%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP090^2 : 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 08:55:28 AM UTC 2026
% Result : Theorem 3.04s 1.69s
% Output : Refutation 3.04s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP090^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n015.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 08:26:16 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.21/0.46 ---- Original DTF file ---
% 0.21/0.46 thf(spec,logic,$$dhol).
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % File : ITP090^2 : TPTP v9.2.1. Released v7.5.0.
% 0.21/0.46 % Domain : Interactive Theorem Proving
% 0.21/0.46 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_426__3295732_1
% 0.21/0.46 % Version : Especial.
% 0.21/0.46 % English :
% 0.21/0.46
% 0.21/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.21/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.21/0.46 % Source : [Des21]
% 0.21/0.46 % Names : KnowledgeKeysSecrets/prob_426__3295732_1 [Des21]
% 0.21/0.46
% 0.21/0.46 % Status : Theorem
% 0.21/0.46 % Rating : 0.00 v7.5.0
% 0.21/0.46 % Syntax : Number of formulae : 353 ( 112 unt; 72 typ; 0 def)
% 0.21/0.46 % Number of atoms : 1057 ( 280 equ; 0 cnn)
% 0.21/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.21/0.46 % Number of connectives : 4596 ( 220 ~; 35 |; 96 &;3700 @)
% 0.21/0.46 % ( 0 <=>; 545 =>; 0 <=; 0 <~>)
% 0.21/0.46 % Maximal formula depth : 20 ( 8 avg)
% 0.21/0.46 % Number of types : 8 ( 7 usr)
% 0.21/0.46 % Number of type conns : 132 ( 132 >; 0 *; 0 +; 0 <<)
% 0.21/0.46 % Number of symbols : 66 ( 65 usr; 5 con; 0-4 aty)
% 0.21/0.46 % Number of variables : 960 ( 61 ^; 850 !; 29 ?; 960 :)
% 0.21/0.46 % ( 20 !>; 0 ?*; 0 @-; 0 @+)
% 0.21/0.46 % SPC : TH1_THM_EQU_NAR
% 0.21/0.46
% 0.21/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:20:52.568
% 0.21/0.46 %------------------------------------------------------------------------------
% 0.21/0.46 % Could-be-implicit typings (9)
% 0.21/0.46 thf(ty_t_Secrecy__types_OExpression,type,
% 0.21/0.46 secrecy_Expression: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Secrecy__types_OSecrets,type,
% 0.21/0.46 secrecy_Secrets: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Secrecy__types_OspecID,type,
% 0.21/0.46 secrecy_specID: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Secrecy__types_OchanID,type,
% 0.21/0.46 secrecy_chanID: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Secrecy__types_OKeys,type,
% 0.21/0.46 secrecy_Keys: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Secrecy__types_OKS,type,
% 0.21/0.46 secrecy_KS: $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_List_Olist,type,
% 0.21/0.46 list: $tType > $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Set_Oset,type,
% 0.21/0.46 set: $tType > $tType ).
% 0.21/0.46
% 0.21/0.46 thf(ty_t_Nat_Onat,type,
% 0.21/0.46 nat: $tType ).
% 0.21/0.46
% 0.21/0.46 % Explicit typings (63)
% 0.21/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.21/0.46 bounded_lattice:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_HOL_Otype,type,
% 0.21/0.46 type:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.21/0.46 bot:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.21/0.46 ord:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.21/0.46 order:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.21/0.46 linorder:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.21/0.46 preorder:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.21/0.46 bounde1808546759up_bot:
% 0.21/0.46 !>[A: $tType] : $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.21/0.46 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 0.21/0.46 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 0.21/0.46 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows,type,
% 0.21/0.46 knowle2055185861_knows: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.21/0.46 sup_sup:
% 0.21/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_ListExtras_Omem,type,
% 0.21/0.46 mem:
% 0.21/0.46 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.21/0.46 bot_bot:
% 0.21/0.46 !>[A: $tType] : A ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.21/0.46 ord_less_eq:
% 0.21/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_ODecr,type,
% 0.21/0.46 decr: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OEnc,type,
% 0.21/0.46 enc: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.21/0.46 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OExt,type,
% 0.21/0.46 ext: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OSign,type,
% 0.21/0.46 sign: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.21/0.46 correctCompositionKS: secrecy_specID > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.21/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OeoutM,type,
% 0.21/0.46 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OexprChannel,type,
% 0.21/0.46 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.21/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OineM,type,
% 0.21/0.46 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.21/0.46 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.21/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.21/0.46 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.21/0.46 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.21/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.21/0.46 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.21/0.46 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.21/0.46 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.21/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.21/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.21/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 0.21/0.46 secrecy_case_KS:
% 0.21/0.46 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.21/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 0.21/0.46 secrecy_rec_KS:
% 0.21/0.46 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.21/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Set_OCollect,type,
% 0.21/0.46 collect:
% 0.21/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Set_Oinsert,type,
% 0.21/0.46 insert:
% 0.21/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Set_Ois__empty,type,
% 0.21/0.46 is_empty:
% 0.21/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Set_Ois__singleton,type,
% 0.21/0.46 is_singleton:
% 0.21/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.21/0.46 the_elem:
% 0.21/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.21/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.21/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.21/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_OinStream,type,
% 0.21/0.46 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_Oins,type,
% 0.21/0.46 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_Oloc,type,
% 0.21/0.46 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_OlocStream,type,
% 0.21/0.46 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_Oout,type,
% 0.21/0.46 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_OoutStream,type,
% 0.21/0.46 outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.21/0.46 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_c_member,type,
% 0.21/0.46 member:
% 0.21/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.21/0.46
% 0.21/0.46 thf(sy_v_P,type,
% 0.21/0.46 p: secrecy_specID ).
% 0.21/0.46
% 0.21/0.46 thf(sy_v_PQ,type,
% 0.21/0.46 pq: secrecy_specID ).
% 0.21/0.46
% 0.21/0.46 thf(sy_v_Q,type,
% 0.21/0.46 q: secrecy_specID ).
% 0.21/0.46
% 0.21/0.46 thf(sy_v_key____,type,
% 0.21/0.46 key: secrecy_Keys ).
% 0.21/0.46
% 0.21/0.46 thf(sy_v_m,type,
% 0.21/0.46 m: secrecy_KS ).
% 0.21/0.46
% 0.21/0.46 % Relevant facts (256)
% 0.21/0.46 thf(fact_0_not__knowQm,axiom,
% 0.21/0.46 ~ ( knowle1437066798e_know @ q @ m ) ).
% 0.21/0.46
% 0.21/0.46 % not_knowQm
% 0.21/0.46 thf(fact_1_a1,axiom,
% 0.21/0.46 ( m
% 0.21/0.46 = ( secrecy_kKS @ key ) ) ).
% 0.21/0.46
% 0.21/0.46 % a1
% 0.21/0.46 thf(fact_2_knowPQ,axiom,
% 0.21/0.46 knowle1437066798e_know @ pq @ m ).
% 0.21/0.46
% 0.21/0.46 % knowPQ
% 0.21/0.46 thf(fact_3_sg2,axiom,
% 0.21/0.46 member @ secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ pq ) ).
% 0.21/0.46
% 0.21/0.46 % sg2
% 0.21/0.46 thf(fact_4_KS_Oinject_I1_J,axiom,
% 0.21/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.21/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.21/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.21/0.46 = ( X1 = Y1 ) ) ).
% 0.21/0.46
% 0.21/0.46 % KS.inject(1)
% 0.21/0.46 thf(fact_5_sg3a,axiom,
% 0.21/0.46 ~ ( ine @ q @ ( secrecy_kE @ key ) ) ).
% 0.21/0.46
% 0.21/0.46 % sg3a
% 0.21/0.46 thf(fact_6_cCompLoc,axiom,
% 0.21/0.46 correc965049635ionLoc @ pq ).
% 0.21/0.46
% 0.21/0.46 % cCompLoc
% 0.21/0.46 thf(fact_7_a12,axiom,
% 0.21/0.46 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 0.21/0.46
% 0.21/0.46 % a12
% 0.21/0.46 thf(fact_8_KS_Osimps_I7_J,axiom,
% 0.21/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.21/0.46 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.21/0.46 = ( F1 @ X1 ) ) ).
% 0.21/0.46
% 0.21/0.46 % KS.simps(7)
% 0.21/0.46 thf(fact_9_KS_Osimps_I5_J,axiom,
% 0.21/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.21/0.46 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.21/0.46 = ( F1 @ X1 ) ) ).
% 0.21/0.46
% 0.21/0.46 % KS.simps(5)
% 0.21/0.46 thf(fact_10_know_Osimps_I1_J,axiom,
% 0.21/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.21/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.21/0.46 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 0.21/0.46 | ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % know.simps(1)
% 0.21/0.46 thf(fact_11_subPQ,axiom,
% 0.21/0.46 ( ( subcomponents @ pq )
% 0.21/0.46 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % subPQ
% 0.21/0.46 thf(fact_12_knows4,axiom,
% 0.21/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 0.21/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.21/0.46 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K2 ) )
% 0.21/0.46 & ( knowle2055185861_knows @ A2 @ ( enc @ K1 @ E ) ) )
% 0.21/0.46 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.21/0.46
% 0.21/0.46 % knows4
% 0.21/0.46 thf(fact_13_knows5,axiom,
% 0.21/0.46 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 0.21/0.46 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.21/0.46 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K1 ) )
% 0.21/0.46 & ( knowle2055185861_knows @ A2 @ ( sign @ K2 @ E ) ) )
% 0.21/0.46 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 0.21/0.46
% 0.21/0.46 % knows5
% 0.21/0.46 thf(fact_14_knows6,axiom,
% 0.21/0.46 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 0.21/0.46 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 0.21/0.46 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 0.21/0.46 => ( knowle2055185861_knows @ A2 @ ( enc @ K @ E1 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % knows6
% 0.21/0.46 thf(fact_15_Expression_Oinject_I1_J,axiom,
% 0.21/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.21/0.46 ( ( ( secrecy_kE @ X1 )
% 0.21/0.46 = ( secrecy_kE @ Y1 ) )
% 0.21/0.46 = ( X1 = Y1 ) ) ).
% 0.21/0.46
% 0.21/0.46 % Expression.inject(1)
% 0.21/0.46 thf(fact_16_cCompI,axiom,
% 0.21/0.46 correctCompositionIn @ pq ).
% 0.21/0.46
% 0.21/0.46 % cCompI
% 0.21/0.46 thf(fact_17_not__know__k__not__ine,axiom,
% 0.21/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.21/0.46 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.21/0.46 => ~ ( ine @ A2 @ ( secrecy_kE @ M ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % not_know_k_not_ine
% 0.21/0.46 thf(fact_18_knows7,axiom,
% 0.21/0.46 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 0.21/0.46 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 0.21/0.46 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 0.21/0.46 => ( knowle2055185861_knows @ A2 @ ( sign @ K @ E1 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % knows7
% 0.21/0.46 thf(fact_19_LocalSecretsComposition__ine1__k,axiom,
% 0.21/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.46 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.21/0.46 => ( ( ( subcomponents @ PQ )
% 0.21/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.21/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.21/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.21/0.46 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % LocalSecretsComposition_ine1_k
% 0.21/0.46 thf(fact_20_LocalSecretsComposition__ine2__k,axiom,
% 0.21/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.46 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.21/0.46 => ( ( ( subcomponents @ PQ )
% 0.21/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.21/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.21/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.21/0.46 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % LocalSecretsComposition_ine2_k
% 0.21/0.46 thf(fact_21_LocalSecretsComposition__neg1__k,axiom,
% 0.21/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.21/0.46 ( ( ( subcomponents @ PQ )
% 0.21/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.21/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.21/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.21/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.21/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % LocalSecretsComposition_neg1_k
% 0.21/0.46 thf(fact_22_singletonI,axiom,
% 0.21/0.46 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % singletonI
% 0.21/0.46 thf(fact_23_LocalSecretsComposition1,axiom,
% 0.21/0.46 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.46 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.21/0.46 => ( ( ( subcomponents @ PQ )
% 0.21/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.46 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % LocalSecretsComposition1
% 0.21/0.46 thf(fact_24_know__composition__neg__ine__k,axiom,
% 0.21/0.46 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.46 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_kKS @ Key ) )
% 0.21/0.46 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ Key ) )
% 0.21/0.46 => ( ( ( subcomponents @ PQ )
% 0.21/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.46 => ( ( correctCompositionIn @ PQ )
% 0.21/0.46 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % know_composition_neg_ine_k
% 0.21/0.46 thf(fact_25_insertCI,axiom,
% 0.21/0.46 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 0.21/0.46 ( ( ~ ( member @ A @ A3 @ B )
% 0.21/0.46 => ( A3 = B2 ) )
% 0.21/0.46 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % insertCI
% 0.21/0.46 thf(fact_26_insert__iff,axiom,
% 0.21/0.46 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.21/0.46 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.21/0.46 = ( ( A3 = B2 )
% 0.21/0.46 | ( member @ A @ A3 @ A2 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % insert_iff
% 0.21/0.46 thf(fact_27_insert__absorb2,axiom,
% 0.21/0.46 ! [A: $tType,X: A,A2: set @ A] :
% 0.21/0.46 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 0.21/0.46 = ( insert @ A @ X @ A2 ) ) ).
% 0.21/0.46
% 0.21/0.46 % insert_absorb2
% 0.21/0.46 thf(fact_28_empty__iff,axiom,
% 0.21/0.46 ! [A: $tType,C: A] :
% 0.21/0.46 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % empty_iff
% 0.21/0.46 thf(fact_29_empty__Collect__eq,axiom,
% 0.21/0.46 ! [A: $tType,P: A > $o] :
% 0.21/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.21/0.46 = ( collect @ A @ P ) )
% 0.21/0.46 = ( ! [X2: A] :
% 0.21/0.46 ~ ( P @ X2 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % empty_Collect_eq
% 0.21/0.46 thf(fact_30_Collect__empty__eq,axiom,
% 0.21/0.46 ! [A: $tType,P: A > $o] :
% 0.21/0.46 ( ( ( collect @ A @ P )
% 0.21/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.46 = ( ! [X2: A] :
% 0.21/0.46 ~ ( P @ X2 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % Collect_empty_eq
% 0.21/0.46 thf(fact_31_all__not__in__conv,axiom,
% 0.21/0.46 ! [A: $tType,A2: set @ A] :
% 0.21/0.46 ( ( ! [X2: A] :
% 0.21/0.46 ~ ( member @ A @ X2 @ A2 ) )
% 0.21/0.46 = ( A2
% 0.21/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % all_not_in_conv
% 0.21/0.46 thf(fact_32_ex__in__conv,axiom,
% 0.21/0.46 ! [A: $tType,A2: set @ A] :
% 0.21/0.46 ( ( ? [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.21/0.46 = ( A2
% 0.21/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % ex_in_conv
% 0.21/0.46 thf(fact_33_equals0I,axiom,
% 0.21/0.46 ! [A: $tType,A2: set @ A] :
% 0.21/0.46 ( ! [Y: A] :
% 0.21/0.46 ~ ( member @ A @ Y @ A2 )
% 0.21/0.46 => ( A2
% 0.21/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % equals0I
% 0.21/0.46 thf(fact_34_equals0D,axiom,
% 0.21/0.46 ! [A: $tType,A2: set @ A,A3: A] :
% 0.21/0.46 ( ( A2
% 0.21/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.46 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 0.21/0.46
% 0.21/0.46 % equals0D
% 0.21/0.46 thf(fact_35_emptyE,axiom,
% 0.21/0.46 ! [A: $tType,A3: A] :
% 0.21/0.46 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % emptyE
% 0.21/0.46 thf(fact_36_mk__disjoint__insert,axiom,
% 0.21/0.46 ! [A: $tType,A3: A,A2: set @ A] :
% 0.21/0.46 ( ( member @ A @ A3 @ A2 )
% 0.21/0.46 => ? [B3: set @ A] :
% 0.21/0.46 ( ( A2
% 0.21/0.46 = ( insert @ A @ A3 @ B3 ) )
% 0.21/0.46 & ~ ( member @ A @ A3 @ B3 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % mk_disjoint_insert
% 0.21/0.46 thf(fact_37_insert__commute,axiom,
% 0.21/0.46 ! [A: $tType,X: A,Y2: A,A2: set @ A] :
% 0.21/0.46 ( ( insert @ A @ X @ ( insert @ A @ Y2 @ A2 ) )
% 0.21/0.46 = ( insert @ A @ Y2 @ ( insert @ A @ X @ A2 ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % insert_commute
% 0.21/0.46 thf(fact_38_insert__eq__iff,axiom,
% 0.21/0.46 ! [A: $tType,A3: A,A2: set @ A,B2: A,B: set @ A] :
% 0.21/0.46 ( ~ ( member @ A @ A3 @ A2 )
% 0.21/0.46 => ( ~ ( member @ A @ B2 @ B )
% 0.21/0.46 => ( ( ( insert @ A @ A3 @ A2 )
% 0.21/0.46 = ( insert @ A @ B2 @ B ) )
% 0.21/0.46 = ( ( ( A3 = B2 )
% 0.21/0.46 => ( A2 = B ) )
% 0.21/0.46 & ( ( A3 != B2 )
% 0.21/0.46 => ? [C2: set @ A] :
% 0.21/0.46 ( ( A2
% 0.21/0.46 = ( insert @ A @ B2 @ C2 ) )
% 0.21/0.46 & ~ ( member @ A @ B2 @ C2 )
% 0.21/0.46 & ( B
% 0.21/0.46 = ( insert @ A @ A3 @ C2 ) )
% 0.21/0.46 & ~ ( member @ A @ A3 @ C2 ) ) ) ) ) ) ) ).
% 0.21/0.46
% 0.21/0.46 % insert_eq_iff
% 0.21/0.46 thf(fact_39_insert__absorb,axiom,
% 0.21/0.46 ! [A: $tType,A3: A,A2: set @ A] :
% 0.21/0.46 ( ( member @ A @ A3 @ A2 )
% 0.21/0.47 => ( ( insert @ A @ A3 @ A2 )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_absorb
% 0.21/0.47 thf(fact_40_insert__ident,axiom,
% 0.21/0.47 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ~ ( member @ A @ X @ A2 )
% 0.21/0.47 => ( ~ ( member @ A @ X @ B )
% 0.21/0.47 => ( ( ( insert @ A @ X @ A2 )
% 0.21/0.47 = ( insert @ A @ X @ B ) )
% 0.21/0.47 = ( A2 = B ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_ident
% 0.21/0.47 thf(fact_41_Set_Oset__insert,axiom,
% 0.21/0.47 ! [A: $tType,X: A,A2: set @ A] :
% 0.21/0.47 ( ( member @ A @ X @ A2 )
% 0.21/0.47 => ~ ! [B3: set @ A] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 = ( insert @ A @ X @ B3 ) )
% 0.21/0.47 => ( member @ A @ X @ B3 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Set.set_insert
% 0.21/0.47 thf(fact_42_insertI2,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 0.21/0.47 ( ( member @ A @ A3 @ B )
% 0.21/0.47 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertI2
% 0.21/0.47 thf(fact_43_insertI1,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,B: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertI1
% 0.21/0.47 thf(fact_44_insertE,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.21/0.47 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.21/0.47 => ( ( A3 != B2 )
% 0.21/0.47 => ( member @ A @ A3 @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insertE
% 0.21/0.47 thf(fact_45_mem__Collect__eq,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,P: A > $o] :
% 0.21/0.47 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.21/0.47 = ( P @ A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % mem_Collect_eq
% 0.21/0.47 thf(fact_46_Collect__mem__eq,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] :
% 0.21/0.47 ( ( collect @ A
% 0.21/0.47 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mem_eq
% 0.21/0.47 thf(fact_47_Collect__cong,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 = ( Q @ X3 ) )
% 0.21/0.47 => ( ( collect @ A @ P )
% 0.21/0.47 = ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_cong
% 0.21/0.47 thf(fact_48_ext,axiom,
% 0.21/0.47 ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( F @ X3 )
% 0.21/0.47 = ( G @ X3 ) )
% 0.21/0.47 => ( F = G ) ) ).
% 0.21/0.47
% 0.21/0.47 % ext
% 0.21/0.47 thf(fact_49_know__composition__neg1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( knowle1437066798e_know @ P @ M )
% 0.21/0.47 => ( ~ ( knowle1437066798e_know @ Q @ M )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ~ ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % know_composition_neg1
% 0.21/0.47 thf(fact_50_singleton__inject,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,B2: A] :
% 0.21/0.47 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 => ( A3 = B2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_inject
% 0.21/0.47 thf(fact_51_insert__not__empty,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,A2: set @ A] :
% 0.21/0.47 ( ( insert @ A @ A3 @ A2 )
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_not_empty
% 0.21/0.47 thf(fact_52_doubleton__eq__iff,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,B2: A,C: A,D: A] :
% 0.21/0.47 ( ( ( insert @ A @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.21/0.47 = ( ( ( A3 = C )
% 0.21/0.47 & ( B2 = D ) )
% 0.21/0.47 | ( ( A3 = D )
% 0.21/0.47 & ( B2 = C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % doubleton_eq_iff
% 0.21/0.47 thf(fact_53_singleton__iff,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A3: A] :
% 0.21/0.47 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( B2 = A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_iff
% 0.21/0.47 thf(fact_54_singletonD,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A3: A] :
% 0.21/0.47 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 => ( B2 = A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % singletonD
% 0.21/0.47 thf(fact_55_TBtheorem3a,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( ine @ P @ E2 )
% 0.21/0.47 => ( ~ ( ine @ Q @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem3a
% 0.21/0.47 thf(fact_56_TBtheorem1a,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( ine @ PQ @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ine @ P @ E2 )
% 0.21/0.47 | ( ine @ Q @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem1a
% 0.21/0.47 thf(fact_57_the__elem__eq,axiom,
% 0.21/0.47 ! [A: $tType,X: A] :
% 0.21/0.47 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = X ) ).
