y4 )
% 0.32/0.47 => ( Y
% 0.32/0.47 = ( cons @ A @ X @ ( remdups_adj @ A @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.elims
% 0.32/0.47 thf(fact_251_remdups__adj_Osimps_I3_J,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Y: A,Xs: list @ A] :
% 0.32/0.47 ( ( ( X3 = Y )
% 0.32/0.47 => ( ( remdups_adj @ A @ ( cons @ A @ X3 @ ( cons @ A @ Y @ Xs ) ) )
% 0.32/0.47 = ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs ) ) ) )
% 0.32/0.47 & ( ( X3 != Y )
% 0.32/0.47 => ( ( remdups_adj @ A @ ( cons @ A @ X3 @ ( cons @ A @ Y @ Xs ) ) )
% 0.32/0.47 = ( cons @ A @ X3 @ ( remdups_adj @ A @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.simps(3)
% 0.32/0.47 thf(fact_252_remdups__adj_Osimps_I1_J,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( remdups_adj @ A @ ( nil @ A ) )
% 0.32/0.47 = ( nil @ A ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj.simps(1)
% 0.32/0.47 thf(fact_253_remdups__adj__append__two,axiom,
% 0.32/0.47 ! [A: $tType,Xs: list @ A,X3: A,Y: A] :
% 0.32/0.47 ( ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) )
% 0.32/0.47 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) @ ( if @ ( list @ A ) @ ( X3 = Y ) @ ( nil @ A ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % remdups_adj_append_two
% 0.32/0.47 thf(fact_254_lexordp__eq_Oinducts,axiom,
% 0.32/0.47 ! [A: $tType] :
% 0.32/0.47 ( ( ord @ A )
% 0.32/0.47 => ! [X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 0.32/0.47 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 0.32/0.47 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 0.32/0.47 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ( ord_less @ A @ X @ Y4 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 0.32/0.47 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 0.32/0.47 ( ~ ( ord_less @ A @ X @ Y4 )
% 0.32/0.47 => ( ~ ( ord_less @ A @ Y4 @ X )
% 0.32/0.47 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys3 )
% 0.32/0.47 => ( ( P @ Xs2 @ Ys3 )
% 0.32/0.47 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 0.32/0.47 => ( P @ X1 @ X2 ) ) ) ) ) ) ).
% 0.32/0.47
% 0.32/0.47 % lexordp_eq.inducts
% 0.32/0.47
% 0.32/0.47 % Type constructors (4)
% 0.32/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.32/0.47 ! [A5: $tType,A6: $tType] :
% 0.32/0.47 ( ( ord @ A6 )
% 0.32/0.47 => ( ord @ ( A5 > A6 ) ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 0.32/0.47 ! [A5: $tType] : ( ord @ ( set @ A5 ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 0.32/0.47 linorder @ $o ).
% 0.32/0.47
% 0.32/0.47 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 0.32/0.47 ord @ $o ).
% 0.32/0.47
% 0.32/0.47 % Helper facts (3)
% 0.32/0.47 thf(help_If_3_1_T,axiom,
% 0.32/0.47 ! [P: $o] :
% 0.32/0.47 ( ( P = $true )
% 0.32/0.47 | ( P = $false ) ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_2_1_T,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Y: A] :
% 0.32/0.47 ( ( if @ A @ $false @ X3 @ Y )
% 0.32/0.47 = Y ) ).
% 0.32/0.47
% 0.32/0.47 thf(help_If_1_1_T,axiom,
% 0.32/0.47 ! [A: $tType,X3: A,Y: A] :
% 0.32/0.47 ( ( if @ A @ $true @ X3 @ Y )
% 0.32/0.47 = X3 ) ).
% 0.32/0.47
% 0.32/0.47 % Conjectures (1)
% 0.32/0.47 thf(conj_0,conjecture,
% 0.32/0.47 knowle1437066798e_know @ a @ ( secrecy_sKS @ m ) ).
% 0.32/0.47
% 0.32/0.47 %------------------------------------------------------------------------------
% 0.32/0.47 ------------------------
% 2.65/1.53 ---- Embedded in THF ---
% 2.65/1.53 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.65/1.53 %%% Generated on Tue Feb 24 08:26:02 EST 2026
% 2.65/1.53 %%% using '$$dhol' embedding, version 1.3.0.
% 2.65/1.53 %%% Logic specification used:
% 2.65/1.53 %%% thf(spec, logic, $$dhol).
% 2.65/1.53
% 2.65/1.53 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MVbIzHpABw/DTF2DTF22724.p
% 2.65/1.53 thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 2.65/1.53 thf(ty_t_Secrecy__types_OSecrets, type, secrecy_Secrets: $tType).
% 2.65/1.53 thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 2.65/1.53 thf(ty_t_Secrecy__types_OKeys, type, secrecy_Keys: $tType).
% 2.65/1.53 thf(ty_t_Secrecy__types_OKS, type, secrecy_KS: $tType).
% 2.65/1.53 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.65/1.53 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.65/1.53 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.65/1.53 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.65/1.53 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.65/1.53 thf(sy_c_BNF__Greatest__Fixpoint_OShift, type, bNF_Greatest_Shift: (!> [A:$tType]: (((set @ (list @ A)) > (A > (set @ (list @ A))))))).
% 2.65/1.53 thf(sy_c_BNF__Greatest__Fixpoint_OSucc, type, bNF_Greatest_Succ: (!> [A:$tType]: (((set @ (list @ A)) > ((list @ A) > (set @ A)))))).
% 2.65/1.53 thf(sy_c_BNF__Greatest__Fixpoint_Oshift, type, bNF_Greatest_shift: (!> [A:$tType,B:$tType]: ((((list @ A) > B) > (A > ((list @ A) > B)))))).
% 2.65/1.53 thf(sy_c_CompLocalSecrets_OLocalSecrets, type, localSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.65/1.53 thf(sy_c_If, type, if: (!> [A:$tType]: (($o > (A > (A > A)))))).
% 2.65/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect, type, knowle1667810483orrect: (secrecy_specID > (secrecy_KS > $o))).
% 2.65/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowsECorrect, type, knowle1893229345orrect: (secrecy_specID > (secrecy_Expression > $o))).
% 2.65/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow, type, knowle1437066798e_know: (secrecy_specID > (secrecy_KS > $o))).
% 2.65/1.53 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows, type, knowle2055185861_knows: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.65/1.53 thf(sy_c_ListExtras_Omem, type, mem: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 2.65/1.53 thf(sy_c_List_Oappend, type, append: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.53 thf(sy_c_List_Oarg__min__list, type, arg_min_list: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > A))))).
% 2.65/1.53 thf(sy_c_List_Obind, type, bind: (!> [A:$tType,B:$tType]: (((list @ A) > ((A > (list @ B)) > (list @ B)))))).
% 2.65/1.53 thf(sy_c_List_Obutlast, type, butlast: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.65/1.53 thf(sy_c_List_Oconcat, type, concat: (!> [A:$tType]: (((list @ (list @ A)) > (list @ A))))).
% 2.65/1.53 thf(sy_c_List_Odistinct__adj, type, distinct_adj: (!> [A:$tType]: (((list @ A) > $o)))).
% 2.65/1.53 thf(sy_c_List_Ofoldr, type, foldr: (!> [A:$tType,B:$tType]: (((A > (B > B)) > ((list @ A) > (B > B)))))).
% 2.65/1.53 thf(sy_c_List_Oinsert, type, insert: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.65/1.53 thf(sy_c_List_Olast, type, last: (!> [A:$tType]: (((list @ A) > A)))).
% 2.65/1.53 thf(sy_c_List_Olist_OCons, type, cons: (!> [A:$tType]: ((A > ((list @ A) > (list @ A)))))).
% 2.65/1.53 thf(sy_c_List_Olist_ONil, type, nil: (!> [A:$tType]: ((list @ A)))).
% 2.65/1.53 thf(sy_c_List_Olist_Ocase__list, type, case_list: (!> [B:$tType,A:$tType]: ((B > ((A > ((list @ A) > B)) > ((list @ A) > B)))))).
% 2.65/1.53 thf(sy_c_List_Olist_Ohd, type, hd: (!> [A:$tType]: (((list @ A) > A)))).
% 2.65/1.53 thf(sy_c_List_Olist_Otl, type, tl: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.65/1.53 thf(sy_c_List_Olist__ex1, type, list_ex1: (!> [A:$tType]: (((A > $o) > ((list @ A) > $o))))).
% 2.65/1.53 thf(sy_c_List_Olistrelp, type, listrelp: (!> [A:$tType,B:$tType]: (((A > (B > $o)) > ((list @ A) > ((list @ B) > $o)))))).
% 2.65/1.53 thf(sy_c_List_Omap__tailrec, type, map_tailrec: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > (list @ B)))))).
% 2.65/1.53 thf(sy_c_List_Omap__tailrec__rev, type, map_tailrec_rev: (!> [A:$tType,B:$tType]: (((A > B) > ((list @ A) > ((list @ B) > (list @ B))))))).
% 2.65/1.53 thf(sy_c_List_Omaps, type, maps: (!> [A:$tType,B:$tType]: (((A > (list @ B)) > ((list @ A) > (list @ B)))))).
% 2.65/1.53 thf(sy_c_List_Omember, type, member: (!> [A:$tType]: (((list @ A) > (A > $o))))).
% 2.65/1.53 thf(sy_c_List_Oord_Olexordp__eq, type, lexordp_eq: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > ((list @ A) > $o)))))).
% 2.65/1.53 thf(sy_c_List_Oord__class_Olexordp__eq, type, ord_lexordp_eq: (!> [A:$tType]: (((list @ A) > ((list @ A) > $o))))).
% 2.65/1.53 thf(sy_c_List_Oproduct__lists, type, product_lists: (!> [A:$tType]: (((list @ (list @ A)) > (list @ (list @ A)))))).
% 2.65/1.53 thf(sy_c_List_Oremdups__adj, type, remdups_adj: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.65/1.53 thf(sy_c_List_Orev, type, rev: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.65/1.53 thf(sy_c_List_Orotate1, type, rotate1: (!> [A:$tType]: (((list @ A) > (list @ A))))).
% 2.65/1.53 thf(sy_c_List_Oshuffles, type, shuffles: (!> [A:$tType]: (((list @ A) > ((list @ A) > (set @ (list @ A))))))).
% 2.65/1.53 thf(sy_c_List_Osplice, type, splice: (!> [A:$tType]: (((list @ A) > ((list @ A) > (list @ A)))))).
% 2.65/1.53 thf(sy_c_List_Osubseqs, type, subseqs: (!> [A:$tType]: (((list @ A) > (list @ (list @ A)))))).
% 2.65/1.53 thf(sy_c_List_Osuccessively, type, successively: (!> [A:$tType]: (((A > (A > $o)) > ((list @ A) > $o))))).
% 2.65/1.53 thf(sy_c_Orderings_Oord__class_Oless, type, ord_less: (!> [A:$tType]: ((A > (A > $o))))).
% 2.65/1.53 thf(sy_c_Secrecy_ODecr, type, decr: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.65/1.53 thf(sy_c_Secrecy_OEnc, type, enc: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.65/1.53 thf(sy_c_Secrecy_OEncrDecrKeys, type, encrDecrKeys: (secrecy_Keys > (secrecy_Keys > $o))).
% 2.65/1.53 thf(sy_c_Secrecy_OExt, type, ext: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.65/1.53 thf(sy_c_Secrecy_OSign, type, sign: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.65/1.53 thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 2.65/1.53 thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 2.65/1.53 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr, type, notSpe1586871396tsExpr: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.65/1.53 thf(sy_c_Secrecy_OspecKeys, type, specKeys: (secrecy_specID > (set @ secrecy_Keys))).
% 2.65/1.53 thf(sy_c_Secrecy_OspecKeysSecrets, type, specKeysSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.65/1.53 thf(sy_c_Secrecy_OspecSecrets, type, specSecrets: (secrecy_specID > (set @ secrecy_Secrets))).
% 2.65/1.53 thf(sy_c_Secrecy__types_OExpression2KSL, type, secrec1371625429on2KSL: ((list @ secrecy_Expression) > (list @ secrecy_KS))).
% 2.65/1.53 thf(sy_c_Secrecy__types_OExpression_OkE, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 2.65/1.53 thf(sy_c_Secrecy__types_OExpression_OsE, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 2.65/1.53 thf(sy_c_Secrecy__types_OKS2Expression, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 2.65/1.53 thf(sy_c_Secrecy__types_OKS_Ocase__KS, type, secrecy_case_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 2.65/1.53 thf(sy_c_Secrecy__types_OKS_OkKS, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 2.65/1.53 thf(sy_c_Secrecy__types_OKS_Orec__KS, type, secrecy_rec_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 2.65/1.53 thf(sy_c_Secrecy__types_OKS_OsKS, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 2.65/1.53 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.65/1.53 thf(sy_c_member, type, member2: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.65/1.53 thf(sy_v_A, type, a: secrecy_specID).
% 2.65/1.53 thf(sy_v_m, type, m: secrecy_Secrets).
% 2.65/1.53 thf(fact_0_assms, axiom, ((knowle2055185861_knows @ a) @ (((cons @ secrecy_Expression) @ (secrecy_sE @ m)) @ (nil @ secrecy_Expression)))).
% 2.65/1.53 thf(fact_1_KS_Oinject_I2_J, axiom, (! [X2:secrecy_Secrets,Y2:secrecy_Secrets]: ((((secrecy_sKS @ X2) = (secrecy_sKS @ Y2)) = (X2 = Y2))))).
% 2.65/1.53 thf(fact_2_know2knows__s, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: ((((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)) => ((knowle2055185861_knows @ A2) @ (((cons @ secrecy_Expression) @ (secrecy_sE @ M)) @ (nil @ secrecy_Expression))))))).
% 2.65/1.53 thf(fact_3_know1s, axiom, (! [C:secrecy_specID,M2:secrecy_Secrets]: ((((knowle2055185861_knows @ C) @ (((cons @ secrecy_Expression) @ (secrec1016742679ession @ (secrecy_sKS @ M2))) @ (nil @ secrecy_Expression))) = ((knowle1437066798e_know @ C) @ (secrecy_sKS @ M2)))))).
% 2.65/1.53 thf(fact_4_KS_Osimps_I8_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X2:secrecy_Secrets]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X2)) = (F2 @ X2))))).
% 2.65/1.53 thf(fact_5_KS_Osimps_I6_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X2:secrecy_Secrets]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X2)) = (F2 @ X2))))).
% 2.65/1.53 thf(fact_6_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)))))))).
% 2.65/1.53 thf(fact_7_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)))))))).
% 2.65/1.53 thf(fact_8_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))))))).
% 2.65/1.53 thf(fact_9_KS2Expression_Osimps_I2_J, axiom, (! [M:secrecy_Secrets]: (((secrec1016742679ession @ (secrecy_sKS @ M)) = (secrecy_sE @ M))))).
% 2.65/1.53 thf(fact_10_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))))).
% 2.65/1.53 thf(fact_11_knows5, axiom, (! [IncrDecrKeys:(secrecy_Keys > (secrecy_Keys > $o)),K1:secrecy_Keys,K2:secrecy_Keys,A2:secrecy_specID,E:(list @ secrecy_Expression)]: (((((IncrDecrKeys @ K1) @ K2) & (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K1)) & ((knowle2055185861_knows @ A2) @ ((sign @ K2) @ E)))) => ((knowle2055185861_knows @ A2) @ E))))).
% 2.65/1.53 thf(fact_12_knows6, axiom, (! [A2:secrecy_specID,K:secrecy_Keys,E1:(list @ secrecy_Expression)]: (((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K)) & ((knowle2055185861_knows @ A2) @ E1)) => ((knowle2055185861_knows @ A2) @ ((enc @ K) @ E1)))))).
% 2.65/1.53 thf(fact_13_KS_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kKS @ X1) = (secrecy_kKS @ Y1)) = (X1 = Y1))))).
% 2.65/1.53 thf(fact_14_Expression_Oinject_I2_J, axiom, (! [X2:secrecy_Secrets,Y2:secrecy_Secrets]: ((((secrecy_sE @ X2) = (secrecy_sE @ Y2)) = (X2 = Y2))))).
% 2.65/1.53 thf(fact_15_KS_Osimps_I7_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 2.65/1.53 thf(fact_16_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))))).
% 2.65/1.53 thf(fact_17_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)))))).
% 2.65/1.53 thf(fact_18_knows__emptyexpression, axiom, (! [C:secrecy_specID]: (((knowle2055185861_knows @ C) @ (nil @ secrecy_Expression))))).
% 2.65/1.53 thf(fact_19_KS_Oexhaust, axiom, (! [Y:secrecy_KS]: (((! [X12:secrecy_Keys]: ((Y != (secrecy_kKS @ X12)))) => (~ ((! [X22:secrecy_Secrets]: ((Y != (secrecy_sKS @ X22)))))))))).
% 2.65/1.53 thf(fact_20_KS_Oinduct, axiom, (! [P:(secrecy_KS > $o),KS:secrecy_KS]: (((! [X:secrecy_Keys]: ((P @ (secrecy_kKS @ X)))) => ((! [X:secrecy_Secrets]: ((P @ (secrecy_sKS @ X)))) => (P @ KS)))))).
% 2.65/1.53 thf(fact_21_KS_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X2:secrecy_Secrets]: (((secrecy_kKS @ X1) != (secrecy_sKS @ X2))))).
% 2.65/1.53 thf(fact_22_knows7, axiom, (! [A2:secrecy_specID,K:secrecy_Keys,E1:(list @ secrecy_Expression)]: (((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ K)) & ((knowle2055185861_knows @ A2) @ E1)) => ((knowle2055185861_knows @ A2) @ ((sign @ K) @ E1)))))).
% 2.65/1.53 thf(fact_23_list_Oinject, axiom, (! [A:$tType,X21:A,X222:(list @ A),Y21:A,Y22:(list @ A)]: ((((((cons @ A) @ X21) @ X222) = (((cons @ A) @ Y21) @ Y22)) = ((X21 = Y21) & (X222 = Y22)))))).
% 2.65/1.53 thf(fact_24_list_Odistinct_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: (((nil @ A) != (((cons @ A) @ X21) @ X222))))).
% 2.65/1.53 thf(fact_25_list_OdiscI, axiom, (! [A:$tType,List:(list @ A),X21:A,X222:(list @ A)]: (((List = (((cons @ A) @ X21) @ X222)) => (List != (nil @ A)))))).
% 2.65/1.53 thf(fact_26_list_Oexhaust, axiom, (! [A:$tType,Y:(list @ A)]: (((Y != (nil @ A)) => (~ ((! [X212:A,X223:(list @ A)]: ((Y != (((cons @ A) @ X212) @ X223)))))))))).
% 2.65/1.53 thf(fact_27_list_Oinducts, axiom, (! [A:$tType,P:((list @ A) > $o),List:(list @ A)]: (((P @ (nil @ A)) => ((! [X12:A,X22:(list @ A)]: (((P @ X22) => (P @ (((cons @ A) @ X12) @ X22))))) => (P @ List)))))).
% 2.65/1.53 thf(fact_28_neq__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) = (? [Y3:A,Ys:(list @ A)]: ((Xs = (((cons @ A) @ Y3) @ Ys)))))))).
% 2.65/1.53 thf(fact_29_list__induct2_H, axiom, (! [A:$tType,B:$tType,P:((list @ A) > ((list @ B) > $o)),Xs:(list @ A),Ys2:(list @ B)]: ((((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Xs2:(list @ A)]: (((P @ (((cons @ A) @ X) @ Xs2)) @ (nil @ B)))) => ((! [Y4:B,Ys3:(list @ B)]: (((P @ (nil @ A)) @ (((cons @ B) @ Y4) @ Ys3)))) => ((! [X:A,Xs2:(list @ A),Y4:B,Ys3:(list @ B)]: ((((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3))))) => ((P @ Xs) @ Ys2)))))))).
% 2.65/1.53 thf(fact_30_splice_Oinduct, axiom, (! [A:$tType,P:((list @ A) > ((list @ A) > $o)),A0:(list @ A),A1:(list @ A)]: (((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((P @ Ys3) @ Xs2) => ((P @ (((cons @ A) @ X) @ Xs2)) @ Ys3)))) => ((P @ A0) @ A1)))))).
% 2.65/1.53 thf(fact_31_induct__list012, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y4:A,Zs:(list @ A)]: (((P @ Zs) => ((P @ (((cons @ A) @ Y4) @ Zs)) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Zs))))))) => (P @ Xs))))))).
% 2.65/1.53 thf(fact_32_min__list_Ocases, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ Xs2)))) => (X3 = (nil @ A))))))))).
% 2.65/1.53 thf(fact_33_min__list_Oinduct, axiom, (! [A:$tType]: (((ord @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((! [X:A,Xs2:(list @ A)]: (((! [X213:A,X224:(list @ A)]: (((Xs2 = (((cons @ A) @ X213) @ X224)) => (P @ Xs2)))) => (P @ (((cons @ A) @ X) @ Xs2))))) => ((P @ (nil @ A)) => (P @ A0))))))))).
% 2.65/1.53 thf(fact_34_not__Cons__self2, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((cons @ A) @ X3) @ Xs) != Xs)))).
% 2.65/1.53 thf(fact_35_strict__sorted_Oinduct, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Ys3:(list @ A)]: (((P @ Ys3) => (P @ (((cons @ A) @ X) @ Ys3))))) => (P @ A0))))))))).
% 2.65/1.53 thf(fact_36_strict__sorted_Ocases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X3:(list @ A)]: (((X3 != (nil @ A)) => (~ ((! [X:A,Ys3:(list @ A)]: ((X3 != (((cons @ A) @ X) @ Ys3))))))))))))).
% 2.65/1.53 thf(fact_37_map__tailrec__rev_Oinduct, axiom, (! [A:$tType,B:$tType,P:((A > B) > ((list @ A) > ((list @ B) > $o))),A0:(A > B),A1:(list @ A),A22:(list @ B)]: (((! [F:(A > B),X_1:(list @ B)]: ((((P @ F) @ (nil @ A)) @ X_1))) => ((! [F:(A > B),A3:A,As:(list @ A),Bs:(list @ B)]: (((((P @ F) @ As) @ (((cons @ B) @ (F @ A3)) @ Bs)) => (((P @ F) @ (((cons @ A) @ A3) @ As)) @ Bs)))) => (((P @ A0) @ A1) @ A22)))))).
% 2.65/1.53 thf(fact_38_list__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((cons @ A) @ X) @ Xs2)))))) => (P @ Xs))))))).
% 2.65/1.53 thf(fact_39_successively_Oinduct, axiom, (! [A:$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 > $o)),X:A,Y4:A,Xs2:(list @ A)]: ((((P @ P2) @ (((cons @ A) @ Y4) @ Xs2)) => ((P @ P2) @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2)))))) => ((P @ A0) @ A1))))))).
% 2.65/1.53 thf(fact_40_arg__min__list_Oinduct, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [P:((A > B) > ((list @ A) > $o)),A0:(A > B),A1:(list @ A)]: (((! [F:(A > B),X:A]: (((P @ F) @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [F:(A > B),X:A,Y4:A,Zs:(list @ A)]: ((((P @ F) @ (((cons @ A) @ Y4) @ Zs)) => ((P @ F) @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Zs)))))) => ((! [A3:(A > B)]: (((P @ A3) @ (nil @ A)))) => ((P @ A0) @ A1)))))))))).
% 2.65/1.53 thf(fact_41_remdups__adj_Oinduct, axiom, (! [A:$tType,P:((list @ A) > $o),A0:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Y4:A,Xs2:(list @ A)]: ((((X = Y4) => (P @ (((cons @ A) @ X) @ Xs2))) => (((X != Y4) => (P @ (((cons @ A) @ Y4) @ Xs2))) => (P @ (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2))))))) => (P @ A0))))))).
% 2.65/1.53 thf(fact_42_sorted__wrt_Oinduct, axiom, (! [A:$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 > $o)),X:A,Ys3:(list @ A)]: ((((P @ P2) @ Ys3) => ((P @ P2) @ (((cons @ A) @ X) @ Ys3))))) => ((P @ A0) @ A1)))))).
% 2.65/1.53 thf(fact_43_remdups__adj_Ocases, axiom, (! [A:$tType,X3:(list @ A)]: (((X3 != (nil @ A)) => ((! [X:A]: ((X3 != (((cons @ A) @ X) @ (nil @ A))))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: ((X3 != (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2)))))))))))).
% 2.65/1.53 thf(fact_44_mem__Collect__eq, axiom, (! [A:$tType,A4:A,P:(A > $o)]: (((((member2 @ A) @ A4) @ ((collect @ A) @ P)) = (P @ A4))))).
% 2.65/1.53 thf(fact_45_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X4:A]: ((((member2 @ A) @ X4) @ A2)))) = A2)))).
% 2.65/1.53 thf(fact_46_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X:A]: (((P @ X) = (Q @ X)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.65/1.53 thf(fact_47_ext, axiom, (! [B:$tType,A:$tType,F3:(A > B),G:(A > B)]: (((! [X:A]: (((F3 @ X) = (G @ X)))) => (F3 = G))))).
% 2.65/1.53 thf(fact_48_transpose_Ocases, axiom, (! [A:$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))))))))))).
% 2.65/1.53 thf(fact_49_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),Y4:A,Ys3:(list @ A)]: ((((P @ Xs2) @ (((cons @ A) @ Y4) @ Ys3)) => (((P @ (((cons @ A) @ X) @ Xs2)) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))) => ((P @ A0) @ A1))))))).
% 2.65/1.53 thf(fact_50_knows1k, 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))))))).
% 2.65/1.53 thf(fact_51_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))))))).
% 2.65/1.53 thf(fact_52_knows2know__k, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: ((((knowle2055185861_knows @ A2) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression))) => ((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))))).
% 2.65/1.53 thf(fact_53_know2knowsPQ__k, axiom, (! [P:secrecy_specID,M:secrecy_Keys,Q:secrecy_specID]: (((((knowle1437066798e_know @ P) @ (secrecy_kKS @ M)) | ((knowle1437066798e_know @ Q) @ (secrecy_kKS @ M))) => (((knowle2055185861_knows @ P) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression))) | ((knowle2055185861_knows @ Q) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression)))))))).
% 2.65/1.53 thf(fact_54_knows2knowPQ__k, axiom, (! [P:secrecy_specID,M:secrecy_Keys,Q:secrecy_specID]: (((((knowle2055185861_knows @ P) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression))) | ((knowle2055185861_knows @ Q) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression)))) => (((knowle1437066798e_know @ P) @ (secrecy_kKS @ M)) | ((knowle1437066798e_know @ Q) @ (secrecy_kKS @ M))))))).
% 2.65/1.53 thf(fact_55_know2knows__neg__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))))))))).
% 2.65/1.53 thf(fact_56_knows2know__neg__k, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: (((~ (((knowle2055185861_knows @ A2) @ (((cons @ secrecy_Expression) @ (secrecy_kE @ M)) @ (nil @ secrecy_Expression))))) => (~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))))))).
% 2.65/1.53 thf(fact_57_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))))))).
% 2.65/1.53 thf(fact_58_insert__Nil, axiom, (! [A:$tType,X3:A]: (((((insert @ A) @ X3) @ (nil @ A)) = (((cons @ A) @ X3) @ (nil @ A)))))).
% 2.65/1.53 thf(fact_59_Expression_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kE @ X1) = (secrecy_kE @ Y1)) = (X1 = Y1))))).
% 2.65/1.53 thf(fact_60_Expression_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X2:secrecy_Secrets]: (((secrecy_kE @ X1) != (secrecy_sE @ X2))))).
% 2.65/1.53 thf(fact_61_KS2Expression_Osimps_I1_J, axiom, (! [M:secrecy_Keys]: (((secrec1016742679ession @ (secrecy_kKS @ M)) = (secrecy_kE @ M))))).
% 2.65/1.53 thf(fact_62_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)))))))).
% 2.65/1.53 thf(fact_63_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)))))))).
% 2.65/1.53 thf(fact_64_eoutKnowsECorrect__L1, axiom, (! [C:secrecy_specID,E:secrecy_Expression]: ((((knowle1893229345orrect @ C) @ E) => (((eout @ C) @ E) => ((? [K3:secrecy_Keys]: (((E = (secrecy_kE @ K3)) & (((member2 @ secrecy_Keys) @ K3) @ (specKeys @ C))))) | ((? [S:secrecy_Secrets]: (((E = (secrecy_sE @ S)) & (((member2 @ secrecy_Secrets) @ S) @ (specSecrets @ C))))) | ((knowle2055185861_knows @ C) @ (((cons @ secrecy_Expression) @ E) @ (nil @ secrecy_Expression)))))))))).