% 0.21/0.47
% 0.21/0.47 % the_elem_eq
% 0.21/0.47 thf(fact_58_bot__apply,axiom,
% 0.21/0.47 ! [C3: $tType,D2: $tType] :
% 0.21/0.47 ( ( bot @ C3 )
% 0.21/0.47 => ( ( bot_bot @ ( D2 > C3 ) )
% 0.21/0.47 = ( ^ [X2: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_apply
% 0.21/0.47 thf(fact_59_is__singletonI,axiom,
% 0.21/0.47 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singletonI
% 0.21/0.47 thf(fact_60_KS2Expression_Osimps_I1_J,axiom,
% 0.21/0.47 ! [M: secrecy_Keys] :
% 0.21/0.47 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.21/0.47 = ( secrecy_kE @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS2Expression.simps(1)
% 0.21/0.47 thf(fact_61_Set_Ois__empty__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_empty @ A )
% 0.21/0.47 = ( ^ [A4: set @ A] :
% 0.21/0.47 ( A4
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Set.is_empty_def
% 0.21/0.47 thf(fact_62_is__singleton__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_singleton @ A )
% 0.21/0.47 = ( ^ [A4: set @ A] :
% 0.21/0.47 ? [X2: A] :
% 0.21/0.47 ( A4
% 0.21/0.47 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singleton_def
% 0.21/0.47 thf(fact_63_is__singletonE,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] :
% 0.21/0.47 ( ( is_singleton @ A @ A2 )
% 0.21/0.47 => ~ ! [X3: A] :
% 0.21/0.47 ( A2
% 0.21/0.47 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singletonE
% 0.21/0.47 thf(fact_64_bot__set__def,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( set @ A ) )
% 0.21/0.47 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_set_def
% 0.21/0.47 thf(fact_65_is__singleton__the__elem,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( is_singleton @ A )
% 0.21/0.47 = ( ^ [A4: set @ A] :
% 0.21/0.47 ( A4
% 0.21/0.47 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singleton_the_elem
% 0.21/0.47 thf(fact_66_is__singletonI_H,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] :
% 0.21/0.47 ( ( A2
% 0.21/0.47 != ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 => ( ! [X3: A,Y: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ A2 )
% 0.21/0.47 => ( ( member @ A @ Y @ A2 )
% 0.21/0.47 => ( X3 = Y ) ) )
% 0.21/0.47 => ( is_singleton @ A @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % is_singletonI'
% 0.21/0.47 thf(fact_67_bot__fun__def,axiom,
% 0.21/0.47 ! [B4: $tType,A: $tType] :
% 0.21/0.47 ( ( bot @ B4 )
% 0.21/0.47 => ( ( bot_bot @ ( A > B4 ) )
% 0.21/0.47 = ( ^ [X2: A] : ( bot_bot @ B4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_fun_def
% 0.21/0.47 thf(fact_68_TBtheorem4a__empty,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ( ine @ P @ E2 )
% 0.21/0.47 | ( ine @ Q @ E2 ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ( loc @ PQ )
% 0.21/0.47 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.21/0.47 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4a_empty
% 0.21/0.47 thf(fact_69_TBtheorem1b,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( ineM @ PQ @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 | ( ineM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem1b
% 0.21/0.47 thf(fact_70_TBtheorem3b,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem3b
% 0.21/0.47 thf(fact_71_DecrEnc,axiom,
% 0.21/0.47 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list @ secrecy_Expression] :
% 0.21/0.47 ( ( encrDecrKeys @ K12 @ K22 )
% 0.21/0.47 => ( ( decr @ K22 @ ( enc @ K12 @ E2 ) )
% 0.21/0.47 = E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % DecrEnc
% 0.21/0.47 thf(fact_72_ExtSign,axiom,
% 0.21/0.47 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list @ secrecy_Expression] :
% 0.21/0.47 ( ( encrDecrKeys @ K12 @ K22 )
% 0.21/0.47 => ( ( ext @ K12 @ ( sign @ K22 @ E2 ) )
% 0.21/0.47 = E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ExtSign
% 0.21/0.47 thf(fact_73_correctCompositionIn__L2,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionIn_L2
% 0.21/0.47 thf(fact_74_correctCompositionIn__prop1,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionIn_prop1
% 0.21/0.47 thf(fact_75_not__ine__ineM,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set @ secrecy_chanID] :
% 0.21/0.47 ( ~ ( ine @ P @ E2 )
% 0.21/0.47 => ~ ( ineM @ P @ M2 @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_ine_ineM
% 0.21/0.47 thf(fact_76_ineM__ine,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ine @ P @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ineM_ine
% 0.21/0.47 thf(fact_77_correctCompositionIn__L1,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionIn_L1
% 0.21/0.47 thf(fact_78_subcomponents__loc,axiom,
% 0.21/0.47 ! [X: secrecy_specID] :
% 0.21/0.47 ( ( correc965049635ionLoc @ X )
% 0.21/0.47 => ( ( ( subcomponents @ X )
% 0.21/0.47 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 0.21/0.47 => ( ( loc @ X )
% 0.21/0.47 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subcomponents_loc
% 0.21/0.47 thf(fact_79_TBtheorem4b__notP1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4b_notP1
% 0.21/0.47 thf(fact_80_TBtheorem4a__notP1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ine @ P @ E2 )
% 0.21/0.47 => ( ~ ( ine @ Q @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4a_notP1
% 0.21/0.47 thf(fact_81_TBtheorem4b__notPQ,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 0.21/0.47 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4b_notPQ
% 0.21/0.47 thf(fact_82_TBtheorem4b__notP2,axiom,
% 0.21/0.47 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.21/0.47 ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4b_notP2
% 0.21/0.47 thf(fact_83_TBtheorem4a__notPQ,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 0.21/0.47 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4a_notPQ
% 0.21/0.47 thf(fact_84_ine__exprChannelSingle__Set,axiom,
% 0.21/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( ine_ex1303305700Single @ P @ Ch @ E2 )
% 0.21/0.47 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_exprChannelSingle_Set
% 0.21/0.47 thf(fact_85_ine__exprChannelSet__Single,axiom,
% 0.21/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 )
% 0.21/0.47 => ( ine_ex1303305700Single @ P @ Ch @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_exprChannelSet_Single
% 0.21/0.47 thf(fact_86_ine__nonempty__exprChannelSet,axiom,
% 0.21/0.47 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.21/0.47 => ( ( ChSet
% 0.21/0.47 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.21/0.47 => ( ine @ P @ E2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_nonempty_exprChannelSet
% 0.21/0.47 thf(fact_87_ine__empty__exprChannelSet,axiom,
% 0.21/0.47 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.21/0.47 => ( ( ChSet
% 0.21/0.47 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.21/0.47 => ~ ( ine @ P @ E2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_empty_exprChannelSet
% 0.21/0.47 thf(fact_88_TBtheorem4a__notP2,axiom,
% 0.21/0.47 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.21/0.47 ( ~ ( ine @ Q @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4a_notP2
% 0.21/0.47 thf(fact_89_locStream__def,axiom,
% 0.21/0.47 ( locStream
% 0.21/0.47 = ( ^ [X2: secrecy_specID] :
% 0.21/0.47 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 0.21/0.47 @ ( loc @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % locStream_def
% 0.21/0.47 thf(fact_90_inStream__def,axiom,
% 0.21/0.47 ( inStream
% 0.21/0.47 = ( ^ [X2: secrecy_specID] :
% 0.21/0.47 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 0.21/0.47 @ ( ins @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % inStream_def
% 0.21/0.47 thf(fact_91_TBtheorem4b__P,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 0.21/0.47 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4b_P
% 0.21/0.47 thf(fact_92_TBtheorem4b__PQ,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 | ( ineM @ Q @ M2 @ E2 ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4b_PQ
% 0.21/0.47 thf(fact_93_TBtheorem4a__P,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( ine @ P @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4a_P
% 0.21/0.47 thf(fact_94_TBtheorem4a__PQ,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ( ine @ P @ E2 )
% 0.21/0.47 | ( ine @ Q @ E2 ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem4a_PQ
% 0.21/0.47 thf(fact_95_ine__ins__neg1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 0.21/0.47 ( ~ ( ine @ P @ M )
% 0.21/0.47 => ( ( exprChannel @ X @ M )
% 0.21/0.47 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_ins_neg1
% 0.21/0.47 thf(fact_96_ine__def,axiom,
% 0.21/0.47 ( ine
% 0.21/0.47 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 0.21/0.47 ? [Ch3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.21/0.47 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_def
% 0.21/0.47 thf(fact_97_ineM__L1,axiom,
% 0.21/0.47 ! [Ch: secrecy_chanID,M2: set @ secrecy_chanID,P: secrecy_specID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch @ M2 )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ E2 )
% 0.21/0.47 => ( ineM @ P @ M2 @ E2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ineM_L1
% 0.21/0.47 thf(fact_98_ineM__def,axiom,
% 0.21/0.47 ( ineM
% 0.21/0.47 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E3: secrecy_Expression] :
% 0.21/0.47 ? [Ch3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 0.21/0.47 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ineM_def
% 0.21/0.47 thf(fact_99_ine__exprChannelSet__def,axiom,
% 0.21/0.47 ( ine_exprChannelSet
% 0.21/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E3: secrecy_Expression] :
% 0.21/0.47 ( ! [X2: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.21/0.47 & ( exprChannel @ X2 @ E3 ) ) )
% 0.21/0.47 & ! [X2: secrecy_chanID] :
% 0.21/0.47 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) ) )
% 0.21/0.47 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_exprChannelSet_def
% 0.21/0.47 thf(fact_100_ine__exprChannelSingle__def,axiom,
% 0.21/0.47 ( ine_ex1303305700Single
% 0.21/0.47 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.21/0.47 & ( exprChannel @ Ch3 @ E3 )
% 0.21/0.47 & ! [X2: secrecy_chanID,T: nat] :
% 0.21/0.47 ( ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 0.21/0.47 & ( X2 != Ch3 ) )
% 0.21/0.47 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ine_exprChannelSingle_def
% 0.21/0.47 thf(fact_101_LocalSecretsComposition__exprChannel__k,axiom,
% 0.21/0.47 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.21/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_exprChannel_k
% 0.21/0.47 thf(fact_102_correctCompositionInLoc__exprChannel,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ M )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ( ins @ PQ ) )
% 0.21/0.47 => ~ ( exprChannel @ X3 @ M ) )
% 0.21/0.47 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionInLoc_exprChannel
% 0.21/0.47 thf(fact_103_TBlemma3b,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.21/0.47 ( ~ ( ineM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ M2 )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.21/0.47 => ~ ( exprChannel @ Ch @ E2 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBlemma3b
% 0.21/0.47 thf(fact_104_bot__empty__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bot_bot @ ( A > $o ) )
% 0.21/0.47 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_empty_eq
% 0.21/0.47 thf(fact_105_Collect__empty__eq__bot,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o] :
% 0.21/0.47 ( ( ( collect @ A @ P )
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( P
% 0.21/0.47 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_empty_eq_bot
% 0.21/0.47 thf(fact_106_LocalSecretsComposition__neg__loc__k,axiom,
% 0.21/0.47 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.21/0.47 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg_loc_k
% 0.21/0.47 thf(fact_107_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ? [Ch4: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_k_Qex
% 0.21/0.47 thf(fact_108_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ? [Ch4: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_k_Pex
% 0.21/0.47 thf(fact_109_correctCompositionKS__PQ,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.21/0.47 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_PQ
% 0.21/0.47 thf(fact_110_correctCompositionKS__neg1,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_neg1
% 0.21/0.47 thf(fact_111_correctCompositionKS__negP,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_negP
% 0.21/0.47 thf(fact_112_correctCompositionKS__negQ,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_negQ
% 0.21/0.47 thf(fact_113_know__composition,axiom,
% 0.21/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ( ( ( knowle1437066798e_know @ P @ M )
% 0.21/0.47 | ( knowle1437066798e_know @ Q @ M ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % know_composition
% 0.21/0.47 thf(fact_114_know__composition1,axiom,
% 0.21/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ( ( knowle1437066798e_know @ P @ M )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % know_composition1
% 0.21/0.47 thf(fact_115_know__composition2,axiom,
% 0.21/0.47 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ( ( knowle1437066798e_know @ Q @ M )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % know_composition2
% 0.21/0.47 thf(fact_116_correctCompositionKS__exprChannel__k__P,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_k_P
% 0.21/0.47 thf(fact_117_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_k_Q
% 0.21/0.47 thf(fact_118_LocalSecretsComposition__neg__k,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.21/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg_k
% 0.21/0.47 thf(fact_119_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ? [Ch4: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_s_Qex
% 0.21/0.47 thf(fact_120_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ? [Ch4: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_s_Pex
% 0.21/0.47 thf(fact_121_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_s_Q
% 0.21/0.47 thf(fact_122_correctCompositionKS__exprChannel__s__P,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.21/0.47 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_exprChannel_s_P
% 0.21/0.47 thf(fact_123_UnCI,axiom,
% 0.21/0.47 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 0.21/0.47 ( ( ~ ( member @ A @ C @ B )
% 0.21/0.47 => ( member @ A @ C @ A2 ) )
% 0.21/0.47 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % UnCI
% 0.21/0.47 thf(fact_124_Un__iff,axiom,
% 0.21/0.47 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 = ( ( member @ A @ C @ A2 )
% 0.21/0.47 | ( member @ A @ C @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_iff
% 0.21/0.47 thf(fact_125_KS_Oinject_I2_J,axiom,
% 0.21/0.47 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.21/0.47 ( ( ( secrecy_sKS @ X22 )
% 0.21/0.47 = ( secrecy_sKS @ Y22 ) )
% 0.21/0.47 = ( X22 = Y22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS.inject(2)
% 0.21/0.47 thf(fact_126_Expression_Oinject_I2_J,axiom,
% 0.21/0.47 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 0.21/0.47 ( ( ( secrecy_sE @ X22 )
% 0.21/0.47 = ( secrecy_sE @ Y22 ) )
% 0.21/0.47 = ( X22 = Y22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Expression.inject(2)
% 0.21/0.47 thf(fact_127_Un__empty,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( ( A2
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_empty
% 0.21/0.47 thf(fact_128_Un__insert__right,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,A3: A,B: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B ) )
% 0.21/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_insert_right
% 0.21/0.47 thf(fact_129_Un__insert__left,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,B: set @ A,C4: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B ) @ C4 )
% 0.21/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_insert_left
% 0.21/0.47 thf(fact_130_Un__empty__left,axiom,
% 0.21/0.47 ! [A: $tType,B: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 0.21/0.47 = B ) ).
% 0.21/0.47
% 0.21/0.47 % Un_empty_left
% 0.21/0.47 thf(fact_131_Un__empty__right,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % Un_empty_right
% 0.21/0.47 thf(fact_132_not__know__s__not__ine,axiom,
% 0.21/0.47 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.21/0.47 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 => ~ ( ine @ A2 @ ( secrecy_sE @ M ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_know_s_not_ine
% 0.21/0.47 thf(fact_133_UnE,axiom,
% 0.21/0.47 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 => ( ~ ( member @ A @ C @ A2 )
% 0.21/0.47 => ( member @ A @ C @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % UnE
% 0.21/0.47 thf(fact_134_UnI1,axiom,
% 0.21/0.47 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( member @ A @ C @ A2 )
% 0.21/0.47 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % UnI1
% 0.21/0.47 thf(fact_135_UnI2,axiom,
% 0.21/0.47 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 0.21/0.47 ( ( member @ A @ C @ B )
% 0.21/0.47 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % UnI2
% 0.21/0.47 thf(fact_136_bex__Un,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 0.21/0.47 ( ( ? [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 & ( P @ X2 ) ) )
% 0.21/0.47 = ( ? [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ A2 )
% 0.21/0.47 & ( P @ X2 ) )
% 0.21/0.47 | ? [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ B )
% 0.21/0.47 & ( P @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bex_Un
% 0.21/0.47 thf(fact_137_ball__Un,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 0.21/0.47 ( ( ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 => ( P @ X2 ) ) )
% 0.21/0.47 = ( ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ A2 )
% 0.21/0.47 => ( P @ X2 ) )
% 0.21/0.47 & ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ B )
% 0.21/0.47 => ( P @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ball_Un
% 0.21/0.47 thf(fact_138_Un__assoc,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 0.21/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_assoc
% 0.21/0.47 thf(fact_139_Un__absorb,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.21/0.47 = A2 ) ).
% 0.21/0.47
% 0.21/0.47 % Un_absorb
% 0.21/0.47 thf(fact_140_Un__commute,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.21/0.47 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_commute
% 0.21/0.47 thf(fact_141_Un__left__absorb,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_left_absorb
% 0.21/0.47 thf(fact_142_Un__left__commute,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 0.21/0.47 = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_left_commute
% 0.21/0.47 thf(fact_143_KS2Expression_Osimps_I2_J,axiom,
% 0.21/0.47 ! [M: secrecy_Secrets] :
% 0.21/0.47 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.21/0.47 = ( secrecy_sE @ M ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS2Expression.simps(2)
% 0.21/0.47 thf(fact_144_KS_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.21/0.47 ( ( secrecy_kKS @ X1 )
% 0.21/0.47 != ( secrecy_sKS @ X22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS.distinct(1)
% 0.21/0.47 thf(fact_145_KS_Oinduct,axiom,
% 0.21/0.47 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.21/0.47 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 0.21/0.47 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 0.21/0.47 => ( P @ KS ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS.induct
% 0.21/0.47 thf(fact_146_KS_Oexhaust,axiom,
% 0.21/0.47 ! [Y2: secrecy_KS] :
% 0.21/0.47 ( ! [X12: secrecy_Keys] :
% 0.21/0.47 ( Y2
% 0.21/0.47 != ( secrecy_kKS @ X12 ) )
% 0.21/0.47 => ~ ! [X23: secrecy_Secrets] :
% 0.21/0.47 ( Y2
% 0.21/0.47 != ( secrecy_sKS @ X23 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS.exhaust
% 0.21/0.47 thf(fact_147_Expression_Odistinct_I1_J,axiom,
% 0.21/0.47 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 0.21/0.47 ( ( secrecy_kE @ X1 )
% 0.21/0.47 != ( secrecy_sE @ X22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Expression.distinct(1)
% 0.21/0.47 thf(fact_148_KS_Osimps_I6_J,axiom,
% 0.21/0.47 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X22: secrecy_Secrets] :
% 0.21/0.47 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X22 ) )
% 0.21/0.47 = ( F2 @ X22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS.simps(6)
% 0.21/0.47 thf(fact_149_know_Osimps_I2_J,axiom,
% 0.21/0.47 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.21/0.47 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 0.21/0.47 | ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % know.simps(2)
% 0.21/0.47 thf(fact_150_KS_Osimps_I8_J,axiom,
% 0.21/0.47 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X22: secrecy_Secrets] :
% 0.21/0.47 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X22 ) )
% 0.21/0.47 = ( F2 @ X22 ) ) ).
% 0.21/0.47
% 0.21/0.47 % KS.simps(8)
% 0.21/0.47 thf(fact_151_singleton__Un__iff,axiom,
% 0.21/0.47 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 = ( ( ( A2
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.21/0.47 | ( ( A2
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 | ( ( A2
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_Un_iff
% 0.21/0.47 thf(fact_152_Un__singleton__iff,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 0.21/0.47 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( ( ( A2
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.21/0.47 | ( ( A2
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 | ( ( A2
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 & ( B
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_singleton_iff
% 0.21/0.47 thf(fact_153_insert__is__Un,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( insert @ A )
% 0.21/0.47 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_is_Un
% 0.21/0.47 thf(fact_154_LocalSecretsComposition__neg__loc__s,axiom,
% 0.21/0.47 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.21/0.47 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.21/0.47 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg_loc_s
% 0.21/0.47 thf(fact_155_LocalSecretsComposition__neg__s,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.21/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg_s
% 0.21/0.47 thf(fact_156_know__composition__neg__ine__s,axiom,
% 0.21/0.47 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_sKS @ Secret ) )
% 0.21/0.47 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correctCompositionIn @ PQ )
% 0.21/0.47 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % know_composition_neg_ine_s
% 0.21/0.47 thf(fact_157_LocalSecretsComposition__neg1__s,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.21/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg1_s
% 0.21/0.47 thf(fact_158_LocalSecretsComposition__ine2__s,axiom,
% 0.21/0.47 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.21/0.47 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_ine2_s
% 0.21/0.47 thf(fact_159_LocalSecretsComposition__ine1__s,axiom,
% 0.21/0.47 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.21/0.47 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_ine1_s
% 0.21/0.47 thf(fact_160_LocalSecretsComposition__exprChannel__s,axiom,
% 0.21/0.47 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.21/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_exprChannel_s
% 0.21/0.47 thf(fact_161_LocalSecretsComposition__neg,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ( correctCompositionKS @ PQ )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.21/0.47 => ( ! [M4: secrecy_Keys] :
% 0.21/0.47 ( ( Ks
% 0.21/0.47 = ( secrecy_kKS @ M4 ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.21/0.47 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.21/0.47 => ( ! [M4: secrecy_Secrets] :
% 0.21/0.47 ( ( Ks
% 0.21/0.47 = ( secrecy_sKS @ M4 ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.21/0.47 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg
% 0.21/0.47 thf(fact_162_LocalSecretsComposition__neg1,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.21/0.47 => ( ! [M4: secrecy_Keys] :
% 0.21/0.47 ( ( Ks
% 0.21/0.47 = ( secrecy_kKS @ M4 ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.21/0.47 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.21/0.47 => ( ! [M4: secrecy_Secrets] :
% 0.21/0.47 ( ( Ks
% 0.21/0.47 = ( secrecy_sKS @ M4 ) )
% 0.21/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.21/0.47 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.21/0.47 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % LocalSecretsComposition_neg1
% 0.21/0.47 thf(fact_163_sup__bot_Oright__neutral,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [A3: A] :
% 0.21/0.47 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 0.21/0.47 = A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_bot.right_neutral
% 0.21/0.47 thf(fact_164_sup__bot_Oneutr__eq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [A3: A,B2: A] :
% 0.21/0.47 ( ( ( bot_bot @ A )
% 0.21/0.47 = ( sup_sup @ A @ A3 @ B2 ) )
% 0.21/0.47 = ( ( A3
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 & ( B2
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_bot.neutr_eq_iff
% 0.21/0.47 thf(fact_165_sup__bot_Oleft__neutral,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [A3: A] :
% 0.21/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 0.21/0.47 = A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_bot.left_neutral
% 0.21/0.47 thf(fact_166_sup__bot_Oeq__neutr__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [A3: A,B2: A] :
% 0.21/0.47 ( ( ( sup_sup @ A @ A3 @ B2 )
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 = ( ( A3
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 & ( B2
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_bot.eq_neutr_iff
% 0.21/0.47 thf(fact_167_sup__bot__left,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.21/0.47 = X ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_bot_left
% 0.21/0.47 thf(fact_168_sup__bot__right,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [X: A] :
% 0.21/0.47 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.21/0.47 = X ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_bot_right
% 0.21/0.47 thf(fact_169_bot__eq__sup__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ( bot_bot @ A )
% 0.21/0.47 = ( sup_sup @ A @ X @ Y2 ) )
% 0.21/0.47 = ( ( X
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 & ( Y2
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % bot_eq_sup_iff
% 0.21/0.47 thf(fact_170_sup__eq__bot__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( bounde1808546759up_bot @ A )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( ( sup_sup @ A @ X @ Y2 )
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 = ( ( X
% 0.21/0.47 = ( bot_bot @ A ) )
% 0.21/0.47 & ( Y2
% 0.21/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % sup_eq_bot_iff
% 0.21/0.47 thf(fact_171_ineM__Un1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,A2: set @ secrecy_chanID,E2: secrecy_Expression,B: set @ secrecy_chanID] :
% 0.21/0.47 ( ( ineM @ P @ A2 @ E2 )
% 0.21/0.47 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A2 @ B ) @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % ineM_Un1
% 0.21/0.47 thf(fact_172_notSpecKeysSecretsExpr__def,axiom,
% 0.21/0.47 ( notSpe1586871396tsExpr
% 0.21/0.47 = ( ^ [P2: secrecy_specID,E4: list @ secrecy_Expression] :
% 0.21/0.47 ( ! [X2: secrecy_Keys] :
% 0.21/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X2 ) @ E4 )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.21/0.47 & ! [Y4: secrecy_Secrets] :
% 0.21/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y4 ) @ E4 )
% 0.21/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % notSpecKeysSecretsExpr_def
% 0.21/0.47 thf(fact_173_TBtheorem5a__empty,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ( eout @ P @ E2 )
% 0.21/0.47 | ( eout @ Q @ E2 ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( ( loc @ PQ )
% 0.21/0.47 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.21/0.47 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5a_empty
% 0.21/0.47 thf(fact_174_correctCompositionKS__subcomp1,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.21/0.47 ( ( correctCompositionKS @ C4 )
% 0.21/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.21/0.47 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 0.21/0.47 => ? [X3: secrecy_specID] :
% 0.21/0.47 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 0.21/0.47 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_subcomp1
% 0.21/0.47 thf(fact_175_TBtheorem2a,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( eout @ PQ @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( eout @ P @ E2 )
% 0.21/0.47 | ( eout @ Q @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem2a
% 0.21/0.47 thf(fact_176_correctCompositionKS__subcomp3,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.21/0.47 ( ( correctCompositionKS @ C4 )
% 0.21/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.21/0.47 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.21/0.47 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_subcomp3
% 0.21/0.47 thf(fact_177_TBtheorem5a__notP1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( eout @ P @ E2 )
% 0.21/0.47 => ( ~ ( eout @ Q @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5a_notP1
% 0.21/0.47 thf(fact_178_TBtheorem5a__notPQ,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 0.21/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5a_notPQ
% 0.21/0.47 thf(fact_179_TBtheorem5a__notP2,axiom,
% 0.21/0.47 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.21/0.47 ( ~ ( eout @ Q @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5a_notP2
% 0.21/0.47 thf(fact_180_out__exprChannelSingle__Set,axiom,
% 0.21/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( out_ex985543062Single @ P @ Ch @ E2 )
% 0.21/0.47 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % out_exprChannelSingle_Set
% 0.21/0.47 thf(fact_181_out__exprChannelSet__Single,axiom,
% 0.21/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 )
% 0.21/0.47 => ( out_ex985543062Single @ P @ Ch @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % out_exprChannelSet_Single
% 0.21/0.47 thf(fact_182_TBtheorem5b__notPQ,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 0.21/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 0.21/0.47 => ( ( M2
% 0.21/0.47 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5b_notPQ
% 0.21/0.47 thf(fact_183_eout__know__k,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 0.21/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 0.21/0.47 = ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 0.21/0.47 = ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 0.21/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eout_know_k
% 0.21/0.47 thf(fact_184_not__know__k__not__eout,axiom,
% 0.21/0.47 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 0.21/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.21/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 0.21/0.47 => ~ ( eout @ A2 @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_know_k_not_eout
% 0.21/0.47 thf(fact_185_not__eout__eoutM,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set @ secrecy_chanID] :
% 0.21/0.47 ( ~ ( eout @ P @ E2 )
% 0.21/0.47 => ~ ( eoutM @ P @ M2 @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_eout_eoutM
% 0.21/0.47 thf(fact_186_eoutM__eout,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.21/0.47 ( ( eoutM @ P @ M2 @ E2 )
% 0.21/0.47 => ( eout @ P @ E2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % eoutM_eout
% 0.21/0.47 thf(fact_187_TBtheorem2b,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( eoutM @ PQ @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( eoutM @ P @ M2 @ E2 )
% 0.21/0.47 | ( eoutM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem2b
% 0.21/0.47 thf(fact_188_TBtheorem5b__notP2,axiom,
% 0.21/0.47 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.21/0.47 ( ~ ( eoutM @ Q @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 0.21/0.47 => ( ! [X3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 0.21/0.47 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5b_notP2
% 0.21/0.47 thf(fact_189_TBtheorem5b__notP1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( eoutM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ~ ( eoutM @ Q @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5b_notP1
% 0.21/0.47 thf(fact_190_eout__know__nonKS__k,axiom,
% 0.21/0.47 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 0.21/0.47 => ( ( eout @ A2 @ ( secrecy_kE @ M ) )
% 0.21/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 0.21/0.47 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eout_know_nonKS_k
% 0.21/0.47 thf(fact_191_eoutKnowCorrect__L1k,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 0.21/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 0.21/0.47 => ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 0.21/0.47 => ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 0.21/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eoutKnowCorrect_L1k
% 0.21/0.47 thf(fact_192_TBtheore54b__P,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( eoutM @ P @ M2 @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 0.21/0.47 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheore54b_P
% 0.21/0.47 thf(fact_193_TBtheorem5b__PQ,axiom,
% 0.21/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ( eoutM @ P @ M2 @ E2 )
% 0.21/0.47 | ( eoutM @ Q @ M2 @ E2 ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5b_PQ
% 0.21/0.47 thf(fact_194_TBtheorem5a__PQ,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.21/0.47 ( ( ( eout @ P @ E2 )
% 0.21/0.47 | ( eout @ Q @ E2 ) )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem5a_PQ
% 0.21/0.47 thf(fact_195_eout__def,axiom,
% 0.21/0.47 ( eout
% 0.21/0.47 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 0.21/0.47 ? [Ch3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.21/0.47 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eout_def
% 0.21/0.47 thf(fact_196_eoutM__def,axiom,
% 0.21/0.47 ( eoutM
% 0.21/0.47 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E3: secrecy_Expression] :
% 0.21/0.47 ? [Ch3: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.21/0.47 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 0.21/0.47 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eoutM_def
% 0.21/0.47 thf(fact_197_out__exprChannelSet__def,axiom,
% 0.21/0.47 ( out_exprChannelSet
% 0.21/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E3: secrecy_Expression] :
% 0.21/0.47 ( ! [X2: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.21/0.47 & ( exprChannel @ X2 @ E3 ) ) )
% 0.21/0.47 & ! [X2: secrecy_chanID] :
% 0.21/0.47 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 0.21/0.47 & ( member @ secrecy_chanID @ X2 @ ( out @ SP ) ) )
% 0.21/0.47 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % out_exprChannelSet_def
% 0.21/0.47 thf(fact_198_out__exprChannelSingle__def,axiom,
% 0.21/0.47 ( out_ex985543062Single
% 0.21/0.47 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.21/0.47 & ( exprChannel @ Ch3 @ E3 )
% 0.21/0.47 & ! [X2: secrecy_chanID,T: nat] :
% 0.21/0.47 ( ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 0.21/0.47 & ( X2 != Ch3 ) )
% 0.21/0.47 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % out_exprChannelSingle_def
% 0.21/0.47 thf(fact_199_correctCompositionOut__prop1,axiom,
% 0.21/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.21/0.47 ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 0.21/0.47 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 0.21/0.47 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionOut_prop1
% 0.21/0.47 thf(fact_200_TBtheorem45a__P,axiom,
% 0.21/0.47 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.21/0.47 ( ( eout @ P @ E2 )
% 0.21/0.47 => ( ( ( subcomponents @ PQ )
% 0.21/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.21/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.21/0.47 => ( ? [Ch2: secrecy_chanID] :
% 0.21/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.21/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.21/0.47 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.21/0.47 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % TBtheorem45a_P
% 0.21/0.47 thf(fact_201_outStream__def,axiom,
% 0.21/0.47 ( outStream
% 0.21/0.47 = ( ^ [X2: secrecy_specID] :
% 0.21/0.47 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 0.21/0.47 @ ( out @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % outStream_def
% 0.21/0.47 thf(fact_202_eout__know__nonKS__s,axiom,
% 0.21/0.47 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 0.21/0.47 => ( ( eout @ A2 @ ( secrecy_sE @ M ) )
% 0.21/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 => ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eout_know_nonKS_s
% 0.21/0.47 thf(fact_203_correctCompositionKS__subcomp4,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.21/0.47 ( ( correctCompositionKS @ C4 )
% 0.21/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.21/0.47 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 0.21/0.47 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_subcomp4
% 0.21/0.47 thf(fact_204_correctCompositionKS__subcomp2,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.21/0.47 ( ( correctCompositionKS @ C4 )
% 0.21/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.21/0.47 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 0.21/0.47 => ? [X3: secrecy_specID] :
% 0.21/0.47 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 0.21/0.47 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % correctCompositionKS_subcomp2
% 0.21/0.47 thf(fact_205_eout__know__s,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 0.21/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 = ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 0.21/0.47 = ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 0.21/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eout_know_s
% 0.21/0.47 thf(fact_206_not__know__s__not__eout,axiom,
% 0.21/0.47 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 0.21/0.47 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 0.21/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 => ~ ( eout @ A2 @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % not_know_s_not_eout
% 0.21/0.47 thf(fact_207_eoutKnowCorrect__L1s,axiom,
% 0.21/0.47 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 0.21/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 => ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 0.21/0.47 => ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 0.21/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eoutKnowCorrect_L1s
% 0.21/0.47 thf(fact_208_adv__not__know2,axiom,
% 0.21/0.47 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Secrets] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 0.21/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.21/0.47 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % adv_not_know2
% 0.21/0.47 thf(fact_209_adv__not__know1,axiom,
% 0.21/0.47 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Keys] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 0.21/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.21/0.47 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % adv_not_know1
% 0.21/0.47 thf(fact_210_order__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_refl
% 0.21/0.47 thf(fact_211_subset__antisym,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 0.21/0.47 => ( A2 = B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_antisym
% 0.21/0.47 thf(fact_212_subsetI,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( member @ A @ X3 @ A2 )
% 0.21/0.47 => ( member @ A @ X3 @ B ) )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % subsetI
% 0.21/0.47 thf(fact_213_empty__subsetI,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 0.21/0.47
% 0.21/0.47 % empty_subsetI
% 0.21/0.47 thf(fact_214_subset__empty,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( A2
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_empty
% 0.21/0.47 thf(fact_215_insert__subset,axiom,
% 0.21/0.47 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B )
% 0.21/0.47 = ( ( member @ A @ X @ B )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % insert_subset
% 0.21/0.47 thf(fact_216_Un__subset__iff,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 0.21/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_subset_iff
% 0.21/0.47 thf(fact_217_singleton__insert__inj__eq,axiom,
% 0.21/0.47 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 0.21/0.47 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 = ( insert @ A @ A3 @ A2 ) )
% 0.21/0.47 = ( ( A3 = B2 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_insert_inj_eq
% 0.21/0.47 thf(fact_218_singleton__insert__inj__eq_H,axiom,
% 0.21/0.47 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 0.21/0.47 ( ( ( insert @ A @ A3 @ A2 )
% 0.21/0.47 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( ( A3 = B2 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % singleton_insert_inj_eq'
% 0.21/0.47 thf(fact_219_subset__singleton__iff,axiom,
% 0.21/0.47 ! [A: $tType,X4: set @ A,A3: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ X4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 = ( ( X4
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 | ( X4
% 0.21/0.47 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_singleton_iff
% 0.21/0.47 thf(fact_220_subset__singletonD,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,X: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.21/0.47 => ( ( A2
% 0.21/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.21/0.47 | ( A2
% 0.21/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_singletonD
% 0.21/0.47 thf(fact_221_Un__mono,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_mono
% 0.21/0.47 thf(fact_222_Un__least,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_least
% 0.21/0.47 thf(fact_223_Un__upper1,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_upper1
% 0.21/0.47 thf(fact_224_Un__upper2,axiom,
% 0.21/0.47 ! [A: $tType,B: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_upper2
% 0.21/0.47 thf(fact_225_Un__absorb1,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 = B ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_absorb1
% 0.21/0.47 thf(fact_226_Un__absorb2,axiom,
% 0.21/0.47 ! [A: $tType,B: set @ A,A2: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 0.21/0.47 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 = A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % Un_absorb2
% 0.21/0.47 thf(fact_227_subset__UnE,axiom,
% 0.21/0.47 ! [A: $tType,C4: set @ A,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.21/0.47 => ~ ! [A6: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 0.21/0.47 => ! [B6: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B )
% 0.21/0.47 => ( C4
% 0.21/0.47 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_UnE
% 0.21/0.47 thf(fact_228_subset__Un__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.21/0.47 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.21/0.47 = B5 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_Un_eq
% 0.21/0.47 thf(fact_229_Collect__mono__iff,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.21/0.47 = ( ! [X2: A] :
% 0.21/0.47 ( ( P @ X2 )
% 0.21/0.47 => ( Q @ X2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mono_iff
% 0.21/0.47 thf(fact_230_set__eq__subset,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 0.21/0.47 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.21/0.47 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % set_eq_subset
% 0.21/0.47 thf(fact_231_subset__trans,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_trans
% 0.21/0.47 thf(fact_232_Collect__mono,axiom,
% 0.21/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.21/0.47 ( ! [X3: A] :
% 0.21/0.47 ( ( P @ X3 )
% 0.21/0.47 => ( Q @ X3 ) )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % Collect_mono
% 0.21/0.47 thf(fact_233_subset__refl,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.21/0.47
% 0.21/0.47 % subset_refl
% 0.21/0.47 thf(fact_234_subset__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.21/0.47 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.21/0.47 ! [T: A] :
% 0.21/0.47 ( ( member @ A @ T @ A4 )
% 0.21/0.47 => ( member @ A @ T @ B5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_iff
% 0.21/0.47 thf(fact_235_equalityD2,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( A2 = B )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ).
% 0.21/0.47
% 0.21/0.47 % equalityD2
% 0.21/0.47 thf(fact_236_equalityD1,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( A2 = B )
% 0.21/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 0.21/0.47
% 0.21/0.47 % equalityD1
% 0.21/0.47 thf(fact_237_subset__eq,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.21/0.47 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.21/0.47 ! [X2: A] :
% 0.21/0.47 ( ( member @ A @ X2 @ A4 )
% 0.21/0.47 => ( member @ A @ X2 @ B5 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subset_eq
% 0.21/0.47 thf(fact_238_equalityE,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.21/0.47 ( ( A2 = B )
% 0.21/0.47 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 => ~ ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % equalityE
% 0.21/0.47 thf(fact_239_subsetD,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 => ( ( member @ A @ C @ A2 )
% 0.21/0.47 => ( member @ A @ C @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % subsetD
% 0.21/0.47 thf(fact_240_in__mono,axiom,
% 0.21/0.47 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 0.21/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.21/0.47 => ( ( member @ A @ X @ A2 )
% 0.21/0.47 => ( member @ A @ X @ B ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % in_mono
% 0.21/0.47 thf(fact_241_dual__order_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B2: A,A3: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.21/0.47 => ( A3 = B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.antisym
% 0.21/0.47 thf(fact_242_dual__order_Oeq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.21/0.47 = ( ^ [A5: A,B7: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B7 @ A5 )
% 0.21/0.47 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.eq_iff
% 0.21/0.47 thf(fact_243_dual__order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [B2: A,A3: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.21/0.47 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.trans
% 0.21/0.47 thf(fact_244_linorder__wlog,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [P: A > A > $o,A3: A,B2: A] :
% 0.21/0.47 ( ! [A7: A,B8: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A7 @ B8 )
% 0.21/0.47 => ( P @ A7 @ B8 ) )
% 0.21/0.47 => ( ! [A7: A,B8: A] :
% 0.21/0.47 ( ( P @ B8 @ A7 )
% 0.21/0.47 => ( P @ A7 @ B8 ) )
% 0.21/0.47 => ( P @ A3 @ B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % linorder_wlog
% 0.21/0.47 thf(fact_245_dual__order_Orefl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.21/0.47
% 0.21/0.47 % dual_order.refl
% 0.21/0.47 thf(fact_246_order__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X: A,Y2: A,Z2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.21/0.47 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_trans
% 0.21/0.47 thf(fact_247_order__class_Oorder_Oantisym,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B2: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.21/0.47 => ( A3 = B2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.antisym
% 0.21/0.47 thf(fact_248_ord__le__eq__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A3: A,B2: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.21/0.47 => ( ( B2 = C )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_le_eq_trans
% 0.21/0.47 thf(fact_249_ord__eq__le__trans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( ord @ A )
% 0.21/0.47 => ! [A3: A,B2: A,C: A] :
% 0.21/0.47 ( ( A3 = B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % ord_eq_le_trans
% 0.21/0.47 thf(fact_250_order__class_Oorder_Oeq__iff,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 0.21/0.47 = ( ^ [A5: A,B7: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A5 @ B7 )
% 0.21/0.47 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order_class.order.eq_iff
% 0.21/0.47 thf(fact_251_antisym__conv,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [Y2: A,X: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 = ( X = Y2 ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % antisym_conv
% 0.21/0.47 thf(fact_252_le__cases3,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X: A,Y2: A,Z2: A] :
% 0.21/0.47 ( ( ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ X )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Y2 @ X ) )
% 0.21/0.47 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.21/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.21/0.47 => ~ ( ord_less_eq @ A @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases3
% 0.21/0.47 thf(fact_253_order_Otrans,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( order @ A )
% 0.21/0.47 => ! [A3: A,B2: A,C: A] :
% 0.21/0.47 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.21/0.47 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.21/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % order.trans
% 0.21/0.47 thf(fact_254_le__cases,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( linorder @ A )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ~ ( ord_less_eq @ A @ X @ Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % le_cases
% 0.21/0.47 thf(fact_255_eq__refl,axiom,
% 0.21/0.47 ! [A: $tType] :
% 0.21/0.47 ( ( preorder @ A )
% 0.21/0.47 => ! [X: A,Y2: A] :
% 0.21/0.47 ( ( X = Y2 )
% 0.21/0.47 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 % eq_refl
% 0.21/0.47
% 0.21/0.47 % Type constructors (24)
% 0.21/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.21/0.47 bounded_lattice @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.21/0.47 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.21/0.47 ! [A8: $tType,A9: $tType] :
% 0.21/0.47 ( ( bounded_lattice @ A9 )
% 0.21/0.47 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.21/0.47 ! [A8: $tType,A9: $tType] :
% 0.21/0.47 ( ( bounded_lattice @ A9 )
% 0.21/0.47 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.21/0.47 ! [A8: $tType,A9: $tType] :
% 0.21/0.47 ( ( preorder @ A9 )
% 0.21/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.21/0.47 ! [A8: $tType,A9: $tType] :
% 0.21/0.47 ( ( order @ A9 )
% 0.21/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.21/0.47 ! [A8: $tType,A9: $tType] :
% 0.21/0.47 ( ( ord @ A9 )
% 0.21/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.21/0.47 ! [A8: $tType,A9: $tType] :
% 0.21/0.47 ( ( bot @ A9 )
% 0.21/0.47 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 0.21/0.47 preorder @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.21/0.47 linorder @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 0.21/0.47 order @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 0.21/0.47 ord @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Nat_Onat___Orderings_Obot_6,axiom,
% 0.21/0.47 bot @ nat ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.21/0.47 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 0.21/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 0.21/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 0.21/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 0.21/0.47 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 0.21/0.47 bounde1808546759up_bot @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.21/0.47 preorder @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 0.21/0.47 linorder @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.21/0.47 order @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.21/0.47 ord @ $o ).
% 0.21/0.47
% 0.21/0.47 thf(tcon_HOL_Obool___Orderings_Obot_17,axiom,
% 0.21/0.47 bot @ $o ).
% 0.21/0.47
% 0.21/0.47 % Conjectures (1)
% 0.21/0.47 thf(conj_0,conjecture,
% 0.21/0.47 ~ ( member @ secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ) ).
% 0.21/0.47
% 0.21/0.47 %------------------------------------------------------------------------------
% 0.21/0.47 ------------------------
% 2.77/1.58 ---- Embedded in THF ---
% 2.77/1.58 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.77/1.58 %%% Generated on Tue Feb 24 08:26:17 EST 2026
% 2.77/1.58 %%% using '$$dhol' embedding, version 1.3.0.
% 2.77/1.58 %%% Logic specification used:
% 2.77/1.58 %%% thf(spec, logic, $$dhol).
% 2.77/1.58
% 2.77/1.58 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.M5SM4yxb8e/DTF2DTF24271.p
% 2.77/1.58 thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 2.77/1.58 thf(ty_t_Secrecy__types_OSecrets, type, secrecy_Secrets: $tType).
% 2.77/1.58 thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 2.77/1.58 thf(ty_t_Secrecy__types_OchanID, type, secrecy_chanID: $tType).
% 2.77/1.58 thf(ty_t_Secrecy__types_OKeys, type, secrecy_Keys: $tType).
% 2.77/1.58 thf(ty_t_Secrecy__types_OKS, type, secrecy_KS: $tType).
% 2.77/1.58 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.77/1.58 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.77/1.58 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.77/1.58 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 2.77/1.58 thf(sy_c_CompLocalSecrets_OLocalSecrets, type, localSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.77/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect, type, knowle1667810483orrect: (secrecy_specID > (secrecy_KS > $o))).
% 2.77/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow, type, knowle1437066798e_know: (secrecy_specID > (secrecy_KS > $o))).
% 2.77/1.58 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows, type, knowle2055185861_knows: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.77/1.58 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.77/1.58 thf(sy_c_ListExtras_Omem, type, mem: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 2.77/1.58 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.77/1.58 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.77/1.58 thf(sy_c_Secrecy_ODecr, type, decr: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.77/1.58 thf(sy_c_Secrecy_OEnc, type, enc: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.77/1.58 thf(sy_c_Secrecy_OEncrDecrKeys, type, encrDecrKeys: (secrecy_Keys > (secrecy_Keys > $o))).
% 2.77/1.58 thf(sy_c_Secrecy_OExt, type, ext: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.77/1.58 thf(sy_c_Secrecy_OSign, type, sign: (secrecy_Keys > ((list @ secrecy_Expression) > (list @ secrecy_Expression)))).
% 2.77/1.58 thf(sy_c_Secrecy_OcorrectCompositionKS, type, correctCompositionKS: (secrecy_specID > $o)).
% 2.77/1.58 thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 2.77/1.58 thf(sy_c_Secrecy_OeoutM, type, eoutM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.77/1.58 thf(sy_c_Secrecy_OexprChannel, type, exprChannel: (secrecy_chanID > (secrecy_Expression > $o))).
% 2.77/1.58 thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 2.77/1.58 thf(sy_c_Secrecy_OineM, type, ineM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.77/1.58 thf(sy_c_Secrecy_Oine__exprChannelSet, type, ine_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.77/1.58 thf(sy_c_Secrecy_Oine__exprChannelSingle, type, ine_ex1303305700Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 2.77/1.58 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr, type, notSpe1586871396tsExpr: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.77/1.58 thf(sy_c_Secrecy_Oout__exprChannelSet, type, out_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.77/1.58 thf(sy_c_Secrecy_Oout__exprChannelSingle, type, out_ex985543062Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 2.77/1.58 thf(sy_c_Secrecy_OspecKeys, type, specKeys: (secrecy_specID > (set @ secrecy_Keys))).
% 2.77/1.58 thf(sy_c_Secrecy_OspecKeysSecrets, type, specKeysSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.77/1.58 thf(sy_c_Secrecy_OspecSecrets, type, specSecrets: (secrecy_specID > (set @ secrecy_Secrets))).
% 2.77/1.58 thf(sy_c_Secrecy__types_OExpression_OkE, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 2.77/1.58 thf(sy_c_Secrecy__types_OExpression_OsE, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 2.77/1.58 thf(sy_c_Secrecy__types_OKS2Expression, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 2.77/1.58 thf(sy_c_Secrecy__types_OKS_Ocase__KS, type, secrecy_case_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 2.77/1.58 thf(sy_c_Secrecy__types_OKS_OkKS, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 2.77/1.58 thf(sy_c_Secrecy__types_OKS_Orec__KS, type, secrecy_rec_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 2.77/1.58 thf(sy_c_Secrecy__types_OKS_OsKS, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 2.77/1.58 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.77/1.58 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.77/1.58 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.77/1.58 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.77/1.58 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.77/1.58 thf(sy_c_inout_OcorrectCompositionIn, type, correctCompositionIn: (secrecy_specID > $o)).
% 2.77/1.58 thf(sy_c_inout_OcorrectCompositionLoc, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 2.77/1.58 thf(sy_c_inout_OcorrectCompositionOut, type, correc990227761ionOut: (secrecy_specID > $o)).
% 2.77/1.58 thf(sy_c_inout_OinStream, type, inStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 2.77/1.58 thf(sy_c_inout_Oins, type, ins: (secrecy_specID > (set @ secrecy_chanID))).
% 2.77/1.58 thf(sy_c_inout_Oloc, type, loc: (secrecy_specID > (set @ secrecy_chanID))).
% 2.77/1.58 thf(sy_c_inout_OlocStream, type, locStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 2.77/1.58 thf(sy_c_inout_Oout, type, out: (secrecy_specID > (set @ secrecy_chanID))).
% 2.77/1.58 thf(sy_c_inout_OoutStream, type, outStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 2.77/1.58 thf(sy_c_inout_Osubcomponents, type, subcomponents: (secrecy_specID > (set @ secrecy_specID))).
% 2.77/1.58 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.77/1.58 thf(sy_v_P, type, p: secrecy_specID).
% 2.77/1.58 thf(sy_v_PQ, type, pq: secrecy_specID).
% 2.77/1.58 thf(sy_v_Q, type, q: secrecy_specID).
% 2.77/1.58 thf(sy_v_key____, type, key: secrecy_Keys).
% 2.77/1.58 thf(sy_v_m, type, m: secrecy_KS).
% 2.77/1.58 thf(fact_0_not__knowQm, axiom, (~ (((knowle1437066798e_know @ q) @ m)))).
% 2.77/1.58 thf(fact_1_a1, axiom, (m = (secrecy_kKS @ key))).
% 2.77/1.58 thf(fact_2_knowPQ, axiom, ((knowle1437066798e_know @ pq) @ m)).
% 2.77/1.58 thf(fact_3_sg2, axiom, (((member @ secrecy_KS) @ (secrecy_kKS @ key)) @ (localSecrets @ pq))).
% 2.77/1.58 thf(fact_4_KS_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kKS @ X1) = (secrecy_kKS @ Y1)) = (X1 = Y1))))).
% 2.77/1.58 thf(fact_5_sg3a, axiom, (~ (((ine @ q) @ (secrecy_kE @ key))))).
% 2.77/1.58 thf(fact_6_cCompLoc, axiom, (correc965049635ionLoc @ pq)).
% 2.77/1.58 thf(fact_7_a12, axiom, (~ (((ine @ pq) @ (secrecy_kE @ key))))).
% 2.77/1.58 thf(fact_8_KS_Osimps_I7_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 2.77/1.58 thf(fact_9_KS_Osimps_I5_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 2.77/1.58 thf(fact_10_know_Osimps_I1_J, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: ((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)) = (((ine @ A2) @ (secrecy_kE @ M)) | (((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (localSecrets @ A2))))))).
% 2.77/1.58 thf(fact_11_subPQ, axiom, ((subcomponents @ pq) = (((insert @ secrecy_specID) @ p) @ (((insert @ secrecy_specID) @ q) @ (bot_bot @ (set @ secrecy_specID)))))).
% 2.77/1.58 thf(fact_12_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))))).
% 2.77/1.58 thf(fact_13_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))))).
% 2.77/1.58 thf(fact_14_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)))))).
% 2.77/1.58 thf(fact_15_Expression_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kE @ X1) = (secrecy_kE @ Y1)) = (X1 = Y1))))).
% 2.77/1.58 thf(fact_16_cCompI, axiom, (correctCompositionIn @ pq)).
% 2.77/1.58 thf(fact_17_not__know__k__not__ine, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: (((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (~ (((ine @ A2) @ (secrecy_kE @ M)))))))).
% 2.77/1.58 thf(fact_18_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)))))).
% 2.77/1.58 thf(fact_19_LocalSecretsComposition__ine1__k, axiom, (! [K:secrecy_Keys,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_kE @ K)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_kE @ K))))))))))).
% 2.77/1.58 thf(fact_20_LocalSecretsComposition__ine2__k, axiom, (! [K:secrecy_Keys,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_kE @ K)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_kE @ K))))))))))).
% 2.77/1.58 thf(fact_21_LocalSecretsComposition__neg1__k, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Keys:secrecy_Keys]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_kE @ Keys)))) => ((~ (((ine @ Q) @ (secrecy_kE @ Keys)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ PQ))))))))))))).
% 2.77/1.58 thf(fact_22_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.77/1.58 thf(fact_23_LocalSecretsComposition1, axiom, (! [Ls:secrecy_KS,P:secrecy_specID,PQ:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ Ls) @ (localSecrets @ P)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => (((member @ secrecy_KS) @ Ls) @ (localSecrets @ PQ))))))).