% 2.65/1.53 thf(fact_65_eoutKnowsECorrect__def, axiom, (knowle1893229345orrect = (^ [C2:secrecy_specID,E2:secrecy_Expression]: ((((eout @ C2) @ E2) = ((? [K4:secrecy_Keys]: (((E2 = (secrecy_kE @ K4)) & (((member2 @ secrecy_Keys) @ K4) @ (specKeys @ C2))))) | ((? [S2:secrecy_Secrets]: (((E2 = (secrecy_sE @ S2)) & (((member2 @ secrecy_Secrets) @ S2) @ (specSecrets @ C2))))) | ((knowle2055185861_knows @ C2) @ (((cons @ secrecy_Expression) @ E2) @ (nil @ secrecy_Expression)))))))))).
% 2.65/1.53 thf(fact_66_product__lists_Osimps_I1_J, axiom, (! [A:$tType]: ((((product_lists @ A) @ (nil @ (list @ A))) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.65/1.53 thf(fact_67_subseqs_Osimps_I1_J, axiom, (! [A:$tType]: ((((subseqs @ A) @ (nil @ A)) = (((cons @ (list @ A)) @ (nil @ A)) @ (nil @ (list @ A))))))).
% 2.65/1.53 thf(fact_68_Expression2KSL_Osimps_I1_J, axiom, ((secrec1371625429on2KSL @ (nil @ secrecy_Expression)) = (nil @ secrecy_KS))).
% 2.65/1.53 thf(fact_69_list__ex1__simps_I1_J, axiom, (! [A:$tType,P:(A > $o)]: ((~ ((((list_ex1 @ A) @ P) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_70_map__tailrec__rev_Oelims, axiom, (! [A:$tType,B:$tType,X3:(A > B),Xa:(list @ A),Xb:(list @ B),Y:(list @ B)]: ((((((((map_tailrec_rev @ A) @ B) @ X3) @ Xa) @ Xb) = Y) => (((Xa = (nil @ A)) => (Y != Xb)) => (~ ((! [A3:A,As:(list @ A)]: (((Xa = (((cons @ A) @ A3) @ As)) => (Y != (((((map_tailrec_rev @ A) @ B) @ X3) @ As) @ (((cons @ B) @ (X3 @ A3)) @ Xb))))))))))))).
% 2.65/1.53 thf(fact_71_arg__min__list_Osimps_I1_J, axiom, (! [B:$tType,A:$tType]: (((linorder @ B) => (! [F3:(A > B),X3:A]: ((((((arg_min_list @ A) @ B) @ F3) @ (((cons @ A) @ X3) @ (nil @ A))) = X3))))))).
% 2.65/1.53 thf(fact_72_ord_Olexordp__eq__simps_I3_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Xs:(list @ A)]: ((~ (((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_73_bind__simps_I1_J, axiom, (! [B:$tType,A:$tType,F3:(B > (list @ A))]: ((((((bind @ B) @ A) @ (nil @ B)) @ F3) = (nil @ A))))).
% 2.65/1.53 thf(fact_74_listrelp_Oinducts, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X1:(list @ A),X2:(list @ B),P:((list @ A) > ((list @ B) > $o))]: (((((((listrelp @ A) @ B) @ R) @ X1) @ X2) => (((P @ (nil @ A)) @ (nil @ B)) => ((! [X:A,Y4:B,Xs2:(list @ A),Ys3:(list @ B)]: ((((R @ X) @ Y4) => ((((((listrelp @ A) @ B) @ R) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ B) @ Y4) @ Ys3))))))) => ((P @ X1) @ X2))))))).
% 2.65/1.53 thf(fact_75_listrelp_Osimps, axiom, (! [B:$tType,A:$tType]: ((((listrelp @ A) @ B) = (^ [R2:(A > (B > $o)),A12:(list @ A),A23:(list @ B)]: ((((A12 = (nil @ A)) & (A23 = (nil @ B))) | (? [X4:A,Y3:B,Xs3:(list @ A),Ys:(list @ B)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ B) @ Y3) @ Ys)) & (((R2 @ X4) @ Y3) & (((((listrelp @ A) @ B) @ R2) @ Xs3) @ Ys))))))))))))).
% 2.65/1.53 thf(fact_76_ord_Olexordp__eq__simps_I4_J, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Xs:(list @ A),Y:A,Ys2:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)) = (((Less @ X3) @ Y) | ((~ (((Less @ Y) @ X3))) & ((((lexordp_eq @ A) @ Less) @ Xs) @ Ys2))))))).
% 2.65/1.53 thf(fact_77_ord_Olexordp__eq__simps_I2_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ Xs) @ (nil @ A)) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_78_ord_Olexordp__eq__simps_I1_J, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys2:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys2)))).
% 2.65/1.53 thf(fact_79_ord_Olexordp__eq__refl, axiom, (! [A:$tType,Less:(A > (A > $o)),Xs:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ Xs) @ Xs)))).
% 2.65/1.53 thf(fact_80_ord_Olexordp__eq_Ocong, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (lexordp_eq @ A))))).
% 2.65/1.53 thf(fact_81_ord_Olexordp__eq_OCons, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: ((((Less @ X3) @ Y) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)))))).
% 2.65/1.53 thf(fact_82_ord_Olexordp__eq_OCons__eq, axiom, (! [A:$tType,Less:(A > (A > $o)),X3:A,Y:A,Xs:(list @ A),Ys2:(list @ A)]: (((~ (((Less @ X3) @ Y))) => ((~ (((Less @ Y) @ X3))) => (((((lexordp_eq @ A) @ Less) @ Xs) @ Ys2) => ((((lexordp_eq @ A) @ Less) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ A) @ Y) @ Ys2)))))))).
% 2.65/1.53 thf(fact_83_ord_Olexordp__eq_ONil, axiom, (! [A:$tType,Less:(A > (A > $o)),Ys2:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ (nil @ A)) @ Ys2)))).
% 2.65/1.53 thf(fact_84_listrelp_OCons, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),X3:A,Y:B,Xs:(list @ A),Ys2:(list @ B)]: ((((R @ X3) @ Y) => ((((((listrelp @ A) @ B) @ R) @ Xs) @ Ys2) => (((((listrelp @ A) @ B) @ R) @ (((cons @ A) @ X3) @ Xs)) @ (((cons @ B) @ Y) @ Ys2))))))).
% 2.65/1.53 thf(fact_85_listrelp_ONil, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o))]: ((((((listrelp @ A) @ B) @ R) @ (nil @ A)) @ (nil @ B))))).
% 2.65/1.53 thf(fact_86_map__tailrec__rev_Osimps_I2_J, axiom, (! [A:$tType,B:$tType,F3:(A > B),A4:A,As2:(list @ A),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F3) @ (((cons @ A) @ A4) @ As2)) @ Bs2) = (((((map_tailrec_rev @ A) @ B) @ F3) @ As2) @ (((cons @ B) @ (F3 @ A4)) @ Bs2)))))).
% 2.65/1.53 thf(fact_87_map__tailrec__rev_Osimps_I1_J, axiom, (! [A:$tType,B:$tType,F3:(A > B),Bs2:(list @ B)]: (((((((map_tailrec_rev @ A) @ B) @ F3) @ (nil @ A)) @ Bs2) = Bs2)))).
% 2.65/1.53 thf(fact_88_ord_Olexordp__eq_Ocases, axiom, (! [A:$tType,Less:(A > (A > $o)),A1:(list @ A),A22:(list @ A)]: ((((((lexordp_eq @ A) @ Less) @ A1) @ A22) => ((A1 != (nil @ A)) => ((! [X:A]: (((? [Xs2:(list @ A)]: ((A1 = (((cons @ A) @ X) @ Xs2)))) => (! [Y4:A]: (((? [Ys3:(list @ A)]: ((A22 = (((cons @ A) @ Y4) @ Ys3)))) => (~ (((Less @ X) @ Y4))))))))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys3:(list @ A)]: (((A22 = (((cons @ A) @ Y4) @ Ys3)) => ((~ (((Less @ X) @ Y4))) => ((~ (((Less @ Y4) @ X))) => (~ (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys3))))))))))))))))))).
% 2.65/1.53 thf(fact_89_ord_Olexordp__eq_Osimps, axiom, (! [A:$tType]: (((lexordp_eq @ A) = (^ [Less2:(A > (A > $o)),A12:(list @ A),A23:(list @ A)]: (((? [Ys:(list @ A)]: (((A12 = (nil @ A)) & (A23 = Ys)))) | ((? [X4:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & ((Less2 @ X4) @ Y3))))) | (? [X4:A,Y3:A,Xs3:(list @ A),Ys:(list @ A)]: (((A12 = (((cons @ A) @ X4) @ Xs3)) & ((A23 = (((cons @ A) @ Y3) @ Ys)) & ((~ (((Less2 @ X4) @ Y3))) & ((~ (((Less2 @ Y3) @ X4))) & ((((lexordp_eq @ A) @ Less2) @ Xs3) @ Ys))))))))))))))).
% 2.65/1.53 thf(fact_90_ord_Olexordp__eq_Oinducts, axiom, (! [A:$tType,Less:(A > (A > $o)),X1:(list @ A),X2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: ((((((lexordp_eq @ A) @ Less) @ X1) @ X2) => ((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: ((((Less @ X) @ Y4) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ (((Less @ X) @ Y4))) => ((~ (((Less @ Y4) @ X))) => (((((lexordp_eq @ A) @ Less) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))))) => ((P @ X1) @ X2)))))))).
% 2.65/1.53 thf(fact_91_listrelp_Ocases, axiom, (! [A:$tType,B:$tType,R:(A > (B > $o)),A1:(list @ A),A22:(list @ B)]: (((((((listrelp @ A) @ B) @ R) @ A1) @ A22) => (((A1 = (nil @ A)) => (A22 != (nil @ B))) => (~ ((! [X:A,Y4:B,Xs2:(list @ A)]: (((A1 = (((cons @ A) @ X) @ Xs2)) => (! [Ys3:(list @ B)]: (((A22 = (((cons @ B) @ Y4) @ Ys3)) => (((R @ X) @ Y4) => (~ ((((((listrelp @ A) @ B) @ R) @ Xs2) @ Ys3))))))))))))))))).
% 2.65/1.53 thf(fact_92_lexordp__eq__simps_I3_J, axiom, (! [A:$tType]: (((ord @ A) => (! [X3:A,Xs:(list @ A)]: ((~ ((((ord_lexordp_eq @ A) @ (((cons @ A) @ X3) @ Xs)) @ (nil @ A)))))))))).
% 2.65/1.53 thf(fact_93_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))))))).
% 2.65/1.53 thf(fact_94_member__rec_I2_J, axiom, (! [A:$tType,Y:A]: ((~ ((((member @ A) @ (nil @ A)) @ Y)))))).
% 2.65/1.53 thf(fact_95_member__rec_I1_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Y:A]: (((((member @ A) @ (((cons @ A) @ X3) @ Xs)) @ Y) = ((X3 = Y) | (((member @ A) @ Xs) @ Y)))))).
% 2.65/1.53 thf(fact_96_splice_Oelims, axiom, (! [A:$tType,X3:(list @ A),Xa:(list @ A),Y:(list @ A)]: ((((((splice @ A) @ X3) @ Xa) = Y) => (((X3 = (nil @ A)) => (Y != Xa)) => (~ ((! [X:A,Xs2:(list @ A)]: (((X3 = (((cons @ A) @ X) @ Xs2)) => (Y != (((cons @ A) @ X) @ (((splice @ A) @ Xa) @ Xs2))))))))))))).
% 2.65/1.53 thf(fact_97_bind__simps_I2_J, axiom, (! [A:$tType,B:$tType,X3:B,Xs:(list @ B),F3:(B > (list @ A))]: ((((((bind @ B) @ A) @ (((cons @ B) @ X3) @ Xs)) @ F3) = (((append @ A) @ (F3 @ X3)) @ ((((bind @ B) @ A) @ Xs) @ F3)))))).
% 2.65/1.53 thf(fact_98_append_Oassoc, axiom, (! [A:$tType,A4:(list @ A),B2:(list @ A),C3:(list @ A)]: (((((append @ A) @ (((append @ A) @ A4) @ B2)) @ C3) = (((append @ A) @ A4) @ (((append @ A) @ B2) @ C3)))))).
% 2.65/1.53 thf(fact_99_append__assoc, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: (((((append @ A) @ (((append @ A) @ Xs) @ Ys2)) @ Zs2) = (((append @ A) @ Xs) @ (((append @ A) @ Ys2) @ Zs2)))))).
% 2.65/1.53 thf(fact_100_append__same__eq, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Ys2) @ Xs) = (((append @ A) @ Zs2) @ Xs)) = (Ys2 = Zs2))))).
% 2.65/1.53 thf(fact_101_same__append__eq, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Xs) @ Zs2)) = (Ys2 = Zs2))))).
% 2.65/1.53 thf(fact_102_append_Oright__neutral, axiom, (! [A:$tType,A4:(list @ A)]: (((((append @ A) @ A4) @ (nil @ A)) = A4)))).
% 2.65/1.53 thf(fact_103_append__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.65/1.53 thf(fact_104_Nil__is__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((nil @ A) = (((append @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.65/1.53 thf(fact_105_self__append__conv2, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (((append @ A) @ Xs) @ Ys2)) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_106_append__self__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Ys2) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_107_self__append__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = (((append @ A) @ Xs) @ Ys2)) = (Ys2 = (nil @ A)))))).
% 2.65/1.53 thf(fact_108_append__self__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = Xs) = (Ys2 = (nil @ A)))))).
% 2.65/1.53 thf(fact_109_append__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((append @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.65/1.53 thf(fact_110_lexordp__eq__simps_I1_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys2:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys2))))))).
% 2.65/1.53 thf(fact_111_lexordp__eq__simps_I2_J, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ (nil @ A)) = (Xs = (nil @ A))))))))).
% 2.65/1.53 thf(fact_112_split__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((((splice @ A) @ Xs) @ Ys2) = (nil @ A)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.65/1.53 thf(fact_113_splice__Nil2, axiom, (! [A:$tType,Xs:(list @ A)]: (((((splice @ A) @ Xs) @ (nil @ A)) = Xs)))).
% 2.65/1.53 thf(fact_114_append1__eq__conv, axiom, (! [A:$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)))))).
% 2.65/1.53 thf(fact_115_append__eq__appendI, axiom, (! [A:$tType,Xs:(list @ A),Xs1:(list @ A),Zs2:(list @ A),Ys2:(list @ A),Us:(list @ A)]: ((((((append @ A) @ Xs) @ Xs1) = Zs2) => ((Ys2 = (((append @ A) @ Xs1) @ Us)) => ((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs2) @ Us))))))).
% 2.65/1.53 thf(fact_116_append__eq__append__conv2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A),Ts:(list @ A)]: ((((((append @ A) @ Xs) @ Ys2) = (((append @ A) @ Zs2) @ Ts)) = (? [Us2:(list @ A)]: ((((Xs = (((append @ A) @ Zs2) @ Us2)) & ((((append @ A) @ Us2) @ Ys2) = Ts)) | (((((append @ A) @ Xs) @ Us2) = Zs2) & (Ys2 = (((append @ A) @ Us2) @ Ts)))))))))).
% 2.65/1.53 thf(fact_117_lexordp__eq__pref, axiom, (! [A:$tType]: (((ord @ A) => (! [U:(list @ A),V:(list @ A)]: ((((ord_lexordp_eq @ A) @ U) @ (((append @ A) @ U) @ V)))))))).
% 2.65/1.53 thf(fact_118_lexordp__eq__refl, axiom, (! [A:$tType]: (((ord @ A) => (! [Xs:(list @ A)]: ((((ord_lexordp_eq @ A) @ Xs) @ Xs))))))).
% 2.65/1.53 thf(fact_119_lexordp__eq__trans, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => ((((ord_lexordp_eq @ A) @ Ys2) @ Zs2) => (((ord_lexordp_eq @ A) @ Xs) @ Zs2))))))))).
% 2.65/1.53 thf(fact_120_lexordp__eq__linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) | (((ord_lexordp_eq @ A) @ Ys2) @ Xs)))))))).
% 2.65/1.53 thf(fact_121_lexordp__eq__antisym, axiom, (! [A:$tType]: (((linorder @ A) => (! [Xs:(list @ A),Ys2:(list @ A)]: (((((ord_lexordp_eq @ A) @ Xs) @ Ys2) => ((((ord_lexordp_eq @ A) @ Ys2) @ Xs) => (Xs = Ys2))))))))).
% 2.65/1.53 thf(fact_122_append__Cons, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys2:(list @ A)]: (((((append @ A) @ (((cons @ A) @ X3) @ Xs)) @ Ys2) = (((cons @ A) @ X3) @ (((append @ A) @ Xs) @ Ys2)))))).
% 2.65/1.53 thf(fact_123_Cons__eq__appendI, axiom, (! [A:$tType,X3:A,Xs1:(list @ A),Ys2:(list @ A),Xs:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X3) @ Xs1) = Ys2) => ((Xs = (((append @ A) @ Xs1) @ Zs2)) => ((((cons @ A) @ X3) @ Xs) = (((append @ A) @ Ys2) @ Zs2))))))).
% 2.65/1.53 thf(fact_124_append_Oleft__neutral, axiom, (! [A:$tType,A4:(list @ A)]: (((((append @ A) @ (nil @ A)) @ A4) = A4)))).
% 2.65/1.53 thf(fact_125_append__Nil, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((append @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.65/1.53 thf(fact_126_eq__Nil__appendI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = Ys2) => (Xs = (((append @ A) @ (nil @ A)) @ Ys2)))))).
% 2.65/1.53 thf(fact_127_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))))).
% 2.65/1.53 thf(fact_128_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))))).
% 2.65/1.53 thf(fact_129_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)))))).
% 2.65/1.53 thf(fact_130_ord_Olexordp__eq__pref, axiom, (! [A:$tType,Less:(A > (A > $o)),U:(list @ A),V:(list @ A)]: (((((lexordp_eq @ A) @ Less) @ U) @ (((append @ A) @ U) @ V))))).
% 2.65/1.53 thf(fact_131_lexordp__eq_ONil, axiom, (! [A:$tType]: (((ord @ A) => (! [Ys2:(list @ A)]: ((((ord_lexordp_eq @ A) @ (nil @ A)) @ Ys2))))))).
% 2.65/1.53 thf(fact_132_notSpecKeysSecretsExpr__L2, axiom, (! [P:secrecy_specID,A4:secrecy_Expression,L:(list @ secrecy_Expression)]: ((((notSpe1586871396tsExpr @ P) @ (((cons @ secrecy_Expression) @ A4) @ L)) => ((notSpe1586871396tsExpr @ P) @ L))))).
% 2.65/1.53 thf(fact_133_splice_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys2:(list @ A)]: (((((splice @ A) @ (((cons @ A) @ X3) @ Xs)) @ Ys2) = (((cons @ A) @ X3) @ (((splice @ A) @ Ys2) @ Xs)))))).
% 2.65/1.53 thf(fact_134_splice_Osimps_I1_J, axiom, (! [A:$tType,Ys2:(list @ A)]: (((((splice @ A) @ (nil @ A)) @ Ys2) = Ys2)))).
% 2.65/1.53 thf(fact_135_rev__nonempty__induct, axiom, (! [A:$tType,Xs:(list @ A),P:((list @ A) > $o)]: (((Xs != (nil @ A)) => ((! [X:A]: ((P @ (((cons @ A) @ X) @ (nil @ A))))) => ((! [X:A,Xs2:(list @ A)]: (((Xs2 != (nil @ A)) => ((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X) @ (nil @ A)))))))) => (P @ Xs))))))).
% 2.65/1.53 thf(fact_136_append__eq__Cons__conv, axiom, (! [A:$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))) | (? [Ys4:(list @ A)]: (((Ys2 = (((cons @ A) @ X3) @ Ys4)) & ((((append @ A) @ Ys4) @ Zs2) = Xs))))))))).
% 2.65/1.53 thf(fact_137_Cons__eq__append__conv, axiom, (! [A:$tType,X3:A,Xs:(list @ A),Ys2:(list @ A),Zs2:(list @ A)]: ((((((cons @ A) @ X3) @ Xs) = (((append @ A) @ Ys2) @ Zs2)) = (((Ys2 = (nil @ A)) & ((((cons @ A) @ X3) @ Xs) = Zs2)) | (? [Ys4:(list @ A)]: ((((((cons @ A) @ X3) @ Ys4) = Ys2) & (Xs = (((append @ A) @ Ys4) @ Zs2)))))))))).
% 2.65/1.53 thf(fact_138_rev__exhaust, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (~ ((! [Ys3:(list @ A),Y4:A]: ((Xs != (((append @ A) @ Ys3) @ (((cons @ A) @ Y4) @ (nil @ A)))))))))))).
% 2.65/1.53 thf(fact_139_rev__induct, axiom, (! [A:$tType,P:((list @ A) > $o),Xs:(list @ A)]: (((P @ (nil @ A)) => ((! [X:A,Xs2:(list @ A)]: (((P @ Xs2) => (P @ (((append @ A) @ Xs2) @ (((cons @ A) @ X) @ (nil @ A))))))) => (P @ Xs)))))).
% 2.65/1.53 thf(fact_140_maps__simps_I1_J, axiom, (! [A:$tType,B:$tType,F3:(B > (list @ A)),X3:B,Xs:(list @ B)]: ((((((maps @ B) @ A) @ F3) @ (((cons @ B) @ X3) @ Xs)) = (((append @ A) @ (F3 @ X3)) @ ((((maps @ B) @ A) @ F3) @ Xs)))))).
% 2.65/1.53 thf(fact_141_ExtSign, axiom, (! [K12:secrecy_Keys,K22:secrecy_Keys,E3:(list @ secrecy_Expression)]: ((((encrDecrKeys @ K12) @ K22) => (((ext @ K12) @ ((sign @ K22) @ E3)) = E3))))).
% 2.65/1.53 thf(fact_142_DecrEnc, axiom, (! [K12:secrecy_Keys,K22:secrecy_Keys,E3:(list @ secrecy_Expression)]: ((((encrDecrKeys @ K12) @ K22) => (((decr @ K22) @ ((enc @ K12) @ E3)) = E3))))).
% 2.65/1.53 thf(fact_143_concat__eq__append__conv, axiom, (! [A:$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),Xs4:(list @ A),Xss22:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss1) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs3) @ Xs4)) @ Xss22))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss1)) @ Xs3)) & (Zs2 = (((append @ A) @ Xs4) @ ((concat @ A) @ Xss22))))))))))))).
% 2.65/1.53 thf(fact_144_rotate1_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((rotate1 @ A) @ (((cons @ A) @ X3) @ Xs)) = (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_145_rotate1__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rotate1 @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_146_concat__append, axiom, (! [A:$tType,Xs:(list @ (list @ A)),Ys2:(list @ (list @ A))]: ((((concat @ A) @ (((append @ (list @ A)) @ Xs) @ Ys2)) = (((append @ A) @ ((concat @ A) @ Xs)) @ ((concat @ A) @ Ys2)))))).
% 2.65/1.53 thf(fact_147_rotate1_Osimps_I1_J, axiom, (! [A:$tType]: ((((rotate1 @ A) @ (nil @ A)) = (nil @ A))))).
% 2.65/1.53 thf(fact_148_concat_Osimps_I1_J, axiom, (! [A:$tType]: ((((concat @ A) @ (nil @ (list @ A))) = (nil @ A))))).
% 2.65/1.53 thf(fact_149_concat_Osimps_I2_J, axiom, (! [A:$tType,X3:(list @ A),Xs:(list @ (list @ A))]: ((((concat @ A) @ (((cons @ (list @ A)) @ X3) @ Xs)) = (((append @ A) @ X3) @ ((concat @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_150_maps__simps_I2_J, axiom, (! [B:$tType,A:$tType,F3:(B > (list @ A))]: ((((((maps @ B) @ A) @ F3) @ (nil @ B)) = (nil @ A))))).
% 2.65/1.53 thf(fact_151_concat__eq__appendD, axiom, (! [A:$tType,Xss2:(list @ (list @ A)),Ys2:(list @ A),Zs2:(list @ A)]: (((((concat @ A) @ Xss2) = (((append @ A) @ Ys2) @ Zs2)) => ((Xss2 != (nil @ (list @ A))) => (? [Xss12:(list @ (list @ A)),Xs2:(list @ A),Xs5:(list @ A),Xss23:(list @ (list @ A))]: (((Xss2 = (((append @ (list @ A)) @ Xss12) @ (((cons @ (list @ A)) @ (((append @ A) @ Xs2) @ Xs5)) @ Xss23))) & ((Ys2 = (((append @ A) @ ((concat @ A) @ Xss12)) @ Xs2)) & (Zs2 = (((append @ A) @ Xs5) @ ((concat @ A) @ Xss23)))))))))))).
% 2.65/1.53 thf(fact_152_butlast__snoc, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((butlast @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A)))) = Xs)))).
% 2.65/1.53 thf(fact_153_last__snoc, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((last @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A)))) = X3)))).
% 2.65/1.53 thf(fact_154_notSpecKeysSecretsExpr__def, axiom, (notSpe1586871396tsExpr = (^ [P3:secrecy_specID,E2:(list @ secrecy_Expression)]: (((! [X4:secrecy_Keys]: (((((mem @ secrecy_Expression) @ (secrecy_kE @ X4)) @ E2) => (~ ((((member2 @ secrecy_KS) @ (secrecy_kKS @ X4)) @ (specKeysSecrets @ P3))))))) & (! [Y3:secrecy_Secrets]: (((((mem @ secrecy_Expression) @ (secrecy_sE @ Y3)) @ E2) => (~ ((((member2 @ secrecy_KS) @ (secrecy_sKS @ Y3)) @ (specKeysSecrets @ P3)))))))))))).
% 2.65/1.53 thf(fact_155_last__appendR, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Ys2)))))).
% 2.65/1.53 thf(fact_156_last__appendL, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: (((Ys2 = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_157_append__butlast__last__id, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((append @ A) @ ((butlast @ A) @ Xs)) @ (((cons @ A) @ ((last @ A) @ Xs)) @ (nil @ A))) = Xs))))).
% 2.65/1.53 thf(fact_158_butlast_Osimps_I1_J, axiom, (! [A:$tType]: ((((butlast @ A) @ (nil @ A)) = (nil @ A))))).
% 2.65/1.53 thf(fact_159_snoc__eq__iff__butlast, axiom, (! [A:$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))))))).
% 2.65/1.53 thf(fact_160_last__ConsR, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: (((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_161_last__ConsL, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: (((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = X3))))).
% 2.65/1.53 thf(fact_162_last_Osimps, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: ((((Xs = (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = X3)) & ((Xs != (nil @ A)) => (((last @ A) @ (((cons @ A) @ X3) @ Xs)) = ((last @ A) @ Xs))))))).
% 2.65/1.53 thf(fact_163_longest__common__suffix, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((? [Ss:(list @ A),Xs5:(list @ A),Ys5:(list @ A)]: (((Xs = (((append @ A) @ Xs5) @ Ss)) & ((Ys2 = (((append @ A) @ Ys5) @ Ss)) & ((Xs5 = (nil @ A)) | ((Ys5 = (nil @ A)) | (((last @ A) @ Xs5) != ((last @ A) @ Ys5))))))))))).
% 2.65/1.53 thf(fact_164_last__append, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: ((((Ys2 = (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Xs))) & ((Ys2 != (nil @ A)) => (((last @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((last @ A) @ Ys2))))))).
% 2.65/1.53 thf(fact_165_butlast_Osimps_I2_J, axiom, (! [A:$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)))))))).
% 2.65/1.53 thf(fact_166_butlast__append, axiom, (! [A:$tType,Ys2:(list @ A),Xs:(list @ A)]: ((((Ys2 = (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((butlast @ A) @ Xs))) & ((Ys2 != (nil @ A)) => (((butlast @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ Xs) @ ((butlast @ A) @ Ys2)))))))).
% 2.65/1.53 thf(fact_167_mem_Osimps_I1_J, axiom, (! [A:$tType,X3:A]: ((~ ((((mem @ A) @ X3) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_168_mem_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Y:A,L:(list @ A)]: (((((mem @ A) @ X3) @ (((cons @ A) @ Y) @ L)) = ((X3 = Y) | (((mem @ A) @ X3) @ L)))))).
% 2.65/1.53 thf(fact_169_concat__conv__foldr, axiom, (! [A:$tType]: (((concat @ A) = (^ [Xss3:(list @ (list @ A))]: ((((((foldr @ (list @ A)) @ (list @ A)) @ (append @ A)) @ Xss3) @ (nil @ A)))))))).
% 2.65/1.53 thf(fact_170_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)))))).