% 2.77/1.58 thf(fact_24_know__composition__neg__ine__k, axiom, (! [P:secrecy_specID,Key:secrecy_Keys,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((knowle1437066798e_know @ P) @ (secrecy_kKS @ Key)))) => ((~ (((knowle1437066798e_know @ Q) @ (secrecy_kKS @ Key)))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ (secrecy_kE @ Key))))))))))).
% 2.77/1.58 thf(fact_25_insertCI, axiom, (! [A:$tType,A3:A,B:(set @ A),B2:A]: ((((~ ((((member @ A) @ A3) @ B))) => (A3 = B2)) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B)))))).
% 2.77/1.58 thf(fact_26_insert__iff, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) = ((A3 = B2) | (((member @ A) @ A3) @ A2)))))).
% 2.77/1.58 thf(fact_27_insert__absorb2, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A2)) = (((insert @ A) @ X) @ A2))))).
% 2.77/1.58 thf(fact_28_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 2.77/1.58 thf(fact_29_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 2.77/1.58 thf(fact_30_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X2:A]: ((~ ((P @ X2))))))))).
% 2.77/1.58 thf(fact_31_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X2:A]: ((~ ((((member @ A) @ X2) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.77/1.58 thf(fact_32_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X2:A]: ((((member @ A) @ X2) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 2.77/1.58 thf(fact_33_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y:A]: ((~ ((((member @ A) @ Y) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 2.77/1.58 thf(fact_34_equals0D, axiom, (! [A:$tType,A2:(set @ A),A3:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A2))))))).
% 2.77/1.58 thf(fact_35_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.77/1.58 thf(fact_36_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => (? [B3:(set @ A)]: (((A2 = (((insert @ A) @ A3) @ B3)) & (~ ((((member @ A) @ A3) @ B3)))))))))).
% 2.77/1.58 thf(fact_37_insert__commute, axiom, (! [A:$tType,X:A,Y2:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y2) @ A2)) = (((insert @ A) @ Y2) @ (((insert @ A) @ X) @ A2)))))).
% 2.77/1.58 thf(fact_38_insert__eq__iff, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A,B:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((~ ((((member @ A) @ B2) @ B))) => (((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ B)) = (((A3 = B2) => (A2 = B)) & ((A3 != B2) => (? [C2:(set @ A)]: (((A2 = (((insert @ A) @ B2) @ C2)) & ((~ ((((member @ A) @ B2) @ C2))) & ((B = (((insert @ A) @ A3) @ C2)) & (~ ((((member @ A) @ A3) @ C2)))))))))))))))).
% 2.77/1.58 thf(fact_39_insert__absorb, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ A2) = A2))))).
% 2.77/1.58 thf(fact_40_insert__ident, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((~ ((((member @ A) @ X) @ B))) => (((((insert @ A) @ X) @ A2) = (((insert @ A) @ X) @ B)) = (A2 = B))))))).
% 2.77/1.58 thf(fact_41_Set_Oset__insert, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((member @ A) @ X) @ A2) => (~ ((! [B3:(set @ A)]: (((A2 = (((insert @ A) @ X) @ B3)) => (((member @ A) @ X) @ B3)))))))))).
% 2.77/1.58 thf(fact_42_insertI2, axiom, (! [A:$tType,A3:A,B:(set @ A),B2:A]: (((((member @ A) @ A3) @ B) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B)))))).
% 2.77/1.58 thf(fact_43_insertI1, axiom, (! [A:$tType,A3:A,B:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B))))).
% 2.77/1.58 thf(fact_44_insertE, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) => ((A3 != B2) => (((member @ A) @ A3) @ A2)))))).
% 2.77/1.58 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.77/1.58 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X2:A]: ((((member @ A) @ X2) @ A2)))) = A2)))).
% 2.77/1.58 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) = (Q @ X3)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.77/1.58 thf(fact_48_ext, axiom, (! [B4:$tType,A:$tType,F:(A > B4),G:(A > B4)]: (((! [X3:A]: (((F @ X3) = (G @ X3)))) => (F = G))))).
% 2.77/1.58 thf(fact_49_know__composition__neg1, axiom, (! [P:secrecy_specID,M:secrecy_KS,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((knowle1437066798e_know @ P) @ M))) => ((~ (((knowle1437066798e_know @ Q) @ M))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionIn @ PQ) => (~ (((knowle1437066798e_know @ PQ) @ M))))))))))).
% 2.77/1.58 thf(fact_50_singleton__inject, axiom, (! [A:$tType,A3:A,B2:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A3 = B2))))).
% 2.77/1.58 thf(fact_51_insert__not__empty, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ A2) != (bot_bot @ (set @ A)))))).
% 2.77/1.58 thf(fact_52_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B2:A,C:A,D:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A3 = C) & (B2 = D)) | ((A3 = D) & (B2 = C))))))).
% 2.77/1.58 thf(fact_53_singleton__iff, axiom, (! [A:$tType,B2:A,A3:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B2 = A3))))).
% 2.77/1.58 thf(fact_54_singletonD, axiom, (! [A:$tType,B2:A,A3:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B2 = A3))))).
% 2.77/1.58 thf(fact_55_TBtheorem3a, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((ine @ P) @ E2))) => ((~ (((ine @ Q) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ E2)))))))))).
% 2.77/1.58 thf(fact_56_TBtheorem1a, axiom, (! [PQ:secrecy_specID,E2:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((ine @ PQ) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((ine @ P) @ E2) | ((ine @ Q) @ E2)))))))).
% 2.77/1.58 thf(fact_57_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 2.77/1.58 thf(fact_58_bot__apply, axiom, (! [C3:$tType,D2:$tType]: (((bot @ C3) => ((bot_bot @ (D2 > C3)) = (^ [X2:D2]: ((bot_bot @ C3)))))))).
% 2.77/1.58 thf(fact_59_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 2.77/1.58 thf(fact_60_KS2Expression_Osimps_I1_J, axiom, (! [M:secrecy_Keys]: (((secrec1016742679ession @ (secrecy_kKS @ M)) = (secrecy_kE @ M))))).
% 2.77/1.58 thf(fact_61_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A4:(set @ A)]: ((A4 = (bot_bot @ (set @ A))))))))).
% 2.77/1.58 thf(fact_62_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((? [X2:A]: ((A4 = (((insert @ A) @ X2) @ (bot_bot @ (set @ A)))))))))))).
% 2.77/1.58 thf(fact_63_is__singletonE, axiom, (! [A:$tType,A2:(set @ A)]: ((((is_singleton @ A) @ A2) => (~ ((! [X3:A]: ((A2 != (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))))))).
% 2.77/1.58 thf(fact_64_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.77/1.58 thf(fact_65_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((A4 = (((insert @ A) @ ((the_elem @ A) @ A4)) @ (bot_bot @ (set @ A)))))))))).
% 2.77/1.58 thf(fact_66_is__singletonI_H, axiom, (! [A:$tType,A2:(set @ A)]: (((A2 != (bot_bot @ (set @ A))) => ((! [X3:A,Y:A]: (((((member @ A) @ X3) @ A2) => ((((member @ A) @ Y) @ A2) => (X3 = Y))))) => ((is_singleton @ A) @ A2)))))).
% 2.77/1.58 thf(fact_67_bot__fun__def, axiom, (! [B4:$tType,A:$tType]: (((bot @ B4) => ((bot_bot @ (A > B4)) = (^ [X2:A]: ((bot_bot @ B4)))))))).
% 2.77/1.58 thf(fact_68_TBtheorem4a__empty, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E2) | ((ine @ Q) @ E2)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((loc @ PQ) = (bot_bot @ (set @ secrecy_chanID))) => ((ine @ PQ) @ E2)))))))).
% 2.77/1.58 thf(fact_69_TBtheorem1b, axiom, (! [PQ:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((ineM @ PQ) @ M2) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ineM @ P) @ M2) @ E2) | (((ineM @ Q) @ M2) @ E2)))))))).
% 2.77/1.58 thf(fact_70_TBtheorem3b, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((ineM @ P) @ M2) @ E2))) => ((~ ((((ineM @ Q) @ M2) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ ((((ineM @ PQ) @ M2) @ E2)))))))))).
% 2.77/1.58 thf(fact_71_DecrEnc, axiom, (! [K12:secrecy_Keys,K22:secrecy_Keys,E2:(list @ secrecy_Expression)]: ((((encrDecrKeys @ K12) @ K22) => (((decr @ K22) @ ((enc @ K12) @ E2)) = E2))))).
% 2.77/1.58 thf(fact_72_ExtSign, axiom, (! [K12:secrecy_Keys,K22:secrecy_Keys,E2:(list @ secrecy_Expression)]: ((((encrDecrKeys @ K12) @ K22) => (((ext @ K12) @ ((sign @ K22) @ E2)) = E2))))).
% 2.77/1.58 thf(fact_73_correctCompositionIn__L2, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch) @ (ins @ Q))))))))).
% 2.77/1.58 thf(fact_74_correctCompositionIn__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ X) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ X) @ (ins @ P)) | (((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))).
% 2.77/1.58 thf(fact_75_not__ine__ineM, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,M2:(set @ secrecy_chanID)]: (((~ (((ine @ P) @ E2))) => (~ ((((ineM @ P) @ M2) @ E2))))))).
% 2.77/1.58 thf(fact_76_ineM__ine, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((((ineM @ P) @ M2) @ E2) => ((ine @ P) @ E2))))).
% 2.77/1.58 thf(fact_77_correctCompositionIn__L1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((member @ secrecy_chanID) @ Ch) @ (ins @ PQ))))))))).
% 2.77/1.58 thf(fact_78_subcomponents__loc, axiom, (! [X:secrecy_specID]: (((correc965049635ionLoc @ X) => (((subcomponents @ X) = (bot_bot @ (set @ secrecy_specID))) => ((loc @ X) = (bot_bot @ (set @ secrecy_chanID)))))))).
% 2.77/1.58 thf(fact_79_TBtheorem4b__notP1, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ineM @ P) @ M2) @ E2) => ((~ ((((ineM @ Q) @ M2) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch2) @ E2) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))) => (~ ((((ineM @ PQ) @ M2) @ E2))))))))))).
% 2.77/1.58 thf(fact_80_TBtheorem4a__notP1, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((ine @ P) @ E2) => ((~ (((ine @ Q) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch2) @ E2) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E2))))))))))).
% 2.77/1.58 thf(fact_81_TBtheorem4b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E2:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M2:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E2) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M2) @ E2)))))))))))).
% 2.77/1.58 thf(fact_82_TBtheorem4b__notP2, axiom, (! [Q:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((ineM @ Q) @ M2) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M2) @ E2))))))))))).
% 2.77/1.58 thf(fact_83_TBtheorem4a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E2:secrecy_Expression,ChSetQ:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E2) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E2)))))))))))).
% 2.77/1.58 thf(fact_84_ine__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E2:secrecy_Expression]: (((((ine_ex1303305700Single @ P) @ Ch) @ E2) => (((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E2))))).
% 2.77/1.58 thf(fact_85_ine__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E2:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E2) => (((ine_ex1303305700Single @ P) @ Ch) @ E2))))).
% 2.77/1.58 thf(fact_86_ine__nonempty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E2:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E2) => ((ChSet != (bot_bot @ (set @ secrecy_chanID))) => ((ine @ P) @ E2)))))).
% 2.77/1.58 thf(fact_87_ine__empty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E2:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E2) => ((ChSet = (bot_bot @ (set @ secrecy_chanID))) => (~ (((ine @ P) @ E2)))))))).
% 2.77/1.58 thf(fact_88_TBtheorem4a__notP2, axiom, (! [Q:secrecy_specID,E2:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((ine @ Q) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E2))))))))))).
% 2.77/1.58 thf(fact_89_locStream__def, axiom, (locStream = (^ [X2:secrecy_specID]: (((^ [Y3:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y3 = Z))) @ (loc @ X2)))))).
% 2.77/1.58 thf(fact_90_inStream__def, axiom, (inStream = (^ [X2:secrecy_specID]: (((^ [Y3:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y3 = Z))) @ (ins @ X2)))))).
% 2.77/1.58 thf(fact_91_TBtheorem4b__P, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((ineM @ P) @ M2) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ Q)) & (((exprChannel @ Ch2) @ E2) & ((~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch2) @ M2)))))) => (((ineM @ PQ) @ M2) @ E2)))))))).
% 2.77/1.58 thf(fact_92_TBtheorem4b__PQ, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((ineM @ P) @ M2) @ E2) | (((ineM @ Q) @ M2) @ E2)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (ins @ Q))) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((exprChannel @ Ch2) @ E2) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))))))) => (((ineM @ PQ) @ M2) @ E2)))))))).
% 2.77/1.58 thf(fact_93_TBtheorem4a__P, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((ine @ P) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ P)) & (((exprChannel @ Ch2) @ E2) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E2)))))))).
% 2.77/1.58 thf(fact_94_TBtheorem4a__PQ, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E2) | ((ine @ Q) @ E2)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (ins @ Q))) & (((exprChannel @ Ch2) @ E2) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E2)))))))).
% 2.77/1.58 thf(fact_95_ine__ins__neg1, axiom, (! [P:secrecy_specID,M:secrecy_Expression,X:secrecy_chanID]: (((~ (((ine @ P) @ M))) => (((exprChannel @ X) @ M) => (~ ((((member @ secrecy_chanID) @ X) @ (ins @ P))))))))).
% 2.77/1.58 thf(fact_96_ine__def, axiom, (ine = (^ [SP:secrecy_specID,E3:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & ((exprChannel @ Ch3) @ E3)))))))).
% 2.77/1.58 thf(fact_97_ineM__L1, axiom, (! [Ch:secrecy_chanID,M2:(set @ secrecy_chanID),P:secrecy_specID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch) @ M2) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ E2) => (((ineM @ P) @ M2) @ E2))))))).
% 2.77/1.58 thf(fact_98_ineM__def, axiom, (ineM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E3:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & ((((member @ secrecy_chanID) @ Ch3) @ M3) & ((exprChannel @ Ch3) @ E3))))))))).
% 2.77/1.58 thf(fact_99_ine__exprChannelSet__def, axiom, (ine_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E3:secrecy_Expression]: (((! [X2:secrecy_chanID]: (((((member @ secrecy_chanID) @ X2) @ ChSet2) => ((((member @ secrecy_chanID) @ X2) @ (ins @ SP)) & ((exprChannel @ X2) @ E3))))) & (! [X2:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X2) @ ChSet2))) & (((member @ secrecy_chanID) @ X2) @ (ins @ SP))) => (~ (((exprChannel @ X2) @ E3))))))))))).
% 2.77/1.58 thf(fact_100_ine__exprChannelSingle__def, axiom, (ine_ex1303305700Single = (^ [SP:secrecy_specID,Ch3:secrecy_chanID,E3:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & (((exprChannel @ Ch3) @ E3) & (! [X2:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X2) @ (ins @ SP)) & (X2 != Ch3)) => (~ (((exprChannel @ X2) @ E3)))))))))))).
% 2.77/1.58 thf(fact_101_LocalSecretsComposition__exprChannel__k, axiom, (! [X:secrecy_chanID,Keys:secrecy_Keys,P:secrecy_specID,Q:secrecy_specID]: ((((exprChannel @ X) @ (secrecy_kE @ Keys)) => ((~ (((ine @ P) @ (secrecy_kE @ Keys)))) => ((~ (((ine @ Q) @ (secrecy_kE @ Keys)))) => ((~ ((((member @ secrecy_chanID) @ X) @ (ins @ P)))) & (~ ((((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))))).
% 2.77/1.58 thf(fact_102_correctCompositionInLoc__exprChannel, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID,M:secrecy_Expression]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ M) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ (ins @ PQ)) => (~ (((exprChannel @ X3) @ M)))))) => (((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))))))))).
% 2.77/1.58 thf(fact_103_TBlemma3b, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((ineM @ P) @ M2) @ E2))) => ((~ ((((ineM @ Q) @ M2) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ M2) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => (~ (((exprChannel @ Ch) @ E2)))))))))))).
% 2.77/1.58 thf(fact_104_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X2:A]: ((((member @ A) @ X2) @ (bot_bot @ (set @ A))))))))).
% 2.77/1.58 thf(fact_105_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.77/1.58 thf(fact_106_LocalSecretsComposition__neg__loc__k, axiom, (! [Key:secrecy_Keys,P:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ P)))) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ P)))) => (~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ P)))))))))).
% 2.77/1.58 thf(fact_107_correctCompositionKS__exprChannel__k__Qex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_kE @ Key))))))))))))))).
% 2.77/1.58 thf(fact_108_correctCompositionKS__exprChannel__k__Pex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_kE @ Key))))))))))))))).
% 2.77/1.58 thf(fact_109_correctCompositionKS__PQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)) => ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)) | (((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q))))))))).
% 2.77/1.58 thf(fact_110_correctCompositionKS__neg1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ))))))))))).
% 2.77/1.58 thf(fact_111_correctCompositionKS__negP, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))))))))).
% 2.77/1.58 thf(fact_112_correctCompositionKS__negQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))))))))).
% 2.77/1.58 thf(fact_113_know__composition, axiom, (! [M:secrecy_KS,P:secrecy_specID,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ Q)))) => ((((knowle1437066798e_know @ P) @ M) | ((knowle1437066798e_know @ Q) @ M)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((correctCompositionKS @ PQ) => ((knowle1437066798e_know @ PQ) @ M)))))))))).
% 2.77/1.58 thf(fact_114_know__composition1, axiom, (! [M:secrecy_KS,P:secrecy_specID,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ Q)))) => (((knowle1437066798e_know @ P) @ M) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((correctCompositionKS @ PQ) => ((knowle1437066798e_know @ PQ) @ M)))))))))).
% 2.77/1.58 thf(fact_115_know__composition2, axiom, (! [M:secrecy_KS,P:secrecy_specID,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ Q)))) => (((knowle1437066798e_know @ Q) @ M) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((correctCompositionKS @ PQ) => ((knowle1437066798e_know @ PQ) @ M)))))))))).
% 2.77/1.58 thf(fact_116_correctCompositionKS__exprChannel__k__P, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_kE @ Key))))))))))))).
% 2.77/1.58 thf(fact_117_correctCompositionKS__exprChannel__k__Q, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_kE @ Key))))))))))))).
% 2.77/1.58 thf(fact_118_LocalSecretsComposition__neg__k, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,M:secrecy_Keys]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (specKeysSecrets @ Q)))) => ((~ (((ine @ P) @ (secrecy_kE @ M)))) => ((~ (((ine @ Q) @ (secrecy_kE @ M)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (localSecrets @ PQ))))))))))))))).
% 2.77/1.58 thf(fact_119_correctCompositionKS__exprChannel__s__Qex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_sE @ Secret))))))))))))))).
% 2.77/1.58 thf(fact_120_correctCompositionKS__exprChannel__s__Pex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_sE @ Secret))))))))))))))).
% 2.77/1.58 thf(fact_121_correctCompositionKS__exprChannel__s__Q, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_sE @ Secret))))))))))))).
% 2.77/1.58 thf(fact_122_correctCompositionKS__exprChannel__s__P, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_sE @ Secret))))))))))))).
% 2.77/1.58 thf(fact_123_UnCI, axiom, (! [A:$tType,C:A,B:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C) @ B))) => (((member @ A) @ C) @ A2)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 2.77/1.58 thf(fact_124_Un__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)) = ((((member @ A) @ C) @ A2) | (((member @ A) @ C) @ B)))))).
% 2.77/1.58 thf(fact_125_KS_Oinject_I2_J, axiom, (! [X22:secrecy_Secrets,Y22:secrecy_Secrets]: ((((secrecy_sKS @ X22) = (secrecy_sKS @ Y22)) = (X22 = Y22))))).
% 2.77/1.58 thf(fact_126_Expression_Oinject_I2_J, axiom, (! [X22:secrecy_Secrets,Y22:secrecy_Secrets]: ((((secrecy_sE @ X22) = (secrecy_sE @ Y22)) = (X22 = Y22))))).
% 2.77/1.58 thf(fact_127_Un__empty, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A2) @ B) = (bot_bot @ (set @ A))) = ((A2 = (bot_bot @ (set @ A))) & (B = (bot_bot @ (set @ A)))))))).
% 2.77/1.58 thf(fact_128_Un__insert__right, axiom, (! [A:$tType,A2:(set @ A),A3:A,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B)) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 2.77/1.58 thf(fact_129_Un__insert__left, axiom, (! [A:$tType,A3:A,B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A3) @ B)) @ C4) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 2.77/1.58 thf(fact_130_Un__empty__left, axiom, (! [A:$tType,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B) = B)))).
% 2.77/1.58 thf(fact_131_Un__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 2.77/1.58 thf(fact_132_not__know__s__not__ine, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: (((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (~ (((ine @ A2) @ (secrecy_sE @ M)))))))).
% 2.77/1.58 thf(fact_133_UnE, axiom, (! [A:$tType,C:A,A2:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)) => ((~ ((((member @ A) @ C) @ A2))) => (((member @ A) @ C) @ B)))))).
% 2.77/1.58 thf(fact_134_UnI1, axiom, (! [A:$tType,C:A,A2:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 2.77/1.58 thf(fact_135_UnI2, axiom, (! [A:$tType,C:A,B:(set @ A),A2:(set @ A)]: (((((member @ A) @ C) @ B) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 2.77/1.58 thf(fact_136_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),P:(A > $o)]: (((? [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B)) & (P @ X2)))) = ((? [X2:A]: (((((member @ A) @ X2) @ A2) & (P @ X2)))) | (? [X2:A]: (((((member @ A) @ X2) @ B) & (P @ X2))))))))).
% 2.77/1.58 thf(fact_137_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),P:(A > $o)]: (((! [X2:A]: (((((member @ A) @ X2) @ (((sup_sup @ (set @ A)) @ A2) @ B)) => (P @ X2)))) = ((! [X2:A]: (((((member @ A) @ X2) @ A2) => (P @ X2)))) & (! [X2:A]: (((((member @ A) @ X2) @ B) => (P @ X2))))))))).
% 2.77/1.58 thf(fact_138_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ C4) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 2.77/1.58 thf(fact_139_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.77/1.58 thf(fact_140_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A4))))))).
% 2.77/1.58 thf(fact_141_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B)) = (((sup_sup @ (set @ A)) @ A2) @ B))))).
% 2.77/1.58 thf(fact_142_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B) @ C4)) = (((sup_sup @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A2) @ C4)))))).
% 2.77/1.58 thf(fact_143_KS2Expression_Osimps_I2_J, axiom, (! [M:secrecy_Secrets]: (((secrec1016742679ession @ (secrecy_sKS @ M)) = (secrecy_sE @ M))))).
% 2.77/1.58 thf(fact_144_KS_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X22:secrecy_Secrets]: (((secrecy_kKS @ X1) != (secrecy_sKS @ X22))))).
% 2.77/1.58 thf(fact_145_KS_Oinduct, axiom, (! [P:(secrecy_KS > $o),KS:secrecy_KS]: (((! [X3:secrecy_Keys]: ((P @ (secrecy_kKS @ X3)))) => ((! [X3:secrecy_Secrets]: ((P @ (secrecy_sKS @ X3)))) => (P @ KS)))))).
% 2.77/1.58 thf(fact_146_KS_Oexhaust, axiom, (! [Y2:secrecy_KS]: (((! [X12:secrecy_Keys]: ((Y2 != (secrecy_kKS @ X12)))) => (~ ((! [X23:secrecy_Secrets]: ((Y2 != (secrecy_sKS @ X23)))))))))).
% 2.77/1.58 thf(fact_147_Expression_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X22:secrecy_Secrets]: (((secrecy_kE @ X1) != (secrecy_sE @ X22))))).
% 2.77/1.58 thf(fact_148_KS_Osimps_I6_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X22:secrecy_Secrets]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X22)) = (F2 @ X22))))).
% 2.77/1.58 thf(fact_149_know_Osimps_I2_J, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: ((((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)) = (((ine @ A2) @ (secrecy_sE @ M)) | (((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (localSecrets @ A2))))))).
% 2.77/1.58 thf(fact_150_KS_Osimps_I8_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X22:secrecy_Secrets]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X22)) = (F2 @ X22))))).
% 2.77/1.58 thf(fact_151_singleton__Un__iff, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A2) @ B)) = (((A2 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.77/1.58 thf(fact_152_Un__singleton__iff, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A2) @ B) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A2 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.77/1.58 thf(fact_153_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A5:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))))))))).
% 2.77/1.58 thf(fact_154_LocalSecretsComposition__neg__loc__s, axiom, (! [Secret:secrecy_Secrets,P:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ P)))) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ P)))) => (~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ P)))))))))).
% 2.77/1.58 thf(fact_155_LocalSecretsComposition__neg__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,M:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (specKeysSecrets @ Q)))) => ((~ (((ine @ P) @ (secrecy_sE @ M)))) => ((~ (((ine @ Q) @ (secrecy_sE @ M)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (localSecrets @ PQ))))))))))))))).