% 2.65/1.53 thf(fact_171_SuccI, axiom, (! [A:$tType,Kl:(list @ A),K:A,Kl2:(set @ (list @ A))]: (((((member2 @ (list @ A)) @ (((append @ A) @ Kl) @ (((cons @ A) @ K) @ (nil @ A)))) @ Kl2) => (((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl2) @ Kl)))))).
% 2.65/1.53 thf(fact_172_SuccD, axiom, (! [A:$tType,K:A,Kl2:(set @ (list @ A)),Kl:(list @ A)]: (((((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl2) @ Kl)) => (((member2 @ (list @ A)) @ (((append @ A) @ Kl) @ (((cons @ A) @ K) @ (nil @ A)))) @ Kl2))))).
% 2.65/1.53 thf(fact_173_rev__eq__Cons__iff, axiom, (! [A:$tType,Xs:(list @ A),Y:A,Ys2:(list @ A)]: (((((rev @ A) @ Xs) = (((cons @ A) @ Y) @ Ys2)) = (Xs = (((append @ A) @ ((rev @ A) @ Ys2)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.65/1.53 thf(fact_174_rev__rev__ident, axiom, (! [A:$tType,Xs:(list @ A)]: ((((rev @ A) @ ((rev @ A) @ Xs)) = Xs)))).
% 2.65/1.53 thf(fact_175_rev__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((rev @ A) @ Xs) = ((rev @ A) @ Ys2)) = (Xs = Ys2))))).
% 2.65/1.53 thf(fact_176_Nil__is__rev__conv, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((rev @ A) @ Xs)) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_177_rev__is__Nil__conv, axiom, (! [A:$tType,Xs:(list @ A)]: (((((rev @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_178_rev__append, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((rev @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((rev @ A) @ Ys2)) @ ((rev @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_179_singleton__rev__conv, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((((cons @ A) @ X3) @ (nil @ A)) = ((rev @ A) @ Xs)) = (Xs = (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_180_rev__singleton__conv, axiom, (! [A:$tType,Xs:(list @ A),X3:A]: (((((rev @ A) @ Xs) = (((cons @ A) @ X3) @ (nil @ A))) = (Xs = (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_181_rev__swap, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((rev @ A) @ Xs) = Ys2) = (Xs = ((rev @ A) @ Ys2)))))).
% 2.65/1.53 thf(fact_182_rev_Osimps_I1_J, axiom, (! [A:$tType]: ((((rev @ A) @ (nil @ A)) = (nil @ A))))).
% 2.65/1.53 thf(fact_183_rev_Osimps_I2_J, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((rev @ A) @ (((cons @ A) @ X3) @ Xs)) = (((append @ A) @ ((rev @ A) @ Xs)) @ (((cons @ A) @ X3) @ (nil @ A))))))).
% 2.65/1.53 thf(fact_184_map__tailrec__def, axiom, (! [B:$tType,A:$tType]: ((((map_tailrec @ A) @ B) = (^ [F4:(A > B),As3:(list @ A)]: (((rev @ B) @ (((((map_tailrec_rev @ A) @ B) @ F4) @ As3) @ (nil @ B))))))))).
% 2.65/1.53 thf(fact_185_shift__def, axiom, (! [B:$tType,A:$tType]: ((((bNF_Greatest_shift @ A) @ B) = (^ [Lab:((list @ A) > B),K4:A,Kl3:(list @ A)]: ((Lab @ (((cons @ A) @ K4) @ Kl3)))))))).
% 2.65/1.53 thf(fact_186_empty__Shift, axiom, (! [A:$tType,Kl2:(set @ (list @ A)),K:A]: (((((member2 @ (list @ A)) @ (nil @ A)) @ Kl2) => ((((member2 @ A) @ K) @ (((bNF_Greatest_Succ @ A) @ Kl2) @ (nil @ A))) => (((member2 @ (list @ A)) @ (nil @ A)) @ (((bNF_Greatest_Shift @ A) @ Kl2) @ K))))))).
% 2.65/1.53 thf(fact_187_ShiftD, axiom, (! [A:$tType,Kl:(list @ A),Kl2:(set @ (list @ A)),K:A]: (((((member2 @ (list @ A)) @ Kl) @ (((bNF_Greatest_Shift @ A) @ Kl2) @ K)) => (((member2 @ (list @ A)) @ (((cons @ A) @ K) @ Kl)) @ Kl2))))).
% 2.65/1.53 thf(fact_188_Succ__Shift, axiom, (! [A:$tType,Kl2:(set @ (list @ A)),K:A,Kl:(list @ A)]: (((((bNF_Greatest_Succ @ A) @ (((bNF_Greatest_Shift @ A) @ Kl2) @ K)) @ Kl) = (((bNF_Greatest_Succ @ A) @ Kl2) @ (((cons @ A) @ K) @ Kl)))))).
% 2.65/1.53 thf(fact_189_last__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((last @ A) @ ((rev @ A) @ Xs)) = ((hd @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_190_hd__rev, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ ((rev @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_191_hd__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs != (nil @ A)) => (((hd @ A) @ (((append @ A) @ Xs) @ Ys2)) = ((hd @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_192_hd__append, axiom, (! [A:$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))))))).
% 2.65/1.53 thf(fact_193_longest__common__prefix, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((? [Ps:(list @ A),Xs5:(list @ A),Ys5:(list @ A)]: (((Xs = (((append @ A) @ Ps) @ Xs5)) & ((Ys2 = (((append @ A) @ Ps) @ Ys5)) & ((Xs5 = (nil @ A)) | ((Ys5 = (nil @ A)) | (((hd @ A) @ Xs5) != ((hd @ A) @ Ys5))))))))))).
% 2.65/1.53 thf(fact_194_hd__concat, axiom, (! [A:$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)))))))).
% 2.65/1.53 thf(fact_195_list_Osel_I1_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: ((((hd @ A) @ (((cons @ A) @ X21) @ X222)) = X21)))).
% 2.65/1.53 thf(fact_196_rotate1__hd__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => (((rotate1 @ A) @ Xs) = (((append @ A) @ ((tl @ A) @ Xs)) @ (((cons @ A) @ ((hd @ A) @ Xs)) @ (nil @ A)))))))).
% 2.65/1.53 thf(fact_197_distinct__adj__append__iff, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((distinct_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((distinct_adj @ A) @ Xs) & (((distinct_adj @ A) @ Ys2) & ((Xs = (nil @ A)) | ((Ys2 = (nil @ A)) | (((last @ A) @ Xs) != ((hd @ A) @ Ys2)))))))))).
% 2.65/1.53 thf(fact_198_distinct__adj__Cons__Cons, axiom, (! [B:$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))))))).
% 2.65/1.53 thf(fact_199_distinct__adj__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((distinct_adj @ A) @ ((rev @ A) @ Xs)) = ((distinct_adj @ A) @ Xs))))).
% 2.65/1.53 thf(fact_200_tl__append2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs != (nil @ A)) => (((tl @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((tl @ A) @ Xs)) @ Ys2)))))).
% 2.65/1.53 thf(fact_201_butlast__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((rev @ A) @ Xs)) = ((rev @ A) @ ((tl @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_202_list_Ocollapse, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List)) = List))))).
% 2.65/1.53 thf(fact_203_hd__Cons__tl, axiom, (! [A:$tType,Xs:(list @ A)]: (((Xs != (nil @ A)) => ((((cons @ A) @ ((hd @ A) @ Xs)) @ ((tl @ A) @ Xs)) = Xs))))).
% 2.65/1.53 thf(fact_204_list_Oexpand, axiom, (! [A:$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)))))).
% 2.65/1.53 thf(fact_205_butlast__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((butlast @ A) @ ((tl @ A) @ Xs)) = ((tl @ A) @ ((butlast @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_206_distinct__adj__appendD1, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((distinct_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) => ((distinct_adj @ A) @ Xs))))).
% 2.65/1.53 thf(fact_207_distinct__adj__appendD2, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((distinct_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) => ((distinct_adj @ A) @ Ys2))))).
% 2.65/1.53 thf(fact_208_distinct__adj__Nil, axiom, (! [A:$tType]: (((distinct_adj @ A) @ (nil @ A))))).
% 2.65/1.53 thf(fact_209_distinct__adj__ConsD, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((distinct_adj @ A) @ (((cons @ A) @ X3) @ Xs)) => ((distinct_adj @ A) @ Xs))))).
% 2.65/1.53 thf(fact_210_list_Osel_I2_J, axiom, (! [A:$tType]: ((((tl @ A) @ (nil @ A)) = (nil @ A))))).
% 2.65/1.53 thf(fact_211_list_Osel_I3_J, axiom, (! [A:$tType,X21:A,X222:(list @ A)]: ((((tl @ A) @ (((cons @ A) @ X21) @ X222)) = X222)))).
% 2.65/1.53 thf(fact_212_tl__Nil, axiom, (! [A:$tType,Xs:(list @ A)]: (((((tl @ A) @ Xs) = (nil @ A)) = ((Xs = (nil @ A)) | (? [X4:A]: ((Xs = (((cons @ A) @ X4) @ (nil @ A)))))))))).
% 2.65/1.53 thf(fact_213_Nil__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((nil @ A) = ((tl @ A) @ Xs)) = ((Xs = (nil @ A)) | (? [X4:A]: ((Xs = (((cons @ A) @ X4) @ (nil @ A)))))))))).
% 2.65/1.53 thf(fact_214_last__tl, axiom, (! [A:$tType,Xs:(list @ A)]: ((((Xs = (nil @ A)) | (((tl @ A) @ Xs) != (nil @ A))) => (((last @ A) @ ((tl @ A) @ Xs)) = ((last @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_215_distinct__adj__singleton, axiom, (! [B:$tType,X3:B]: (((distinct_adj @ B) @ (((cons @ B) @ X3) @ (nil @ B)))))).
% 2.65/1.53 thf(fact_216_list_Oexhaust__sel, axiom, (! [A:$tType,List:(list @ A)]: (((List != (nil @ A)) => (List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))).
% 2.65/1.53 thf(fact_217_distinct__adj__Cons, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: ((((distinct_adj @ A) @ (((cons @ A) @ X3) @ Xs)) = ((Xs = (nil @ A)) | ((X3 != ((hd @ A) @ Xs)) & ((distinct_adj @ A) @ Xs))))))).
% 2.65/1.53 thf(fact_218_list_Osplit__sel__asm, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((list @ A) > B)),List:(list @ A)]: (((P @ (((((case_list @ B) @ A) @ F1) @ F2) @ List)) = (~ ((((List = (nil @ A)) & (~ ((P @ F1)))) | ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) & (~ ((P @ ((F2 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))))))).
% 2.65/1.53 thf(fact_219_list_Osplit__sel, axiom, (! [B:$tType,A:$tType,P:(B > $o),F1:B,F2:(A > ((list @ A) > B)),List:(list @ A)]: (((P @ (((((case_list @ B) @ A) @ F1) @ F2) @ List)) = (((List = (nil @ A)) => (P @ F1)) & ((List = (((cons @ A) @ ((hd @ A) @ List)) @ ((tl @ A) @ List))) => (P @ ((F2 @ ((hd @ A) @ List)) @ ((tl @ A) @ List))))))))).
% 2.65/1.53 thf(fact_220_list_Osimps_I4_J, axiom, (! [A:$tType,B:$tType,F1:B,F2:(A > ((list @ A) > B))]: (((((((case_list @ B) @ A) @ F1) @ F2) @ (nil @ A)) = F1)))).
% 2.65/1.53 thf(fact_221_list_Osimps_I5_J, axiom, (! [B:$tType,A:$tType,F1:B,F2:(A > ((list @ A) > B)),X21:A,X222:(list @ A)]: (((((((case_list @ B) @ A) @ F1) @ F2) @ (((cons @ A) @ X21) @ X222)) = ((F2 @ X21) @ X222))))).
% 2.65/1.53 thf(fact_222_list_Ocase__eq__if, axiom, (! [A:$tType,B:$tType]: ((((case_list @ B) @ A) = (^ [F12:B,F22:(A > ((list @ A) > B)),List3:(list @ A)]: (((((if @ B) @ (List3 = (nil @ A))) @ F12) @ ((F22 @ ((hd @ A) @ List3)) @ ((tl @ A) @ List3))))))))).
% 2.65/1.53 thf(fact_223_successively__append__iff, axiom, (! [A:$tType,P:(A > (A > $o)),Xs:(list @ A),Ys2:(list @ A)]: (((((successively @ A) @ P) @ (((append @ A) @ Xs) @ Ys2)) = ((((successively @ A) @ P) @ Xs) & ((((successively @ A) @ P) @ Ys2) & ((Xs = (nil @ A)) | ((Ys2 = (nil @ A)) | ((P @ ((last @ A) @ Xs)) @ ((hd @ A) @ Ys2)))))))))).
% 2.65/1.53 thf(fact_224_Cons__in__shuffles__iff, axiom, (! [A:$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)))))))))).
% 2.65/1.53 thf(fact_225_Nil__in__shuffles, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((((member2 @ (list @ A)) @ (nil @ A)) @ (((shuffles @ A) @ Xs) @ Ys2)) = ((Xs = (nil @ A)) & (Ys2 = (nil @ A))))))).
% 2.65/1.53 thf(fact_226_splice__in__shuffles, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((member2 @ (list @ A)) @ (((splice @ A) @ Xs) @ Ys2)) @ (((shuffles @ A) @ Xs) @ Ys2))))).
% 2.65/1.53 thf(fact_227_shufflesE, axiom, (! [A:$tType,Zs2:(list @ A),Xs:(list @ A),Ys2:(list @ A)]: (((((member2 @ (list @ A)) @ Zs2) @ (((shuffles @ A) @ Xs) @ Ys2)) => (((Zs2 = Xs) => (Ys2 != (nil @ A))) => (((Zs2 = Ys2) => (Xs != (nil @ A))) => ((! [X:A,Xs5:(list @ A)]: (((Xs = (((cons @ A) @ X) @ Xs5)) => (! [Z2:A,Zs3:(list @ A)]: (((Zs2 = (((cons @ A) @ Z2) @ Zs3)) => ((X = Z2) => (~ ((((member2 @ (list @ A)) @ Zs3) @ (((shuffles @ A) @ Xs5) @ Ys2))))))))))) => (~ ((! [Y4:A,Ys5:(list @ A)]: (((Ys2 = (((cons @ A) @ Y4) @ Ys5)) => (! [Z2:A,Zs3:(list @ A)]: (((Zs2 = (((cons @ A) @ Z2) @ Zs3)) => ((Y4 = Z2) => (~ ((((member2 @ (list @ A)) @ Zs3) @ (((shuffles @ A) @ Xs) @ Ys5)))))))))))))))))))).
% 2.65/1.53 thf(fact_228_successively_Osimps_I2_J, axiom, (! [A:$tType,P:(A > (A > $o)),X3:A]: ((((successively @ A) @ P) @ (((cons @ A) @ X3) @ (nil @ A)))))).
% 2.65/1.53 thf(fact_229_successively_Oelims_I1_J, axiom, (! [A:$tType,X3:(A > (A > $o)),Xa:(list @ A),Y:$o]: ((((((successively @ A) @ X3) @ Xa) = Y) => (((Xa = (nil @ A)) => (~ (Y))) => (((? [X:A]: ((Xa = (((cons @ A) @ X) @ (nil @ A))))) => (~ (Y))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: (((Xa = (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2))) => (Y = (~ ((((X3 @ X) @ Y4) & (((successively @ A) @ X3) @ (((cons @ A) @ Y4) @ Xs2))))))))))))))))).
% 2.65/1.53 thf(fact_230_successively_Oelims_I2_J, axiom, (! [A:$tType,X3:(A > (A > $o)),Xa:(list @ A)]: (((((successively @ A) @ X3) @ Xa) => ((Xa != (nil @ A)) => ((! [X:A]: ((Xa != (((cons @ A) @ X) @ (nil @ A))))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: (((Xa = (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2))) => (~ ((((X3 @ X) @ Y4) & (((successively @ A) @ X3) @ (((cons @ A) @ Y4) @ Xs2)))))))))))))))).
% 2.65/1.53 thf(fact_231_shuffles__commutes, axiom, (! [A:$tType]: (((shuffles @ A) = (^ [Xs3:(list @ A),Ys:(list @ A)]: ((((shuffles @ A) @ Ys) @ Xs3))))))).
% 2.65/1.53 thf(fact_232_successively_Osimps_I1_J, axiom, (! [A:$tType,P:(A > (A > $o))]: ((((successively @ A) @ P) @ (nil @ A))))).
% 2.65/1.53 thf(fact_233_successively_Osimps_I3_J, axiom, (! [A:$tType,P:(A > (A > $o)),X3:A,Y:A,Xs:(list @ A)]: (((((successively @ A) @ P) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y) @ Xs))) = (((P @ X3) @ Y) & (((successively @ A) @ P) @ (((cons @ A) @ Y) @ Xs))))))).
% 2.65/1.53 thf(fact_234_successively_Oelims_I3_J, axiom, (! [A:$tType,X3:(A > (A > $o)),Xa:(list @ A)]: (((~ ((((successively @ A) @ X3) @ Xa))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: (((Xa = (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2))) => (((X3 @ X) @ Y4) & (((successively @ A) @ X3) @ (((cons @ A) @ Y4) @ Xs2)))))))))))).
% 2.65/1.53 thf(fact_235_Nil__in__shufflesI, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: (((Xs = (nil @ A)) => ((Ys2 = (nil @ A)) => (((member2 @ (list @ A)) @ (nil @ A)) @ (((shuffles @ A) @ Xs) @ Ys2))))))).
% 2.65/1.53 thf(fact_236_Cons__in__shuffles__rightI, axiom, (! [A:$tType,Zs2:(list @ A),Xs:(list @ A),Ys2:(list @ A),Z:A]: (((((member2 @ (list @ A)) @ Zs2) @ (((shuffles @ A) @ Xs) @ Ys2)) => (((member2 @ (list @ A)) @ (((cons @ A) @ Z) @ Zs2)) @ (((shuffles @ A) @ Xs) @ (((cons @ A) @ Z) @ Ys2))))))).
% 2.65/1.53 thf(fact_237_Cons__in__shuffles__leftI, axiom, (! [A:$tType,Zs2:(list @ A),Xs:(list @ A),Ys2:(list @ A),Z:A]: (((((member2 @ (list @ A)) @ Zs2) @ (((shuffles @ A) @ Xs) @ Ys2)) => (((member2 @ (list @ A)) @ (((cons @ A) @ Z) @ Zs2)) @ (((shuffles @ A) @ (((cons @ A) @ Z) @ Xs)) @ Ys2)))))).
% 2.65/1.53 thf(fact_238_successively__Cons, axiom, (! [A:$tType,P:(A > (A > $o)),X3:A,Xs:(list @ A)]: (((((successively @ A) @ P) @ (((cons @ A) @ X3) @ Xs)) = ((Xs = (nil @ A)) | (((P @ X3) @ ((hd @ A) @ Xs)) & (((successively @ A) @ P) @ Xs))))))).
% 2.65/1.53 thf(fact_239_remdups__adj__append_H, axiom, (! [A:$tType,Xs:(list @ A),Ys2:(list @ A)]: ((((Xs = (nil @ A)) | ((Ys2 = (nil @ A)) | (((last @ A) @ Xs) != ((hd @ A) @ Ys2)))) => (((remdups_adj @ A) @ (((append @ A) @ Xs) @ Ys2)) = (((append @ A) @ ((remdups_adj @ A) @ Xs)) @ ((remdups_adj @ A) @ Ys2))))))).
% 2.65/1.53 thf(fact_240_remdups__adj__append, axiom, (! [A:$tType,Xs_1:(list @ A),X3:A,Xs_2:(list @ A)]: ((((remdups_adj @ A) @ (((append @ A) @ Xs_1) @ (((cons @ A) @ X3) @ Xs_2))) = (((append @ A) @ ((remdups_adj @ A) @ (((append @ A) @ Xs_1) @ (((cons @ A) @ X3) @ (nil @ A))))) @ ((tl @ A) @ ((remdups_adj @ A) @ (((cons @ A) @ X3) @ Xs_2)))))))).
% 2.65/1.53 thf(fact_241_remdups__adj__Nil__iff, axiom, (! [A:$tType,Xs:(list @ A)]: (((((remdups_adj @ A) @ Xs) = (nil @ A)) = (Xs = (nil @ A)))))).
% 2.65/1.53 thf(fact_242_remdups__adj__rev, axiom, (! [A:$tType,Xs:(list @ A)]: ((((remdups_adj @ A) @ ((rev @ A) @ Xs)) = ((rev @ A) @ ((remdups_adj @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_243_hd__remdups__adj, axiom, (! [A:$tType,Xs:(list @ A)]: ((((hd @ A) @ ((remdups_adj @ A) @ Xs)) = ((hd @ A) @ Xs))))).
% 2.65/1.53 thf(fact_244_last__remdups__adj, axiom, (! [A:$tType,Xs:(list @ A)]: ((((last @ A) @ ((remdups_adj @ A) @ Xs)) = ((last @ A) @ Xs))))).
% 2.65/1.53 thf(fact_245_remdups__adj__Cons__alt, axiom, (! [A:$tType,X3:A,Xs:(list @ A)]: (((((cons @ A) @ X3) @ ((tl @ A) @ ((remdups_adj @ A) @ (((cons @ A) @ X3) @ Xs)))) = ((remdups_adj @ A) @ (((cons @ A) @ X3) @ Xs)))))).
% 2.65/1.53 thf(fact_246_successively__remdups__adjI, axiom, (! [A:$tType,P:(A > (A > $o)),Xs:(list @ A)]: (((((successively @ A) @ P) @ Xs) => (((successively @ A) @ P) @ ((remdups_adj @ A) @ Xs)))))).
% 2.65/1.53 thf(fact_247_distinct__adj__remdups__adj, axiom, (! [A:$tType,Xs:(list @ A)]: (((distinct_adj @ A) @ ((remdups_adj @ A) @ Xs))))).
% 2.65/1.53 thf(fact_248_distinct__adj__altdef, axiom, (! [A:$tType]: (((distinct_adj @ A) = (^ [Xs3:(list @ A)]: ((((remdups_adj @ A) @ Xs3) = Xs3))))))).
% 2.65/1.53 thf(fact_249_remdups__adj_Osimps_I2_J, axiom, (! [A:$tType,X3:A]: ((((remdups_adj @ A) @ (((cons @ A) @ X3) @ (nil @ A))) = (((cons @ A) @ X3) @ (nil @ A)))))).
% 2.65/1.53 thf(fact_250_remdups__adj_Oelims, axiom, (! [A:$tType,X3:(list @ A),Y:(list @ A)]: (((((remdups_adj @ A) @ X3) = Y) => (((X3 = (nil @ A)) => (Y != (nil @ A))) => ((! [X:A]: (((X3 = (((cons @ A) @ X) @ (nil @ A))) => (Y != (((cons @ A) @ X) @ (nil @ A)))))) => (~ ((! [X:A,Y4:A,Xs2:(list @ A)]: (((X3 = (((cons @ A) @ X) @ (((cons @ A) @ Y4) @ Xs2))) => (~ ((((X = Y4) => (Y = ((remdups_adj @ A) @ (((cons @ A) @ X) @ Xs2)))) & ((X != Y4) => (Y = (((cons @ A) @ X) @ ((remdups_adj @ A) @ (((cons @ A) @ Y4) @ Xs2))))))))))))))))))).
% 2.65/1.53 thf(fact_251_remdups__adj_Osimps_I3_J, axiom, (! [A:$tType,X3:A,Y:A,Xs:(list @ A)]: ((((X3 = Y) => (((remdups_adj @ A) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y) @ Xs))) = ((remdups_adj @ A) @ (((cons @ A) @ X3) @ Xs)))) & ((X3 != Y) => (((remdups_adj @ A) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y) @ Xs))) = (((cons @ A) @ X3) @ ((remdups_adj @ A) @ (((cons @ A) @ Y) @ Xs))))))))).
% 2.65/1.53 thf(fact_252_remdups__adj_Osimps_I1_J, axiom, (! [A:$tType]: ((((remdups_adj @ A) @ (nil @ A)) = (nil @ A))))).
% 2.65/1.53 thf(fact_253_remdups__adj__append__two, axiom, (! [A:$tType,Xs:(list @ A),X3:A,Y:A]: ((((remdups_adj @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (((cons @ A) @ Y) @ (nil @ A))))) = (((append @ A) @ ((remdups_adj @ A) @ (((append @ A) @ Xs) @ (((cons @ A) @ X3) @ (nil @ A))))) @ ((((if @ (list @ A)) @ (X3 = Y)) @ (nil @ A)) @ (((cons @ A) @ Y) @ (nil @ A)))))))).
% 2.65/1.53 thf(fact_254_lexordp__eq_Oinducts, axiom, (! [A:$tType]: (((ord @ A) => (! [X1:(list @ A),X2:(list @ A),P:((list @ A) > ((list @ A) > $o))]: (((((ord_lexordp_eq @ A) @ X1) @ X2) => ((! [X_1:(list @ A)]: (((P @ (nil @ A)) @ X_1))) => ((! [X:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((((ord_less @ A) @ X) @ Y4) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3))))) => ((! [X:A,Y4:A,Xs2:(list @ A),Ys3:(list @ A)]: (((~ ((((ord_less @ A) @ X) @ Y4))) => ((~ ((((ord_less @ A) @ Y4) @ X))) => ((((ord_lexordp_eq @ A) @ Xs2) @ Ys3) => (((P @ Xs2) @ Ys3) => ((P @ (((cons @ A) @ X) @ Xs2)) @ (((cons @ A) @ Y4) @ Ys3)))))))) => ((P @ X1) @ X2))))))))))).
% 2.65/1.53 thf(tcon_fun___Orderings_Oord, axiom, (! [A5:$tType,A6:$tType]: (((ord @ A6) => (ord @ (A5 > A6)))))).
% 2.65/1.53 thf(tcon_Set_Oset___Orderings_Oord_1, axiom, (! [A5:$tType]: ((ord @ (set @ A5))))).
% 2.65/1.53 thf(tcon_HOL_Obool___Orderings_Olinorder, axiom, (linorder @ $o)).
% 2.65/1.53 thf(tcon_HOL_Obool___Orderings_Oord_2, axiom, (ord @ $o)).
% 2.65/1.53 thf(help_If_3_1_T, axiom, (! [P:$o]: (((P = $true) | (P = $false))))).
% 2.65/1.53 thf(help_If_2_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $false) @ X3) @ Y) = Y)))).
% 2.65/1.53 thf(help_If_1_1_T, axiom, (! [A:$tType,X3:A,Y:A]: ((((((if @ A) @ $true) @ X3) @ Y) = X3)))).
% 2.65/1.53 thf(conj_0, conjecture, ((knowle1437066798e_know @ a) @ (secrecy_sKS @ m))).
% 2.65/1.53 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.MVbIzHpABw/DTF2DTF22724.p
% 2.65/1.53 ------------------------
% 2.65/1.56 ---- Cleaned THF ---
% 2.65/1.56 thf(ty_t_Secrecy__types_OExpression,type,
% 2.65/1.56 secrecy_Expression: $tType ).
% 2.65/1.56
% 2.65/1.56 thf(ty_t_Secrecy__types_OSecrets,type,
% 2.65/1.56 secrecy_Secrets: $tType ).
% 2.65/1.56
% 2.65/1.56 thf(ty_t_Secrecy__types_OspecID,type,
% 2.65/1.56 secrecy_specID: $tType ).
% 2.65/1.56
% 2.65/1.56 thf(ty_t_Secrecy__types_OKeys,type,
% 2.65/1.56 secrecy_Keys: $tType ).
% 2.65/1.56
% 2.65/1.56 thf(ty_t_Secrecy__types_OKS,type,
% 2.65/1.56 secrecy_KS: $tType ).
% 2.65/1.56
% 2.65/1.56 thf(ty_t_List_Olist,type,
% 2.65/1.56 list: $tType > $tType ).
% 2.65/1.56
% 2.65/1.56 thf(ty_t_Set_Oset,type,
% 2.65/1.56 set: $tType > $tType ).
% 2.65/1.56
% 2.65/1.56 thf(sy_cl_HOL_Otype,type,
% 2.65/1.56 type:
% 2.65/1.56 !>[A: $tType] : $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_cl_Orderings_Oord,type,
% 2.65/1.56 ord:
% 2.65/1.56 !>[A: $tType] : $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_cl_Orderings_Olinorder,type,
% 2.65/1.56 linorder:
% 2.65/1.56 !>[A: $tType] : $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_BNF__Greatest__Fixpoint_OShift,type,
% 2.65/1.56 bNF_Greatest_Shift:
% 2.65/1.56 !>[A: $tType] : ( ( set @ ( list @ A ) ) > A > ( set @ ( list @ A ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_BNF__Greatest__Fixpoint_OSucc,type,
% 2.65/1.56 bNF_Greatest_Succ:
% 2.65/1.56 !>[A: $tType] : ( ( set @ ( list @ A ) ) > ( list @ A ) > ( set @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_BNF__Greatest__Fixpoint_Oshift,type,
% 2.65/1.56 bNF_Greatest_shift:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( ( list @ A ) > B ) > A > ( list @ A ) > B ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.65/1.56 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_If,type,
% 2.65/1.56 if:
% 2.65/1.56 !>[A: $tType] : ( $o > A > A > A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 2.65/1.56 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowsECorrect,type,
% 2.65/1.56 knowle1893229345orrect: secrecy_specID > secrecy_Expression > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 2.65/1.56 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows,type,
% 2.65/1.56 knowle2055185861_knows: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_ListExtras_Omem,type,
% 2.65/1.56 mem:
% 2.65/1.56 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oappend,type,
% 2.65/1.56 append:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oarg__min__list,type,
% 2.65/1.56 arg_min_list:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Obind,type,
% 2.65/1.56 bind:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( list @ A ) > ( A > ( list @ B ) ) > ( list @ B ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Obutlast,type,
% 2.65/1.56 butlast:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oconcat,type,
% 2.65/1.56 concat:
% 2.65/1.56 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Odistinct__adj,type,
% 2.65/1.56 distinct_adj:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Ofoldr,type,
% 2.65/1.56 foldr:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( A > B > B ) > ( list @ A ) > B > B ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oinsert,type,
% 2.65/1.56 insert:
% 2.65/1.56 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olast,type,
% 2.65/1.56 last:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olist_OCons,type,
% 2.65/1.56 cons:
% 2.65/1.56 !>[A: $tType] : ( A > ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olist_ONil,type,
% 2.65/1.56 nil:
% 2.65/1.56 !>[A: $tType] : ( list @ A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olist_Ocase__list,type,
% 2.65/1.56 case_list:
% 2.65/1.56 !>[B: $tType,A: $tType] : ( B > ( A > ( list @ A ) > B ) > ( list @ A ) > B ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olist_Ohd,type,
% 2.65/1.56 hd:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olist_Otl,type,
% 2.65/1.56 tl:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olist__ex1,type,
% 2.65/1.56 list_ex1:
% 2.65/1.56 !>[A: $tType] : ( ( A > $o ) > ( list @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Olistrelp,type,
% 2.65/1.56 listrelp:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( A > B > $o ) > ( list @ A ) > ( list @ B ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Omap__tailrec,type,
% 2.65/1.56 map_tailrec:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Omap__tailrec__rev,type,
% 2.65/1.56 map_tailrec_rev:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( A > B ) > ( list @ A ) > ( list @ B ) > ( list @ B ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Omaps,type,
% 2.65/1.56 maps:
% 2.65/1.56 !>[A: $tType,B: $tType] : ( ( A > ( list @ B ) ) > ( list @ A ) > ( list @ B ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Omember,type,
% 2.65/1.56 member:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > A > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oord_Olexordp__eq,type,
% 2.65/1.56 lexordp_eq:
% 2.65/1.56 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > ( list @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oord__class_Olexordp__eq,type,
% 2.65/1.56 ord_lexordp_eq:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oproduct__lists,type,
% 2.65/1.56 product_lists:
% 2.65/1.56 !>[A: $tType] : ( ( list @ ( list @ A ) ) > ( list @ ( list @ A ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oremdups__adj,type,
% 2.65/1.56 remdups_adj:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Orev,type,
% 2.65/1.56 rev:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Orotate1,type,
% 2.65/1.56 rotate1:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Oshuffles,type,
% 2.65/1.56 shuffles:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( set @ ( list @ A ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Osplice,type,
% 2.65/1.56 splice:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ A ) > ( list @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Osubseqs,type,
% 2.65/1.56 subseqs:
% 2.65/1.56 !>[A: $tType] : ( ( list @ A ) > ( list @ ( list @ A ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_List_Osuccessively,type,
% 2.65/1.56 successively:
% 2.65/1.56 !>[A: $tType] : ( ( A > A > $o ) > ( list @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Orderings_Oord__class_Oless,type,
% 2.65/1.56 ord_less:
% 2.65/1.56 !>[A: $tType] : ( A > A > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_ODecr,type,
% 2.65/1.56 decr: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OEnc,type,
% 2.65/1.56 enc: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 2.65/1.56 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OExt,type,
% 2.65/1.56 ext: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OSign,type,
% 2.65/1.56 sign: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_Oeout,type,
% 2.65/1.56 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_Oine,type,
% 2.65/1.56 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.65/1.56 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OspecKeys,type,
% 2.65/1.56 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.65/1.56 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.65/1.56 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 2.65/1.56 secrec1371625429on2KSL: ( list @ secrecy_Expression ) > ( list @ secrecy_KS ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.65/1.56 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.65/1.56 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.65/1.56 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 2.65/1.56 secrecy_case_KS:
% 2.65/1.56 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.65/1.56 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 2.65/1.56 secrecy_rec_KS:
% 2.65/1.56 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.65/1.56 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_Set_OCollect,type,
% 2.65/1.56 collect:
% 2.65/1.56 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_c_member,type,
% 2.65/1.56 member2:
% 2.65/1.56 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.65/1.56
% 2.65/1.56 thf(sy_v_A,type,
% 2.65/1.56 a: secrecy_specID ).
% 2.65/1.56
% 2.65/1.56 thf(sy_v_m,type,
% 2.65/1.56 m: secrecy_Secrets ).
% 2.65/1.56
% 2.65/1.56 thf(fact_0_assms,axiom,
% 2.65/1.56 knowle2055185861_knows @ a @ ( cons @ secrecy_Expression @ ( secrecy_sE @ m ) @ ( nil @ secrecy_Expression ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_1_KS_Oinject_I2_J,axiom,
% 2.65/1.56 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.65/1.56 ( ( ( secrecy_sKS @ X2 )
% 2.65/1.56 = ( secrecy_sKS @ Y2 ) )
% 2.65/1.56 = ( X2 = Y2 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_2_know2knows__s,axiom,
% 2.65/1.56 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 2.65/1.56 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 2.65/1.56 => ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_sE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_3_know1s,axiom,
% 2.65/1.56 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 2.65/1.56 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ ( nil @ secrecy_Expression ) ) )
% 2.65/1.56 = ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_4_KS_Osimps_I8_J,axiom,
% 2.65/1.56 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 2.65/1.56 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 2.65/1.56 = ( F2 @ X2 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_5_KS_Osimps_I6_J,axiom,
% 2.65/1.56 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 2.65/1.56 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 2.65/1.56 = ( F2 @ X2 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_6_eoutKnowCorrect__L1s,axiom,
% 2.65/1.56 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 2.65/1.56 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 2.65/1.56 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 2.65/1.56 => ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 2.65/1.56 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_7_eout__know__s,axiom,
% 2.65/1.56 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 2.65/1.56 ( ( knowle1667810483orrect @ C @ ( secrecy_sKS @ M ) )
% 2.65/1.56 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 2.65/1.56 = ( ( member2 @ secrecy_Secrets @ M @ ( specSecrets @ C ) )
% 2.65/1.56 | ( knowle1437066798e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_8_know_Osimps_I2_J,axiom,
% 2.65/1.56 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 2.65/1.56 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 2.65/1.56 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 2.65/1.56 | ( member2 @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_9_KS2Expression_Osimps_I2_J,axiom,
% 2.65/1.56 ! [M: secrecy_Secrets] :
% 2.65/1.56 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.65/1.56 = ( secrecy_sE @ M ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_10_knows4,axiom,
% 2.65/1.56 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 2.65/1.56 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.65/1.56 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K2 ) )
% 2.65/1.56 & ( knowle2055185861_knows @ A2 @ ( enc @ K1 @ E ) ) )
% 2.65/1.56 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_11_knows5,axiom,
% 2.65/1.56 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 2.65/1.56 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 2.65/1.56 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K1 ) )
% 2.65/1.56 & ( knowle2055185861_knows @ A2 @ ( sign @ K2 @ E ) ) )
% 2.65/1.56 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_12_knows6,axiom,
% 2.65/1.56 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 2.65/1.56 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 2.65/1.56 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 2.65/1.56 => ( knowle2055185861_knows @ A2 @ ( enc @ K @ E1 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_13_KS_Oinject_I1_J,axiom,
% 2.65/1.56 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.65/1.56 ( ( ( secrecy_kKS @ X1 )
% 2.65/1.56 = ( secrecy_kKS @ Y1 ) )
% 2.65/1.56 = ( X1 = Y1 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_14_Expression_Oinject_I2_J,axiom,
% 2.65/1.56 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.65/1.56 ( ( ( secrecy_sE @ X2 )
% 2.65/1.56 = ( secrecy_sE @ Y2 ) )
% 2.65/1.56 = ( X2 = Y2 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_15_KS_Osimps_I7_J,axiom,
% 2.65/1.56 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 2.65/1.56 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 2.65/1.56 = ( F1 @ X1 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_16_KS_Osimps_I5_J,axiom,
% 2.65/1.56 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 2.65/1.56 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 2.65/1.56 = ( F1 @ X1 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_17_know1k,axiom,
% 2.65/1.56 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 2.65/1.56 ( ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ ( nil @ secrecy_Expression ) ) )
% 2.65/1.56 = ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_18_knows__emptyexpression,axiom,
% 2.65/1.56 ! [C: secrecy_specID] : ( knowle2055185861_knows @ C @ ( nil @ secrecy_Expression ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_19_KS_Oexhaust,axiom,
% 2.65/1.56 ! [Y: secrecy_KS] :
% 2.65/1.56 ( ! [X12: secrecy_Keys] :
% 2.65/1.56 ( Y
% 2.65/1.56 != ( secrecy_kKS @ X12 ) )
% 2.65/1.56 => ~ ! [X22: secrecy_Secrets] :
% 2.65/1.56 ( Y
% 2.65/1.56 != ( secrecy_sKS @ X22 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_20_KS_Oinduct,axiom,
% 2.65/1.56 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.65/1.56 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 2.65/1.56 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 2.65/1.56 => ( P @ KS ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_21_KS_Odistinct_I1_J,axiom,
% 2.65/1.56 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.65/1.56 ( ( secrecy_kKS @ X1 )
% 2.65/1.56 != ( secrecy_sKS @ X2 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_22_knows7,axiom,
% 2.65/1.56 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 2.65/1.56 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 2.65/1.56 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 2.65/1.56 => ( knowle2055185861_knows @ A2 @ ( sign @ K @ E1 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_23_list_Oinject,axiom,
% 2.65/1.56 ! [A: $tType,X21: A,X222: list @ A,Y21: A,Y22: list @ A] :
% 2.65/1.56 ( ( ( cons @ A @ X21 @ X222 )
% 2.65/1.56 = ( cons @ A @ Y21 @ Y22 ) )
% 2.65/1.56 = ( ( X21 = Y21 )
% 2.65/1.56 & ( X222 = Y22 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_24_list_Odistinct_I1_J,axiom,
% 2.65/1.56 ! [A: $tType,X21: A,X222: list @ A] :
% 2.65/1.56 ( ( nil @ A )
% 2.65/1.56 != ( cons @ A @ X21 @ X222 ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_25_list_OdiscI,axiom,
% 2.65/1.56 ! [A: $tType,List: list @ A,X21: A,X222: list @ A] :
% 2.65/1.56 ( ( List
% 2.65/1.56 = ( cons @ A @ X21 @ X222 ) )
% 2.65/1.56 => ( List
% 2.65/1.56 != ( nil @ A ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_26_list_Oexhaust,axiom,
% 2.65/1.56 ! [A: $tType,Y: list @ A] :
% 2.65/1.56 ( ( Y
% 2.65/1.56 != ( nil @ A ) )
% 2.65/1.56 => ~ ! [X212: A,X223: list @ A] :
% 2.65/1.56 ( Y
% 2.65/1.56 != ( cons @ A @ X212 @ X223 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_27_list_Oinducts,axiom,
% 2.65/1.56 ! [A: $tType,P: ( list @ A ) > $o,List: list @ A] :
% 2.65/1.56 ( ( P @ ( nil @ A ) )
% 2.65/1.56 => ( ! [X12: A,X22: list @ A] :
% 2.65/1.56 ( ( P @ X22 )
% 2.65/1.56 => ( P @ ( cons @ A @ X12 @ X22 ) ) )
% 2.65/1.56 => ( P @ List ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_28_neq__Nil__conv,axiom,
% 2.65/1.56 ! [A: $tType,Xs: list @ A] :
% 2.65/1.56 ( ( Xs
% 2.65/1.56 != ( nil @ A ) )
% 2.65/1.56 = ( ? [Y3: A,Ys: list @ A] :
% 2.65/1.56 ( Xs
% 2.65/1.56 = ( cons @ A @ Y3 @ Ys ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_29_list__induct2_H,axiom,
% 2.65/1.56 ! [A: $tType,B: $tType,P: ( list @ A ) > ( list @ B ) > $o,Xs: list @ A,Ys2: list @ B] :
% 2.65/1.56 ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.65/1.56 => ( ! [X: A,Xs2: list @ A] : ( P @ ( cons @ A @ X @ Xs2 ) @ ( nil @ B ) )
% 2.65/1.56 => ( ! [Y4: B,Ys3: list @ B] : ( P @ ( nil @ A ) @ ( cons @ B @ Y4 @ Ys3 ) )
% 2.65/1.56 => ( ! [X: A,Xs2: list @ A,Y4: B,Ys3: list @ B] :
% 2.65/1.56 ( ( P @ Xs2 @ Ys3 )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) )
% 2.65/1.56 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_30_splice_Oinduct,axiom,
% 2.65/1.56 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.65/1.56 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.65/1.56 => ( ! [X: A,Xs2: list @ A,Ys3: list @ A] :
% 2.65/1.56 ( ( P @ Ys3 @ Xs2 )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 ) )
% 2.65/1.56 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_31_induct__list012,axiom,
% 2.65/1.56 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.65/1.56 ( ( P @ ( nil @ A ) )
% 2.65/1.56 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.56 => ( ! [X: A,Y4: A,Zs: list @ A] :
% 2.65/1.56 ( ( P @ Zs )
% 2.65/1.56 => ( ( P @ ( cons @ A @ Y4 @ Zs ) )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs ) ) ) ) )
% 2.65/1.56 => ( P @ Xs ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_32_min__list_Ocases,axiom,
% 2.65/1.56 ! [A: $tType] :
% 2.65/1.56 ( ( ord @ A )
% 2.65/1.56 => ! [X3: list @ A] :
% 2.65/1.56 ( ! [X: A,Xs2: list @ A] :
% 2.65/1.56 ( X3
% 2.65/1.56 != ( cons @ A @ X @ Xs2 ) )
% 2.65/1.56 => ( X3
% 2.65/1.56 = ( nil @ A ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_33_min__list_Oinduct,axiom,
% 2.65/1.56 ! [A: $tType] :
% 2.65/1.56 ( ( ord @ A )
% 2.65/1.56 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.65/1.56 ( ! [X: A,Xs2: list @ A] :
% 2.65/1.56 ( ! [X213: A,X224: list @ A] :
% 2.65/1.56 ( ( Xs2
% 2.65/1.56 = ( cons @ A @ X213 @ X224 ) )
% 2.65/1.56 => ( P @ Xs2 ) )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 2.65/1.56 => ( ( P @ ( nil @ A ) )
% 2.65/1.56 => ( P @ A0 ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_34_not__Cons__self2,axiom,
% 2.65/1.56 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.56 ( ( cons @ A @ X3 @ Xs )
% 2.65/1.56 != Xs ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_35_strict__sorted_Oinduct,axiom,
% 2.65/1.56 ! [A: $tType] :
% 2.65/1.56 ( ( linorder @ A )
% 2.65/1.56 => ! [P: ( list @ A ) > $o,A0: list @ A] :
% 2.65/1.56 ( ( P @ ( nil @ A ) )
% 2.65/1.56 => ( ! [X: A,Ys3: list @ A] :
% 2.65/1.56 ( ( P @ Ys3 )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ Ys3 ) ) )
% 2.65/1.56 => ( P @ A0 ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_36_strict__sorted_Ocases,axiom,
% 2.65/1.56 ! [A: $tType] :
% 2.65/1.56 ( ( linorder @ A )
% 2.65/1.56 => ! [X3: list @ A] :
% 2.65/1.56 ( ( X3
% 2.65/1.56 != ( nil @ A ) )
% 2.65/1.56 => ~ ! [X: A,Ys3: list @ A] :
% 2.65/1.56 ( X3
% 2.65/1.56 != ( cons @ A @ X @ Ys3 ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_37_map__tailrec__rev_Oinduct,axiom,
% 2.65/1.56 ! [A: $tType,B: $tType,P: ( A > B ) > ( list @ A ) > ( list @ B ) > $o,A0: A > B,A1: list @ A,A22: list @ B] :
% 2.65/1.56 ( ! [F: A > B,X_1: list @ B] : ( P @ F @ ( nil @ A ) @ X_1 )
% 2.65/1.56 => ( ! [F: A > B,A3: A,As: list @ A,Bs: list @ B] :
% 2.65/1.56 ( ( P @ F @ As @ ( cons @ B @ ( F @ A3 ) @ Bs ) )
% 2.65/1.56 => ( P @ F @ ( cons @ A @ A3 @ As ) @ Bs ) )
% 2.65/1.56 => ( P @ A0 @ A1 @ A22 ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_38_list__nonempty__induct,axiom,
% 2.65/1.56 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.65/1.56 ( ( Xs
% 2.65/1.56 != ( nil @ A ) )
% 2.65/1.56 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.56 => ( ! [X: A,Xs2: list @ A] :
% 2.65/1.56 ( ( Xs2
% 2.65/1.56 != ( nil @ A ) )
% 2.65/1.56 => ( ( P @ Xs2 )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ Xs2 ) ) ) )
% 2.65/1.56 => ( P @ Xs ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_39_successively_Oinduct,axiom,
% 2.65/1.56 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.65/1.56 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.65/1.56 => ( ! [P2: A > A > $o,X: A] : ( P @ P2 @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.56 => ( ! [P2: A > A > $o,X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.56 ( ( P @ P2 @ ( cons @ A @ Y4 @ Xs2 ) )
% 2.65/1.56 => ( P @ P2 @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) )
% 2.65/1.56 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_40_arg__min__list_Oinduct,axiom,
% 2.65/1.56 ! [B: $tType,A: $tType] :
% 2.65/1.56 ( ( linorder @ B )
% 2.65/1.56 => ! [P: ( A > B ) > ( list @ A ) > $o,A0: A > B,A1: list @ A] :
% 2.65/1.56 ( ! [F: A > B,X: A] : ( P @ F @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.56 => ( ! [F: A > B,X: A,Y4: A,Zs: list @ A] :
% 2.65/1.56 ( ( P @ F @ ( cons @ A @ Y4 @ Zs ) )
% 2.65/1.56 => ( P @ F @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Zs ) ) ) )
% 2.65/1.56 => ( ! [A3: A > B] : ( P @ A3 @ ( nil @ A ) )
% 2.65/1.56 => ( P @ A0 @ A1 ) ) ) ) ) ).
% 2.65/1.56
% 2.65/1.56 thf(fact_41_remdups__adj_Oinduct,axiom,
% 2.65/1.56 ! [A: $tType,P: ( list @ A ) > $o,A0: list @ A] :
% 2.65/1.56 ( ( P @ ( nil @ A ) )
% 2.65/1.56 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.56 => ( ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.56 ( ( ( X = Y4 )
% 2.65/1.56 => ( P @ ( cons @ A @ X @ Xs2 ) ) )
% 2.65/1.56 => ( ( ( X != Y4 )
% 2.65/1.57 => ( P @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) )
% 2.65/1.57 => ( P @ A0 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_42_sorted__wrt_Oinduct,axiom,
% 2.65/1.57 ! [A: $tType,P: ( A > A > $o ) > ( list @ A ) > $o,A0: A > A > $o,A1: list @ A] :
% 2.65/1.57 ( ! [P2: A > A > $o] : ( P @ P2 @ ( nil @ A ) )
% 2.65/1.57 => ( ! [P2: A > A > $o,X: A,Ys3: list @ A] :
% 2.65/1.57 ( ( P @ P2 @ Ys3 )
% 2.65/1.57 => ( P @ P2 @ ( cons @ A @ X @ Ys3 ) ) )
% 2.65/1.57 => ( P @ A0 @ A1 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_43_remdups__adj_Ocases,axiom,
% 2.65/1.57 ! [A: $tType,X3: list @ A] :
% 2.65/1.57 ( ( X3
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ! [X: A] :
% 2.65/1.57 ( X3
% 2.65/1.57 != ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.57 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.57 ( X3
% 2.65/1.57 != ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_44_mem__Collect__eq,axiom,
% 2.65/1.57 ! [A: $tType,A4: A,P: A > $o] :
% 2.65/1.57 ( ( member2 @ A @ A4 @ ( collect @ A @ P ) )
% 2.65/1.57 = ( P @ A4 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_45_Collect__mem__eq,axiom,
% 2.65/1.57 ! [A: $tType,A2: set @ A] :
% 2.65/1.57 ( ( collect @ A
% 2.65/1.57 @ ^ [X4: A] : ( member2 @ A @ X4 @ A2 ) )
% 2.65/1.57 = A2 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_46_Collect__cong,axiom,
% 2.65/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.65/1.57 ( ! [X: A] :
% 2.65/1.57 ( ( P @ X )
% 2.65/1.57 = ( Q @ X ) )
% 2.65/1.57 => ( ( collect @ A @ P )
% 2.65/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_47_ext,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,F3: A > B,G: A > B] :
% 2.65/1.57 ( ! [X: A] :
% 2.65/1.57 ( ( F3 @ X )
% 2.65/1.57 = ( G @ X ) )
% 2.65/1.57 => ( F3 = G ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_48_transpose_Ocases,axiom,
% 2.65/1.57 ! [A: $tType,X3: list @ ( list @ A )] :
% 2.65/1.57 ( ( X3
% 2.65/1.57 != ( nil @ ( list @ A ) ) )
% 2.65/1.57 => ( ! [Xss: list @ ( list @ A )] :
% 2.65/1.57 ( X3
% 2.65/1.57 != ( cons @ ( list @ A ) @ ( nil @ A ) @ Xss ) )
% 2.65/1.57 => ~ ! [X: A,Xs2: list @ A,Xss: list @ ( list @ A )] :
% 2.65/1.57 ( X3
% 2.65/1.57 != ( cons @ ( list @ A ) @ ( cons @ A @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_49_shuffles_Oinduct,axiom,
% 2.65/1.57 ! [A: $tType,P: ( list @ A ) > ( list @ A ) > $o,A0: list @ A,A1: list @ A] :
% 2.65/1.57 ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.65/1.57 => ( ! [Xs2: list @ A] : ( P @ Xs2 @ ( nil @ A ) )
% 2.65/1.57 => ( ! [X: A,Xs2: list @ A,Y4: A,Ys3: list @ A] :
% 2.65/1.57 ( ( P @ Xs2 @ ( cons @ A @ Y4 @ Ys3 ) )
% 2.65/1.57 => ( ( P @ ( cons @ A @ X @ Xs2 ) @ Ys3 )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) )
% 2.65/1.57 => ( P @ A0 @ A1 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_50_knows1k,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.65/1.57 = ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_51_know2knows__k,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.65/1.57 => ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_52_knows2know__k,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 2.65/1.57 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_53_know2knowsPQ__k,axiom,
% 2.65/1.57 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 2.65/1.57 ( ( ( knowle1437066798e_know @ P @ ( secrecy_kKS @ M ) )
% 2.65/1.57 | ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ M ) ) )
% 2.65/1.57 => ( ( knowle2055185861_knows @ P @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 2.65/1.57 | ( knowle2055185861_knows @ Q @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_54_knows2knowPQ__k,axiom,
% 2.65/1.57 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 2.65/1.57 ( ( ( knowle2055185861_knows @ P @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 2.65/1.57 | ( knowle2055185861_knows @ Q @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) )
% 2.65/1.57 => ( ( knowle1437066798e_know @ P @ ( secrecy_kKS @ M ) )
% 2.65/1.57 | ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ M ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_55_know2knows__neg__k,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.65/1.57 => ~ ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_56_knows2know__neg__k,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ~ ( knowle2055185861_knows @ A2 @ ( cons @ secrecy_Expression @ ( secrecy_kE @ M ) @ ( nil @ secrecy_Expression ) ) )
% 2.65/1.57 => ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_57_know_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.65/1.57 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 2.65/1.57 | ( member2 @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_58_insert__Nil,axiom,
% 2.65/1.57 ! [A: $tType,X3: A] :
% 2.65/1.57 ( ( insert @ A @ X3 @ ( nil @ A ) )
% 2.65/1.57 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_59_Expression_Oinject_I1_J,axiom,
% 2.65/1.57 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.65/1.57 ( ( ( secrecy_kE @ X1 )
% 2.65/1.57 = ( secrecy_kE @ Y1 ) )
% 2.65/1.57 = ( X1 = Y1 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_60_Expression_Odistinct_I1_J,axiom,
% 2.65/1.57 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.65/1.57 ( ( secrecy_kE @ X1 )
% 2.65/1.57 != ( secrecy_sE @ X2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_61_KS2Expression_Osimps_I1_J,axiom,
% 2.65/1.57 ! [M: secrecy_Keys] :
% 2.65/1.57 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.65/1.57 = ( secrecy_kE @ M ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_62_eoutKnowCorrect__L1k,axiom,
% 2.65/1.57 ! [C: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 2.65/1.57 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 2.65/1.57 => ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 2.65/1.57 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_63_eout__know__k,axiom,
% 2.65/1.57 ! [C: secrecy_specID,M: secrecy_Keys] :
% 2.65/1.57 ( ( knowle1667810483orrect @ C @ ( secrecy_kKS @ M ) )
% 2.65/1.57 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 2.65/1.57 = ( ( member2 @ secrecy_Keys @ M @ ( specKeys @ C ) )
% 2.65/1.57 | ( knowle1437066798e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_64_eoutKnowsECorrect__L1,axiom,
% 2.65/1.57 ! [C: secrecy_specID,E: secrecy_Expression] :
% 2.65/1.57 ( ( knowle1893229345orrect @ C @ E )
% 2.65/1.57 => ( ( eout @ C @ E )
% 2.65/1.57 => ( ? [K3: secrecy_Keys] :
% 2.65/1.57 ( ( E
% 2.65/1.57 = ( secrecy_kE @ K3 ) )
% 2.65/1.57 & ( member2 @ secrecy_Keys @ K3 @ ( specKeys @ C ) ) )
% 2.65/1.57 | ? [S: secrecy_Secrets] :
% 2.65/1.57 ( ( E
% 2.65/1.57 = ( secrecy_sE @ S ) )
% 2.65/1.57 & ( member2 @ secrecy_Secrets @ S @ ( specSecrets @ C ) ) )
% 2.65/1.57 | ( knowle2055185861_knows @ C @ ( cons @ secrecy_Expression @ E @ ( nil @ secrecy_Expression ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_65_eoutKnowsECorrect__def,axiom,
% 2.65/1.57 ( knowle1893229345orrect
% 2.65/1.57 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 2.65/1.57 ( ( eout @ C2 @ E2 )
% 2.65/1.57 = ( ? [K4: secrecy_Keys] :
% 2.65/1.57 ( ( E2
% 2.65/1.57 = ( secrecy_kE @ K4 ) )
% 2.65/1.57 & ( member2 @ secrecy_Keys @ K4 @ ( specKeys @ C2 ) ) )
% 2.65/1.57 | ? [S2: secrecy_Secrets] :
% 2.65/1.57 ( ( E2
% 2.65/1.57 = ( secrecy_sE @ S2 ) )
% 2.65/1.57 & ( member2 @ secrecy_Secrets @ S2 @ ( specSecrets @ C2 ) ) )
% 2.65/1.57 | ( knowle2055185861_knows @ C2 @ ( cons @ secrecy_Expression @ E2 @ ( nil @ secrecy_Expression ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_66_product__lists_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( product_lists @ A @ ( nil @ ( list @ A ) ) )
% 2.65/1.57 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_67_subseqs_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( subseqs @ A @ ( nil @ A ) )