% 2.77/1.58 thf(fact_156_know__composition__neg__ine__s, axiom, (! [P:secrecy_specID,Secret:secrecy_Secrets,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((knowle1437066798e_know @ P) @ (secrecy_sKS @ Secret)))) => ((~ (((knowle1437066798e_know @ Q) @ (secrecy_sKS @ Secret)))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ (secrecy_sE @ Secret))))))))))).
% 2.77/1.58 thf(fact_157_LocalSecretsComposition__neg1__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,S:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ))))))))))))).
% 2.77/1.58 thf(fact_158_LocalSecretsComposition__ine2__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_sE @ S))))))))))).
% 2.77/1.58 thf(fact_159_LocalSecretsComposition__ine1__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_sE @ S))))))))))).
% 2.77/1.58 thf(fact_160_LocalSecretsComposition__exprChannel__s, axiom, (! [X:secrecy_chanID,Secrets:secrecy_Secrets,P:secrecy_specID,Q:secrecy_specID]: ((((exprChannel @ X) @ (secrecy_sE @ Secrets)) => ((~ (((ine @ P) @ (secrecy_sE @ Secrets)))) => ((~ (((ine @ Q) @ (secrecy_sE @ Secrets)))) => ((~ ((((member @ secrecy_chanID) @ X) @ (ins @ P)))) & (~ ((((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))))).
% 2.77/1.58 thf(fact_161_LocalSecretsComposition__neg, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))) => ((! [M4:secrecy_Keys]: (((Ks = (secrecy_kKS @ M4)) => ((~ (((ine @ P) @ (secrecy_kE @ M4)))) & (~ (((ine @ Q) @ (secrecy_kE @ M4)))))))) => ((! [M4:secrecy_Secrets]: (((Ks = (secrecy_sKS @ M4)) => ((~ (((ine @ P) @ (secrecy_sE @ M4)))) & (~ (((ine @ Q) @ (secrecy_sE @ M4)))))))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ PQ))))))))))))))).
% 2.77/1.58 thf(fact_162_LocalSecretsComposition__neg1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((! [M4:secrecy_Keys]: (((Ks = (secrecy_kKS @ M4)) => ((~ (((ine @ P) @ (secrecy_kE @ M4)))) & (~ (((ine @ Q) @ (secrecy_kE @ M4)))))))) => ((! [M4:secrecy_Secrets]: (((Ks = (secrecy_sKS @ M4)) => ((~ (((ine @ P) @ (secrecy_sE @ M4)))) & (~ (((ine @ Q) @ (secrecy_sE @ M4)))))))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ PQ))))))))))))).
% 2.77/1.58 thf(fact_163_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ (bot_bot @ A)) = A3))))))).
% 2.77/1.58 thf(fact_164_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A3) @ B2)) = ((A3 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 2.77/1.58 thf(fact_165_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A3) = A3))))))).
% 2.77/1.58 thf(fact_166_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B2:A]: ((((((sup_sup @ A) @ A3) @ B2) = (bot_bot @ A)) = ((A3 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 2.77/1.58 thf(fact_167_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 2.77/1.58 thf(fact_168_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 2.77/1.58 thf(fact_169_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y2)) = ((X = (bot_bot @ A)) & (Y2 = (bot_bot @ A)))))))))).
% 2.77/1.58 thf(fact_170_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y2:A]: ((((((sup_sup @ A) @ X) @ Y2) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y2 = (bot_bot @ A)))))))))).
% 2.77/1.58 thf(fact_171_ineM__Un1, axiom, (! [P:secrecy_specID,A2:(set @ secrecy_chanID),E2:secrecy_Expression,B:(set @ secrecy_chanID)]: (((((ineM @ P) @ A2) @ E2) => (((ineM @ P) @ (((sup_sup @ (set @ secrecy_chanID)) @ A2) @ B)) @ E2))))).
% 2.77/1.58 thf(fact_172_notSpecKeysSecretsExpr__def, axiom, (notSpe1586871396tsExpr = (^ [P2:secrecy_specID,E4:(list @ secrecy_Expression)]: (((! [X2:secrecy_Keys]: (((((mem @ secrecy_Expression) @ (secrecy_kE @ X2)) @ E4) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ X2)) @ (specKeysSecrets @ P2))))))) & (! [Y4:secrecy_Secrets]: (((((mem @ secrecy_Expression) @ (secrecy_sE @ Y4)) @ E4) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Y4)) @ (specKeysSecrets @ P2)))))))))))).
% 2.77/1.58 thf(fact_173_TBtheorem5a__empty, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E2) | ((eout @ Q) @ E2)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((loc @ PQ) = (bot_bot @ (set @ secrecy_chanID))) => ((eout @ PQ) @ E2)))))))).
% 2.77/1.58 thf(fact_174_correctCompositionKS__subcomp1, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Keys]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xa) @ (specKeys @ C4)) => (? [X3:secrecy_specID]: (((((member @ secrecy_specID) @ X3) @ (subcomponents @ C4)) & (((member @ secrecy_Keys) @ Xa) @ (specKeys @ X3))))))))))).
% 2.77/1.58 thf(fact_175_TBtheorem2a, axiom, (! [PQ:secrecy_specID,E2:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((eout @ PQ) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((eout @ P) @ E2) | ((eout @ Q) @ E2)))))))).
% 2.77/1.58 thf(fact_176_correctCompositionKS__subcomp3, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Keys]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xa) @ (specKeys @ X)) => (((member @ secrecy_Keys) @ Xa) @ (specKeys @ C4)))))))).
% 2.77/1.58 thf(fact_177_TBtheorem5a__notP1, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((eout @ P) @ E2) => ((~ (((eout @ Q) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch2) @ E2) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E2))))))))))).
% 2.77/1.58 thf(fact_178_TBtheorem5a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E2:secrecy_Expression,ChSetQ:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSetP) @ E2) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E2)))))))))))).
% 2.77/1.58 thf(fact_179_TBtheorem5a__notP2, axiom, (! [Q:secrecy_specID,E2:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((eout @ Q) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E2))))))))))).
% 2.77/1.58 thf(fact_180_out__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E2:secrecy_Expression]: (((((out_ex985543062Single @ P) @ Ch) @ E2) => (((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E2))))).
% 2.77/1.58 thf(fact_181_out__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E2:secrecy_Expression]: (((((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E2) => (((out_ex985543062Single @ P) @ Ch) @ E2))))).
% 2.77/1.58 thf(fact_182_TBtheorem5b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E2:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M2:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSetP) @ E2) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E2) => ((M2 = (((sup_sup @ (set @ secrecy_chanID)) @ ChSetP) @ ChSetQ)) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetP) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSetQ) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M2) @ E2))))))))))))).
% 2.77/1.58 thf(fact_183_eout__know__k, axiom, (! [C4:secrecy_specID,M:secrecy_Keys]: ((((knowle1667810483orrect @ C4) @ (secrecy_kKS @ M)) = (((eout @ C4) @ (secrecy_kE @ M)) = ((((member @ secrecy_Keys) @ M) @ (specKeys @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_kKS @ M)))))))).
% 2.77/1.58 thf(fact_184_not__know__k__not__eout, axiom, (! [M:secrecy_Keys,A2:secrecy_specID]: (((~ ((((member @ secrecy_Keys) @ M) @ (specKeys @ A2)))) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (((knowle1667810483orrect @ A2) @ (secrecy_kKS @ M)) => (~ (((eout @ A2) @ (secrecy_kE @ M)))))))))).
% 2.77/1.58 thf(fact_185_not__eout__eoutM, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,M2:(set @ secrecy_chanID)]: (((~ (((eout @ P) @ E2))) => (~ ((((eoutM @ P) @ M2) @ E2))))))).
% 2.77/1.58 thf(fact_186_eoutM__eout, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((((eoutM @ P) @ M2) @ E2) => ((eout @ P) @ E2))))).
% 2.77/1.58 thf(fact_187_TBtheorem2b, axiom, (! [PQ:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ PQ) @ M2) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((eoutM @ P) @ M2) @ E2) | (((eoutM @ Q) @ M2) @ E2)))))))).
% 2.77/1.58 thf(fact_188_TBtheorem5b__notP2, axiom, (! [Q:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((eoutM @ Q) @ M2) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E2) => ((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet) => (((member @ secrecy_chanID) @ X3) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M2) @ E2))))))))))).
% 2.77/1.58 thf(fact_189_TBtheorem5b__notP1, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eoutM @ P) @ M2) @ E2) => ((~ ((((eoutM @ Q) @ M2) @ E2))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch2) @ E2) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))) => (~ ((((eoutM @ PQ) @ M2) @ E2))))))))))).
% 2.77/1.58 thf(fact_190_eout__know__nonKS__k, axiom, (! [M:secrecy_Keys,A2:secrecy_specID]: (((~ ((((member @ secrecy_Keys) @ M) @ (specKeys @ A2)))) => (((eout @ A2) @ (secrecy_kE @ M)) => (((knowle1667810483orrect @ A2) @ (secrecy_kKS @ M)) => ((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))))))).
% 2.77/1.58 thf(fact_191_eoutKnowCorrect__L1k, axiom, (! [C4:secrecy_specID,M:secrecy_Keys]: ((((knowle1667810483orrect @ C4) @ (secrecy_kKS @ M)) => (((eout @ C4) @ (secrecy_kE @ M)) => ((((member @ secrecy_Keys) @ M) @ (specKeys @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_kKS @ M)))))))).
% 2.77/1.58 thf(fact_192_TBtheore54b__P, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ P) @ M2) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ Q)) & (((exprChannel @ Ch2) @ E2) & ((~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch2) @ M2)))))) => (((eoutM @ PQ) @ M2) @ E2)))))))).
% 2.77/1.58 thf(fact_193_TBtheorem5b__PQ, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((eoutM @ P) @ M2) @ E2) | (((eoutM @ Q) @ M2) @ E2)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (out @ Q))) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((exprChannel @ Ch2) @ E2) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))))))) => (((eoutM @ PQ) @ M2) @ E2)))))))).
% 2.77/1.58 thf(fact_194_TBtheorem5a__PQ, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E2) | ((eout @ Q) @ E2)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (out @ Q))) & (((exprChannel @ Ch2) @ E2) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E2)))))))).
% 2.77/1.58 thf(fact_195_eout__def, axiom, (eout = (^ [SP:secrecy_specID,E3:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & ((exprChannel @ Ch3) @ E3)))))))).
% 2.77/1.58 thf(fact_196_eoutM__def, axiom, (eoutM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E3:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & ((((member @ secrecy_chanID) @ Ch3) @ M3) & ((exprChannel @ Ch3) @ E3))))))))).
% 2.77/1.58 thf(fact_197_out__exprChannelSet__def, axiom, (out_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E3:secrecy_Expression]: (((! [X2:secrecy_chanID]: (((((member @ secrecy_chanID) @ X2) @ ChSet2) => ((((member @ secrecy_chanID) @ X2) @ (out @ SP)) & ((exprChannel @ X2) @ E3))))) & (! [X2:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X2) @ ChSet2))) & (((member @ secrecy_chanID) @ X2) @ (out @ SP))) => (~ (((exprChannel @ X2) @ E3))))))))))).
% 2.77/1.58 thf(fact_198_out__exprChannelSingle__def, axiom, (out_ex985543062Single = (^ [SP:secrecy_specID,Ch3:secrecy_chanID,E3:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & (((exprChannel @ Ch3) @ E3) & (! [X2:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X2) @ (out @ SP)) & (X2 != Ch3)) => (~ (((exprChannel @ X2) @ E3)))))))))))).
% 2.77/1.58 thf(fact_199_correctCompositionOut__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((member @ secrecy_chanID) @ X) @ (out @ PQ)) => ((((member @ secrecy_chanID) @ X) @ (out @ P)) | (((member @ secrecy_chanID) @ X) @ (out @ Q))))))))).
% 2.77/1.58 thf(fact_200_TBtheorem45a__P, axiom, (! [P:secrecy_specID,E2:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((eout @ P) @ E2) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ P)) & (((exprChannel @ Ch2) @ E2) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E2)))))))).
% 2.77/1.58 thf(fact_201_outStream__def, axiom, (outStream = (^ [X2:secrecy_specID]: (((^ [Y3:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y3 = Z))) @ (out @ X2)))))).
% 2.77/1.58 thf(fact_202_eout__know__nonKS__s, axiom, (! [M:secrecy_Secrets,A2:secrecy_specID]: (((~ ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ A2)))) => (((eout @ A2) @ (secrecy_sE @ M)) => (((knowle1667810483orrect @ A2) @ (secrecy_sKS @ M)) => ((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))))))).
% 2.77/1.58 thf(fact_203_correctCompositionKS__subcomp4, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Secrets]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X)) => (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ C4)))))))).
% 2.77/1.58 thf(fact_204_correctCompositionKS__subcomp2, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Secrets]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ C4)) => (? [X3:secrecy_specID]: (((((member @ secrecy_specID) @ X3) @ (subcomponents @ C4)) & (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X3))))))))))).
% 2.77/1.58 thf(fact_205_eout__know__s, axiom, (! [C4:secrecy_specID,M:secrecy_Secrets]: ((((knowle1667810483orrect @ C4) @ (secrecy_sKS @ M)) = (((eout @ C4) @ (secrecy_sE @ M)) = ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_sKS @ M)))))))).
% 2.77/1.58 thf(fact_206_not__know__s__not__eout, axiom, (! [M:secrecy_Secrets,A2:secrecy_specID]: (((~ ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ A2)))) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (((knowle1667810483orrect @ A2) @ (secrecy_sKS @ M)) => (~ (((eout @ A2) @ (secrecy_sE @ M)))))))))).
% 2.77/1.58 thf(fact_207_eoutKnowCorrect__L1s, axiom, (! [C4:secrecy_specID,M:secrecy_Secrets]: ((((knowle1667810483orrect @ C4) @ (secrecy_sKS @ M)) => (((eout @ C4) @ (secrecy_sE @ M)) => ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_sKS @ M)))))))).
% 2.77/1.58 thf(fact_208_adv__not__know2, axiom, (! [P:secrecy_specID,A2:secrecy_specID,M:secrecy_Secrets]: (((((ord_less_eq @ (set @ secrecy_chanID)) @ (out @ P)) @ (ins @ A2)) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (~ (((eout @ P) @ (secrecy_sE @ M))))))))).
% 2.77/1.58 thf(fact_209_adv__not__know1, axiom, (! [P:secrecy_specID,A2:secrecy_specID,M:secrecy_Keys]: (((((ord_less_eq @ (set @ secrecy_chanID)) @ (out @ P)) @ (ins @ A2)) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (~ (((eout @ P) @ (secrecy_kE @ M))))))))).
% 2.77/1.58 thf(fact_210_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.77/1.58 thf(fact_211_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ A2) => (A2 = B)))))).
% 2.77/1.58 thf(fact_212_subsetI, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((! [X3:A]: (((((member @ A) @ X3) @ A2) => (((member @ A) @ X3) @ B)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B))))).
% 2.77/1.58 thf(fact_213_empty__subsetI, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2)))).
% 2.77/1.58 thf(fact_214_subset__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.77/1.58 thf(fact_215_insert__subset, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ B) = ((((member @ A) @ X) @ B) & (((ord_less_eq @ (set @ A)) @ A2) @ B)))))).
% 2.77/1.58 thf(fact_216_Un__subset__iff, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A2) @ C4) & (((ord_less_eq @ (set @ A)) @ B) @ C4)))))).
% 2.77/1.58 thf(fact_217_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A3:A,A2:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A2)) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.77/1.58 thf(fact_218_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A]: ((((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 2.77/1.58 thf(fact_219_subset__singleton__iff, axiom, (! [A:$tType,X4:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ X4) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = ((X4 = (bot_bot @ (set @ A))) | (X4 = (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))))).
% 2.77/1.58 thf(fact_220_subset__singletonD, axiom, (! [A:$tType,A2:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) => ((A2 = (bot_bot @ (set @ A))) | (A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))).
% 2.77/1.58 thf(fact_221_Un__mono, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ (((sup_sup @ (set @ A)) @ C4) @ D3))))))).
% 2.77/1.58 thf(fact_222_Un__least, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ C4)))))).
% 2.77/1.58 thf(fact_223_Un__upper1, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B))))).
% 2.77/1.58 thf(fact_224_Un__upper2, axiom, (! [A:$tType,B:(set @ A),A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A2) @ B))))).
% 2.77/1.58 thf(fact_225_Un__absorb1, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((sup_sup @ (set @ A)) @ A2) @ B) = B))))).
% 2.77/1.58 thf(fact_226_Un__absorb2, axiom, (! [A:$tType,B:(set @ A),A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B) @ A2) => ((((sup_sup @ (set @ A)) @ A2) @ B) = A2))))).
% 2.77/1.58 thf(fact_227_subset__UnE, axiom, (! [A:$tType,C4:(set @ A),A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((sup_sup @ (set @ A)) @ A2) @ B)) => (~ ((! [A6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ A2) => (! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ B) => (C4 != (((sup_sup @ (set @ A)) @ A6) @ B6)))))))))))))).
% 2.77/1.58 thf(fact_228_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ B5) = B5))))))).
% 2.77/1.58 thf(fact_229_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X2:A]: (((P @ X2) => (Q @ X2)))))))).
% 2.77/1.58 thf(fact_230_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y3:(set @ A),Z:(set @ A)]: ((Y3 = Z))) = (^ [A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))).
% 2.77/1.58 thf(fact_231_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ A2) @ C4)))))).
% 2.77/1.58 thf(fact_232_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X3:A]: (((P @ X3) => (Q @ X3)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.77/1.58 thf(fact_233_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 2.77/1.58 thf(fact_234_subset__iff, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((! [T:A]: (((((member @ A) @ T) @ A4) => (((member @ A) @ T) @ B5)))))))))).
% 2.77/1.58 thf(fact_235_equalityD2, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((A2 = B) => (((ord_less_eq @ (set @ A)) @ B) @ A2))))).
% 2.77/1.58 thf(fact_236_equalityD1, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((A2 = B) => (((ord_less_eq @ (set @ A)) @ A2) @ B))))).
% 2.77/1.58 thf(fact_237_subset__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((! [X2:A]: (((((member @ A) @ X2) @ A4) => (((member @ A) @ X2) @ B5)))))))))).
% 2.77/1.58 thf(fact_238_equalityE, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((A2 = B) => (~ (((((ord_less_eq @ (set @ A)) @ A2) @ B) => (~ ((((ord_less_eq @ (set @ A)) @ B) @ A2)))))))))).
% 2.77/1.58 thf(fact_239_subsetD, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B)))))).
% 2.77/1.58 thf(fact_240_in__mono, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B)))))).
% 2.77/1.58 thf(fact_241_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ A3) @ B2) => (A3 = B2))))))))).
% 2.77/1.58 thf(fact_242_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ B7) @ A5) & (((ord_less_eq @ A) @ A5) @ B7))))))))).
% 2.77/1.58 thf(fact_243_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A3))))))))).
% 2.77/1.58 thf(fact_244_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B2:A]: (((! [A7:A,B8:A]: (((((ord_less_eq @ A) @ A7) @ B8) => ((P @ A7) @ B8)))) => ((! [A7:A,B8:A]: ((((P @ B8) @ A7) => ((P @ A7) @ B8)))) => ((P @ A3) @ B2))))))))).
% 2.77/1.58 thf(fact_245_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.77/1.58 thf(fact_246_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y2:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y2) => ((((ord_less_eq @ A) @ Y2) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.77/1.58 thf(fact_247_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ A3) => (A3 = B2))))))))).
% 2.77/1.58 thf(fact_248_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.77/1.58 thf(fact_249_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B2:A,C:A]: (((A3 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.77/1.58 thf(fact_250_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y3:A,Z:A]: ((Y3 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ A5) @ B7) & (((ord_less_eq @ A) @ B7) @ A5))))))))).
% 2.77/1.58 thf(fact_251_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y2:A,X:A]: (((((ord_less_eq @ A) @ Y2) @ X) => ((((ord_less_eq @ A) @ X) @ Y2) = (X = Y2))))))))).
% 2.77/1.58 thf(fact_252_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y2:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ Z2)))) => (((((ord_less_eq @ A) @ Y2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y2)))) => (((((ord_less_eq @ A) @ Z2) @ Y2) => (~ ((((ord_less_eq @ A) @ Y2) @ X)))) => (((((ord_less_eq @ A) @ Y2) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y2))))))))))))))))).
% 2.77/1.58 thf(fact_253_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.77/1.58 thf(fact_254_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y2:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y2))) => (((ord_less_eq @ A) @ Y2) @ X)))))))).
% 2.77/1.58 thf(fact_255_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y2:A]: (((X = Y2) => (((ord_less_eq @ A) @ X) @ Y2)))))))).
% 2.77/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.77/1.58 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 2.77/1.58 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 2.77/1.58 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounde1808546759up_bot @ (A8 > A9)))))).
% 2.77/1.58 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 2.77/1.58 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.77/1.58 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 2.77/1.58 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 2.77/1.58 thf(tcon_Nat_Onat___Orderings_Opreorder_3, axiom, (preorder @ nat)).
% 2.77/1.58 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.77/1.58 thf(tcon_Nat_Onat___Orderings_Oorder_4, axiom, (order @ nat)).
% 2.77/1.58 thf(tcon_Nat_Onat___Orderings_Oord_5, axiom, (ord @ nat)).
% 2.77/1.58 thf(tcon_Nat_Onat___Orderings_Obot_6, axiom, (bot @ nat)).
% 2.77/1.58 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, axiom, (! [A8:$tType]: ((bounde1808546759up_bot @ (set @ A8))))).
% 2.77/1.58 thf(tcon_Set_Oset___Orderings_Opreorder_8, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 2.77/1.58 thf(tcon_Set_Oset___Orderings_Oorder_9, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.77/1.58 thf(tcon_Set_Oset___Orderings_Oord_10, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 2.77/1.58 thf(tcon_Set_Oset___Orderings_Obot_11, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 2.77/1.58 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, axiom, (bounde1808546759up_bot @ $o)).
% 2.77/1.58 thf(tcon_HOL_Obool___Orderings_Opreorder_13, axiom, (preorder @ $o)).
% 2.77/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder_14, axiom, (linorder @ $o)).
% 2.77/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_15, axiom, (order @ $o)).
% 2.77/1.58 thf(tcon_HOL_Obool___Orderings_Oord_16, axiom, (ord @ $o)).
% 2.77/1.58 thf(tcon_HOL_Obool___Orderings_Obot_17, axiom, (bot @ $o)).
% 2.77/1.58 thf(conj_0, conjecture, (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ key)) @ (localSecrets @ q))))).
% 2.77/1.58 % SZS output end ListOfTHF for /export/starexec/sandbox2/tmp/tmp.M5SM4yxb8e/DTF2DTF24271.p
% 2.77/1.58 ------------------------
% 3.04/1.61 ---- Cleaned THF ---
% 3.04/1.61 thf(ty_t_Secrecy__types_OExpression,type,
% 3.04/1.61 secrecy_Expression: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Secrecy__types_OSecrets,type,
% 3.04/1.61 secrecy_Secrets: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Secrecy__types_OspecID,type,
% 3.04/1.61 secrecy_specID: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Secrecy__types_OchanID,type,
% 3.04/1.61 secrecy_chanID: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Secrecy__types_OKeys,type,
% 3.04/1.61 secrecy_Keys: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Secrecy__types_OKS,type,
% 3.04/1.61 secrecy_KS: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_List_Olist,type,
% 3.04/1.61 list: $tType > $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Set_Oset,type,
% 3.04/1.61 set: $tType > $tType ).