% 2.65/1.57 = ( cons @ ( list @ A ) @ ( nil @ A ) @ ( nil @ ( list @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_68_Expression2KSL_Osimps_I1_J,axiom,
% 2.65/1.57 ( ( secrec1371625429on2KSL @ ( nil @ secrecy_Expression ) )
% 2.65/1.57 = ( nil @ secrecy_KS ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_69_list__ex1__simps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,P: A > $o] :
% 2.65/1.57 ~ ( list_ex1 @ A @ P @ ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_70_map__tailrec__rev_Oelims,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,X3: A > B,Xa: list @ A,Xb: list @ B,Y: list @ B] :
% 2.65/1.57 ( ( ( map_tailrec_rev @ A @ B @ X3 @ Xa @ Xb )
% 2.65/1.57 = Y )
% 2.65/1.57 => ( ( ( Xa
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( Y != Xb ) )
% 2.65/1.57 => ~ ! [A3: A,As: list @ A] :
% 2.65/1.57 ( ( Xa
% 2.65/1.57 = ( cons @ A @ A3 @ As ) )
% 2.65/1.57 => ( Y
% 2.65/1.57 != ( map_tailrec_rev @ A @ B @ X3 @ As @ ( cons @ B @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_71_arg__min__list_Osimps_I1_J,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType] :
% 2.65/1.57 ( ( linorder @ B )
% 2.65/1.57 => ! [F3: A > B,X3: A] :
% 2.65/1.57 ( ( arg_min_list @ A @ B @ F3 @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.65/1.57 = X3 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_72_ord_Olexordp__eq__simps_I3_J,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A] :
% 2.65/1.57 ~ ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_73_bind__simps_I1_J,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 2.65/1.57 ( ( bind @ B @ A @ ( nil @ B ) @ F3 )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_74_listrelp_Oinducts,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,R: A > B > $o,X1: list @ A,X2: list @ B,P: ( list @ A ) > ( list @ B ) > $o] :
% 2.65/1.57 ( ( listrelp @ A @ B @ R @ X1 @ X2 )
% 2.65/1.57 => ( ( P @ ( nil @ A ) @ ( nil @ B ) )
% 2.65/1.57 => ( ! [X: A,Y4: B,Xs2: list @ A,Ys3: list @ B] :
% 2.65/1.57 ( ( R @ X @ Y4 )
% 2.65/1.57 => ( ( listrelp @ A @ B @ R @ Xs2 @ Ys3 )
% 2.65/1.57 => ( ( P @ Xs2 @ Ys3 )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ B @ Y4 @ Ys3 ) ) ) ) )
% 2.65/1.57 => ( P @ X1 @ X2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_75_listrelp_Osimps,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType] :
% 2.65/1.57 ( ( listrelp @ A @ B )
% 2.65/1.57 = ( ^ [R2: A > B > $o,A12: list @ A,A23: list @ B] :
% 2.65/1.57 ( ( ( A12
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( A23
% 2.65/1.57 = ( nil @ B ) ) )
% 2.65/1.57 | ? [X4: A,Y3: B,Xs3: list @ A,Ys: list @ B] :
% 2.65/1.57 ( ( A12
% 2.65/1.57 = ( cons @ A @ X4 @ Xs3 ) )
% 2.65/1.57 & ( A23
% 2.65/1.57 = ( cons @ B @ Y3 @ Ys ) )
% 2.65/1.57 & ( R2 @ X4 @ Y3 )
% 2.65/1.57 & ( listrelp @ A @ B @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_76_ord_Olexordp__eq__simps_I4_J,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,X3: A,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.65/1.57 ( ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) )
% 2.65/1.57 = ( ( Less @ X3 @ Y )
% 2.65/1.57 | ( ~ ( Less @ Y @ X3 )
% 2.65/1.57 & ( lexordp_eq @ A @ Less @ Xs @ Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_77_ord_Olexordp__eq__simps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,Xs: list @ A] :
% 2.65/1.57 ( ( lexordp_eq @ A @ Less @ Xs @ ( nil @ A ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_78_ord_Olexordp__eq__simps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_79_ord_Olexordp__eq__refl,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,Xs: list @ A] : ( lexordp_eq @ A @ Less @ Xs @ Xs ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_80_ord_Olexordp__eq_Ocong,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( lexordp_eq @ A )
% 2.65/1.57 = ( lexordp_eq @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_81_ord_Olexordp__eq_OCons,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( Less @ X3 @ Y )
% 2.65/1.57 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_82_ord_Olexordp__eq_OCons__eq,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,X3: A,Y: A,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ~ ( Less @ X3 @ Y )
% 2.65/1.57 => ( ~ ( Less @ Y @ X3 )
% 2.65/1.57 => ( ( lexordp_eq @ A @ Less @ Xs @ Ys2 )
% 2.65/1.57 => ( lexordp_eq @ A @ Less @ ( cons @ A @ X3 @ Xs ) @ ( cons @ A @ Y @ Ys2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_83_ord_Olexordp__eq_ONil,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,Ys2: list @ A] : ( lexordp_eq @ A @ Less @ ( nil @ A ) @ Ys2 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_84_listrelp_OCons,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,R: A > B > $o,X3: A,Y: B,Xs: list @ A,Ys2: list @ B] :
% 2.65/1.57 ( ( R @ X3 @ Y )
% 2.65/1.57 => ( ( listrelp @ A @ B @ R @ Xs @ Ys2 )
% 2.65/1.57 => ( listrelp @ A @ B @ R @ ( cons @ A @ X3 @ Xs ) @ ( cons @ B @ Y @ Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_85_listrelp_ONil,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,R: A > B > $o] : ( listrelp @ A @ B @ R @ ( nil @ A ) @ ( nil @ B ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_86_map__tailrec__rev_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,F3: A > B,A4: A,As2: list @ A,Bs2: list @ B] :
% 2.65/1.57 ( ( map_tailrec_rev @ A @ B @ F3 @ ( cons @ A @ A4 @ As2 ) @ Bs2 )
% 2.65/1.57 = ( map_tailrec_rev @ A @ B @ F3 @ As2 @ ( cons @ B @ ( F3 @ A4 ) @ Bs2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_87_map__tailrec__rev_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,F3: A > B,Bs2: list @ B] :
% 2.65/1.57 ( ( map_tailrec_rev @ A @ B @ F3 @ ( nil @ A ) @ Bs2 )
% 2.65/1.57 = Bs2 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_88_ord_Olexordp__eq_Ocases,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,A1: list @ A,A22: list @ A] :
% 2.65/1.57 ( ( lexordp_eq @ A @ Less @ A1 @ A22 )
% 2.65/1.57 => ( ( A1
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ! [X: A] :
% 2.65/1.57 ( ? [Xs2: list @ A] :
% 2.65/1.57 ( A1
% 2.65/1.57 = ( cons @ A @ X @ Xs2 ) )
% 2.65/1.57 => ! [Y4: A] :
% 2.65/1.57 ( ? [Ys3: list @ A] :
% 2.65/1.57 ( A22
% 2.65/1.57 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.65/1.57 => ~ ( Less @ X @ Y4 ) ) )
% 2.65/1.57 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.57 ( ( A1
% 2.65/1.57 = ( cons @ A @ X @ Xs2 ) )
% 2.65/1.57 => ! [Ys3: list @ A] :
% 2.65/1.57 ( ( A22
% 2.65/1.57 = ( cons @ A @ Y4 @ Ys3 ) )
% 2.65/1.57 => ( ~ ( Less @ X @ Y4 )
% 2.65/1.57 => ( ~ ( Less @ Y4 @ X )
% 2.65/1.57 => ~ ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_89_ord_Olexordp__eq_Osimps,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( lexordp_eq @ A )
% 2.65/1.57 = ( ^ [Less2: A > A > $o,A12: list @ A,A23: list @ A] :
% 2.65/1.57 ( ? [Ys: list @ A] :
% 2.65/1.57 ( ( A12
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( A23 = Ys ) )
% 2.65/1.57 | ? [X4: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.65/1.57 ( ( A12
% 2.65/1.57 = ( cons @ A @ X4 @ Xs3 ) )
% 2.65/1.57 & ( A23
% 2.65/1.57 = ( cons @ A @ Y3 @ Ys ) )
% 2.65/1.57 & ( Less2 @ X4 @ Y3 ) )
% 2.65/1.57 | ? [X4: A,Y3: A,Xs3: list @ A,Ys: list @ A] :
% 2.65/1.57 ( ( A12
% 2.65/1.57 = ( cons @ A @ X4 @ Xs3 ) )
% 2.65/1.57 & ( A23
% 2.65/1.57 = ( cons @ A @ Y3 @ Ys ) )
% 2.65/1.57 & ~ ( Less2 @ X4 @ Y3 )
% 2.65/1.57 & ~ ( Less2 @ Y3 @ X4 )
% 2.65/1.57 & ( lexordp_eq @ A @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_90_ord_Olexordp__eq_Oinducts,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.65/1.57 ( ( lexordp_eq @ A @ Less @ X1 @ X2 )
% 2.65/1.57 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.65/1.57 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.65/1.57 ( ( Less @ X @ Y4 )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.65/1.57 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.65/1.57 ( ~ ( Less @ X @ Y4 )
% 2.65/1.57 => ( ~ ( Less @ Y4 @ X )
% 2.65/1.57 => ( ( lexordp_eq @ A @ Less @ Xs2 @ Ys3 )
% 2.65/1.57 => ( ( P @ Xs2 @ Ys3 )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 2.65/1.57 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_91_listrelp_Ocases,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,R: A > B > $o,A1: list @ A,A22: list @ B] :
% 2.65/1.57 ( ( listrelp @ A @ B @ R @ A1 @ A22 )
% 2.65/1.57 => ( ( ( A1
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( A22
% 2.65/1.57 != ( nil @ B ) ) )
% 2.65/1.57 => ~ ! [X: A,Y4: B,Xs2: list @ A] :
% 2.65/1.57 ( ( A1
% 2.65/1.57 = ( cons @ A @ X @ Xs2 ) )
% 2.65/1.57 => ! [Ys3: list @ B] :
% 2.65/1.57 ( ( A22
% 2.65/1.57 = ( cons @ B @ Y4 @ Ys3 ) )
% 2.65/1.57 => ( ( R @ X @ Y4 )
% 2.65/1.57 => ~ ( listrelp @ A @ B @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_92_lexordp__eq__simps_I3_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [X3: A,Xs: list @ A] :
% 2.65/1.57 ~ ( ord_lexordp_eq @ A @ ( cons @ A @ X3 @ Xs ) @ ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_93_notSpecKeysSecretsExpr__L1,axiom,
% 2.65/1.57 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 2.65/1.57 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 2.65/1.57 => ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ ( nil @ secrecy_Expression ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_94_member__rec_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,Y: A] :
% 2.65/1.57 ~ ( member @ A @ ( nil @ A ) @ Y ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_95_member__rec_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A,Y: A] :
% 2.65/1.57 ( ( member @ A @ ( cons @ A @ X3 @ Xs ) @ Y )
% 2.65/1.57 = ( ( X3 = Y )
% 2.65/1.57 | ( member @ A @ Xs @ Y ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_96_splice_Oelims,axiom,
% 2.65/1.57 ! [A: $tType,X3: list @ A,Xa: list @ A,Y: list @ A] :
% 2.65/1.57 ( ( ( splice @ A @ X3 @ Xa )
% 2.65/1.57 = Y )
% 2.65/1.57 => ( ( ( X3
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( Y != Xa ) )
% 2.65/1.57 => ~ ! [X: A,Xs2: list @ A] :
% 2.65/1.57 ( ( X3
% 2.65/1.57 = ( cons @ A @ X @ Xs2 ) )
% 2.65/1.57 => ( Y
% 2.65/1.57 != ( cons @ A @ X @ ( splice @ A @ Xa @ Xs2 ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_97_bind__simps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,X3: B,Xs: list @ B,F3: B > ( list @ A )] :
% 2.65/1.57 ( ( bind @ B @ A @ ( cons @ B @ X3 @ Xs ) @ F3 )
% 2.65/1.57 = ( append @ A @ ( F3 @ X3 ) @ ( bind @ B @ A @ Xs @ F3 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_98_append_Oassoc,axiom,
% 2.65/1.57 ! [A: $tType,A4: list @ A,B2: list @ A,C3: list @ A] :
% 2.65/1.57 ( ( append @ A @ ( append @ A @ A4 @ B2 ) @ C3 )
% 2.65/1.57 = ( append @ A @ A4 @ ( append @ A @ B2 @ C3 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_99_append__assoc,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( append @ A @ ( append @ A @ Xs @ Ys2 ) @ Zs2 )
% 2.65/1.57 = ( append @ A @ Xs @ ( append @ A @ Ys2 @ Zs2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_100_append__same__eq,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Ys2 @ Xs )
% 2.65/1.57 = ( append @ A @ Zs2 @ Xs ) )
% 2.65/1.57 = ( Ys2 = Zs2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_101_same__append__eq,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ Ys2 )
% 2.65/1.57 = ( append @ A @ Xs @ Zs2 ) )
% 2.65/1.57 = ( Ys2 = Zs2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_102_append_Oright__neutral,axiom,
% 2.65/1.57 ! [A: $tType,A4: list @ A] :
% 2.65/1.57 ( ( append @ A @ A4 @ ( nil @ A ) )
% 2.65/1.57 = A4 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_103_append__is__Nil__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ Ys2 )
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_104_Nil__is__append__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( nil @ A )
% 2.65/1.57 = ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_105_self__append__conv2,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.65/1.57 ( ( Ys2
% 2.65/1.57 = ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_106_append__self__conv2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ Ys2 )
% 2.65/1.57 = Ys2 )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_107_self__append__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 = ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( Ys2
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_108_append__self__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ Ys2 )
% 2.65/1.57 = Xs )
% 2.65/1.57 = ( Ys2
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_109_append__Nil2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( append @ A @ Xs @ ( nil @ A ) )
% 2.65/1.57 = Xs ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_110_lexordp__eq__simps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_111_lexordp__eq__simps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [Xs: list @ A] :
% 2.65/1.57 ( ( ord_lexordp_eq @ A @ Xs @ ( nil @ A ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_112_split__Nil__iff,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( splice @ A @ Xs @ Ys2 )
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_113_splice__Nil2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( splice @ A @ Xs @ ( nil @ A ) )
% 2.65/1.57 = Xs ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_114_append1__eq__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A,Y: A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.65/1.57 = ( append @ A @ Ys2 @ ( cons @ A @ Y @ ( nil @ A ) ) ) )
% 2.65/1.57 = ( ( Xs = Ys2 )
% 2.65/1.57 & ( X3 = Y ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_115_append__eq__appendI,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Xs1: list @ A,Zs2: list @ A,Ys2: list @ A,Us: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ Xs1 )
% 2.65/1.57 = Zs2 )
% 2.65/1.57 => ( ( Ys2
% 2.65/1.57 = ( append @ A @ Xs1 @ Us ) )
% 2.65/1.57 => ( ( append @ A @ Xs @ Ys2 )
% 2.65/1.57 = ( append @ A @ Zs2 @ Us ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_116_append__eq__append__conv2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A,Zs2: list @ A,Ts: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ Ys2 )
% 2.65/1.57 = ( append @ A @ Zs2 @ Ts ) )
% 2.65/1.57 = ( ? [Us2: list @ A] :
% 2.65/1.57 ( ( ( Xs
% 2.65/1.57 = ( append @ A @ Zs2 @ Us2 ) )
% 2.65/1.57 & ( ( append @ A @ Us2 @ Ys2 )
% 2.65/1.57 = Ts ) )
% 2.65/1.57 | ( ( ( append @ A @ Xs @ Us2 )
% 2.65/1.57 = Zs2 )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( append @ A @ Us2 @ Ts ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_117_lexordp__eq__pref,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [U: list @ A,V: list @ A] : ( ord_lexordp_eq @ A @ U @ ( append @ A @ U @ V ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_118_lexordp__eq__refl,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [Xs: list @ A] : ( ord_lexordp_eq @ A @ Xs @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_119_lexordp__eq__trans,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( linorder @ A )
% 2.65/1.57 => ! [Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.65/1.57 => ( ( ord_lexordp_eq @ A @ Ys2 @ Zs2 )
% 2.65/1.57 => ( ord_lexordp_eq @ A @ Xs @ Zs2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_120_lexordp__eq__linear,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( linorder @ A )
% 2.65/1.57 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.65/1.57 | ( ord_lexordp_eq @ A @ Ys2 @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_121_lexordp__eq__antisym,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( linorder @ A )
% 2.65/1.57 => ! [Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ord_lexordp_eq @ A @ Xs @ Ys2 )
% 2.65/1.57 => ( ( ord_lexordp_eq @ A @ Ys2 @ Xs )
% 2.65/1.57 => ( Xs = Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_122_append__Cons,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( append @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 2.65/1.57 = ( cons @ A @ X3 @ ( append @ A @ Xs @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_123_Cons__eq__appendI,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs1: list @ A,Ys2: list @ A,Xs: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ( cons @ A @ X3 @ Xs1 )
% 2.65/1.57 = Ys2 )
% 2.65/1.57 => ( ( Xs
% 2.65/1.57 = ( append @ A @ Xs1 @ Zs2 ) )
% 2.65/1.57 => ( ( cons @ A @ X3 @ Xs )
% 2.65/1.57 = ( append @ A @ Ys2 @ Zs2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_124_append_Oleft__neutral,axiom,
% 2.65/1.57 ! [A: $tType,A4: list @ A] :
% 2.65/1.57 ( ( append @ A @ ( nil @ A ) @ A4 )
% 2.65/1.57 = A4 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_125_append__Nil,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A] :
% 2.65/1.57 ( ( append @ A @ ( nil @ A ) @ Ys2 )
% 2.65/1.57 = Ys2 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_126_eq__Nil__appendI,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( Xs = Ys2 )
% 2.65/1.57 => ( Xs
% 2.65/1.57 = ( append @ A @ ( nil @ A ) @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_127_knows2b,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,E: list @ secrecy_Expression,E1: list @ secrecy_Expression] :
% 2.65/1.57 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E @ E1 ) )
% 2.65/1.57 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_128_knows2a,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E: list @ secrecy_Expression] :
% 2.65/1.57 ( ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E ) )
% 2.65/1.57 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_129_knows3,axiom,
% 2.65/1.57 ! [A2: secrecy_specID,E1: list @ secrecy_Expression,E22: list @ secrecy_Expression] :
% 2.65/1.57 ( ( ( knowle2055185861_knows @ A2 @ E1 )
% 2.65/1.57 & ( knowle2055185861_knows @ A2 @ E22 ) )
% 2.65/1.57 => ( knowle2055185861_knows @ A2 @ ( append @ secrecy_Expression @ E1 @ E22 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_130_ord_Olexordp__eq__pref,axiom,
% 2.65/1.57 ! [A: $tType,Less: A > A > $o,U: list @ A,V: list @ A] : ( lexordp_eq @ A @ Less @ U @ ( append @ A @ U @ V ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_131_lexordp__eq_ONil,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [Ys2: list @ A] : ( ord_lexordp_eq @ A @ ( nil @ A ) @ Ys2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_132_notSpecKeysSecretsExpr__L2,axiom,
% 2.65/1.57 ! [P: secrecy_specID,A4: secrecy_Expression,L: list @ secrecy_Expression] :
% 2.65/1.57 ( ( notSpe1586871396tsExpr @ P @ ( cons @ secrecy_Expression @ A4 @ L ) )
% 2.65/1.57 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_133_splice_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( splice @ A @ ( cons @ A @ X3 @ Xs ) @ Ys2 )
% 2.65/1.57 = ( cons @ A @ X3 @ ( splice @ A @ Ys2 @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_134_splice_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A] :
% 2.65/1.57 ( ( splice @ A @ ( nil @ A ) @ Ys2 )
% 2.65/1.57 = Ys2 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_135_rev__nonempty__induct,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,P: ( list @ A ) > $o] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ! [X: A] : ( P @ ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.57 => ( ! [X: A,Xs2: list @ A] :
% 2.65/1.57 ( ( Xs2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( P @ Xs2 )
% 2.65/1.57 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) ) )
% 2.65/1.57 => ( P @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_136_append__eq__Cons__conv,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Zs2: list @ A,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Ys2 @ Zs2 )
% 2.65/1.57 = ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( Zs2
% 2.65/1.57 = ( cons @ A @ X3 @ Xs ) ) )
% 2.65/1.57 | ? [Ys4: list @ A] :
% 2.65/1.57 ( ( Ys2
% 2.65/1.57 = ( cons @ A @ X3 @ Ys4 ) )
% 2.65/1.57 & ( ( append @ A @ Ys4 @ Zs2 )
% 2.65/1.57 = Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_137_Cons__eq__append__conv,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A,Ys2: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ( cons @ A @ X3 @ Xs )
% 2.65/1.57 = ( append @ A @ Ys2 @ Zs2 ) )
% 2.65/1.57 = ( ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( ( cons @ A @ X3 @ Xs )
% 2.65/1.57 = Zs2 ) )
% 2.65/1.57 | ? [Ys4: list @ A] :
% 2.65/1.57 ( ( ( cons @ A @ X3 @ Ys4 )
% 2.65/1.57 = Ys2 )
% 2.65/1.57 & ( Xs
% 2.65/1.57 = ( append @ A @ Ys4 @ Zs2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_138_rev__exhaust,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ~ ! [Ys3: list @ A,Y4: A] :
% 2.65/1.57 ( Xs
% 2.65/1.57 != ( append @ A @ Ys3 @ ( cons @ A @ Y4 @ ( nil @ A ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_139_rev__induct,axiom,
% 2.65/1.57 ! [A: $tType,P: ( list @ A ) > $o,Xs: list @ A] :
% 2.65/1.57 ( ( P @ ( nil @ A ) )
% 2.65/1.57 => ( ! [X: A,Xs2: list @ A] :
% 2.65/1.57 ( ( P @ Xs2 )
% 2.65/1.57 => ( P @ ( append @ A @ Xs2 @ ( cons @ A @ X @ ( nil @ A ) ) ) ) )
% 2.65/1.57 => ( P @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_140_maps__simps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,F3: B > ( list @ A ),X3: B,Xs: list @ B] :
% 2.65/1.57 ( ( maps @ B @ A @ F3 @ ( cons @ B @ X3 @ Xs ) )
% 2.65/1.57 = ( append @ A @ ( F3 @ X3 ) @ ( maps @ B @ A @ F3 @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_141_ExtSign,axiom,
% 2.65/1.57 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list @ secrecy_Expression] :
% 2.65/1.57 ( ( encrDecrKeys @ K12 @ K22 )
% 2.65/1.57 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 2.65/1.57 = E3 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_142_DecrEnc,axiom,
% 2.65/1.57 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list @ secrecy_Expression] :
% 2.65/1.57 ( ( encrDecrKeys @ K12 @ K22 )
% 2.65/1.57 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 2.65/1.57 = E3 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_143_concat__eq__append__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ( concat @ A @ Xss2 )
% 2.65/1.57 = ( append @ A @ Ys2 @ Zs2 ) )
% 2.65/1.57 = ( ( ( Xss2
% 2.65/1.57 = ( nil @ ( list @ A ) ) )
% 2.65/1.57 => ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( Zs2
% 2.65/1.57 = ( nil @ A ) ) ) )
% 2.65/1.57 & ( ( Xss2
% 2.65/1.57 != ( nil @ ( list @ A ) ) )
% 2.65/1.57 => ? [Xss1: list @ ( list @ A ),Xs3: list @ A,Xs4: list @ A,Xss22: list @ ( list @ A )] :
% 2.65/1.57 ( ( Xss2
% 2.65/1.57 = ( append @ ( list @ A ) @ Xss1 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( append @ A @ ( concat @ A @ Xss1 ) @ Xs3 ) )
% 2.65/1.57 & ( Zs2
% 2.65/1.57 = ( append @ A @ Xs4 @ ( concat @ A @ Xss22 ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_144_rotate1_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( rotate1 @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_145_rotate1__is__Nil__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( rotate1 @ A @ Xs )
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_146_concat__append,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ ( list @ A ),Ys2: list @ ( list @ A )] :
% 2.65/1.57 ( ( concat @ A @ ( append @ ( list @ A ) @ Xs @ Ys2 ) )
% 2.65/1.57 = ( append @ A @ ( concat @ A @ Xs ) @ ( concat @ A @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_147_rotate1_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( rotate1 @ A @ ( nil @ A ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_148_concat_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( concat @ A @ ( nil @ ( list @ A ) ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_149_concat_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: list @ A,Xs: list @ ( list @ A )] :
% 2.65/1.57 ( ( concat @ A @ ( cons @ ( list @ A ) @ X3 @ Xs ) )
% 2.65/1.57 = ( append @ A @ X3 @ ( concat @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_150_maps__simps_I2_J,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,F3: B > ( list @ A )] :
% 2.65/1.57 ( ( maps @ B @ A @ F3 @ ( nil @ B ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_151_concat__eq__appendD,axiom,
% 2.65/1.57 ! [A: $tType,Xss2: list @ ( list @ A ),Ys2: list @ A,Zs2: list @ A] :
% 2.65/1.57 ( ( ( concat @ A @ Xss2 )
% 2.65/1.57 = ( append @ A @ Ys2 @ Zs2 ) )
% 2.65/1.57 => ( ( Xss2
% 2.65/1.57 != ( nil @ ( list @ A ) ) )
% 2.65/1.57 => ? [Xss12: list @ ( list @ A ),Xs2: list @ A,Xs5: list @ A,Xss23: list @ ( list @ A )] :
% 2.65/1.57 ( ( Xss2
% 2.65/1.57 = ( append @ ( list @ A ) @ Xss12 @ ( cons @ ( list @ A ) @ ( append @ A @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( append @ A @ ( concat @ A @ Xss12 ) @ Xs2 ) )
% 2.65/1.57 & ( Zs2
% 2.65/1.57 = ( append @ A @ Xs5 @ ( concat @ A @ Xss23 ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_152_butlast__snoc,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( butlast @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 2.65/1.57 = Xs ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_153_last__snoc,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( last @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) )
% 2.65/1.57 = X3 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_154_notSpecKeysSecretsExpr__def,axiom,
% 2.65/1.57 ( notSpe1586871396tsExpr
% 2.65/1.57 = ( ^ [P3: secrecy_specID,E2: list @ secrecy_Expression] :
% 2.65/1.57 ( ! [X4: secrecy_Keys] :
% 2.65/1.57 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X4 ) @ E2 )
% 2.65/1.57 => ~ ( member2 @ secrecy_KS @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 2.65/1.57 & ! [Y3: secrecy_Secrets] :
% 2.65/1.57 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y3 ) @ E2 )
% 2.65/1.57 => ~ ( member2 @ secrecy_KS @ ( secrecy_sKS @ Y3 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_155_last__appendR,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.65/1.57 ( ( Ys2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( last @ A @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_156_last__appendL,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.65/1.57 ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_157_append__butlast__last__id,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( append @ A @ ( butlast @ A @ Xs ) @ ( cons @ A @ ( last @ A @ Xs ) @ ( nil @ A ) ) )
% 2.65/1.57 = Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_158_butlast_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( butlast @ A @ ( nil @ A ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_159_snoc__eq__iff__butlast,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.65/1.57 = Ys2 )
% 2.65/1.57 = ( ( Ys2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 & ( ( butlast @ A @ Ys2 )
% 2.65/1.57 = Xs )
% 2.65/1.57 & ( ( last @ A @ Ys2 )
% 2.65/1.57 = X3 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_160_last__ConsR,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_161_last__ConsL,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = X3 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_162_last_Osimps,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = X3 ) )
% 2.65/1.57 & ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_163_longest__common__suffix,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ? [Ss: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 = ( append @ A @ Xs5 @ Ss ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( append @ A @ Ys5 @ Ss ) )
% 2.65/1.57 & ( ( Xs5
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( Ys5
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( last @ A @ Xs5 )
% 2.65/1.57 != ( last @ A @ Ys5 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_164_last__append,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.65/1.57 ( ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) )
% 2.65/1.57 & ( ( Ys2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( last @ A @ Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_165_butlast_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( nil @ A ) ) )
% 2.65/1.57 & ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( butlast @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( cons @ A @ X3 @ ( butlast @ A @ Xs ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_166_butlast__append,axiom,
% 2.65/1.57 ! [A: $tType,Ys2: list @ A,Xs: list @ A] :
% 2.65/1.57 ( ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( butlast @ A @ Xs ) ) )
% 2.65/1.57 & ( ( Ys2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( butlast @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( append @ A @ Xs @ ( butlast @ A @ Ys2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_167_mem_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A] :
% 2.65/1.57 ~ ( mem @ A @ X3 @ ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_168_mem_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Y: A,L: list @ A] :
% 2.65/1.57 ( ( mem @ A @ X3 @ ( cons @ A @ Y @ L ) )
% 2.65/1.57 = ( ( X3 = Y )
% 2.65/1.57 | ( mem @ A @ X3 @ L ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_169_concat__conv__foldr,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( concat @ A )
% 2.65/1.57 = ( ^ [Xss3: list @ ( list @ A )] : ( foldr @ ( list @ A ) @ ( list @ A ) @ ( append @ A ) @ Xss3 @ ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_170_foldr__append,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,F3: B > A > A,Xs: list @ B,Ys2: list @ B,A4: A] :
% 2.65/1.57 ( ( foldr @ B @ A @ F3 @ ( append @ B @ Xs @ Ys2 ) @ A4 )
% 2.65/1.57 = ( foldr @ B @ A @ F3 @ Xs @ ( foldr @ B @ A @ F3 @ Ys2 @ A4 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_171_SuccI,axiom,
% 2.65/1.57 ! [A: $tType,Kl: list @ A,K: A,Kl2: set @ ( list @ A )] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ ( append @ A @ Kl @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl2 )
% 2.65/1.57 => ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl2 @ Kl ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_172_SuccD,axiom,
% 2.65/1.57 ! [A: $tType,K: A,Kl2: set @ ( list @ A ),Kl: list @ A] :
% 2.65/1.57 ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl2 @ Kl ) )
% 2.65/1.57 => ( member2 @ ( list @ A ) @ ( append @ A @ Kl @ ( cons @ A @ K @ ( nil @ A ) ) ) @ Kl2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_173_rev__eq__Cons__iff,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Y: A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( rev @ A @ Xs )
% 2.65/1.57 = ( cons @ A @ Y @ Ys2 ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_174_rev__rev__ident,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( rev @ A @ ( rev @ A @ Xs ) )
% 2.65/1.57 = Xs ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_175_rev__is__rev__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( rev @ A @ Xs )
% 2.65/1.57 = ( rev @ A @ Ys2 ) )
% 2.65/1.57 = ( Xs = Ys2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_176_Nil__is__rev__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( nil @ A )
% 2.65/1.57 = ( rev @ A @ Xs ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_177_rev__is__Nil__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( rev @ A @ Xs )
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_178_rev__append,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( rev @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( append @ A @ ( rev @ A @ Ys2 ) @ ( rev @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_179_singleton__rev__conv,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( ( cons @ A @ X3 @ ( nil @ A ) )
% 2.65/1.57 = ( rev @ A @ Xs ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_180_rev__singleton__conv,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A] :
% 2.65/1.57 ( ( ( rev @ A @ Xs )
% 2.65/1.57 = ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_181_rev__swap,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( rev @ A @ Xs )
% 2.65/1.57 = Ys2 )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( rev @ A @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_182_rev_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( rev @ A @ ( nil @ A ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_183_rev_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( rev @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( append @ A @ ( rev @ A @ Xs ) @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_184_map__tailrec__def,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType] :
% 2.65/1.57 ( ( map_tailrec @ A @ B )
% 2.65/1.57 = ( ^ [F4: A > B,As3: list @ A] : ( rev @ B @ ( map_tailrec_rev @ A @ B @ F4 @ As3 @ ( nil @ B ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_185_shift__def,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType] :
% 2.65/1.57 ( ( bNF_Greatest_shift @ A @ B )
% 2.65/1.57 = ( ^ [Lab: ( list @ A ) > B,K4: A,Kl3: list @ A] : ( Lab @ ( cons @ A @ K4 @ Kl3 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_186_empty__Shift,axiom,
% 2.65/1.57 ! [A: $tType,Kl2: set @ ( list @ A ),K: A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ Kl2 )
% 2.65/1.57 => ( ( member2 @ A @ K @ ( bNF_Greatest_Succ @ A @ Kl2 @ ( nil @ A ) ) )
% 2.65/1.57 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( bNF_Greatest_Shift @ A @ Kl2 @ K ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_187_ShiftD,axiom,
% 2.65/1.57 ! [A: $tType,Kl: list @ A,Kl2: set @ ( list @ A ),K: A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ Kl @ ( bNF_Greatest_Shift @ A @ Kl2 @ K ) )
% 2.65/1.57 => ( member2 @ ( list @ A ) @ ( cons @ A @ K @ Kl ) @ Kl2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_188_Succ__Shift,axiom,
% 2.65/1.57 ! [A: $tType,Kl2: set @ ( list @ A ),K: A,Kl: list @ A] :
% 2.65/1.57 ( ( bNF_Greatest_Succ @ A @ ( bNF_Greatest_Shift @ A @ Kl2 @ K ) @ Kl )
% 2.65/1.57 = ( bNF_Greatest_Succ @ A @ Kl2 @ ( cons @ A @ K @ Kl ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_189_last__rev,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( last @ A @ ( rev @ A @ Xs ) )
% 2.65/1.57 = ( hd @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_190_hd__rev,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( hd @ A @ ( rev @ A @ Xs ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_191_hd__append2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( hd @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_192_hd__append,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( hd @ A @ Ys2 ) ) )
% 2.65/1.57 & ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( hd @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( hd @ A @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_193_longest__common__prefix,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ? [Ps: list @ A,Xs5: list @ A,Ys5: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 = ( append @ A @ Ps @ Xs5 ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( append @ A @ Ps @ Ys5 ) )
% 2.65/1.57 & ( ( Xs5
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( Ys5
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( hd @ A @ Xs5 )
% 2.65/1.57 != ( hd @ A @ Ys5 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_194_hd__concat,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ ( list @ A )] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ ( list @ A ) ) )
% 2.65/1.57 => ( ( ( hd @ ( list @ A ) @ Xs )
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( hd @ A @ ( concat @ A @ Xs ) )
% 2.65/1.57 = ( hd @ A @ ( hd @ ( list @ A ) @ Xs ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_195_list_Osel_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,X21: A,X222: list @ A] :
% 2.65/1.57 ( ( hd @ A @ ( cons @ A @ X21 @ X222 ) )
% 2.65/1.57 = X21 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_196_rotate1__hd__tl,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( rotate1 @ A @ Xs )
% 2.65/1.57 = ( append @ A @ ( tl @ A @ Xs ) @ ( cons @ A @ ( hd @ A @ Xs ) @ ( nil @ A ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_197_distinct__adj__append__iff,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( ( distinct_adj @ A @ Xs )
% 2.65/1.57 & ( distinct_adj @ A @ Ys2 )
% 2.65/1.57 & ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( last @ A @ Xs )
% 2.65/1.57 != ( hd @ A @ Ys2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_198_distinct__adj__Cons__Cons,axiom,
% 2.65/1.57 ! [B: $tType,X3: B,Y: B,Xs: list @ B] :
% 2.65/1.57 ( ( distinct_adj @ B @ ( cons @ B @ X3 @ ( cons @ B @ Y @ Xs ) ) )
% 2.65/1.57 = ( ( X3 != Y )
% 2.65/1.57 & ( distinct_adj @ B @ ( cons @ B @ Y @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_199_distinct__adj__rev,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( distinct_adj @ A @ ( rev @ A @ Xs ) )
% 2.65/1.57 = ( distinct_adj @ A @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_200_tl__append2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( tl @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( append @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_201_butlast__rev,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( butlast @ A @ ( rev @ A @ Xs ) )
% 2.65/1.57 = ( rev @ A @ ( tl @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_202_list_Ocollapse,axiom,
% 2.65/1.57 ! [A: $tType,List: list @ A] :
% 2.65/1.57 ( ( List
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) )
% 2.65/1.57 = List ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_203_hd__Cons__tl,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( cons @ A @ ( hd @ A @ Xs ) @ ( tl @ A @ Xs ) )
% 2.65/1.57 = Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_204_list_Oexpand,axiom,
% 2.65/1.57 ! [A: $tType,List: list @ A,List2: list @ A] :
% 2.65/1.57 ( ( ( List
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( List2
% 2.65/1.57 = ( nil @ A ) ) )
% 2.65/1.57 => ( ( ( List
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( List2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ( ( hd @ A @ List )
% 2.65/1.57 = ( hd @ A @ List2 ) )
% 2.65/1.57 & ( ( tl @ A @ List )
% 2.65/1.57 = ( tl @ A @ List2 ) ) ) ) )
% 2.65/1.57 => ( List = List2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_205_butlast__tl,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( butlast @ A @ ( tl @ A @ Xs ) )
% 2.65/1.57 = ( tl @ A @ ( butlast @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_206_distinct__adj__appendD1,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 => ( distinct_adj @ A @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_207_distinct__adj__appendD2,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( distinct_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 => ( distinct_adj @ A @ Ys2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_208_distinct__adj__Nil,axiom,
% 2.65/1.57 ! [A: $tType] : ( distinct_adj @ A @ ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_209_distinct__adj__ConsD,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 => ( distinct_adj @ A @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_210_list_Osel_I2_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( tl @ A @ ( nil @ A ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_211_list_Osel_I3_J,axiom,
% 2.65/1.57 ! [A: $tType,X21: A,X222: list @ A] :
% 2.65/1.57 ( ( tl @ A @ ( cons @ A @ X21 @ X222 ) )
% 2.65/1.57 = X222 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_212_tl__Nil,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( tl @ A @ Xs )
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ? [X4: A] :
% 2.65/1.57 ( Xs
% 2.65/1.57 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_213_Nil__tl,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( nil @ A )
% 2.65/1.57 = ( tl @ A @ Xs ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ? [X4: A] :
% 2.65/1.57 ( Xs
% 2.65/1.57 = ( cons @ A @ X4 @ ( nil @ A ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_214_last__tl,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( tl @ A @ Xs )
% 2.65/1.57 != ( nil @ A ) ) )
% 2.65/1.57 => ( ( last @ A @ ( tl @ A @ Xs ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_215_distinct__adj__singleton,axiom,
% 2.65/1.57 ! [B: $tType,X3: B] : ( distinct_adj @ B @ ( cons @ B @ X3 @ ( nil @ B ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_216_list_Oexhaust__sel,axiom,
% 2.65/1.57 ! [A: $tType,List: list @ A] :
% 2.65/1.57 ( ( List
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( List
% 2.65/1.57 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_217_distinct__adj__Cons,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( distinct_adj @ A @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( X3
% 2.65/1.57 != ( hd @ A @ Xs ) )
% 2.65/1.57 & ( distinct_adj @ A @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_218_list_Osplit__sel__asm,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 2.65/1.57 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 2.65/1.57 = ( ~ ( ( ( List
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ~ ( P @ F1 ) )
% 2.65/1.57 | ( ( List
% 2.65/1.57 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 2.65/1.57 & ~ ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_219_list_Osplit__sel,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,P: B > $o,F1: B,F2: A > ( list @ A ) > B,List: list @ A] :
% 2.65/1.57 ( ( P @ ( case_list @ B @ A @ F1 @ F2 @ List ) )
% 2.65/1.57 = ( ( ( List
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( P @ F1 ) )
% 2.65/1.57 & ( ( List
% 2.65/1.57 = ( cons @ A @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) )
% 2.65/1.57 => ( P @ ( F2 @ ( hd @ A @ List ) @ ( tl @ A @ List ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_220_list_Osimps_I4_J,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType,F1: B,F2: A > ( list @ A ) > B] :
% 2.65/1.57 ( ( case_list @ B @ A @ F1 @ F2 @ ( nil @ A ) )
% 2.65/1.57 = F1 ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_221_list_Osimps_I5_J,axiom,
% 2.65/1.57 ! [B: $tType,A: $tType,F1: B,F2: A > ( list @ A ) > B,X21: A,X222: list @ A] :
% 2.65/1.57 ( ( case_list @ B @ A @ F1 @ F2 @ ( cons @ A @ X21 @ X222 ) )
% 2.65/1.57 = ( F2 @ X21 @ X222 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_222_list_Ocase__eq__if,axiom,
% 2.65/1.57 ! [A: $tType,B: $tType] :
% 2.65/1.57 ( ( case_list @ B @ A )
% 2.65/1.57 = ( ^ [F12: B,F22: A > ( list @ A ) > B,List3: list @ A] :
% 2.65/1.57 ( if @ B
% 2.65/1.57 @ ( List3
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 @ F12
% 2.65/1.57 @ ( F22 @ ( hd @ A @ List3 ) @ ( tl @ A @ List3 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_223_successively__append__iff,axiom,
% 2.65/1.57 ! [A: $tType,P: A > A > $o,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( successively @ A @ P @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( ( successively @ A @ P @ Xs )
% 2.65/1.57 & ( successively @ A @ P @ Ys2 )
% 2.65/1.57 & ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( P @ ( last @ A @ Xs ) @ ( hd @ A @ Ys2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_224_Cons__in__shuffles__iff,axiom,
% 2.65/1.57 ! [A: $tType,Z: A,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( ( ( Xs
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 & ( ( hd @ A @ Xs )
% 2.65/1.57 = Z )
% 2.65/1.57 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ ( tl @ A @ Xs ) @ Ys2 ) ) )
% 2.65/1.57 | ( ( Ys2
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 & ( ( hd @ A @ Ys2 )
% 2.65/1.57 = Z )
% 2.65/1.57 & ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ ( tl @ A @ Ys2 ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_225_Nil__in__shuffles,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( shuffles @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 & ( Ys2
% 2.65/1.57 = ( nil @ A ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_226_splice__in__shuffles,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] : ( member2 @ ( list @ A ) @ ( splice @ A @ Xs @ Ys2 ) @ ( shuffles @ A @ Xs @ Ys2 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_227_shufflesE,axiom,
% 2.65/1.57 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 2.65/1.57 => ( ( ( Zs2 = Xs )
% 2.65/1.57 => ( Ys2
% 2.65/1.57 != ( nil @ A ) ) )
% 2.65/1.57 => ( ( ( Zs2 = Ys2 )
% 2.65/1.57 => ( Xs
% 2.65/1.57 != ( nil @ A ) ) )
% 2.65/1.57 => ( ! [X: A,Xs5: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 = ( cons @ A @ X @ Xs5 ) )
% 2.65/1.57 => ! [Z2: A,Zs3: list @ A] :
% 2.65/1.57 ( ( Zs2
% 2.65/1.57 = ( cons @ A @ Z2 @ Zs3 ) )
% 2.65/1.57 => ( ( X = Z2 )
% 2.65/1.57 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs5 @ Ys2 ) ) ) ) )
% 2.65/1.57 => ~ ! [Y4: A,Ys5: list @ A] :
% 2.65/1.57 ( ( Ys2
% 2.65/1.57 = ( cons @ A @ Y4 @ Ys5 ) )
% 2.65/1.57 => ! [Z2: A,Zs3: list @ A] :
% 2.65/1.57 ( ( Zs2
% 2.65/1.57 = ( cons @ A @ Z2 @ Zs3 ) )
% 2.65/1.57 => ( ( Y4 = Z2 )
% 2.65/1.57 => ~ ( member2 @ ( list @ A ) @ Zs3 @ ( shuffles @ A @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_228_successively_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,P: A > A > $o,X3: A] : ( successively @ A @ P @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_229_successively_Oelims_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A > A > $o,Xa: list @ A,Y: $o] :
% 2.65/1.57 ( ( ( successively @ A @ X3 @ Xa )
% 2.65/1.57 = Y )
% 2.65/1.57 => ( ( ( Xa
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ~ Y )
% 2.65/1.57 => ( ( ? [X: A] :
% 2.65/1.57 ( Xa
% 2.65/1.57 = ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.57 => ~ Y )
% 2.65/1.57 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.57 ( ( Xa
% 2.65/1.57 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.65/1.57 => ( Y
% 2.65/1.57 = ( ~ ( ( X3 @ X @ Y4 )
% 2.65/1.57 & ( successively @ A @ X3 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_230_successively_Oelims_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A > A > $o,Xa: list @ A] :
% 2.65/1.57 ( ( successively @ A @ X3 @ Xa )
% 2.65/1.57 => ( ( Xa
% 2.65/1.57 != ( nil @ A ) )
% 2.65/1.57 => ( ! [X: A] :
% 2.65/1.57 ( Xa
% 2.65/1.57 != ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.57 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.57 ( ( Xa
% 2.65/1.57 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.65/1.57 => ~ ( ( X3 @ X @ Y4 )
% 2.65/1.57 & ( successively @ A @ X3 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_231_shuffles__commutes,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( shuffles @ A )
% 2.65/1.57 = ( ^ [Xs3: list @ A,Ys: list @ A] : ( shuffles @ A @ Ys @ Xs3 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_232_successively_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType,P: A > A > $o] : ( successively @ A @ P @ ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_233_successively_Osimps_I3_J,axiom,
% 2.65/1.57 ! [A: $tType,P: A > A > $o,X3: A,Y: A,Xs: list @ A] :
% 2.65/1.57 ( ( successively @ A @ P @ ( cons @ A @ X3 @ ( cons @ A @ Y @ Xs ) ) )
% 2.65/1.57 = ( ( P @ X3 @ Y )
% 2.65/1.57 & ( successively @ A @ P @ ( cons @ A @ Y @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_234_successively_Oelims_I3_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A > A > $o,Xa: list @ A] :
% 2.65/1.57 ( ~ ( successively @ A @ X3 @ Xa )
% 2.65/1.57 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.57 ( ( Xa
% 2.65/1.57 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.65/1.57 => ( ( X3 @ X @ Y4 )
% 2.65/1.57 & ( successively @ A @ X3 @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_235_Nil__in__shufflesI,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( member2 @ ( list @ A ) @ ( nil @ A ) @ ( shuffles @ A @ Xs @ Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_236_Cons__in__shuffles__rightI,axiom,
% 2.65/1.57 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A,Z: A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 2.65/1.57 => ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ Xs @ ( cons @ A @ Z @ Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_237_Cons__in__shuffles__leftI,axiom,
% 2.65/1.57 ! [A: $tType,Zs2: list @ A,Xs: list @ A,Ys2: list @ A,Z: A] :
% 2.65/1.57 ( ( member2 @ ( list @ A ) @ Zs2 @ ( shuffles @ A @ Xs @ Ys2 ) )
% 2.65/1.57 => ( member2 @ ( list @ A ) @ ( cons @ A @ Z @ Zs2 ) @ ( shuffles @ A @ ( cons @ A @ Z @ Xs ) @ Ys2 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_238_successively__Cons,axiom,
% 2.65/1.57 ! [A: $tType,P: A > A > $o,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( successively @ A @ P @ ( cons @ A @ X3 @ Xs ) )
% 2.65/1.57 = ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( P @ X3 @ ( hd @ A @ Xs ) )
% 2.65/1.57 & ( successively @ A @ P @ Xs ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_239_remdups__adj__append_H,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,Ys2: list @ A] :
% 2.65/1.57 ( ( ( Xs
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( Ys2
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 | ( ( last @ A @ Xs )
% 2.65/1.57 != ( hd @ A @ Ys2 ) ) )
% 2.65/1.57 => ( ( remdups_adj @ A @ ( append @ A @ Xs @ Ys2 ) )
% 2.65/1.57 = ( append @ A @ ( remdups_adj @ A @ Xs ) @ ( remdups_adj @ A @ Ys2 ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_240_remdups__adj__append,axiom,
% 2.65/1.57 ! [A: $tType,Xs_1: list @ A,X3: A,Xs_2: list @ A] :
% 2.65/1.57 ( ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X3 @ Xs_2 ) ) )
% 2.65/1.57 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs_1 @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs_2 ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_241_remdups__adj__Nil__iff,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( ( remdups_adj @ A @ Xs )
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 = ( Xs
% 2.65/1.57 = ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_242_remdups__adj__rev,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( remdups_adj @ A @ ( rev @ A @ Xs ) )
% 2.65/1.57 = ( rev @ A @ ( remdups_adj @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_243_hd__remdups__adj,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( hd @ A @ ( remdups_adj @ A @ Xs ) )
% 2.65/1.57 = ( hd @ A @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_244_last__remdups__adj,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] :
% 2.65/1.57 ( ( last @ A @ ( remdups_adj @ A @ Xs ) )
% 2.65/1.57 = ( last @ A @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_245_remdups__adj__Cons__alt,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Xs: list @ A] :
% 2.65/1.57 ( ( cons @ A @ X3 @ ( tl @ A @ ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs ) ) ) )
% 2.65/1.57 = ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_246_successively__remdups__adjI,axiom,
% 2.65/1.57 ! [A: $tType,P: A > A > $o,Xs: list @ A] :
% 2.65/1.57 ( ( successively @ A @ P @ Xs )
% 2.65/1.57 => ( successively @ A @ P @ ( remdups_adj @ A @ Xs ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_247_distinct__adj__remdups__adj,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A] : ( distinct_adj @ A @ ( remdups_adj @ A @ Xs ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_248_distinct__adj__altdef,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( distinct_adj @ A )
% 2.65/1.57 = ( ^ [Xs3: list @ A] :
% 2.65/1.57 ( ( remdups_adj @ A @ Xs3 )
% 2.65/1.57 = Xs3 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_249_remdups__adj_Osimps_I2_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A] :
% 2.65/1.57 ( ( remdups_adj @ A @ ( cons @ A @ X3 @ ( nil @ A ) ) )
% 2.65/1.57 = ( cons @ A @ X3 @ ( nil @ A ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_250_remdups__adj_Oelims,axiom,
% 2.65/1.57 ! [A: $tType,X3: list @ A,Y: list @ A] :
% 2.65/1.57 ( ( ( remdups_adj @ A @ X3 )
% 2.65/1.57 = Y )
% 2.65/1.57 => ( ( ( X3
% 2.65/1.57 = ( nil @ A ) )
% 2.65/1.57 => ( Y
% 2.65/1.57 != ( nil @ A ) ) )
% 2.65/1.57 => ( ! [X: A] :
% 2.65/1.57 ( ( X3
% 2.65/1.57 = ( cons @ A @ X @ ( nil @ A ) ) )
% 2.65/1.57 => ( Y
% 2.65/1.57 != ( cons @ A @ X @ ( nil @ A ) ) ) )
% 2.65/1.57 => ~ ! [X: A,Y4: A,Xs2: list @ A] :
% 2.65/1.57 ( ( X3
% 2.65/1.57 = ( cons @ A @ X @ ( cons @ A @ Y4 @ Xs2 ) ) )
% 2.65/1.57 => ~ ( ( ( X = Y4 )
% 2.65/1.57 => ( Y
% 2.65/1.57 = ( remdups_adj @ A @ ( cons @ A @ X @ Xs2 ) ) ) )
% 2.65/1.57 & ( ( X != Y4 )
% 2.65/1.57 => ( Y
% 2.65/1.57 = ( cons @ A @ X @ ( remdups_adj @ A @ ( cons @ A @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_251_remdups__adj_Osimps_I3_J,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Y: A,Xs: list @ A] :
% 2.65/1.57 ( ( ( X3 = Y )
% 2.65/1.57 => ( ( remdups_adj @ A @ ( cons @ A @ X3 @ ( cons @ A @ Y @ Xs ) ) )
% 2.65/1.57 = ( remdups_adj @ A @ ( cons @ A @ X3 @ Xs ) ) ) )
% 2.65/1.57 & ( ( X3 != Y )
% 2.65/1.57 => ( ( remdups_adj @ A @ ( cons @ A @ X3 @ ( cons @ A @ Y @ Xs ) ) )
% 2.65/1.57 = ( cons @ A @ X3 @ ( remdups_adj @ A @ ( cons @ A @ Y @ Xs ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_252_remdups__adj_Osimps_I1_J,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( remdups_adj @ A @ ( nil @ A ) )
% 2.65/1.57 = ( nil @ A ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_253_remdups__adj__append__two,axiom,
% 2.65/1.57 ! [A: $tType,Xs: list @ A,X3: A,Y: A] :
% 2.65/1.57 ( ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) )
% 2.65/1.57 = ( append @ A @ ( remdups_adj @ A @ ( append @ A @ Xs @ ( cons @ A @ X3 @ ( nil @ A ) ) ) ) @ ( if @ ( list @ A ) @ ( X3 = Y ) @ ( nil @ A ) @ ( cons @ A @ Y @ ( nil @ A ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(fact_254_lexordp__eq_Oinducts,axiom,
% 2.65/1.57 ! [A: $tType] :
% 2.65/1.57 ( ( ord @ A )
% 2.65/1.57 => ! [X1: list @ A,X2: list @ A,P: ( list @ A ) > ( list @ A ) > $o] :
% 2.65/1.57 ( ( ord_lexordp_eq @ A @ X1 @ X2 )
% 2.65/1.57 => ( ! [X_1: list @ A] : ( P @ ( nil @ A ) @ X_1 )
% 2.65/1.57 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.65/1.57 ( ( ord_less @ A @ X @ Y4 )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) )
% 2.65/1.57 => ( ! [X: A,Y4: A,Xs2: list @ A,Ys3: list @ A] :
% 2.65/1.57 ( ~ ( ord_less @ A @ X @ Y4 )
% 2.65/1.57 => ( ~ ( ord_less @ A @ Y4 @ X )
% 2.65/1.57 => ( ( ord_lexordp_eq @ A @ Xs2 @ Ys3 )
% 2.65/1.57 => ( ( P @ Xs2 @ Ys3 )
% 2.65/1.57 => ( P @ ( cons @ A @ X @ Xs2 ) @ ( cons @ A @ Y4 @ Ys3 ) ) ) ) ) )
% 2.65/1.57 => ( P @ X1 @ X2 ) ) ) ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(tcon_fun___Orderings_Oord,axiom,
% 2.65/1.57 ! [A5: $tType,A6: $tType] :
% 2.65/1.57 ( ( ord @ A6 )
% 2.65/1.57 => ( ord @ ( A5 > A6 ) ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(tcon_Set_Oset___Orderings_Oord_1,axiom,
% 2.65/1.57 ! [A5: $tType] : ( ord @ ( set @ A5 ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(tcon_HOL_Obool___Orderings_Olinorder,axiom,
% 2.65/1.57 linorder @ $o ).
% 2.65/1.57
% 2.65/1.57 thf(tcon_HOL_Obool___Orderings_Oord_2,axiom,
% 2.65/1.57 ord @ $o ).
% 2.65/1.57
% 2.65/1.57 thf(help_If_3_1_T,axiom,
% 2.65/1.57 ! [P: $o] :
% 2.65/1.57 ( ( P = $true )
% 2.65/1.57 | ( P = $false ) ) ).
% 2.65/1.57
% 2.65/1.57 thf(help_If_2_1_T,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Y: A] :
% 2.65/1.57 ( ( if @ A @ $false @ X3 @ Y )
% 2.65/1.57 = Y ) ).
% 2.65/1.57
% 2.65/1.57 thf(help_If_1_1_T,axiom,
% 2.65/1.57 ! [A: $tType,X3: A,Y: A] :
% 2.65/1.57 ( ( if @ A @ $true @ X3 @ Y )
% 2.65/1.57 = X3 ) ).
% 2.65/1.57
% 2.65/1.57 thf(conj_0,conjecture,
% 2.65/1.57 knowle1437066798e_know @ a @ ( secrecy_sKS @ m ) ).
% 2.65/1.57 ------------------------
% 2.65/1.59 % (22903)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/2Mi)
% 2.65/1.59 % (22903)Instruction limit reached!
% 2.65/1.59 % (22903)------------------------------
% 2.65/1.59 % (22903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.59 % (22903)Termination reason: Unknown
% 2.65/1.59 % (22903)Termination phase: shuffling
% 2.65/1.59
% 2.65/1.59 % (22903)Memory used [KB]: 1279
% 2.65/1.59 % (22903)Time elapsed: 0.002 s
% 2.65/1.59 % (22903)Instructions burned: 2 (million)
% 2.65/1.59 % (22903)------------------------------
% 2.65/1.59 % (22903)------------------------------
% 2.65/1.59 % (22904)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_22724 for (2999ds/2Mi)
% 2.65/1.59 % (22901)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_22724 for (2999ds/4Mi)
% 2.65/1.60 % (22902)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_22724 for (2999ds/27Mi)
% 2.65/1.60 % (22904)Instruction limit reached!
% 2.65/1.60 % (22904)------------------------------
% 2.65/1.60 % (22904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.65/1.60 % (22900)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/183Mi)
% 2.65/1.60 % (22904)Termination reason: Unknown
% 2.65/1.60 % (22904)Termination phase: shuffling
% 2.65/1.60
% 2.65/1.60 % (22904)Memory used [KB]: 1407
% 2.65/1.60 % (22904)Time elapsed: 0.003 s
% 2.65/1.60 % (22904)Instructions burned: 4 (million)
% 2.65/1.60 % (22904)------------------------------
% 2.65/1.60 % (22904)------------------------------
% 2.65/1.60 % (22905)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_22724 for (2999ds/275Mi)
% 2.73/1.60 % (22901)Instruction limit reached!
% 2.73/1.60 % (22901)------------------------------
% 2.73/1.60 % (22901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.60 % (22901)Termination reason: Unknown
% 2.73/1.60 % (22901)Termination phase: shuffling
% 2.73/1.60
% 2.73/1.60 % (22901)Memory used [KB]: 1407
% 2.73/1.60 % (22901)Time elapsed: 0.004 s
% 2.73/1.60 % (22901)Instructions burned: 5 (million)
% 2.73/1.60 % (22901)------------------------------
% 2.73/1.60 % (22901)------------------------------
% 2.73/1.60 % (22908)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/3Mi)
% 2.73/1.60 % (22908)Instruction limit reached!