% 3.04/1.61
% 3.04/1.61 thf(ty_t_Nat_Onat,type,
% 3.04/1.61 nat: $tType ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.04/1.61 bounded_lattice:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_HOL_Otype,type,
% 3.04/1.61 type:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Obot,type,
% 3.04/1.61 bot:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Oord,type,
% 3.04/1.61 ord:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Oorder,type,
% 3.04/1.61 order:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Olinorder,type,
% 3.04/1.61 linorder:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Orderings_Opreorder,type,
% 3.04/1.61 preorder:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 3.04/1.61 bounde1808546759up_bot:
% 3.04/1.61 !>[A: $tType] : $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 3.04/1.61 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 3.04/1.61 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 3.04/1.61 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknows,type,
% 3.04/1.61 knowle2055185861_knows: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Lattices_Osup__class_Osup,type,
% 3.04/1.61 sup_sup:
% 3.04/1.61 !>[A: $tType] : ( A > A > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_ListExtras_Omem,type,
% 3.04/1.61 mem:
% 3.04/1.61 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.04/1.61 bot_bot:
% 3.04/1.61 !>[A: $tType] : A ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.04/1.61 ord_less_eq:
% 3.04/1.61 !>[A: $tType] : ( A > A > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_ODecr,type,
% 3.04/1.61 decr: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OEnc,type,
% 3.04/1.61 enc: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 3.04/1.61 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OExt,type,
% 3.04/1.61 ext: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OSign,type,
% 3.04/1.61 sign: secrecy_Keys > ( list @ secrecy_Expression ) > ( list @ secrecy_Expression ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 3.04/1.61 correctCompositionKS: secrecy_specID > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_Oeout,type,
% 3.04/1.61 eout: secrecy_specID > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OeoutM,type,
% 3.04/1.61 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OexprChannel,type,
% 3.04/1.61 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_Oine,type,
% 3.04/1.61 ine: secrecy_specID > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OineM,type,
% 3.04/1.61 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 3.04/1.61 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 3.04/1.61 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 3.04/1.61 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 3.04/1.61 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 3.04/1.61 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OspecKeys,type,
% 3.04/1.61 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 3.04/1.61 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy_OspecSecrets,type,
% 3.04/1.61 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 3.04/1.61 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 3.04/1.61 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 3.04/1.61 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 3.04/1.61 secrecy_case_KS:
% 3.04/1.61 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 3.04/1.61 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 3.04/1.61 secrecy_rec_KS:
% 3.04/1.61 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 3.04/1.61 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Set_OCollect,type,
% 3.04/1.61 collect:
% 3.04/1.61 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Set_Oinsert,type,
% 3.04/1.61 insert:
% 3.04/1.61 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Set_Ois__empty,type,
% 3.04/1.61 is_empty:
% 3.04/1.61 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Set_Ois__singleton,type,
% 3.04/1.61 is_singleton:
% 3.04/1.61 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_Set_Othe__elem,type,
% 3.04/1.61 the_elem:
% 3.04/1.61 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_OcorrectCompositionIn,type,
% 3.04/1.61 correctCompositionIn: secrecy_specID > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 3.04/1.61 correc965049635ionLoc: secrecy_specID > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_OcorrectCompositionOut,type,
% 3.04/1.61 correc990227761ionOut: secrecy_specID > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_OinStream,type,
% 3.04/1.61 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_Oins,type,
% 3.04/1.61 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_Oloc,type,
% 3.04/1.61 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_OlocStream,type,
% 3.04/1.61 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_Oout,type,
% 3.04/1.61 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_OoutStream,type,
% 3.04/1.61 outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_inout_Osubcomponents,type,
% 3.04/1.61 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_c_member,type,
% 3.04/1.61 member:
% 3.04/1.61 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_P,type,
% 3.04/1.61 p: secrecy_specID ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_PQ,type,
% 3.04/1.61 pq: secrecy_specID ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_Q,type,
% 3.04/1.61 q: secrecy_specID ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_key____,type,
% 3.04/1.61 key: secrecy_Keys ).
% 3.04/1.61
% 3.04/1.61 thf(sy_v_m,type,
% 3.04/1.61 m: secrecy_KS ).
% 3.04/1.61
% 3.04/1.61 thf(fact_0_not__knowQm,axiom,
% 3.04/1.61 ~ ( knowle1437066798e_know @ q @ m ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_1_a1,axiom,
% 3.04/1.61 ( m
% 3.04/1.61 = ( secrecy_kKS @ key ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_2_knowPQ,axiom,
% 3.04/1.61 knowle1437066798e_know @ pq @ m ).
% 3.04/1.61
% 3.04/1.61 thf(fact_3_sg2,axiom,
% 3.04/1.61 member @ secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ pq ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_4_KS_Oinject_I1_J,axiom,
% 3.04/1.61 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.04/1.61 ( ( ( secrecy_kKS @ X1 )
% 3.04/1.61 = ( secrecy_kKS @ Y1 ) )
% 3.04/1.61 = ( X1 = Y1 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_5_sg3a,axiom,
% 3.04/1.61 ~ ( ine @ q @ ( secrecy_kE @ key ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_6_cCompLoc,axiom,
% 3.04/1.61 correc965049635ionLoc @ pq ).
% 3.04/1.61
% 3.04/1.61 thf(fact_7_a12,axiom,
% 3.04/1.61 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_8_KS_Osimps_I7_J,axiom,
% 3.04/1.61 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 3.04/1.61 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 3.04/1.61 = ( F1 @ X1 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_9_KS_Osimps_I5_J,axiom,
% 3.04/1.61 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 3.04/1.61 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 3.04/1.61 = ( F1 @ X1 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_10_know_Osimps_I1_J,axiom,
% 3.04/1.61 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 3.04/1.61 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 3.04/1.61 | ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_11_subPQ,axiom,
% 3.04/1.61 ( ( subcomponents @ pq )
% 3.04/1.61 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_12_knows4,axiom,
% 3.04/1.61 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 3.04/1.61 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 3.04/1.61 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K2 ) )
% 3.04/1.61 & ( knowle2055185861_knows @ A2 @ ( enc @ K1 @ E ) ) )
% 3.04/1.61 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_13_knows5,axiom,
% 3.04/1.61 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A2: secrecy_specID,E: list @ secrecy_Expression] :
% 3.04/1.61 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 3.04/1.61 & ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K1 ) )
% 3.04/1.61 & ( knowle2055185861_knows @ A2 @ ( sign @ K2 @ E ) ) )
% 3.04/1.61 => ( knowle2055185861_knows @ A2 @ E ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_14_knows6,axiom,
% 3.04/1.61 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 3.04/1.61 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 3.04/1.61 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 3.04/1.61 => ( knowle2055185861_knows @ A2 @ ( enc @ K @ E1 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_15_Expression_Oinject_I1_J,axiom,
% 3.04/1.61 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.04/1.61 ( ( ( secrecy_kE @ X1 )
% 3.04/1.61 = ( secrecy_kE @ Y1 ) )
% 3.04/1.61 = ( X1 = Y1 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_16_cCompI,axiom,
% 3.04/1.61 correctCompositionIn @ pq ).
% 3.04/1.61
% 3.04/1.61 thf(fact_17_not__know__k__not__ine,axiom,
% 3.04/1.61 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 3.04/1.61 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 => ~ ( ine @ A2 @ ( secrecy_kE @ M ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_18_knows7,axiom,
% 3.04/1.61 ! [A2: secrecy_specID,K: secrecy_Keys,E1: list @ secrecy_Expression] :
% 3.04/1.61 ( ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ K ) )
% 3.04/1.61 & ( knowle2055185861_knows @ A2 @ E1 ) )
% 3.04/1.61 => ( knowle2055185861_knows @ A2 @ ( sign @ K @ E1 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_19_LocalSecretsComposition__ine1__k,axiom,
% 3.04/1.61 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.04/1.61 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_20_LocalSecretsComposition__ine2__k,axiom,
% 3.04/1.61 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.04/1.61 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_21_LocalSecretsComposition__neg1__k,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_22_singletonI,axiom,
% 3.04/1.61 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_23_LocalSecretsComposition1,axiom,
% 3.04/1.61 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_24_know__composition__neg__ine__k,axiom,
% 3.04/1.61 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_kKS @ Key ) )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ Key ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_25_insertCI,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 3.04/1.61 ( ( ~ ( member @ A @ A3 @ B )
% 3.04/1.61 => ( A3 = B2 ) )
% 3.04/1.61 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_26_insert__iff,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 3.04/1.61 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 3.04/1.61 = ( ( A3 = B2 )
% 3.04/1.61 | ( member @ A @ A3 @ A2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_27_insert__absorb2,axiom,
% 3.04/1.61 ! [A: $tType,X: A,A2: set @ A] :
% 3.04/1.61 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 3.04/1.61 = ( insert @ A @ X @ A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_28_empty__iff,axiom,
% 3.04/1.61 ! [A: $tType,C: A] :
% 3.04/1.61 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_29_empty__Collect__eq,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o] :
% 3.04/1.61 ( ( ( bot_bot @ ( set @ A ) )
% 3.04/1.61 = ( collect @ A @ P ) )
% 3.04/1.61 = ( ! [X2: A] :
% 3.04/1.61 ~ ( P @ X2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_30_Collect__empty__eq,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o] :
% 3.04/1.61 ( ( ( collect @ A @ P )
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( ! [X2: A] :
% 3.04/1.61 ~ ( P @ X2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_31_all__not__in__conv,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( ! [X2: A] :
% 3.04/1.61 ~ ( member @ A @ X2 @ A2 ) )
% 3.04/1.61 = ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_32_ex__in__conv,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( ? [X2: A] : ( member @ A @ X2 @ A2 ) )
% 3.04/1.61 = ( A2
% 3.04/1.61 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_33_equals0I,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ! [Y: A] :
% 3.04/1.61 ~ ( member @ A @ Y @ A2 )
% 3.04/1.61 => ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_34_equals0D,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,A3: A] :
% 3.04/1.61 ( ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_35_emptyE,axiom,
% 3.04/1.61 ! [A: $tType,A3: A] :
% 3.04/1.61 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_36_mk__disjoint__insert,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,A2: set @ A] :
% 3.04/1.61 ( ( member @ A @ A3 @ A2 )
% 3.04/1.61 => ? [B3: set @ A] :
% 3.04/1.61 ( ( A2
% 3.04/1.61 = ( insert @ A @ A3 @ B3 ) )
% 3.04/1.61 & ~ ( member @ A @ A3 @ B3 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_37_insert__commute,axiom,
% 3.04/1.61 ! [A: $tType,X: A,Y2: A,A2: set @ A] :
% 3.04/1.61 ( ( insert @ A @ X @ ( insert @ A @ Y2 @ A2 ) )
% 3.04/1.61 = ( insert @ A @ Y2 @ ( insert @ A @ X @ A2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_38_insert__eq__iff,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,A2: set @ A,B2: A,B: set @ A] :
% 3.04/1.61 ( ~ ( member @ A @ A3 @ A2 )
% 3.04/1.61 => ( ~ ( member @ A @ B2 @ B )
% 3.04/1.61 => ( ( ( insert @ A @ A3 @ A2 )
% 3.04/1.61 = ( insert @ A @ B2 @ B ) )
% 3.04/1.61 = ( ( ( A3 = B2 )
% 3.04/1.61 => ( A2 = B ) )
% 3.04/1.61 & ( ( A3 != B2 )
% 3.04/1.61 => ? [C2: set @ A] :
% 3.04/1.61 ( ( A2
% 3.04/1.61 = ( insert @ A @ B2 @ C2 ) )
% 3.04/1.61 & ~ ( member @ A @ B2 @ C2 )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( insert @ A @ A3 @ C2 ) )
% 3.04/1.61 & ~ ( member @ A @ A3 @ C2 ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_39_insert__absorb,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,A2: set @ A] :
% 3.04/1.61 ( ( member @ A @ A3 @ A2 )
% 3.04/1.61 => ( ( insert @ A @ A3 @ A2 )
% 3.04/1.61 = A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_40_insert__ident,axiom,
% 3.04/1.61 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ~ ( member @ A @ X @ A2 )
% 3.04/1.61 => ( ~ ( member @ A @ X @ B )
% 3.04/1.61 => ( ( ( insert @ A @ X @ A2 )
% 3.04/1.61 = ( insert @ A @ X @ B ) )
% 3.04/1.61 = ( A2 = B ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_41_Set_Oset__insert,axiom,
% 3.04/1.61 ! [A: $tType,X: A,A2: set @ A] :
% 3.04/1.61 ( ( member @ A @ X @ A2 )
% 3.04/1.61 => ~ ! [B3: set @ A] :
% 3.04/1.61 ( ( A2
% 3.04/1.61 = ( insert @ A @ X @ B3 ) )
% 3.04/1.61 => ( member @ A @ X @ B3 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_42_insertI2,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 3.04/1.61 ( ( member @ A @ A3 @ B )
% 3.04/1.61 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_43_insertI1,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_44_insertE,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 3.04/1.61 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 3.04/1.61 => ( ( A3 != B2 )
% 3.04/1.61 => ( member @ A @ A3 @ A2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_45_mem__Collect__eq,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,P: A > $o] :
% 3.04/1.61 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 3.04/1.61 = ( P @ A3 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_46_Collect__mem__eq,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( collect @ A
% 3.04/1.61 @ ^ [X2: A] : ( member @ A @ X2 @ A2 ) )
% 3.04/1.61 = A2 ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_47_Collect__cong,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( P @ X3 )
% 3.04/1.61 = ( Q @ X3 ) )
% 3.04/1.61 => ( ( collect @ A @ P )
% 3.04/1.61 = ( collect @ A @ Q ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_48_ext,axiom,
% 3.04/1.61 ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( F @ X3 )
% 3.04/1.61 = ( G @ X3 ) )
% 3.04/1.61 => ( F = G ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_49_know__composition__neg1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( knowle1437066798e_know @ P @ M )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ Q @ M )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ~ ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_50_singleton__inject,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B2: A] :
% 3.04/1.61 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 => ( A3 = B2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_51_insert__not__empty,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,A2: set @ A] :
% 3.04/1.61 ( ( insert @ A @ A3 @ A2 )
% 3.04/1.61 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_52_doubleton__eq__iff,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B2: A,C: A,D: A] :
% 3.04/1.61 ( ( ( insert @ A @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.04/1.61 = ( ( ( A3 = C )
% 3.04/1.61 & ( B2 = D ) )
% 3.04/1.61 | ( ( A3 = D )
% 3.04/1.61 & ( B2 = C ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_53_singleton__iff,axiom,
% 3.04/1.61 ! [A: $tType,B2: A,A3: A] :
% 3.04/1.61 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 = ( B2 = A3 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_54_singletonD,axiom,
% 3.04/1.61 ! [A: $tType,B2: A,A3: A] :
% 3.04/1.61 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 => ( B2 = A3 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_55_TBtheorem3a,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( ine @ P @ E2 )
% 3.04/1.61 => ( ~ ( ine @ Q @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_56_TBtheorem1a,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( ine @ PQ @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ine @ P @ E2 )
% 3.04/1.61 | ( ine @ Q @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_57_the__elem__eq,axiom,
% 3.04/1.61 ! [A: $tType,X: A] :
% 3.04/1.61 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 = X ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_58_bot__apply,axiom,
% 3.04/1.61 ! [C3: $tType,D2: $tType] :
% 3.04/1.61 ( ( bot @ C3 )
% 3.04/1.61 => ( ( bot_bot @ ( D2 > C3 ) )
% 3.04/1.61 = ( ^ [X2: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_59_is__singletonI,axiom,
% 3.04/1.61 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_60_KS2Expression_Osimps_I1_J,axiom,
% 3.04/1.61 ! [M: secrecy_Keys] :
% 3.04/1.61 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 3.04/1.61 = ( secrecy_kE @ M ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_61_Set_Ois__empty__def,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( is_empty @ A )
% 3.04/1.61 = ( ^ [A4: set @ A] :
% 3.04/1.61 ( A4
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_62_is__singleton__def,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( is_singleton @ A )
% 3.04/1.61 = ( ^ [A4: set @ A] :
% 3.04/1.61 ? [X2: A] :
% 3.04/1.61 ( A4
% 3.04/1.61 = ( insert @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_63_is__singletonE,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( is_singleton @ A @ A2 )
% 3.04/1.61 => ~ ! [X3: A] :
% 3.04/1.61 ( A2
% 3.04/1.61 != ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_64_bot__set__def,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bot_bot @ ( set @ A ) )
% 3.04/1.61 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_65_is__singleton__the__elem,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( is_singleton @ A )
% 3.04/1.61 = ( ^ [A4: set @ A] :
% 3.04/1.61 ( A4
% 3.04/1.61 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_66_is__singletonI_H,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( A2
% 3.04/1.61 != ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 => ( ! [X3: A,Y: A] :
% 3.04/1.61 ( ( member @ A @ X3 @ A2 )
% 3.04/1.61 => ( ( member @ A @ Y @ A2 )
% 3.04/1.61 => ( X3 = Y ) ) )
% 3.04/1.61 => ( is_singleton @ A @ A2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_67_bot__fun__def,axiom,
% 3.04/1.61 ! [B4: $tType,A: $tType] :
% 3.04/1.61 ( ( bot @ B4 )
% 3.04/1.61 => ( ( bot_bot @ ( A > B4 ) )
% 3.04/1.61 = ( ^ [X2: A] : ( bot_bot @ B4 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_68_TBtheorem4a__empty,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ( ine @ P @ E2 )
% 3.04/1.61 | ( ine @ Q @ E2 ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ( loc @ PQ )
% 3.04/1.61 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.04/1.61 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_69_TBtheorem1b,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( ineM @ PQ @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 | ( ineM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_70_TBtheorem3b,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_71_DecrEnc,axiom,
% 3.04/1.61 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list @ secrecy_Expression] :
% 3.04/1.61 ( ( encrDecrKeys @ K12 @ K22 )
% 3.04/1.61 => ( ( decr @ K22 @ ( enc @ K12 @ E2 ) )
% 3.04/1.61 = E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_72_ExtSign,axiom,
% 3.04/1.61 ! [K12: secrecy_Keys,K22: secrecy_Keys,E2: list @ secrecy_Expression] :
% 3.04/1.61 ( ( encrDecrKeys @ K12 @ K22 )
% 3.04/1.61 => ( ( ext @ K12 @ ( sign @ K22 @ E2 ) )
% 3.04/1.61 = E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_73_correctCompositionIn__L2,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_74_correctCompositionIn__prop1,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_75_not__ine__ineM,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set @ secrecy_chanID] :
% 3.04/1.61 ( ~ ( ine @ P @ E2 )
% 3.04/1.61 => ~ ( ineM @ P @ M2 @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_76_ineM__ine,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ine @ P @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_77_correctCompositionIn__L1,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_78_subcomponents__loc,axiom,
% 3.04/1.61 ! [X: secrecy_specID] :
% 3.04/1.61 ( ( correc965049635ionLoc @ X )
% 3.04/1.61 => ( ( ( subcomponents @ X )
% 3.04/1.61 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 3.04/1.61 => ( ( loc @ X )
% 3.04/1.61 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_79_TBtheorem4b__notP1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_80_TBtheorem4a__notP1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ine @ P @ E2 )
% 3.04/1.61 => ( ~ ( ine @ Q @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( ine_ex1303305700Single @ P @ Ch2 @ E2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_81_TBtheorem4b__notPQ,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 3.04/1.61 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_82_TBtheorem4b__notP2,axiom,
% 3.04/1.61 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.04/1.61 ( ~ ( ineM @ Q @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_83_TBtheorem4a__notPQ,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ine_exprChannelSet @ P @ ChSetP @ E2 )
% 3.04/1.61 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_84_ine__exprChannelSingle__Set,axiom,
% 3.04/1.61 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( ine_ex1303305700Single @ P @ Ch @ E2 )
% 3.04/1.61 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_85_ine__exprChannelSet__Single,axiom,
% 3.04/1.61 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 )
% 3.04/1.61 => ( ine_ex1303305700Single @ P @ Ch @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_86_ine__nonempty__exprChannelSet,axiom,
% 3.04/1.61 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 3.04/1.61 => ( ( ChSet
% 3.04/1.61 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.04/1.61 => ( ine @ P @ E2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_87_ine__empty__exprChannelSet,axiom,
% 3.04/1.61 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 3.04/1.61 => ( ( ChSet
% 3.04/1.61 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.04/1.61 => ~ ( ine @ P @ E2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_88_TBtheorem4a__notP2,axiom,
% 3.04/1.61 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.04/1.61 ( ~ ( ine @ Q @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( ine_exprChannelSet @ P @ ChSet @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( ine @ PQ @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_89_locStream__def,axiom,
% 3.04/1.61 ( locStream
% 3.04/1.61 = ( ^ [X2: secrecy_specID] :
% 3.04/1.61 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 3.04/1.61 @ ( loc @ X2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_90_inStream__def,axiom,
% 3.04/1.61 ( inStream
% 3.04/1.61 = ( ^ [X2: secrecy_specID] :
% 3.04/1.61 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 3.04/1.61 @ ( ins @ X2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_91_TBtheorem4b__P,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 3.04/1.61 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_92_TBtheorem4b__PQ,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 | ( ineM @ Q @ M2 @ E2 ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ineM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_93_TBtheorem4a__P,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( ine @ P @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_94_TBtheorem4a__PQ,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ( ine @ P @ E2 )
% 3.04/1.61 | ( ine @ Q @ E2 ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ine @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_95_ine__ins__neg1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 3.04/1.61 ( ~ ( ine @ P @ M )
% 3.04/1.61 => ( ( exprChannel @ X @ M )
% 3.04/1.61 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_96_ine__def,axiom,
% 3.04/1.61 ( ine
% 3.04/1.61 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 3.04/1.61 ? [Ch3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 3.04/1.61 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_97_ineM__L1,axiom,
% 3.04/1.61 ! [Ch: secrecy_chanID,M2: set @ secrecy_chanID,P: secrecy_specID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch @ M2 )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ E2 )
% 3.04/1.61 => ( ineM @ P @ M2 @ E2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_98_ineM__def,axiom,
% 3.04/1.61 ( ineM
% 3.04/1.61 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E3: secrecy_Expression] :
% 3.04/1.61 ? [Ch3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 3.04/1.61 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_99_ine__exprChannelSet__def,axiom,
% 3.04/1.61 ( ine_exprChannelSet
% 3.04/1.61 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E3: secrecy_Expression] :
% 3.04/1.61 ( ! [X2: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 3.04/1.61 & ( exprChannel @ X2 @ E3 ) ) )
% 3.04/1.61 & ! [X2: secrecy_chanID] :
% 3.04/1.61 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) ) )
% 3.04/1.61 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_100_ine__exprChannelSingle__def,axiom,
% 3.04/1.61 ( ine_ex1303305700Single
% 3.04/1.61 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 3.04/1.61 & ( exprChannel @ Ch3 @ E3 )
% 3.04/1.61 & ! [X2: secrecy_chanID,T: nat] :
% 3.04/1.61 ( ( ( member @ secrecy_chanID @ X2 @ ( ins @ SP ) )
% 3.04/1.61 & ( X2 != Ch3 ) )
% 3.04/1.61 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_101_LocalSecretsComposition__exprChannel__k,axiom,
% 3.04/1.61 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_102_correctCompositionInLoc__exprChannel,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ M )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ( ins @ PQ ) )
% 3.04/1.61 => ~ ( exprChannel @ X3 @ M ) )
% 3.04/1.61 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_103_TBlemma3b,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 3.04/1.61 ( ~ ( ineM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ~ ( ineM @ Q @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ M2 )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.04/1.61 => ~ ( exprChannel @ Ch @ E2 ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_104_bot__empty__eq,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bot_bot @ ( A > $o ) )
% 3.04/1.61 = ( ^ [X2: A] : ( member @ A @ X2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_105_Collect__empty__eq__bot,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o] :
% 3.04/1.61 ( ( ( collect @ A @ P )
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( P
% 3.04/1.61 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_106_LocalSecretsComposition__neg__loc__k,axiom,
% 3.04/1.61 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.04/1.61 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_107_correctCompositionKS__exprChannel__k__Qex,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ? [Ch4: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_108_correctCompositionKS__exprChannel__k__Pex,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ? [Ch4: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_109_correctCompositionKS__PQ,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.04/1.61 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_110_correctCompositionKS__neg1,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_111_correctCompositionKS__negP,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_112_correctCompositionKS__negQ,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_113_know__composition,axiom,
% 3.04/1.61 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ( ( ( knowle1437066798e_know @ P @ M )
% 3.04/1.61 | ( knowle1437066798e_know @ Q @ M ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_114_know__composition1,axiom,
% 3.04/1.61 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ( ( knowle1437066798e_know @ P @ M )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_115_know__composition2,axiom,
% 3.04/1.61 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ( ( knowle1437066798e_know @ Q @ M )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_116_correctCompositionKS__exprChannel__k__P,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_117_correctCompositionKS__exprChannel__k__Q,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_118_LocalSecretsComposition__neg__k,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_119_correctCompositionKS__exprChannel__s__Qex,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ? [Ch4: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_120_correctCompositionKS__exprChannel__s__Pex,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ? [Ch4: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_121_correctCompositionKS__exprChannel__s__Q,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_122_correctCompositionKS__exprChannel__s__P,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.04/1.61 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_123_UnCI,axiom,
% 3.04/1.61 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 3.04/1.61 ( ( ~ ( member @ A @ C @ B )
% 3.04/1.61 => ( member @ A @ C @ A2 ) )
% 3.04/1.61 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_124_Un__iff,axiom,
% 3.04/1.61 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 = ( ( member @ A @ C @ A2 )
% 3.04/1.61 | ( member @ A @ C @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_125_KS_Oinject_I2_J,axiom,
% 3.04/1.61 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 3.04/1.61 ( ( ( secrecy_sKS @ X22 )
% 3.04/1.61 = ( secrecy_sKS @ Y22 ) )
% 3.04/1.61 = ( X22 = Y22 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_126_Expression_Oinject_I2_J,axiom,
% 3.04/1.61 ! [X22: secrecy_Secrets,Y22: secrecy_Secrets] :
% 3.04/1.61 ( ( ( secrecy_sE @ X22 )
% 3.04/1.61 = ( secrecy_sE @ Y22 ) )
% 3.04/1.61 = ( X22 = Y22 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_127_Un__empty,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_128_Un__insert__right,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,A3: A,B: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B ) )
% 3.04/1.61 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_129_Un__insert__left,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,B: set @ A,C4: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B ) @ C4 )
% 3.04/1.61 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_130_Un__empty__left,axiom,
% 3.04/1.61 ! [A: $tType,B: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 3.04/1.61 = B ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_131_Un__empty__right,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = A2 ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_132_not__know__s__not__ine,axiom,
% 3.04/1.61 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 3.04/1.61 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 => ~ ( ine @ A2 @ ( secrecy_sE @ M ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_133_UnE,axiom,
% 3.04/1.61 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 => ( ~ ( member @ A @ C @ A2 )
% 3.04/1.61 => ( member @ A @ C @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_134_UnI1,axiom,
% 3.04/1.61 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( member @ A @ C @ A2 )
% 3.04/1.61 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_135_UnI2,axiom,
% 3.04/1.61 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 3.04/1.61 ( ( member @ A @ C @ B )