% 2.73/1.60 % (22908)------------------------------
% 2.73/1.60 % (22908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.60 % (22908)Termination reason: Unknown
% 2.73/1.60 % (22908)Termination phase: shuffling
% 2.73/1.60
% 2.73/1.60 % (22908)Memory used [KB]: 1407
% 2.73/1.60 % (22908)Time elapsed: 0.003 s
% 2.73/1.60 % (22908)Instructions burned: 5 (million)
% 2.73/1.60 % (22908)------------------------------
% 2.73/1.60 % (22908)------------------------------
% 2.73/1.61 % (22906)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/18Mi)
% 2.73/1.61 % (22902)Instruction limit reached!
% 2.73/1.61 % (22902)------------------------------
% 2.73/1.61 % (22902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.61 % (22902)Termination reason: Unknown
% 2.73/1.61 % (22902)Termination phase: Property scanning
% 2.73/1.61
% 2.73/1.61 % (22902)Memory used [KB]: 1791
% 2.73/1.61 % (22902)Time elapsed: 0.016 s
% 2.73/1.61 % (22902)Instructions burned: 27 (million)
% 2.73/1.61 % (22902)------------------------------
% 2.73/1.61 % (22902)------------------------------
% 2.73/1.61 % (22910)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_22724 for (2999ds/37Mi)
% 2.73/1.61 % (22912)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_22724 for (2999ds/3Mi)
% 2.73/1.61 % (22912)Instruction limit reached!
% 2.73/1.61 % (22912)------------------------------
% 2.73/1.61 % (22912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.61 % (22912)Termination reason: Unknown
% 2.73/1.61 % (22912)Termination phase: shuffling
% 2.73/1.61
% 2.73/1.61 % (22912)Memory used [KB]: 1407
% 2.73/1.61 % (22912)Time elapsed: 0.002 s
% 2.73/1.61 % (22912)Instructions burned: 3 (million)
% 2.73/1.61 % (22912)------------------------------
% 2.73/1.61 % (22912)------------------------------
% 2.73/1.61 % (22911)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_22724 for (2999ds/15Mi)
% 2.73/1.62 % (22911)Instruction limit reached!
% 2.73/1.62 % (22911)------------------------------
% 2.73/1.62 % (22911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.62 % (22911)Termination reason: Unknown
% 2.73/1.62 % (22911)Termination phase: shuffling
% 2.73/1.62
% 2.73/1.62 % (22911)Memory used [KB]: 1663
% 2.73/1.62 % (22911)Time elapsed: 0.009 s
% 2.73/1.62 % (22911)Instructions burned: 15 (million)
% 2.73/1.62 % (22911)------------------------------
% 2.73/1.62 % (22911)------------------------------
% 2.73/1.62 % (22906)Instruction limit reached!
% 2.73/1.62 % (22906)------------------------------
% 2.73/1.62 % (22906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.62 % (22906)Termination reason: Unknown
% 2.73/1.62 % (22906)Termination phase: shuffling
% 2.73/1.62
% 2.73/1.62 % (22906)Memory used [KB]: 1791
% 2.73/1.62 % (22906)Time elapsed: 0.017 s
% 2.73/1.62 % (22906)Instructions burned: 19 (million)
% 2.73/1.62 % (22906)------------------------------
% 2.73/1.62 % (22906)------------------------------
% 2.73/1.62 % (22905)Refutation not found, incomplete strategy
% 2.73/1.62 % (22905)------------------------------
% 2.73/1.62 % (22905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.62 % (22905)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.62
% 2.73/1.62
% 2.73/1.62 % (22905)Memory used [KB]: 6396
% 2.73/1.62 % (22905)Time elapsed: 0.029 s
% 2.73/1.62 % (22905)Instructions burned: 50 (million)
% 2.73/1.62 % (22905)------------------------------
% 2.73/1.62 % (22905)------------------------------
% 2.73/1.62 % (22915)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/7Mi)
% 2.73/1.63 % (22914)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_22724 for (2999ds/1041Mi)
% 2.73/1.63 % (22915)Instruction limit reached!
% 2.73/1.63 % (22915)------------------------------
% 2.73/1.63 % (22915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.63 % (22915)Termination reason: Unknown
% 2.73/1.63 % (22915)Termination phase: shuffling
% 2.73/1.63
% 2.73/1.63 % (22915)Memory used [KB]: 1535
% 2.73/1.63 % (22915)Time elapsed: 0.004 s
% 2.73/1.63 % (22915)Instructions burned: 9 (million)
% 2.73/1.63 % (22915)------------------------------
% 2.73/1.63 % (22915)------------------------------
% 2.73/1.63 % (22910)Instruction limit reached!
% 2.73/1.63 % (22910)------------------------------
% 2.73/1.63 % (22910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.63 % (22910)Termination reason: Unknown
% 2.73/1.63 % (22910)Termination phase: shuffling
% 2.73/1.63
% 2.73/1.63 % (22910)Memory used [KB]: 2174
% 2.73/1.63 % (22910)Time elapsed: 0.019 s
% 2.73/1.63 % (22910)Instructions burned: 38 (million)
% 2.73/1.63 % (22910)------------------------------
% 2.73/1.63 % (22910)------------------------------
% 2.73/1.64 % (22919)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/7Mi)
% 2.73/1.64 % (22916)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/16Mi)
% 2.73/1.64 % (22917)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_22724 for (2999ds/3Mi)
% 2.73/1.64 % (22919)Instruction limit reached!
% 2.73/1.64 % (22919)------------------------------
% 2.73/1.64 % (22919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.64 % (22919)Termination reason: Unknown
% 2.73/1.64 % (22919)Termination phase: shuffling
% 2.73/1.64
% 2.73/1.64 % (22919)Memory used [KB]: 1535
% 2.73/1.64 % (22919)Time elapsed: 0.005 s
% 2.73/1.64 % (22919)Instructions burned: 9 (million)
% 2.73/1.64 % (22919)------------------------------
% 2.73/1.64 % (22919)------------------------------
% 2.73/1.64 % (22918)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_22724 for (2999ds/3Mi)
% 2.73/1.64 % (22917)Instruction limit reached!
% 2.73/1.64 % (22917)------------------------------
% 2.73/1.64 % (22917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.64 % (22917)Termination reason: Unknown
% 2.73/1.64 % (22917)Termination phase: shuffling
% 2.73/1.64
% 2.73/1.64 % (22917)Memory used [KB]: 1407
% 2.73/1.64 % (22917)Time elapsed: 0.004 s
% 2.73/1.64 % (22917)Instructions burned: 4 (million)
% 2.73/1.64 % (22917)------------------------------
% 2.73/1.64 % (22917)------------------------------
% 2.73/1.64 % (22918)Instruction limit reached!
% 2.73/1.64 % (22918)------------------------------
% 2.73/1.64 % (22918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.64 % (22918)Termination reason: Unknown
% 2.73/1.64 % (22918)Termination phase: shuffling
% 2.73/1.64
% 2.73/1.64 % (22918)Memory used [KB]: 1407
% 2.73/1.64 % (22918)Time elapsed: 0.004 s
% 2.73/1.64 % (22918)Instructions burned: 4 (million)
% 2.73/1.64 % (22918)------------------------------
% 2.73/1.64 % (22918)------------------------------
% 2.73/1.65 % (22920)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/3Mi)
% 2.73/1.65 % (22916)Instruction limit reached!
% 2.73/1.65 % (22916)------------------------------
% 2.73/1.65 % (22916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.65 % (22916)Termination reason: Unknown
% 2.73/1.65 % (22916)Termination phase: shuffling
% 2.73/1.65
% 2.73/1.65 % (22916)Memory used [KB]: 1791
% 2.73/1.65 % (22916)Time elapsed: 0.010 s
% 2.73/1.65 % (22916)Instructions burned: 17 (million)
% 2.73/1.65 % (22916)------------------------------
% 2.73/1.65 % (22916)------------------------------
% 2.73/1.65 % (22920)Instruction limit reached!
% 2.73/1.65 % (22920)------------------------------
% 2.73/1.65 % (22920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.65 % (22920)Termination reason: Unknown
% 2.73/1.65 % (22920)Termination phase: shuffling
% 2.73/1.65
% 2.73/1.65 % (22920)Memory used [KB]: 1407
% 2.73/1.65 % (22920)Time elapsed: 0.003 s
% 2.73/1.65 % (22920)Instructions burned: 3 (million)
% 2.73/1.65 % (22920)------------------------------
% 2.73/1.65 % (22920)------------------------------
% 2.73/1.65 % (22921)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/4Mi)
% 2.73/1.65 % (22921)Instruction limit reached!
% 2.73/1.65 % (22921)------------------------------
% 2.73/1.65 % (22921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.65 % (22921)Termination reason: Unknown
% 2.73/1.65 % (22921)Termination phase: shuffling
% 2.73/1.65
% 2.73/1.65 % (22921)Memory used [KB]: 1407
% 2.73/1.65 % (22921)Time elapsed: 0.003 s
% 2.73/1.65 % (22921)Instructions burned: 6 (million)
% 2.73/1.65 % (22921)------------------------------
% 2.73/1.65 % (22921)------------------------------
% 2.73/1.66 % (22922)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/18Mi)
% 2.73/1.66 % (22923)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/710Mi)
% 2.73/1.66 % (22924)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/6Mi)
% 2.73/1.66 % (22925)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_22724 for (2999ds/902Mi)
% 2.73/1.66 % (22926)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_22724 for (2999ds/21Mi)
% 2.73/1.67 % (22924)Instruction limit reached!
% 2.73/1.67 % (22924)------------------------------
% 2.73/1.67 % (22924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.67 % (22924)Termination reason: Unknown
% 2.73/1.67 % (22924)Termination phase: shuffling
% 2.73/1.67
% 2.73/1.67 % (22924)Memory used [KB]: 1407
% 2.73/1.67 % (22924)Time elapsed: 0.005 s
% 2.73/1.67 % (22924)Instructions burned: 8 (million)
% 2.73/1.67 % (22924)------------------------------
% 2.73/1.67 % (22924)------------------------------
% 2.73/1.67 % (22922)Instruction limit reached!
% 2.73/1.67 % (22922)------------------------------
% 2.73/1.67 % (22922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.67 % (22922)Termination reason: Unknown
% 2.73/1.67 % (22922)Termination phase: shuffling
% 2.73/1.67
% 2.73/1.67 % (22922)Memory used [KB]: 1791
% 2.73/1.67 % (22922)Time elapsed: 0.012 s
% 2.73/1.67 % (22922)Instructions burned: 18 (million)
% 2.73/1.67 % (22922)------------------------------
% 2.73/1.67 % (22922)------------------------------
% 2.73/1.67 % (22926)Instruction limit reached!
% 2.73/1.67 % (22926)------------------------------
% 2.73/1.67 % (22926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.67 % (22926)Termination reason: Unknown
% 2.73/1.67 % (22926)Termination phase: shuffling
% 2.73/1.67
% 2.73/1.67 % (22926)Memory used [KB]: 1791
% 2.73/1.67 % (22926)Time elapsed: 0.009 s
% 2.73/1.67 % (22926)Instructions burned: 22 (million)
% 2.73/1.67 % (22926)------------------------------
% 2.73/1.67 % (22926)------------------------------
% 2.73/1.68 % (22931)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/377Mi)
% 2.73/1.68 % (22928)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_22724 for (2999ds/5Mi)
% 2.73/1.68 % (22900)Instruction limit reached!
% 2.73/1.68 % (22900)------------------------------
% 2.73/1.68 % (22900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.68 % (22900)Termination reason: Unknown
% 2.73/1.68 % (22900)Termination phase: Saturation
% 2.73/1.68
% 2.73/1.68 % (22900)Memory used [KB]: 7164
% 2.73/1.68 % (22900)Time elapsed: 0.090 s
% 2.73/1.68 % (22900)Instructions burned: 183 (million)
% 2.73/1.68 % (22900)------------------------------
% 2.73/1.68 % (22900)------------------------------
% 2.73/1.68 % (22928)Instruction limit reached!
% 2.73/1.68 % (22928)------------------------------
% 2.73/1.68 % (22928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.68 % (22928)Termination reason: Unknown
% 2.73/1.68 % (22928)Termination phase: shuffling
% 2.73/1.68
% 2.73/1.68 % (22928)Memory used [KB]: 1407
% 2.73/1.68 % (22928)Time elapsed: 0.004 s
% 2.73/1.68 % (22928)Instructions burned: 6 (million)
% 2.73/1.68 % (22928)------------------------------
% 2.73/1.68 % (22928)------------------------------
% 2.73/1.69 % (22930)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_22724 for (2999ds/6Mi)
% 2.73/1.69 % (22930)Instruction limit reached!
% 2.73/1.69 % (22930)------------------------------
% 2.73/1.69 % (22930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.69 % (22930)Termination reason: Unknown
% 2.73/1.69 % (22930)Termination phase: shuffling
% 2.73/1.69
% 2.73/1.69 % (22930)Memory used [KB]: 1407
% 2.73/1.69 % (22930)Time elapsed: 0.005 s
% 2.73/1.69 % (22930)Instructions burned: 6 (million)
% 2.73/1.69 % (22930)------------------------------
% 2.73/1.69 % (22930)------------------------------
% 2.73/1.69 % (22935)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_22724 for (2998ds/19Mi)
% 2.73/1.70 % (22933)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_22724 for (2998ds/779Mi)
% 2.73/1.70 % (22935)Instruction limit reached!
% 2.73/1.70 % (22935)------------------------------
% 2.73/1.70 % (22935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.70 % (22935)Termination reason: Unknown
% 2.73/1.70 % (22935)Termination phase: shuffling
% 2.73/1.70
% 2.73/1.70 % (22935)Memory used [KB]: 1791
% 2.73/1.70 % (22935)Time elapsed: 0.007 s
% 2.73/1.70 % (22935)Instructions burned: 21 (million)
% 2.73/1.70 % (22935)------------------------------
% 2.73/1.70 % (22935)------------------------------
% 2.73/1.70 % (22937)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_22724 for (2998ds/879Mi)
% 2.73/1.71 % (22940)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_22724 for (2998ds/17Mi)
% 2.73/1.72 % (22940)Instruction limit reached!
% 2.73/1.72 % (22940)------------------------------
% 2.73/1.72 % (22940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.72 % (22940)Termination reason: Unknown
% 2.73/1.72 % (22940)Termination phase: shuffling
% 2.73/1.72
% 2.73/1.72 % (22940)Memory used [KB]: 1791
% 2.73/1.72 % (22940)Time elapsed: 0.007 s
% 2.73/1.72 % (22940)Instructions burned: 19 (million)
% 2.73/1.72 % (22940)------------------------------
% 2.73/1.72 % (22940)------------------------------
% 2.73/1.72 % (22925)Refutation not found, incomplete strategy
% 2.73/1.72 % (22925)------------------------------
% 2.73/1.72 % (22925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.72 % (22925)Termination reason: Refutation not found, incomplete strategy
% 2.73/1.72
% 2.73/1.72
% 2.73/1.72 % (22925)Memory used [KB]: 7419
% 2.73/1.72 % (22925)Time elapsed: 0.060 s
% 2.73/1.72 % (22925)Instructions burned: 153 (million)
% 2.73/1.72 % (22925)------------------------------
% 2.73/1.72 % (22925)------------------------------
% 2.73/1.73 % (22941)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_22724 for (2998ds/3Mi)
% 2.73/1.73 % (22941)Instruction limit reached!
% 2.73/1.73 % (22941)------------------------------
% 2.73/1.73 % (22941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.73 % (22941)Termination reason: Unknown
% 2.73/1.73 % (22941)Termination phase: shuffling
% 2.73/1.73
% 2.73/1.73 % (22941)Memory used [KB]: 1407
% 2.73/1.73 % (22941)Time elapsed: 0.003 s
% 2.73/1.73 % (22941)Instructions burned: 6 (million)
% 2.73/1.73 % (22941)------------------------------
% 2.73/1.73 % (22941)------------------------------
% 2.73/1.73 % (22942)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_22724 for (2998ds/30Mi)
% 2.73/1.74 % (22943)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_22724 for (2998ds/127Mi)
% 2.73/1.74 % (22942)Instruction limit reached!
% 2.73/1.74 % (22942)------------------------------
% 2.73/1.74 % (22942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.74 % (22942)Termination reason: Unknown
% 2.73/1.74 % (22942)Termination phase: Property scanning
% 2.73/1.74
% 2.73/1.74 % (22942)Memory used [KB]: 1918
% 2.73/1.74 % (22942)Time elapsed: 0.012 s
% 2.73/1.74 % (22942)Instructions burned: 33 (million)
% 2.73/1.74 % (22942)------------------------------
% 2.73/1.74 % (22942)------------------------------
% 2.73/1.75 % (22944)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_22724 for (2998ds/100Mi)
% 2.73/1.77 % (22943)Instruction limit reached!
% 2.73/1.77 % (22943)------------------------------
% 2.73/1.77 % (22943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.77 % (22943)Termination reason: Unknown
% 2.73/1.77 % (22943)Termination phase: Saturation
% 2.73/1.77
% 2.73/1.77 % (22943)Memory used [KB]: 7036
% 2.73/1.77 % (22943)Time elapsed: 0.039 s
% 2.73/1.77 % (22943)Instructions burned: 129 (million)
% 2.73/1.77 % (22943)------------------------------
% 2.73/1.77 % (22943)------------------------------
% 2.73/1.78 % (22944)Instruction limit reached!
% 2.73/1.78 % (22944)------------------------------
% 2.73/1.78 % (22944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.78 % (22944)Termination reason: Unknown
% 2.73/1.78 % (22944)Termination phase: Property scanning
% 2.73/1.78
% 2.73/1.78 % (22944)Memory used [KB]: 2430
% 2.73/1.78 % (22944)Time elapsed: 0.030 s
% 2.73/1.78 % (22944)Instructions burned: 104 (million)
% 2.73/1.78 % (22944)------------------------------
% 2.73/1.78 % (22944)------------------------------
% 2.73/1.78 % (22945)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_22724 for (2998ds/3Mi)
% 2.73/1.78 % (22945)Instruction limit reached!
% 2.73/1.78 % (22945)------------------------------
% 2.73/1.78 % (22945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.78 % (22945)Termination reason: Unknown
% 2.73/1.78 % (22945)Termination phase: shuffling
% 2.73/1.78
% 2.73/1.78 % (22945)Memory used [KB]: 1407
% 2.73/1.78 % (22945)Time elapsed: 0.002 s
% 2.73/1.78 % (22945)Instructions burned: 4 (million)
% 2.73/1.78 % (22945)------------------------------
% 2.73/1.78 % (22945)------------------------------
% 2.73/1.79 % (22946)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_22724 for (2997ds/20Mi)
% 2.73/1.79 % (22947)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_22724 for (2997ds/86Mi)
% 2.73/1.80 % (22946)Instruction limit reached!
% 2.73/1.80 % (22946)------------------------------
% 2.73/1.80 % (22946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.80 % (22946)Termination reason: Unknown
% 2.73/1.80 % (22946)Termination phase: shuffling
% 2.73/1.80
% 2.73/1.80 % (22946)Memory used [KB]: 1791
% 2.73/1.80 % (22946)Time elapsed: 0.008 s
% 2.73/1.80 % (22946)Instructions burned: 20 (million)
% 2.73/1.80 % (22946)------------------------------
% 2.73/1.80 % (22946)------------------------------
% 2.73/1.81 % (22951)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_22724 for (2997ds/107Mi)
% 2.73/1.82 % (22947)Instruction limit reached!
% 2.73/1.82 % (22947)------------------------------
% 2.73/1.82 % (22947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.82 % (22947)Termination reason: Unknown
% 2.73/1.82 % (22947)Termination phase: Property scanning
% 2.73/1.82
% 2.73/1.82 % (22947)Memory used [KB]: 2430
% 2.73/1.82 % (22947)Time elapsed: 0.027 s
% 2.73/1.82 % (22947)Instructions burned: 88 (million)
% 2.73/1.82 % (22947)------------------------------
% 2.73/1.82 % (22947)------------------------------
% 2.73/1.83 % (22958)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_22724 for (2997ds/39Mi)
% 2.73/1.84 % (22931)Instruction limit reached!
% 2.73/1.84 % (22931)------------------------------
% 2.73/1.84 % (22931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.84 % (22931)Termination reason: Unknown
% 2.73/1.84 % (22931)Termination phase: Saturation
% 2.73/1.84
% 2.73/1.84 % (22931)Memory used [KB]: 8187
% 2.73/1.84 % (22931)Time elapsed: 0.156 s
% 2.73/1.84 % (22931)Instructions burned: 379 (million)
% 2.73/1.84 % (22931)------------------------------
% 2.73/1.84 % (22931)------------------------------
% 2.73/1.84 % (22951)Instruction limit reached!
% 2.73/1.84 % (22951)------------------------------
% 2.73/1.84 % (22951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.84 % (22951)Termination reason: Unknown
% 2.73/1.84 % (22951)Termination phase: Saturation
% 2.73/1.84
% 2.73/1.84 % (22951)Memory used [KB]: 6908
% 2.73/1.84 % (22951)Time elapsed: 0.033 s
% 2.73/1.84 % (22951)Instructions burned: 109 (million)
% 2.73/1.84 % (22951)------------------------------
% 2.73/1.84 % (22951)------------------------------
% 2.73/1.84 % (22958)Instruction limit reached!
% 2.73/1.84 % (22958)------------------------------
% 2.73/1.84 % (22958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.84 % (22958)Termination reason: Unknown
% 2.73/1.84 % (22958)Termination phase: shuffling
% 2.73/1.84
% 2.73/1.84 % (22958)Memory used [KB]: 2174
% 2.73/1.84 % (22958)Time elapsed: 0.012 s
% 2.73/1.84 % (22958)Instructions burned: 40 (million)
% 2.73/1.84 % (22958)------------------------------
% 2.73/1.84 % (22958)------------------------------
% 2.73/1.85 % (22965)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_22724 for (2997ds/448Mi)
% 2.73/1.85 % (22967)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_22724 for (2997ds/46Mi)
% 2.73/1.85 % (22969)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_22724 for (2997ds/98Mi)
% 2.73/1.86 % (22967)Instruction limit reached!
% 2.73/1.86 % (22967)------------------------------
% 2.73/1.86 % (22967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.86 % (22967)Termination reason: Unknown
% 2.73/1.86 % (22967)Termination phase: Preprocessing 3
% 2.73/1.86
% 2.73/1.86 % (22967)Memory used [KB]: 1918
% 2.73/1.86 % (22967)Time elapsed: 0.015 s
% 2.73/1.86 % (22967)Instructions burned: 46 (million)
% 2.73/1.86 % (22967)------------------------------
% 2.73/1.86 % (22967)------------------------------
% 2.73/1.87 % (22978)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_22724 for (2997ds/507Mi)
% 2.73/1.88 % (22969)Instruction limit reached!
% 2.73/1.88 % (22969)------------------------------
% 2.73/1.88 % (22969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.88 % (22969)Termination reason: Unknown
% 2.73/1.88 % (22969)Termination phase: Property scanning
% 2.73/1.88
% 2.73/1.88 % (22969)Memory used [KB]: 2430
% 2.73/1.88 % (22969)Time elapsed: 0.028 s
% 2.73/1.88 % (22969)Instructions burned: 100 (million)
% 2.73/1.88 % (22969)------------------------------
% 2.73/1.88 % (22969)------------------------------
% 2.73/1.89 % (22985)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_22724 for (2996ds/149Mi)
% 2.73/1.90 % (22923)Instruction limit reached!
% 2.73/1.90 % (22923)------------------------------
% 2.73/1.90 % (22923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.90 % (22923)Termination reason: Unknown
% 2.73/1.90 % (22923)Termination phase: Saturation
% 2.73/1.90
% 2.73/1.90 % (22923)Memory used [KB]: 7803
% 2.73/1.90 % (22923)Time elapsed: 0.236 s
% 2.73/1.90 % (22923)Instructions burned: 710 (million)
% 2.73/1.90 % (22923)------------------------------
% 2.73/1.90 % (22923)------------------------------
% 2.73/1.90 % (22993)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_22724 for (2996ds/39Mi)
% 2.73/1.92 % (22993)Instruction limit reached!
% 2.73/1.92 % (22993)------------------------------
% 2.73/1.92 % (22993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.92 % (22993)Termination reason: Unknown
% 2.73/1.92 % (22993)Termination phase: Naming
% 2.73/1.92
% 2.73/1.92 % (22993)Memory used [KB]: 1918
% 2.73/1.92 % (22993)Time elapsed: 0.013 s
% 2.73/1.92 % (22993)Instructions burned: 39 (million)
% 2.73/1.92 % (22993)------------------------------
% 2.73/1.92 % (22993)------------------------------
% 2.73/1.93 % (22996)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_22724 for (2996ds/6Mi)
% 2.73/1.93 % (22985)Instruction limit reached!
% 2.73/1.93 % (22985)------------------------------
% 2.73/1.93 % (22985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.93 % (22985)Termination reason: Unknown
% 2.73/1.93 % (22985)Termination phase: Saturation
% 2.73/1.93
% 2.73/1.93 % (22985)Memory used [KB]: 6908
% 2.73/1.93 % (22985)Time elapsed: 0.043 s
% 2.73/1.93 % (22985)Instructions burned: 149 (million)
% 2.73/1.93 % (22985)------------------------------
% 2.73/1.93 % (22985)------------------------------
% 2.73/1.93 % (22996)Instruction limit reached!
% 2.73/1.93 % (22996)------------------------------
% 2.73/1.93 % (22996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.93 % (22996)Termination reason: Unknown
% 2.73/1.93 % (22996)Termination phase: shuffling
% 2.73/1.93
% 2.73/1.93 % (22996)Memory used [KB]: 1407
% 2.73/1.93 % (22996)Time elapsed: 0.003 s
% 2.73/1.93 % (22996)Instructions burned: 6 (million)
% 2.73/1.93 % (22996)------------------------------
% 2.73/1.93 % (22996)------------------------------
% 2.73/1.94 % (22997)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_22724 for (2996ds/1087Mi)
% 2.73/1.94 % (22998)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_22724 for (2996ds/47Mi)
% 2.73/1.94 % (22933)Instruction limit reached!
% 2.73/1.94 % (22933)------------------------------
% 2.73/1.94 % (22933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.94 % (22933)Termination reason: Unknown
% 2.73/1.94 % (22933)Termination phase: Saturation
% 2.73/1.94
% 2.73/1.94 % (22933)Memory used [KB]: 7803
% 2.73/1.94 % (22933)Time elapsed: 0.269 s
% 2.73/1.94 % (22933)Instructions burned: 781 (million)
% 2.73/1.94 % (22933)------------------------------
% 2.73/1.94 % (22933)------------------------------
% 2.73/1.95 % (22998)Instruction limit reached!
% 2.73/1.95 % (22998)------------------------------
% 2.73/1.95 % (22998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.95 % (22998)Termination reason: Unknown
% 2.73/1.95 % (22998)Termination phase: Preprocessing 3
% 2.73/1.95
% 2.73/1.95 % (22998)Memory used [KB]: 2046
% 2.73/1.95 % (22998)Time elapsed: 0.016 s
% 2.73/1.95 % (22998)Instructions burned: 49 (million)
% 2.73/1.95 % (22998)------------------------------
% 2.73/1.95 % (22998)------------------------------
% 2.73/1.95 % (22999)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_22724 for (2996ds/44Mi)
% 2.73/1.96 % (23001)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_22724 for (2996ds/432Mi)
% 2.73/1.97 % (22999)Instruction limit reached!
% 2.73/1.97 % (22999)------------------------------
% 2.73/1.97 % (22999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.97 % (22999)Termination reason: Unknown
% 2.73/1.97 % (22999)Termination phase: shuffling
% 2.73/1.97
% 2.73/1.97 % (22999)Memory used [KB]: 2174
% 2.73/1.97 % (22999)Time elapsed: 0.014 s
% 2.73/1.97 % (22999)Instructions burned: 45 (million)
% 2.73/1.97 % (22999)------------------------------
% 2.73/1.97 % (22999)------------------------------
% 2.73/1.97 % (22914)Instruction limit reached!
% 2.73/1.97 % (22914)------------------------------
% 2.73/1.97 % (22914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.97 % (22914)Termination reason: Unknown
% 2.73/1.97 % (22914)Termination phase: Saturation
% 2.73/1.97
% 2.73/1.97 % (22914)Memory used [KB]: 9850
% 2.73/1.97 % (22914)Time elapsed: 0.347 s
% 2.73/1.97 % (22914)Instructions burned: 1041 (million)
% 2.73/1.97 % (22914)------------------------------
% 2.73/1.97 % (22914)------------------------------
% 2.73/1.98 % (23007)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_22724 for (2996ds/62Mi)
% 2.73/1.98 % (23010)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_22724 for (2995ds/31Mi)
% 2.73/1.98 % (22937)Instruction limit reached!
% 2.73/1.98 % (22937)------------------------------
% 2.73/1.98 % (22937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.98 % (22937)Termination reason: Unknown
% 2.73/1.98 % (22937)Termination phase: Saturation
% 2.73/1.98
% 2.73/1.98 % (22937)Memory used [KB]: 8315
% 2.73/1.98 % (22937)Time elapsed: 0.303 s
% 2.73/1.98 % (22937)Instructions burned: 879 (million)
% 2.73/1.98 % (22937)------------------------------
% 2.73/1.98 % (22937)------------------------------
% 2.73/1.99 % (22965)Instruction limit reached!
% 2.73/1.99 % (22965)------------------------------
% 2.73/1.99 % (22965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.99 % (22965)Termination reason: Unknown
% 2.73/1.99 % (22965)Termination phase: Saturation
% 2.73/1.99
% 2.73/1.99 % (22965)Memory used [KB]: 7803
% 2.73/1.99 % (22965)Time elapsed: 0.141 s
% 2.73/1.99 % (22965)Instructions burned: 449 (million)
% 2.73/1.99 % (22965)------------------------------
% 2.73/1.99 % (22965)------------------------------
% 2.73/1.99 % (23010)Instruction limit reached!
% 2.73/1.99 % (23010)------------------------------
% 2.73/1.99 % (23010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.99 % (23010)Termination reason: Unknown
% 2.73/1.99 % (23010)Termination phase: Property scanning
% 2.73/1.99
% 2.73/1.99 % (23010)Memory used [KB]: 1791
% 2.73/1.99 % (23010)Time elapsed: 0.011 s
% 2.73/1.99 % (23010)Instructions burned: 31 (million)
% 2.73/1.99 % (23010)------------------------------
% 2.73/1.99 % (23010)------------------------------
% 2.73/1.99 % (23007)Instruction limit reached!
% 2.73/1.99 % (23007)------------------------------
% 2.73/1.99 % (23007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.73/1.99 % (23007)Termination reason: Unknown
% 2.73/1.99 % (23007)Termination phase: Property scanning
% 2.73/1.99
% 2.73/1.99 % (23007)Memory used [KB]: 2302
% 2.73/1.99 % (23007)Time elapsed: 0.018 s
% 2.73/1.99 % (23007)Instructions burned: 62 (million)
% 2.73/1.99 % (23007)------------------------------
% 2.73/1.99 % (23007)------------------------------
% 2.73/1.99 % (23015)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_22724 for (2995ds/96Mi)
% 2.73/2.00 % (23020)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_22724 for (2995ds/71Mi)
% 2.73/2.00 % (23021)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_22724 for (2995ds/83Mi)
% 2.73/2.01 % (23018)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_22724 for (2995ds/453Mi)
% 5.72/2.02 % (23015)Instruction limit reached!
% 5.72/2.02 % (23015)------------------------------
% 5.72/2.02 % (23015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.02 % (23015)Termination reason: Unknown
% 5.72/2.02 % (23015)Termination phase: Property scanning
% 5.72/2.02
% 5.72/2.02 % (23015)Memory used [KB]: 2430
% 5.72/2.02 % (23015)Time elapsed: 0.029 s
% 5.72/2.02 % (23015)Instructions burned: 97 (million)
% 5.72/2.02 % (23015)------------------------------
% 5.72/2.02 % (23015)------------------------------
% 5.72/2.02 % (23020)Instruction limit reached!
% 5.72/2.02 % (23020)------------------------------
% 5.72/2.02 % (23020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.02 % (23020)Termination reason: Unknown
% 5.72/2.02 % (23020)Termination phase: Property scanning
% 5.72/2.02
% 5.72/2.02 % (23020)Memory used [KB]: 2302
% 5.72/2.02 % (23020)Time elapsed: 0.023 s
% 5.72/2.02 % (23020)Instructions burned: 72 (million)
% 5.72/2.02 % (23020)------------------------------
% 5.72/2.02 % (23020)------------------------------
% 5.72/2.02 % (22978)Instruction limit reached!
% 5.72/2.02 % (22978)------------------------------
% 5.72/2.02 % (22978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.02 % (22978)Termination reason: Unknown
% 5.72/2.02 % (22978)Termination phase: Saturation
% 5.72/2.02
% 5.72/2.02 % (22978)Memory used [KB]: 8571
% 5.72/2.02 % (22978)Time elapsed: 0.154 s
% 5.72/2.02 % (22978)Instructions burned: 509 (million)
% 5.72/2.02 % (22978)------------------------------
% 5.72/2.02 % (22978)------------------------------
% 5.72/2.03 % (23021)Instruction limit reached!
% 5.72/2.03 % (23021)------------------------------
% 5.72/2.03 % (23021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.03 % (23021)Termination reason: Unknown
% 5.72/2.03 % (23021)Termination phase: Saturation
% 5.72/2.03
% 5.72/2.03 % (23021)Memory used [KB]: 6524
% 5.72/2.03 % (23021)Time elapsed: 0.027 s
% 5.72/2.03 % (23021)Instructions burned: 83 (million)
% 5.72/2.03 % (23021)------------------------------
% 5.72/2.03 % (23021)------------------------------
% 5.72/2.03 % (23033)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_22724 for (2995ds/11Mi)
% 5.72/2.03 % (23034)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_22724 for (2995ds/41Mi)
% 5.72/2.03 % (23033)Instruction limit reached!
% 5.72/2.03 % (23033)------------------------------
% 5.72/2.03 % (23033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.03 % (23033)Termination reason: Unknown
% 5.72/2.03 % (23033)Termination phase: shuffling
% 5.72/2.03
% 5.72/2.03 % (23033)Memory used [KB]: 1535
% 5.72/2.03 % (23033)Time elapsed: 0.004 s
% 5.72/2.03 % (23033)Instructions burned: 11 (million)
% 5.72/2.03 % (23033)------------------------------
% 5.72/2.03 % (23033)------------------------------
% 5.72/2.03 % (23035)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_22724 for (2995ds/6Mi)
% 5.72/2.04 % (23035)Instruction limit reached!
% 5.72/2.04 % (23035)------------------------------
% 5.72/2.04 % (23035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.04 % (23035)Termination reason: Unknown
% 5.72/2.04 % (23035)Termination phase: shuffling
% 5.72/2.04
% 5.72/2.04 % (23035)Memory used [KB]: 1407
% 5.72/2.04 % (23035)Time elapsed: 0.003 s
% 5.72/2.04 % (23035)Instructions burned: 6 (million)
% 5.72/2.04 % (23035)------------------------------
% 5.72/2.04 % (23035)------------------------------
% 5.72/2.04 % (23036)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_22724 for (2995ds/150Mi)
% 5.72/2.04 % (23037)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_22724 for (2995ds/343Mi)
% 5.72/2.04 % (23034)Instruction limit reached!
% 5.72/2.04 % (23034)------------------------------
% 5.72/2.04 % (23034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.04 % (23034)Termination reason: Unknown
% 5.72/2.04 % (23034)Termination phase: shuffling
% 5.72/2.04
% 5.72/2.04 % (23034)Memory used [KB]: 2174
% 5.72/2.04 % (23034)Time elapsed: 0.013 s
% 5.72/2.04 % (23034)Instructions burned: 43 (million)
% 5.72/2.04 % (23034)------------------------------
% 5.72/2.04 % (23034)------------------------------
% 5.72/2.05 % (23038)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_22724 for (2995ds/109Mi)
% 5.72/2.05 % (23047)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_22724 for (2995ds/253Mi)
% 5.72/2.08 % (23038)Instruction limit reached!
% 5.72/2.08 % (23038)------------------------------
% 5.72/2.08 % (23038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.08 % (23038)Termination reason: Unknown
% 5.72/2.08 % (23038)Termination phase: Saturation
% 5.72/2.08
% 5.72/2.08 % (23038)Memory used [KB]: 6908
% 5.72/2.08 % (23038)Time elapsed: 0.033 s
% 5.72/2.08 % (23038)Instructions burned: 109 (million)
% 5.72/2.08 % (23038)------------------------------
% 5.72/2.08 % (23038)------------------------------
% 5.72/2.08 % (23036)Instruction limit reached!
% 5.72/2.08 % (23036)------------------------------
% 5.72/2.08 % (23036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.08 % (23036)Termination reason: Unknown
% 5.72/2.08 % (23036)Termination phase: Saturation
% 5.72/2.08
% 5.72/2.08 % (23036)Memory used [KB]: 7164
% 5.72/2.08 % (23036)Time elapsed: 0.045 s
% 5.72/2.08 % (23036)Instructions burned: 151 (million)
% 5.72/2.08 % (23036)------------------------------
% 5.72/2.08 % (23036)------------------------------
% 5.72/2.08 % (23047)Refutation not found, incomplete strategy
% 5.72/2.08 % (23047)------------------------------
% 5.72/2.08 % (23047)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.08 % (23047)Termination reason: Refutation not found, incomplete strategy
% 5.72/2.08
% 5.72/2.08
% 5.72/2.08 % (23047)Memory used [KB]: 6780
% 5.72/2.08 % (23047)Time elapsed: 0.030 s
% 5.72/2.08 % (23047)Instructions burned: 91 (million)
% 5.72/2.08 % (23047)------------------------------
% 5.72/2.08 % (23047)------------------------------
% 5.72/2.09 % (23060)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_22724 for (2994ds/140Mi)
% 5.72/2.09 % (23061)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_22724 for (2994ds/614Mi)
% 5.72/2.09 % (23064)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_22724 for (2994ds/202Mi)
% 5.72/2.09 % (23001)Instruction limit reached!
% 5.72/2.09 % (23001)------------------------------
% 5.72/2.09 % (23001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.09 % (23001)Termination reason: Unknown
% 5.72/2.09 % (23001)Termination phase: Saturation
% 5.72/2.09
% 5.72/2.09 % (23001)Memory used [KB]: 3709
% 5.72/2.09 % (23001)Time elapsed: 0.133 s
% 5.72/2.09 % (23001)Instructions burned: 433 (million)
% 5.72/2.09 % (23001)------------------------------
% 5.72/2.09 % (23001)------------------------------
% 5.72/2.10 % (23075)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_22724 for (2994ds/339Mi)
% 5.72/2.11 % (23064)Refutation not found, incomplete strategy
% 5.72/2.11 % (23064)------------------------------
% 5.72/2.11 % (23064)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.72/2.11 % (23064)Termination reason: Refutation not found, incomplete strategy
% 5.72/2.11
% 5.72/2.11
% 5.72/2.11 % (23064)Memory used [KB]: 6652
% 5.72/2.11 % (23064)Time elapsed: 0.021 s
% 5.72/2.11 % (23064)Instructions burned: 63 (million)
% 5.72/2.11 % (23064)------------------------------
% 5.72/2.11 % (23064)------------------------------
% 5.72/2.12 % (23060)First to succeed.
% 6.28/2.12 % (23060)Refutation found. Thanks to Tanya!
% 6.28/2.12 % SZS status Theorem for DTF2THF_22724
% 6.28/2.12 % SZS output start Proof for DTF2THF_22724
% 6.28/2.12 thf(type_def_5, type, list: ($tType) > $tType).
% 6.28/2.12 thf(type_def_6, type, set: ($tType) > $tType).
% 6.28/2.12 thf(type_def_8, type, secrecy_specID: $tType).
% 6.28/2.12 thf(type_def_9, type, secrecy_KS: $tType).
% 6.28/2.12 thf(type_def_10, type, secrecy_Expression: $tType).
% 6.28/2.12 thf(type_def_11, type, secrecy_Keys: $tType).
% 6.28/2.12 thf(type_def_12, type, secrecy_Secrets: $tType).
% 6.28/2.12 thf(func_def_0, type, secrecy_Expression: $tType).
% 6.28/2.12 thf(func_def_1, type, secrecy_Secrets: $tType).
% 6.28/2.12 thf(func_def_2, type, secrecy_specID: $tType).
% 6.28/2.12 thf(func_def_3, type, secrecy_Keys: $tType).
% 6.28/2.12 thf(func_def_4, type, secrecy_KS: $tType).
% 6.28/2.12 thf(func_def_5, type, list: ($tType) > $tType).
% 6.28/2.12 thf(func_def_6, type, set: ($tType) > $tType).
% 6.28/2.12 thf(func_def_7, type, type: !>[X0: $tType]:($o)).
% 6.28/2.12 thf(func_def_8, type, ord: !>[X0: $tType]:($o)).
% 6.28/2.12 thf(func_def_9, type, linorder: !>[X0: $tType]:($o)).
% 6.28/2.12 thf(func_def_10, type, bNF_Greatest_Shift: !>[X0: $tType]:(set @ list @ X0 > X0 > set @ list @ X0)).
% 6.28/2.12 thf(func_def_11, type, bNF_Greatest_Succ: !>[X0: $tType]:(set @ list @ X0 > list @ X0 > set @ X0)).
% 6.28/2.12 thf(func_def_12, type, bNF_Greatest_shift: !>[X0: $tType, X1: $tType]:((list @ X0 > X1) > X0 > list @ X0 > X1)).
% 6.28/2.12 thf(func_def_13, type, localSecrets: secrecy_specID > set @ secrecy_KS).
% 6.28/2.12 thf(func_def_14, type, if: !>[X0: $tType]:($o > X0 > X0 > X0)).
% 6.28/2.12 thf(func_def_15, type, knowle1667810483orrect: secrecy_specID > secrecy_KS > $o).
% 6.28/2.12 thf(func_def_16, type, knowle1893229345orrect: secrecy_specID > secrecy_Expression > $o).
% 6.28/2.12 thf(func_def_17, type, knowle1437066798e_know: secrecy_specID > secrecy_KS > $o).
% 6.28/2.12 thf(func_def_18, type, knowle2055185861_knows: secrecy_specID > list @ secrecy_Expression > $o).
% 6.28/2.12 thf(func_def_19, type, mem: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 6.28/2.12 thf(func_def_20, type, append: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_21, type, arg_min_list: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > X0)).
% 6.28/2.12 thf(func_def_22, type, bind: !>[X0: $tType, X1: $tType]:(list @ X0 > (X0 > list @ X1) > list @ X1)).
% 6.28/2.12 thf(func_def_23, type, butlast: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_24, type, concat: !>[X0: $tType]:(list @ list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_25, type, distinct_adj: !>[X0: $tType]:(list @ X0 > $o)).
% 6.28/2.12 thf(func_def_26, type, foldr: !>[X0: $tType, X1: $tType]:((X0 > X1 > X1) > list @ X0 > X1 > X1)).
% 6.28/2.12 thf(func_def_27, type, insert: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_28, type, last: !>[X0: $tType]:(list @ X0 > X0)).
% 6.28/2.12 thf(func_def_29, type, cons: !>[X0: $tType]:(X0 > list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_30, type, nil: !>[X0: $tType]:(list @ X0)).
% 6.28/2.12 thf(func_def_31, type, case_list: !>[X0: $tType, X1: $tType]:(X0 > (X1 > list @ X1 > X0) > list @ X1 > X0)).
% 6.28/2.12 thf(func_def_32, type, hd: !>[X0: $tType]:(list @ X0 > X0)).
% 6.28/2.12 thf(func_def_33, type, tl: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_34, type, list_ex1: !>[X0: $tType]:((X0 > $o) > list @ X0 > $o)).
% 6.28/2.12 thf(func_def_35, type, listrelp: !>[X0: $tType, X1: $tType]:((X0 > X1 > $o) > list @ X0 > list @ X1 > $o)).
% 6.28/2.12 thf(func_def_36, type, map_tailrec: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1)).
% 6.28/2.12 thf(func_def_37, type, map_tailrec_rev: !>[X0: $tType, X1: $tType]:((X0 > X1) > list @ X0 > list @ X1 > list @ X1)).
% 6.28/2.12 thf(func_def_38, type, maps: !>[X0: $tType, X1: $tType]:((X0 > list @ X1) > list @ X0 > list @ X1)).
% 6.28/2.12 thf(func_def_39, type, member: !>[X0: $tType]:(list @ X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_40, type, lexordp_eq: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > list @ X0 > $o)).
% 6.28/2.12 thf(func_def_41, type, ord_lexordp_eq: !>[X0: $tType]:(list @ X0 > list @ X0 > $o)).
% 6.28/2.12 thf(func_def_42, type, product_lists: !>[X0: $tType]:(list @ list @ X0 > list @ list @ X0)).
% 6.28/2.12 thf(func_def_43, type, remdups_adj: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_44, type, rev: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_45, type, rotate1: !>[X0: $tType]:(list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_46, type, shuffles: !>[X0: $tType]:(list @ X0 > list @ X0 > set @ list @ X0)).
% 6.28/2.12 thf(func_def_47, type, splice: !>[X0: $tType]:(list @ X0 > list @ X0 > list @ X0)).
% 6.28/2.12 thf(func_def_48, type, subseqs: !>[X0: $tType]:(list @ X0 > list @ list @ X0)).
% 6.28/2.12 thf(func_def_49, type, successively: !>[X0: $tType]:((X0 > X0 > $o) > list @ X0 > $o)).
% 6.28/2.12 thf(func_def_50, type, ord_less: !>[X0: $tType]:(X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_51, type, decr: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 6.28/2.12 thf(func_def_52, type, enc: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 6.28/2.12 thf(func_def_53, type, encrDecrKeys: secrecy_Keys > secrecy_Keys > $o).
% 6.28/2.12 thf(func_def_54, type, ext: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 6.28/2.12 thf(func_def_55, type, sign: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 6.28/2.12 thf(func_def_56, type, eout: secrecy_specID > secrecy_Expression > $o).
% 6.28/2.12 thf(func_def_57, type, ine: secrecy_specID > secrecy_Expression > $o).
% 6.28/2.12 thf(func_def_58, type, notSpe1586871396tsExpr: secrecy_specID > list @ secrecy_Expression > $o).
% 6.28/2.12 thf(func_def_59, type, specKeys: secrecy_specID > set @ secrecy_Keys).
% 6.28/2.12 thf(func_def_60, type, specKeysSecrets: secrecy_specID > set @ secrecy_KS).
% 6.28/2.12 thf(func_def_61, type, specSecrets: secrecy_specID > set @ secrecy_Secrets).
% 6.28/2.12 thf(func_def_62, type, secrec1371625429on2KSL: list @ secrecy_Expression > list @ secrecy_KS).
% 6.28/2.12 thf(func_def_63, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 6.28/2.12 thf(func_def_64, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 6.28/2.12 thf(func_def_65, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 6.28/2.12 thf(func_def_66, type, secrecy_case_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 6.28/2.12 thf(func_def_67, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 6.28/2.12 thf(func_def_68, type, secrecy_rec_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 6.28/2.12 thf(func_def_69, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 6.28/2.12 thf(func_def_70, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 6.28/2.12 thf(func_def_71, type, member2: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 6.28/2.12 thf(func_def_72, type, a: secrecy_specID).
% 6.28/2.12 thf(func_def_73, type, m: secrecy_Secrets).
% 6.28/2.12 thf(func_def_92, type, sK0: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_93, type, sK1: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_94, type, sK2: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_95, type, sK3: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_96, type, sK4: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_97, type, sK5: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_98, type, sK6: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_99, type, sK7: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_100, type, sK8: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_101, type, sK9: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_102, type, sK10: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_103, type, sK11: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_104, type, sK12: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_105, type, sK13: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_106, type, sK14: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_107, type, sK15: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_108, type, sK16: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_109, type, sK17: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_110, type, sK18: !>[X0: $tType]:((list @ X0 > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_111, type, sK19: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_112, type, sK20: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_113, type, sK21: !>[X0: $tType]:((list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_114, type, sK22: !>[X0: $tType]:((list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_115, type, sK23: secrecy_KS > secrecy_Secrets).
% 6.28/2.12 thf(func_def_116, type, sK24: secrecy_KS > secrecy_Keys).
% 6.28/2.12 thf(func_def_117, type, sK25: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_118, type, sK26: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_119, type, sK27: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_120, type, sK28: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_121, type, sK29: (secrecy_KS > $o) > secrecy_Keys).
% 6.28/2.12 thf(func_def_122, type, sK30: (secrecy_KS > $o) > secrecy_Secrets).
% 6.28/2.12 thf(func_def_123, type, sK31: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 6.28/2.12 thf(func_def_124, type, sK32: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_125, type, sK33: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 6.28/2.12 thf(func_def_126, type, sK34: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 6.28/2.12 thf(func_def_127, type, sK35: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X0)).
% 6.28/2.12 thf(func_def_128, type, sK36: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_129, type, sK37: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > X1)).
% 6.28/2.12 thf(func_def_130, type, sK38: !>[X0: $tType, X1: $tType]:((list @ X0 > list @ X1 > $o) > list @ X1)).
% 6.28/2.12 thf(func_def_131, type, sK39: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 6.28/2.12 thf(func_def_132, type, sK40: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_133, type, sK41: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_134, type, sK42: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_135, type, sK43: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_136, type, sK44: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_137, type, sK45: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0)).
% 6.28/2.12 thf(func_def_138, type, sK46: !>[X0: $tType]:(((X0 > X0 > $o) > list @ X0 > $o) > X0 > X0 > $o)).
% 6.28/2.12 thf(func_def_139, type, sK47: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 6.28/2.12 thf(func_def_140, type, sK48: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 6.28/2.12 thf(func_def_141, type, sK49: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0 > X1)).
% 6.28/2.12 thf(func_def_142, type, sK50: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > X0)).
% 6.28/2.12 thf(func_def_143, type, sK51: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X0)).
% 6.28/2.12 thf(func_def_144, type, sK52: !>[X0: $tType, X1: $tType]:(((X0 > X1) > list @ X0 > list @ X1 > $o) > list @ X1)).
% 6.28/2.12 thf(func_def_146, type, ph54: !>[X0: $tType]:(X0)).
% 6.28/2.12 thf(f930,plain,(
% 6.28/2.12 $false),
% 6.28/2.12 inference(subsumption_resolution,[status(thm)],[f928,f885])).
% 6.28/2.12 thf(f885,plain,(
% 6.28/2.12 ((knowle1437066798e_know @ a @ (secrecy_sKS @ m)) != $true)),
% 6.28/2.12 inference(cnf_transformation,[status(thm)],[f782])).
% 6.28/2.12 thf(f782,plain,(
% 6.28/2.12 ((knowle1437066798e_know @ a @ (secrecy_sKS @ m)) != $true)),
% 6.28/2.12 inference(flattening,[status(thm)],[f380])).
% 6.28/2.12 thf(f380,plain,(
% 6.28/2.12 ~((knowle1437066798e_know @ a @ (secrecy_sKS @ m)) = $true)),
% 6.28/2.12 inference(fool_elimination,[status(thm)],[f379])).
% 6.28/2.12 thf(f379,plain,(
% 6.28/2.12 ~(knowle1437066798e_know @ a @ (secrecy_sKS @ m))),
% 6.28/2.12 inference(rectify,[status(thm)],[f264])).
% 6.28/2.12 thf(f264,negated_conjecture,(
% 6.28/2.12 ~(knowle1437066798e_know @ a @ (secrecy_sKS @ m))),
% 6.28/2.12 inference(negated_conjecture,[status(cth)],[f263])).
% 6.28/2.12 thf(f263,conjecture,(
% 6.28/2.12 (knowle1437066798e_know @ a @ (secrecy_sKS @ m))),
% 6.28/2.12 file('/export/starexec/sandbox2/tmp/tmp.MVbIzHpABw/DTF2THF_22724.p',conj_0)).
% 6.28/2.12 thf(f928,plain,(
% 6.28/2.12 ((knowle1437066798e_know @ a @ (secrecy_sKS @ m)) = $true)),
% 6.28/2.12 inference(superposition,[status(thm)],[f893,f859])).
% 6.28/2.12 thf(f859,plain,(
% 6.28/2.12 ((knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_sE @ m) @ nil @ secrecy_Expression)) = $true)),
% 6.28/2.12 inference(cnf_transformation,[status(thm)],[f777])).
% 6.28/2.12 thf(f777,plain,(
% 6.28/2.12 ((knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_sE @ m) @ nil @ secrecy_Expression)) = $true)),
% 6.28/2.12 inference(fool_elimination,[status(thm)],[f776])).
% 6.28/2.12 thf(f776,plain,(
% 6.28/2.12 (knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_sE @ m) @ nil @ secrecy_Expression))),
% 6.28/2.12 inference(rectify,[status(thm)],[f1])).
% 6.28/2.12 thf(f1,axiom,(
% 6.28/2.12 (knowle2055185861_knows @ a @ (cons @ secrecy_Expression @ (secrecy_sE @ m) @ nil @ secrecy_Expression))),
% 6.28/2.12 file('/export/starexec/sandbox2/tmp/tmp.MVbIzHpABw/DTF2THF_22724.p',fact_0_assms)).
% 6.28/2.12 thf(f893,plain,(
% 6.28/2.12 ( ! [X0 : secrecy_specID,X1 : secrecy_Secrets] : (((knowle1437066798e_know @ X0 @ (secrecy_sKS @ X1)) = (knowle2055185861_knows @ X0 @ (cons @ secrecy_Expression @ (secrecy_sE @ X1) @ nil @ secrecy_Expression)))) )),
% 6.28/2.12 inference(backward_demodulation,[status(thm)],[f886,f853])).
% 6.28/2.12 thf(f853,plain,(
% 6.28/2.12 ( ! [X0 : secrecy_Secrets] : (((secrecy_sE @ X0) = (secrec1016742679ession @ (secrecy_sKS @ X0)))) )),
% 6.28/2.12 inference(cnf_transformation,[status(thm)],[f461])).
% 6.28/2.12 thf(f461,plain,(
% 6.28/2.12 ! [X0 : secrecy_Secrets] : ((secrecy_sE @ X0) = (secrec1016742679ession @ (secrecy_sKS @ X0)))),
% 6.28/2.12 inference(fool_elimination,[status(thm)],[f460])).
% 6.28/2.12 thf(f460,plain,(
% 6.28/2.12 ! [X0 : secrecy_Secrets] : ((secrecy_sE @ X0) = (secrec1016742679ession @ (secrecy_sKS @ X0)))),
% 6.28/2.12 inference(rectify,[status(thm)],[f10])).
% 6.28/2.12 thf(f10,axiom,(
% 6.28/2.12 ! [X5 : secrecy_Secrets] : ((secrecy_sE @ X5) = (secrec1016742679ession @ (secrecy_sKS @ X5)))),
% 6.28/2.12 file('/export/starexec/sandbox2/tmp/tmp.MVbIzHpABw/DTF2THF_22724.p',fact_9_KS2Expression_Osimps_I2_J)).
% 6.28/2.12 thf(f886,plain,(
% 6.28/2.12 ( ! [X0 : secrecy_specID,X1 : secrecy_Secrets] : (((knowle2055185861_knows @ X0 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_sKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X0 @ (secrecy_sKS @ X1)))) )),
% 6.28/2.12 inference(cnf_transformation,[status(thm)],[f285])).
% 6.28/2.12 thf(f285,plain,(
% 6.28/2.12 ! [X0 : secrecy_specID,X1 : secrecy_Secrets] : ((knowle2055185861_knows @ X0 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_sKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X0 @ (secrecy_sKS @ X1)))),
% 6.28/2.12 inference(fool_elimination,[status(thm)],[f284])).
% 6.28/2.12 thf(f284,plain,(
% 6.28/2.12 ! [X0 : secrecy_specID,X1 : secrecy_Secrets] : ((knowle2055185861_knows @ X0 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_sKS @ X1)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X0 @ (secrecy_sKS @ X1)))),
% 6.28/2.12 inference(rectify,[status(thm)],[f4])).
% 6.28/2.12 thf(f4,axiom,(
% 6.28/2.12 ! [X6 : secrecy_specID,X7 : secrecy_Secrets] : ((knowle2055185861_knows @ X6 @ (cons @ secrecy_Expression @ (secrec1016742679ession @ (secrecy_sKS @ X7)) @ nil @ secrecy_Expression)) = (knowle1437066798e_know @ X6 @ (secrecy_sKS @ X7)))),
% 6.28/2.12 file('/export/starexec/sandbox2/tmp/tmp.MVbIzHpABw/DTF2THF_22724.p',fact_3_know1s)).
% 6.28/2.12 % SZS output end Proof for DTF2THF_22724
% 6.28/2.12 % (23060)------------------------------
% 6.28/2.12 % (23060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.28/2.12 % (23060)Termination reason: Refutation
% 6.28/2.12
% 6.28/2.12 % (23060)Memory used [KB]: 6908
% 6.28/2.12 % (23060)Time elapsed: 0.031 s
% 6.28/2.12 % (23060)Instructions burned: 90 (million)
% 6.28/2.12 % (23060)------------------------------
% 6.28/2.12 % (23060)------------------------------
% 6.28/2.12 % (22898)Success in time 0.537 s
%------------------------------------------------------------------------------