% 3.04/1.61 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_136_bex__Un,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 3.04/1.61 ( ( ? [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 & ( P @ X2 ) ) )
% 3.04/1.61 = ( ? [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ A2 )
% 3.04/1.61 & ( P @ X2 ) )
% 3.04/1.61 | ? [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ B )
% 3.04/1.61 & ( P @ X2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_137_ball__Un,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 3.04/1.61 ( ( ! [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 => ( P @ X2 ) ) )
% 3.04/1.61 = ( ! [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ A2 )
% 3.04/1.61 => ( P @ X2 ) )
% 3.04/1.61 & ! [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ B )
% 3.04/1.61 => ( P @ X2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_138_Un__assoc,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 3.04/1.61 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_139_Un__absorb,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 3.04/1.61 = A2 ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_140_Un__commute,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) )
% 3.04/1.61 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_141_Un__left__absorb,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 = ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_142_Un__left__commute,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 3.04/1.61 = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_143_KS2Expression_Osimps_I2_J,axiom,
% 3.04/1.61 ! [M: secrecy_Secrets] :
% 3.04/1.61 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 3.04/1.61 = ( secrecy_sE @ M ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_144_KS_Odistinct_I1_J,axiom,
% 3.04/1.61 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 3.04/1.61 ( ( secrecy_kKS @ X1 )
% 3.04/1.61 != ( secrecy_sKS @ X22 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_145_KS_Oinduct,axiom,
% 3.04/1.61 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 3.04/1.61 ( ! [X3: secrecy_Keys] : ( P @ ( secrecy_kKS @ X3 ) )
% 3.04/1.61 => ( ! [X3: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X3 ) )
% 3.04/1.61 => ( P @ KS ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_146_KS_Oexhaust,axiom,
% 3.04/1.61 ! [Y2: secrecy_KS] :
% 3.04/1.61 ( ! [X12: secrecy_Keys] :
% 3.04/1.61 ( Y2
% 3.04/1.61 != ( secrecy_kKS @ X12 ) )
% 3.04/1.61 => ~ ! [X23: secrecy_Secrets] :
% 3.04/1.61 ( Y2
% 3.04/1.61 != ( secrecy_sKS @ X23 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_147_Expression_Odistinct_I1_J,axiom,
% 3.04/1.61 ! [X1: secrecy_Keys,X22: secrecy_Secrets] :
% 3.04/1.61 ( ( secrecy_kE @ X1 )
% 3.04/1.61 != ( secrecy_sE @ X22 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_148_KS_Osimps_I6_J,axiom,
% 3.04/1.61 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X22: secrecy_Secrets] :
% 3.04/1.61 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X22 ) )
% 3.04/1.61 = ( F2 @ X22 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_149_know_Osimps_I2_J,axiom,
% 3.04/1.61 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 3.04/1.61 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 3.04/1.61 | ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_150_KS_Osimps_I8_J,axiom,
% 3.04/1.61 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X22: secrecy_Secrets] :
% 3.04/1.61 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X22 ) )
% 3.04/1.61 = ( F2 @ X22 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_151_singleton__Un__iff,axiom,
% 3.04/1.61 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 = ( ( ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.04/1.61 | ( ( A2
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 | ( ( A2
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_152_Un__singleton__iff,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 3.04/1.61 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 = ( ( ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.04/1.61 | ( ( A2
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 | ( ( A2
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 & ( B
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_153_insert__is__Un,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( insert @ A )
% 3.04/1.61 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_154_LocalSecretsComposition__neg__loc__s,axiom,
% 3.04/1.61 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.04/1.61 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_155_LocalSecretsComposition__neg__s,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_156_know__composition__neg__ine__s,axiom,
% 3.04/1.61 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_sKS @ Secret ) )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correctCompositionIn @ PQ )
% 3.04/1.61 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_157_LocalSecretsComposition__neg1__s,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_158_LocalSecretsComposition__ine2__s,axiom,
% 3.04/1.61 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.04/1.61 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_159_LocalSecretsComposition__ine1__s,axiom,
% 3.04/1.61 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.04/1.61 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_160_LocalSecretsComposition__exprChannel__s,axiom,
% 3.04/1.61 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 3.04/1.61 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_161_LocalSecretsComposition__neg,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ( correctCompositionKS @ PQ )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.04/1.61 => ( ! [M4: secrecy_Keys] :
% 3.04/1.61 ( ( Ks
% 3.04/1.61 = ( secrecy_kKS @ M4 ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.04/1.61 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.04/1.61 => ( ! [M4: secrecy_Secrets] :
% 3.04/1.61 ( ( Ks
% 3.04/1.61 = ( secrecy_sKS @ M4 ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.04/1.61 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_162_LocalSecretsComposition__neg1,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc965049635ionLoc @ PQ )
% 3.04/1.61 => ( ! [M4: secrecy_Keys] :
% 3.04/1.61 ( ( Ks
% 3.04/1.61 = ( secrecy_kKS @ M4 ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.04/1.61 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.04/1.61 => ( ! [M4: secrecy_Secrets] :
% 3.04/1.61 ( ( Ks
% 3.04/1.61 = ( secrecy_sKS @ M4 ) )
% 3.04/1.61 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.04/1.61 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 3.04/1.61 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_163_sup__bot_Oright__neutral,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [A3: A] :
% 3.04/1.61 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 3.04/1.61 = A3 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_164_sup__bot_Oneutr__eq__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [A3: A,B2: A] :
% 3.04/1.61 ( ( ( bot_bot @ A )
% 3.04/1.61 = ( sup_sup @ A @ A3 @ B2 ) )
% 3.04/1.61 = ( ( A3
% 3.04/1.61 = ( bot_bot @ A ) )
% 3.04/1.61 & ( B2
% 3.04/1.61 = ( bot_bot @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_165_sup__bot_Oleft__neutral,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [A3: A] :
% 3.04/1.61 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 3.04/1.61 = A3 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_166_sup__bot_Oeq__neutr__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [A3: A,B2: A] :
% 3.04/1.61 ( ( ( sup_sup @ A @ A3 @ B2 )
% 3.04/1.61 = ( bot_bot @ A ) )
% 3.04/1.61 = ( ( A3
% 3.04/1.61 = ( bot_bot @ A ) )
% 3.04/1.61 & ( B2
% 3.04/1.61 = ( bot_bot @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_167_sup__bot__left,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [X: A] :
% 3.04/1.61 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 3.04/1.61 = X ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_168_sup__bot__right,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [X: A] :
% 3.04/1.61 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 3.04/1.61 = X ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_169_bot__eq__sup__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [X: A,Y2: A] :
% 3.04/1.61 ( ( ( bot_bot @ A )
% 3.04/1.61 = ( sup_sup @ A @ X @ Y2 ) )
% 3.04/1.61 = ( ( X
% 3.04/1.61 = ( bot_bot @ A ) )
% 3.04/1.61 & ( Y2
% 3.04/1.61 = ( bot_bot @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_170_sup__eq__bot__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( bounde1808546759up_bot @ A )
% 3.04/1.61 => ! [X: A,Y2: A] :
% 3.04/1.61 ( ( ( sup_sup @ A @ X @ Y2 )
% 3.04/1.61 = ( bot_bot @ A ) )
% 3.04/1.61 = ( ( X
% 3.04/1.61 = ( bot_bot @ A ) )
% 3.04/1.61 & ( Y2
% 3.04/1.61 = ( bot_bot @ A ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_171_ineM__Un1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,A2: set @ secrecy_chanID,E2: secrecy_Expression,B: set @ secrecy_chanID] :
% 3.04/1.61 ( ( ineM @ P @ A2 @ E2 )
% 3.04/1.61 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A2 @ B ) @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_172_notSpecKeysSecretsExpr__def,axiom,
% 3.04/1.61 ( notSpe1586871396tsExpr
% 3.04/1.61 = ( ^ [P2: secrecy_specID,E4: list @ secrecy_Expression] :
% 3.04/1.61 ( ! [X2: secrecy_Keys] :
% 3.04/1.61 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X2 ) @ E4 )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X2 ) @ ( specKeysSecrets @ P2 ) ) )
% 3.04/1.61 & ! [Y4: secrecy_Secrets] :
% 3.04/1.61 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y4 ) @ E4 )
% 3.04/1.61 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y4 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_173_TBtheorem5a__empty,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ( eout @ P @ E2 )
% 3.04/1.61 | ( eout @ Q @ E2 ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( ( loc @ PQ )
% 3.04/1.61 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.04/1.61 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_174_correctCompositionKS__subcomp1,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.04/1.61 ( ( correctCompositionKS @ C4 )
% 3.04/1.61 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.04/1.61 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 3.04/1.61 => ? [X3: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 3.04/1.61 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X3 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_175_TBtheorem2a,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( eout @ PQ @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( eout @ P @ E2 )
% 3.04/1.61 | ( eout @ Q @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_176_correctCompositionKS__subcomp3,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.04/1.61 ( ( correctCompositionKS @ C4 )
% 3.04/1.61 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.04/1.61 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 3.04/1.61 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_177_TBtheorem5a__notP1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( eout @ P @ E2 )
% 3.04/1.61 => ( ~ ( eout @ Q @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_178_TBtheorem5a__notPQ,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 3.04/1.61 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_179_TBtheorem5a__notP2,axiom,
% 3.04/1.61 ! [Q: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.04/1.61 ( ~ ( eout @ Q @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( eout @ PQ @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_180_out__exprChannelSingle__Set,axiom,
% 3.04/1.61 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( out_ex985543062Single @ P @ Ch @ E2 )
% 3.04/1.61 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_181_out__exprChannelSet__Single,axiom,
% 3.04/1.61 ! [P: secrecy_specID,Ch: secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E2 )
% 3.04/1.61 => ( out_ex985543062Single @ P @ Ch @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_182_TBtheorem5b__notPQ,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E2: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( out_exprChannelSet @ P @ ChSetP @ E2 )
% 3.04/1.61 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E2 )
% 3.04/1.61 => ( ( M2
% 3.04/1.61 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetP )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSetQ )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_183_eout__know__k,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 3.04/1.61 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 = ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 3.04/1.61 = ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 3.04/1.61 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_184_not__know__k__not__eout,axiom,
% 3.04/1.61 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 => ~ ( eout @ A2 @ ( secrecy_kE @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_185_not__eout__eoutM,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,M2: set @ secrecy_chanID] :
% 3.04/1.61 ( ~ ( eout @ P @ E2 )
% 3.04/1.61 => ~ ( eoutM @ P @ M2 @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_186_eoutM__eout,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.04/1.61 ( ( eoutM @ P @ M2 @ E2 )
% 3.04/1.61 => ( eout @ P @ E2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_187_TBtheorem2b,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( eoutM @ PQ @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( eoutM @ P @ M2 @ E2 )
% 3.04/1.61 | ( eoutM @ Q @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_188_TBtheorem5b__notP2,axiom,
% 3.04/1.61 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.04/1.61 ( ~ ( eoutM @ Q @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( out_exprChannelSet @ P @ ChSet @ E2 )
% 3.04/1.61 => ( ! [X3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X3 @ ChSet )
% 3.04/1.61 => ( member @ secrecy_chanID @ X3 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_189_TBtheorem5b__notP1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( eoutM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ~ ( eoutM @ Q @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( out_ex985543062Single @ P @ Ch2 @ E2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ~ ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_190_eout__know__nonKS__k,axiom,
% 3.04/1.61 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 3.04/1.61 => ( ( eout @ A2 @ ( secrecy_kE @ M ) )
% 3.04/1.61 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_191_eoutKnowCorrect__L1k,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 3.04/1.61 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 => ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 3.04/1.61 => ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 3.04/1.61 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_192_TBtheore54b__P,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( eoutM @ P @ M2 @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 3.04/1.61 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_193_TBtheorem5b__PQ,axiom,
% 3.04/1.61 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ( eoutM @ P @ M2 @ E2 )
% 3.04/1.61 | ( eoutM @ Q @ M2 @ E2 ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( eoutM @ PQ @ M2 @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_194_TBtheorem5a__PQ,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.04/1.61 ( ( ( eout @ P @ E2 )
% 3.04/1.61 | ( eout @ Q @ E2 ) )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_195_eout__def,axiom,
% 3.04/1.61 ( eout
% 3.04/1.61 = ( ^ [SP: secrecy_specID,E3: secrecy_Expression] :
% 3.04/1.61 ? [Ch3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 3.04/1.61 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_196_eoutM__def,axiom,
% 3.04/1.61 ( eoutM
% 3.04/1.61 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E3: secrecy_Expression] :
% 3.04/1.61 ? [Ch3: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 3.04/1.61 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 3.04/1.61 & ( exprChannel @ Ch3 @ E3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_197_out__exprChannelSet__def,axiom,
% 3.04/1.61 ( out_exprChannelSet
% 3.04/1.61 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E3: secrecy_Expression] :
% 3.04/1.61 ( ! [X2: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 3.04/1.61 & ( exprChannel @ X2 @ E3 ) ) )
% 3.04/1.61 & ! [X2: secrecy_chanID] :
% 3.04/1.61 ( ( ~ ( member @ secrecy_chanID @ X2 @ ChSet2 )
% 3.04/1.61 & ( member @ secrecy_chanID @ X2 @ ( out @ SP ) ) )
% 3.04/1.61 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_198_out__exprChannelSingle__def,axiom,
% 3.04/1.61 ( out_ex985543062Single
% 3.04/1.61 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E3: secrecy_Expression] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 3.04/1.61 & ( exprChannel @ Ch3 @ E3 )
% 3.04/1.61 & ! [X2: secrecy_chanID,T: nat] :
% 3.04/1.61 ( ( ( member @ secrecy_chanID @ X2 @ ( out @ SP ) )
% 3.04/1.61 & ( X2 != Ch3 ) )
% 3.04/1.61 => ~ ( exprChannel @ X2 @ E3 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_199_correctCompositionOut__prop1,axiom,
% 3.04/1.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.04/1.61 ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 3.04/1.61 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 3.04/1.61 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_200_TBtheorem45a__P,axiom,
% 3.04/1.61 ! [P: secrecy_specID,E2: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.04/1.61 ( ( eout @ P @ E2 )
% 3.04/1.61 => ( ( ( subcomponents @ PQ )
% 3.04/1.61 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.04/1.61 => ( ( correc990227761ionOut @ PQ )
% 3.04/1.61 => ( ? [Ch2: secrecy_chanID] :
% 3.04/1.61 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 3.04/1.61 & ( exprChannel @ Ch2 @ E2 )
% 3.04/1.61 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.04/1.61 => ( eout @ PQ @ E2 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_201_outStream__def,axiom,
% 3.04/1.61 ( outStream
% 3.04/1.61 = ( ^ [X2: secrecy_specID] :
% 3.04/1.61 ( ^ [Y3: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y3 = Z )
% 3.04/1.61 @ ( out @ X2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_202_eout__know__nonKS__s,axiom,
% 3.04/1.61 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 3.04/1.61 => ( ( eout @ A2 @ ( secrecy_sE @ M ) )
% 3.04/1.61 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 => ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_203_correctCompositionKS__subcomp4,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.04/1.61 ( ( correctCompositionKS @ C4 )
% 3.04/1.61 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.04/1.61 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 3.04/1.61 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_204_correctCompositionKS__subcomp2,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.04/1.61 ( ( correctCompositionKS @ C4 )
% 3.04/1.61 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.04/1.61 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 3.04/1.61 => ? [X3: secrecy_specID] :
% 3.04/1.61 ( ( member @ secrecy_specID @ X3 @ ( subcomponents @ C4 ) )
% 3.04/1.61 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X3 ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_205_eout__know__s,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 3.04/1.61 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 = ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 3.04/1.61 = ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 3.04/1.61 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_206_not__know__s__not__eout,axiom,
% 3.04/1.61 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 3.04/1.61 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 => ~ ( eout @ A2 @ ( secrecy_sE @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_207_eoutKnowCorrect__L1s,axiom,
% 3.04/1.61 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 3.04/1.61 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 => ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 3.04/1.61 => ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 3.04/1.61 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_208_adv__not__know2,axiom,
% 3.04/1.61 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Secrets] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.04/1.61 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_209_adv__not__know1,axiom,
% 3.04/1.61 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Keys] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 3.04/1.61 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.04/1.61 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_210_order__refl,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_211_subset__antisym,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 3.04/1.61 => ( A2 = B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_212_subsetI,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( member @ A @ X3 @ A2 )
% 3.04/1.61 => ( member @ A @ X3 @ B ) )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_213_empty__subsetI,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_214_subset__empty,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_215_insert__subset,axiom,
% 3.04/1.61 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B )
% 3.04/1.61 = ( ( member @ A @ X @ B )
% 3.04/1.61 & ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_216_Un__subset__iff,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 3.04/1.61 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 3.04/1.61 & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_217_singleton__insert__inj__eq,axiom,
% 3.04/1.61 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 3.04/1.61 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 = ( insert @ A @ A3 @ A2 ) )
% 3.04/1.61 = ( ( A3 = B2 )
% 3.04/1.61 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_218_singleton__insert__inj__eq_H,axiom,
% 3.04/1.61 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 3.04/1.61 ( ( ( insert @ A @ A3 @ A2 )
% 3.04/1.61 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 = ( ( A3 = B2 )
% 3.04/1.61 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_219_subset__singleton__iff,axiom,
% 3.04/1.61 ! [A: $tType,X4: set @ A,A3: A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ X4 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 = ( ( X4
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 | ( X4
% 3.04/1.61 = ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_220_subset__singletonD,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,X: A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.04/1.61 => ( ( A2
% 3.04/1.61 = ( bot_bot @ ( set @ A ) ) )
% 3.04/1.61 | ( A2
% 3.04/1.61 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_221_Un__mono,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 3.04/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_222_Un__least,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 3.04/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_223_Un__upper1,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_224_Un__upper2,axiom,
% 3.04/1.61 ! [A: $tType,B: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_225_Un__absorb1,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 = B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_226_Un__absorb2,axiom,
% 3.04/1.61 ! [A: $tType,B: set @ A,A2: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 3.04/1.61 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 = A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_227_subset__UnE,axiom,
% 3.04/1.61 ! [A: $tType,C4: set @ A,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.04/1.61 => ~ ! [A6: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 3.04/1.61 => ! [B6: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B )
% 3.04/1.61 => ( C4
% 3.04/1.61 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_228_subset__Un__eq,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 3.04/1.61 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.04/1.61 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 3.04/1.61 = B5 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_229_Collect__mono__iff,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 3.04/1.61 = ( ! [X2: A] :
% 3.04/1.61 ( ( P @ X2 )
% 3.04/1.61 => ( Q @ X2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_230_set__eq__subset,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ^ [Y3: set @ A,Z: set @ A] : ( Y3 = Z ) )
% 3.04/1.61 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 3.04/1.61 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_231_subset__trans,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_232_Collect__mono,axiom,
% 3.04/1.61 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.04/1.61 ( ! [X3: A] :
% 3.04/1.61 ( ( P @ X3 )
% 3.04/1.61 => ( Q @ X3 ) )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_233_subset__refl,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_234_subset__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 3.04/1.61 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.04/1.61 ! [T: A] :
% 3.04/1.61 ( ( member @ A @ T @ A4 )
% 3.04/1.61 => ( member @ A @ T @ B5 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_235_equalityD2,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( A2 = B )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_236_equalityD1,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( A2 = B )
% 3.04/1.61 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_237_subset__eq,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) )
% 3.04/1.61 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.04/1.61 ! [X2: A] :
% 3.04/1.61 ( ( member @ A @ X2 @ A4 )
% 3.04/1.61 => ( member @ A @ X2 @ B5 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_238_equalityE,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.04/1.61 ( ( A2 = B )
% 3.04/1.61 => ~ ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 => ~ ( ord_less_eq @ ( set @ A ) @ B @ A2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_239_subsetD,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,C: A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 => ( ( member @ A @ C @ A2 )
% 3.04/1.61 => ( member @ A @ C @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_240_in__mono,axiom,
% 3.04/1.61 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 3.04/1.61 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.04/1.61 => ( ( member @ A @ X @ A2 )
% 3.04/1.61 => ( member @ A @ X @ B ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_241_dual__order_Oantisym,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [B2: A,A3: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.04/1.61 => ( A3 = B2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_242_dual__order_Oeq__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.04/1.61 = ( ^ [A5: A,B7: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ B7 @ A5 )
% 3.04/1.61 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_243_dual__order_Otrans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [B2: A,A3: A,C: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ C @ B2 )
% 3.04/1.61 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_244_linorder__wlog,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [P: A > A > $o,A3: A,B2: A] :
% 3.04/1.61 ( ! [A7: A,B8: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A7 @ B8 )
% 3.04/1.61 => ( P @ A7 @ B8 ) )
% 3.04/1.61 => ( ! [A7: A,B8: A] :
% 3.04/1.61 ( ( P @ B8 @ A7 )
% 3.04/1.61 => ( P @ A7 @ B8 ) )
% 3.04/1.61 => ( P @ A3 @ B2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_245_dual__order_Orefl,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_246_order__trans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [X: A,Y2: A,Z2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ X @ Y2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 3.04/1.61 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_247_order__class_Oorder_Oantisym,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [A3: A,B2: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.04/1.61 => ( A3 = B2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_248_ord__le__eq__trans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord @ A )
% 3.04/1.61 => ! [A3: A,B2: A,C: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.04/1.61 => ( ( B2 = C )
% 3.04/1.61 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_249_ord__eq__le__trans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( ord @ A )
% 3.04/1.61 => ! [A3: A,B2: A,C: A] :
% 3.04/1.61 ( ( A3 = B2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.04/1.61 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_250_order__class_Oorder_Oeq__iff,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ( ( ^ [Y3: A,Z: A] : ( Y3 = Z ) )
% 3.04/1.61 = ( ^ [A5: A,B7: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A5 @ B7 )
% 3.04/1.61 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_251_antisym__conv,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [Y2: A,X: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ Y2 @ X )
% 3.04/1.61 => ( ( ord_less_eq @ A @ X @ Y2 )
% 3.04/1.61 = ( X = Y2 ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_252_le__cases3,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [X: A,Y2: A,Z2: A] :
% 3.04/1.61 ( ( ( ord_less_eq @ A @ X @ Y2 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Y2 @ Z2 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ Y2 @ X )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Z2 @ Y2 ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ Z2 @ Y2 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Y2 @ X ) )
% 3.04/1.61 => ( ( ( ord_less_eq @ A @ Y2 @ Z2 )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 3.04/1.61 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 3.04/1.61 => ~ ( ord_less_eq @ A @ X @ Y2 ) ) ) ) ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_253_order_Otrans,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( order @ A )
% 3.04/1.61 => ! [A3: A,B2: A,C: A] :
% 3.04/1.61 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.04/1.61 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.04/1.61 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_254_le__cases,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( linorder @ A )
% 3.04/1.61 => ! [X: A,Y2: A] :
% 3.04/1.61 ( ~ ( ord_less_eq @ A @ X @ Y2 )
% 3.04/1.61 => ( ord_less_eq @ A @ Y2 @ X ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(fact_255_eq__refl,axiom,
% 3.04/1.61 ! [A: $tType] :
% 3.04/1.61 ( ( preorder @ A )
% 3.04/1.61 => ! [X: A,Y2: A] :
% 3.04/1.61 ( ( X = Y2 )
% 3.04/1.61 => ( ord_less_eq @ A @ X @ Y2 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 3.04/1.61 bounded_lattice @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 3.04/1.61 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 3.04/1.61 ! [A8: $tType,A9: $tType] :
% 3.04/1.61 ( ( bounded_lattice @ A9 )
% 3.04/1.61 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 3.04/1.61 ! [A8: $tType,A9: $tType] :
% 3.04/1.61 ( ( bounded_lattice @ A9 )
% 3.04/1.61 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.04/1.61 ! [A8: $tType,A9: $tType] :
% 3.04/1.61 ( ( preorder @ A9 )
% 3.04/1.61 => ( preorder @ ( A8 > A9 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.04/1.61 ! [A8: $tType,A9: $tType] :
% 3.04/1.61 ( ( order @ A9 )
% 3.04/1.61 => ( order @ ( A8 > A9 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_fun___Orderings_Oord,axiom,
% 3.04/1.61 ! [A8: $tType,A9: $tType] :
% 3.04/1.61 ( ( ord @ A9 )
% 3.04/1.61 => ( ord @ ( A8 > A9 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_fun___Orderings_Obot,axiom,
% 3.04/1.61 ! [A8: $tType,A9: $tType] :
% 3.04/1.61 ( ( bot @ A9 )
% 3.04/1.61 => ( bot @ ( A8 > A9 ) ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 3.04/1.61 preorder @ nat ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.04/1.61 linorder @ nat ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 3.04/1.61 order @ nat ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 3.04/1.61 ord @ nat ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Nat_Onat___Orderings_Obot_6,axiom,
% 3.04/1.61 bot @ nat ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 3.04/1.61 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 3.04/1.61 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 3.04/1.61 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 3.04/1.61 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 3.04/1.61 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 3.04/1.61 bounde1808546759up_bot @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 3.04/1.61 preorder @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 3.04/1.61 linorder @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 3.04/1.61 order @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 3.04/1.61 ord @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(tcon_HOL_Obool___Orderings_Obot_17,axiom,
% 3.04/1.61 bot @ $o ).
% 3.04/1.61
% 3.04/1.61 thf(conj_0,conjecture,
% 3.04/1.61 ~ ( member @ secrecy_KS @ ( secrecy_kKS @ key ) @ ( localSecrets @ q ) ) ).
% 3.04/1.61 ------------------------
% 3.04/1.63 % (24441)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_24271 for (2999ds/4Mi)
% 3.04/1.63 % (24442)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_24271 for (2999ds/27Mi)
% 3.04/1.63 % (24440)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/183Mi)
% 3.04/1.63 % (24445)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_24271 for (2999ds/275Mi)
% 3.04/1.63 % (24443)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/2Mi)
% 3.04/1.63 % (24443)Instruction limit reached!
% 3.04/1.63 % (24443)------------------------------
% 3.04/1.63 % (24443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.63 % (24443)Termination reason: Unknown
% 3.04/1.63 % (24443)Termination phase: shuffling
% 3.04/1.63
% 3.04/1.63 % (24443)Memory used [KB]: 1279
% 3.04/1.63 % (24443)Time elapsed: 0.002 s
% 3.04/1.63 % (24443)Instructions burned: 2 (million)
% 3.04/1.63 % (24443)------------------------------
% 3.04/1.63 % (24443)------------------------------
% 3.04/1.63 % (24444)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_24271 for (2999ds/2Mi)
% 3.04/1.63 % (24441)Instruction limit reached!
% 3.04/1.63 % (24441)------------------------------
% 3.04/1.63 % (24441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.63 % (24441)Termination reason: Unknown
% 3.04/1.63 % (24441)Termination phase: shuffling
% 3.04/1.63
% 3.04/1.63 % (24441)Memory used [KB]: 1407
% 3.04/1.63 % (24441)Time elapsed: 0.004 s
% 3.04/1.63 % (24441)Instructions burned: 7 (million)
% 3.04/1.63 % (24441)------------------------------
% 3.04/1.63 % (24441)------------------------------
% 3.04/1.63 % (24444)Instruction limit reached!
% 3.04/1.63 % (24444)------------------------------
% 3.04/1.63 % (24444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.63 % (24444)Termination reason: Unknown
% 3.04/1.63 % (24444)Termination phase: shuffling
% 3.04/1.63
% 3.04/1.63 % (24444)Memory used [KB]: 1407
% 3.04/1.63 % (24444)Time elapsed: 0.004 s
% 3.04/1.63 % (24444)Instructions burned: 3 (million)
% 3.04/1.63 % (24444)------------------------------
% 3.04/1.63 % (24444)------------------------------
% 3.04/1.63 % (24446)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/18Mi)
% 3.04/1.64 % (24442)Instruction limit reached!
% 3.04/1.64 % (24442)------------------------------
% 3.04/1.64 % (24442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (24442)Termination reason: Unknown
% 3.04/1.64 % (24442)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (24442)Memory used [KB]: 1791
% 3.04/1.64 % (24442)Time elapsed: 0.011 s
% 3.04/1.64 % (24442)Instructions burned: 28 (million)
% 3.04/1.64 % (24442)------------------------------
% 3.04/1.64 % (24442)------------------------------
% 3.04/1.64 % (24447)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/3Mi)
% 3.04/1.64 % (24448)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_24271 for (2999ds/37Mi)
% 3.04/1.64 % (24447)Instruction limit reached!
% 3.04/1.64 % (24447)------------------------------
% 3.04/1.64 % (24447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (24447)Termination reason: Unknown
% 3.04/1.64 % (24447)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (24447)Memory used [KB]: 1407
% 3.04/1.64 % (24447)Time elapsed: 0.002 s
% 3.04/1.64 % (24447)Instructions burned: 3 (million)
% 3.04/1.64 % (24447)------------------------------
% 3.04/1.64 % (24447)------------------------------
% 3.04/1.64 % (24446)Instruction limit reached!
% 3.04/1.64 % (24446)------------------------------
% 3.04/1.64 % (24446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.64 % (24446)Termination reason: Unknown
% 3.04/1.64 % (24446)Termination phase: shuffling
% 3.04/1.64
% 3.04/1.64 % (24446)Memory used [KB]: 1663
% 3.04/1.64 % (24446)Time elapsed: 0.012 s
% 3.04/1.64 % (24446)Instructions burned: 18 (million)
% 3.04/1.64 % (24446)------------------------------
% 3.04/1.64 % (24446)------------------------------
% 3.04/1.65 % (24450)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_24271 for (2999ds/3Mi)
% 3.04/1.65 % (24450)Instruction limit reached!
% 3.04/1.65 % (24450)------------------------------
% 3.04/1.65 % (24450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.65 % (24450)Termination reason: Unknown
% 3.04/1.65 % (24450)Termination phase: shuffling
% 3.04/1.65
% 3.04/1.65 % (24450)Memory used [KB]: 1407
% 3.04/1.65 % (24450)Time elapsed: 0.002 s
% 3.04/1.65 % (24450)Instructions burned: 3 (million)
% 3.04/1.65 % (24450)------------------------------
% 3.04/1.65 % (24450)------------------------------
% 3.04/1.65 % (24449)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_24271 for (2999ds/15Mi)
% 3.04/1.65 % (24445)Refutation not found, incomplete strategy
% 3.04/1.65 % (24445)------------------------------
% 3.04/1.65 % (24445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.65 % (24445)Termination reason: Refutation not found, incomplete strategy
% 3.04/1.65
% 3.04/1.65
% 3.04/1.65 % (24445)Memory used [KB]: 6524
% 3.04/1.65 % (24445)Time elapsed: 0.021 s
% 3.04/1.65 % (24445)Instructions burned: 65 (million)
% 3.04/1.65 % (24445)------------------------------
% 3.04/1.65 % (24445)------------------------------
% 3.04/1.65 % (24451)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_24271 for (2999ds/1041Mi)
% 3.04/1.65 % (24448)Instruction limit reached!
% 3.04/1.65 % (24448)------------------------------
% 3.04/1.65 % (24448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.65 % (24448)Termination reason: Unknown
% 3.04/1.65 % (24448)Termination phase: shuffling
% 3.04/1.65
% 3.04/1.65 % (24448)Memory used [KB]: 2046
% 3.04/1.65 % (24448)Time elapsed: 0.011 s
% 3.04/1.65 % (24448)Instructions burned: 37 (million)
% 3.04/1.65 % (24448)------------------------------
% 3.04/1.65 % (24448)------------------------------
% 3.04/1.65 % (24452)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/7Mi)
% 3.04/1.66 % (24452)Instruction limit reached!
% 3.04/1.66 % (24452)------------------------------
% 3.04/1.66 % (24452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (24452)Termination reason: Unknown
% 3.04/1.66 % (24452)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (24452)Memory used [KB]: 1407
% 3.04/1.66 % (24452)Time elapsed: 0.005 s
% 3.04/1.66 % (24452)Instructions burned: 9 (million)
% 3.04/1.66 % (24452)------------------------------
% 3.04/1.66 % (24452)------------------------------
% 3.04/1.66 % (24453)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/16Mi)
% 3.04/1.66 % (24449)Instruction limit reached!
% 3.04/1.66 % (24449)------------------------------
% 3.04/1.66 % (24449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (24449)Termination reason: Unknown
% 3.04/1.66 % (24449)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (24449)Memory used [KB]: 1663
% 3.04/1.66 % (24449)Time elapsed: 0.012 s
% 3.04/1.66 % (24449)Instructions burned: 16 (million)
% 3.04/1.66 % (24449)------------------------------
% 3.04/1.66 % (24449)------------------------------
% 3.04/1.66 % (24454)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_24271 for (2999ds/3Mi)
% 3.04/1.66 % (24455)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_24271 for (2999ds/3Mi)
% 3.04/1.66 % (24455)Instruction limit reached!
% 3.04/1.66 % (24455)------------------------------
% 3.04/1.66 % (24455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (24455)Termination reason: Unknown
% 3.04/1.66 % (24455)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (24455)Memory used [KB]: 1407
% 3.04/1.66 % (24455)Time elapsed: 0.002 s
% 3.04/1.66 % (24455)Instructions burned: 3 (million)
% 3.04/1.66 % (24455)------------------------------
% 3.04/1.66 % (24455)------------------------------
% 3.04/1.66 % (24454)Instruction limit reached!
% 3.04/1.66 % (24454)------------------------------
% 3.04/1.66 % (24454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (24454)Termination reason: Unknown
% 3.04/1.66 % (24454)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (24454)Memory used [KB]: 1407
% 3.04/1.66 % (24454)Time elapsed: 0.003 s
% 3.04/1.66 % (24454)Instructions burned: 6 (million)
% 3.04/1.66 % (24454)------------------------------
% 3.04/1.66 % (24454)------------------------------
% 3.04/1.66 % (24453)Instruction limit reached!
% 3.04/1.66 % (24453)------------------------------
% 3.04/1.66 % (24453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.66 % (24453)Termination reason: Unknown
% 3.04/1.66 % (24453)Termination phase: shuffling
% 3.04/1.66
% 3.04/1.66 % (24453)Memory used [KB]: 1535
% 3.04/1.66 % (24453)Time elapsed: 0.006 s
% 3.04/1.66 % (24453)Instructions burned: 16 (million)
% 3.04/1.66 % (24453)------------------------------
% 3.04/1.66 % (24453)------------------------------
% 3.04/1.67 % (24458)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/7Mi)
% 3.04/1.67 % (24458)Instruction limit reached!
% 3.04/1.67 % (24458)------------------------------
% 3.04/1.67 % (24458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.67 % (24458)Termination reason: Unknown
% 3.04/1.67 % (24458)Termination phase: shuffling
% 3.04/1.67
% 3.04/1.67 % (24458)Memory used [KB]: 1535
% 3.04/1.67 % (24458)Time elapsed: 0.005 s
% 3.04/1.67 % (24458)Instructions burned: 9 (million)
% 3.04/1.67 % (24458)------------------------------
% 3.04/1.67 % (24458)------------------------------
% 3.04/1.67 % (24461)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/4Mi)
% 3.04/1.67 % (24463)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/18Mi)
% 3.04/1.67 % (24461)Instruction limit reached!
% 3.04/1.67 % (24461)------------------------------
% 3.04/1.67 % (24461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.67 % (24461)Termination reason: Unknown
% 3.04/1.67 % (24461)Termination phase: shuffling
% 3.04/1.67
% 3.04/1.67 % (24461)Memory used [KB]: 1407
% 3.04/1.67 % (24461)Time elapsed: 0.003 s
% 3.04/1.67 % (24461)Instructions burned: 6 (million)
% 3.04/1.67 % (24461)------------------------------
% 3.04/1.67 % (24461)------------------------------
% 3.04/1.67 % (24464)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/710Mi)
% 3.04/1.68 % (24463)Instruction limit reached!
% 3.04/1.68 % (24463)------------------------------
% 3.04/1.68 % (24463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.68 % (24463)Termination reason: Unknown
% 3.04/1.68 % (24463)Termination phase: shuffling
% 3.04/1.68
% 3.04/1.68 % (24463)Memory used [KB]: 1535
% 3.04/1.68 % (24463)Time elapsed: 0.007 s
% 3.04/1.68 % (24463)Instructions burned: 18 (million)
% 3.04/1.68 % (24463)------------------------------
% 3.04/1.68 % (24463)------------------------------
% 3.04/1.68 % (24460)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/3Mi)
% 3.04/1.68 % (24460)Instruction limit reached!
% 3.04/1.68 % (24460)------------------------------
% 3.04/1.68 % (24460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.68 % (24460)Termination reason: Unknown
% 3.04/1.68 % (24460)Termination phase: shuffling
% 3.04/1.68
% 3.04/1.68 % (24460)Memory used [KB]: 1407
% 3.04/1.68 % (24460)Time elapsed: 0.004 s
% 3.04/1.68 % (24460)Instructions burned: 4 (million)
% 3.04/1.68 % (24460)------------------------------
% 3.04/1.68 % (24460)------------------------------
% 3.04/1.68 % (24468)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/6Mi)
% 3.04/1.68 % (24440)Instruction limit reached!
% 3.04/1.68 % (24440)------------------------------
% 3.04/1.68 % (24440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.68 % (24440)Termination reason: Unknown
% 3.04/1.68 % (24440)Termination phase: Saturation
% 3.04/1.68
% 3.04/1.68 % (24440)Memory used [KB]: 6908
% 3.04/1.68 % (24440)Time elapsed: 0.052 s
% 3.04/1.68 % (24440)Instructions burned: 184 (million)
% 3.04/1.68 % (24440)------------------------------
% 3.04/1.68 % (24440)------------------------------
% 3.04/1.68 % (24468)Instruction limit reached!
% 3.04/1.68 % (24468)------------------------------
% 3.04/1.68 % (24468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.68 % (24468)Termination reason: Unknown
% 3.04/1.68 % (24468)Termination phase: shuffling
% 3.04/1.68
% 3.04/1.68 % (24468)Memory used [KB]: 1407
% 3.04/1.68 % (24468)Time elapsed: 0.004 s
% 3.04/1.68 % (24468)Instructions burned: 6 (million)
% 3.04/1.68 % (24468)------------------------------
% 3.04/1.68 % (24468)------------------------------
% 3.04/1.68 % (24470)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_24271 for (2999ds/902Mi)
% 3.04/1.69 % (24473)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_24271 for (2999ds/21Mi)
% 3.04/1.69 % (24476)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_24271 for (2999ds/6Mi)
% 3.04/1.69 % (24464)First to succeed.
% 3.04/1.69 % (24475)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/5Mi)
% 3.04/1.69 % (24476)Instruction limit reached!
% 3.04/1.69 % (24476)------------------------------
% 3.04/1.69 % (24476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.69 % (24476)Termination reason: Unknown
% 3.04/1.69 % (24476)Termination phase: shuffling
% 3.04/1.69
% 3.04/1.69 % (24476)Memory used [KB]: 1407
% 3.04/1.69 % (24476)Time elapsed: 0.003 s
% 3.04/1.69 % (24476)Instructions burned: 7 (million)
% 3.04/1.69 % (24476)------------------------------
% 3.04/1.69 % (24476)------------------------------
% 3.04/1.69 % (24478)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_24271 for (2999ds/377Mi)
% 3.04/1.69 % (24464)Refutation found. Thanks to Tanya!
% 3.04/1.69 % SZS status Theorem for DTF2THF_24271
% 3.04/1.69 % SZS output start Proof for DTF2THF_24271
% 3.04/1.69 thf(type_def_5, type, secrecy_specID: $tType).
% 3.04/1.69 thf(type_def_6, type, secrecy_KS: $tType).
% 3.04/1.69 thf(type_def_7, type, set: ($tType) > $tType).
% 3.04/1.69 thf(type_def_9, type, secrecy_Expression: $tType).
% 3.04/1.69 thf(type_def_10, type, list: ($tType) > $tType).
% 3.04/1.69 thf(type_def_11, type, secrecy_Keys: $tType).
% 3.04/1.69 thf(type_def_12, type, secrecy_chanID: $tType).
% 3.04/1.69 thf(type_def_13, type, secrecy_Secrets: $tType).
% 3.04/1.69 thf(type_def_14, type, nat: $tType).
% 3.04/1.69 thf(func_def_0, type, secrecy_Expression: $tType).
% 3.04/1.69 thf(func_def_1, type, secrecy_Secrets: $tType).
% 3.04/1.69 thf(func_def_2, type, secrecy_specID: $tType).
% 3.04/1.69 thf(func_def_3, type, secrecy_chanID: $tType).
% 3.04/1.69 thf(func_def_4, type, secrecy_Keys: $tType).
% 3.04/1.69 thf(func_def_5, type, secrecy_KS: $tType).
% 3.04/1.69 thf(func_def_6, type, list: ($tType) > $tType).
% 3.04/1.69 thf(func_def_7, type, set: ($tType) > $tType).
% 3.04/1.69 thf(func_def_8, type, nat: $tType).
% 3.04/1.69 thf(func_def_9, type, bounded_lattice: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_12, type, ord: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_16, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 3.04/1.69 thf(func_def_17, type, localSecrets: secrecy_specID > set @ secrecy_KS).
% 3.04/1.69 thf(func_def_18, type, knowle1667810483orrect: secrecy_specID > secrecy_KS > $o).
% 3.04/1.69 thf(func_def_19, type, knowle1437066798e_know: secrecy_specID > secrecy_KS > $o).
% 3.04/1.69 thf(func_def_20, type, knowle2055185861_knows: secrecy_specID > list @ secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_21, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 3.04/1.69 thf(func_def_22, type, mem: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 3.04/1.69 thf(func_def_23, type, bot_bot: !>[X0: $tType]:(X0)).
% 3.04/1.69 thf(func_def_24, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 3.04/1.69 thf(func_def_25, type, decr: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 3.04/1.69 thf(func_def_26, type, enc: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 3.04/1.69 thf(func_def_27, type, encrDecrKeys: secrecy_Keys > secrecy_Keys > $o).
% 3.04/1.69 thf(func_def_28, type, ext: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 3.04/1.69 thf(func_def_29, type, sign: secrecy_Keys > list @ secrecy_Expression > list @ secrecy_Expression).
% 3.04/1.69 thf(func_def_30, type, correctCompositionKS: secrecy_specID > $o).
% 3.04/1.69 thf(func_def_31, type, eout: secrecy_specID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_32, type, eoutM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_33, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_34, type, ine: secrecy_specID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_35, type, ineM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_36, type, ine_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_37, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_38, type, notSpe1586871396tsExpr: secrecy_specID > list @ secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_39, type, out_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_40, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 3.04/1.69 thf(func_def_41, type, specKeys: secrecy_specID > set @ secrecy_Keys).
% 3.04/1.69 thf(func_def_42, type, specKeysSecrets: secrecy_specID > set @ secrecy_KS).
% 3.04/1.69 thf(func_def_43, type, specSecrets: secrecy_specID > set @ secrecy_Secrets).
% 3.04/1.69 thf(func_def_44, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 3.04/1.69 thf(func_def_45, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 3.04/1.69 thf(func_def_46, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 3.04/1.69 thf(func_def_47, type, secrecy_case_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 3.04/1.69 thf(func_def_48, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 3.04/1.69 thf(func_def_49, type, secrecy_rec_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 3.04/1.69 thf(func_def_50, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 3.04/1.69 thf(func_def_51, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 3.04/1.69 thf(func_def_52, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 3.04/1.69 thf(func_def_53, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 3.04/1.69 thf(func_def_54, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 3.04/1.69 thf(func_def_55, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 3.04/1.69 thf(func_def_56, type, correctCompositionIn: secrecy_specID > $o).
% 3.04/1.69 thf(func_def_57, type, correc965049635ionLoc: secrecy_specID > $o).
% 3.04/1.69 thf(func_def_58, type, correc990227761ionOut: secrecy_specID > $o).
% 3.04/1.69 thf(func_def_59, type, inStream: secrecy_specID > set @ secrecy_chanID > $o).
% 3.04/1.69 thf(func_def_60, type, ins: secrecy_specID > set @ secrecy_chanID).
% 3.04/1.69 thf(func_def_61, type, loc: secrecy_specID > set @ secrecy_chanID).
% 3.04/1.69 thf(func_def_62, type, locStream: secrecy_specID > set @ secrecy_chanID > $o).
% 3.04/1.69 thf(func_def_63, type, out: secrecy_specID > set @ secrecy_chanID).
% 3.04/1.69 thf(func_def_64, type, outStream: secrecy_specID > set @ secrecy_chanID > $o).
% 3.04/1.69 thf(func_def_65, type, subcomponents: secrecy_specID > set @ secrecy_specID).
% 3.04/1.69 thf(func_def_66, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 3.04/1.69 thf(func_def_67, type, p: secrecy_specID).
% 3.04/1.69 thf(func_def_68, type, pq: secrecy_specID).
% 3.04/1.69 thf(func_def_69, type, q: secrecy_specID).
% 3.04/1.69 thf(func_def_70, type, key: secrecy_Keys).
% 3.04/1.69 thf(func_def_71, type, m: secrecy_KS).
% 3.04/1.69 thf(func_def_86, type, sK0: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 3.04/1.69 thf(f824,plain,(
% 3.04/1.69 $false),
% 3.04/1.69 inference(subsumption_resolution,[status(thm)],[f822,f817])).
% 3.04/1.69 thf(f817,plain,(
% 3.04/1.69 ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) != $true)),
% 3.04/1.69 inference(definition_unfolding,[status(thm)],[f805,f804])).
% 3.04/1.69 thf(f804,plain,(
% 3.04/1.69 (m = (secrecy_kKS @ key))),
% 3.04/1.69 inference(cnf_transformation,[status(thm)],[f2])).
% 3.04/1.69 thf(f2,axiom,(
% 3.04/1.69 (m = (secrecy_kKS @ key))),
% 3.04/1.69 file('/export/starexec/sandbox2/tmp/tmp.M5SM4yxb8e/DTF2THF_24271.p',fact_1_a1)).
% 3.04/1.69 thf(f805,plain,(
% 3.04/1.69 ((knowle1437066798e_know @ q @ m) != $true)),
% 3.04/1.69 inference(cnf_transformation,[status(thm)],[f791])).
% 3.04/1.69 thf(f791,plain,(
% 3.04/1.69 ((knowle1437066798e_know @ q @ m) != $true)),
% 3.04/1.69 inference(flattening,[status(thm)],[f753])).
% 3.04/1.69 thf(f753,plain,(
% 3.04/1.69 ~((knowle1437066798e_know @ q @ m) = $true)),
% 3.04/1.69 inference(fool_elimination,[status(thm)],[f752])).
% 3.04/1.69 thf(f752,plain,(
% 3.04/1.69 ~(knowle1437066798e_know @ q @ m)),
% 3.04/1.69 inference(rectify,[status(thm)],[f1])).
% 3.04/1.69 thf(f1,axiom,(
% 3.04/1.69 ~(knowle1437066798e_know @ q @ m)),
% 3.04/1.69 file('/export/starexec/sandbox2/tmp/tmp.M5SM4yxb8e/DTF2THF_24271.p',fact_0_not__knowQm)).
% 3.04/1.69 thf(f822,plain,(
% 3.04/1.69 ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) = $true)),
% 3.04/1.69 inference(trivial_inequality_removal,[status(thm)],[f820])).
% 3.04/1.69 thf(f820,plain,(
% 3.04/1.69 ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) = $true) | ($true != $true)),
% 3.04/1.69 inference(superposition,[status(thm)],[f807,f816])).
% 3.04/1.69 thf(f816,plain,(
% 3.04/1.69 ((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q)) = $true)),
% 3.04/1.69 inference(cnf_transformation,[status(thm)],[f790])).
% 3.04/1.69 thf(f790,plain,(
% 3.04/1.69 ((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q)) = $true)),
% 3.04/1.69 inference(flattening,[status(thm)],[f335])).
% 3.04/1.69 thf(f335,plain,(
% 3.04/1.69 ~~((member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q)) = $true)),
% 3.04/1.69 inference(fool_elimination,[status(thm)],[f334])).
% 3.04/1.69 thf(f334,plain,(
% 3.04/1.69 ~~(member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 3.04/1.69 inference(rectify,[status(thm)],[f282])).
% 3.04/1.69 thf(f282,negated_conjecture,(
% 3.04/1.69 ~~(member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 3.04/1.69 inference(negated_conjecture,[status(cth)],[f281])).
% 3.04/1.69 thf(f281,conjecture,(
% 3.04/1.69 ~(member @ secrecy_KS @ (secrecy_kKS @ key) @ (localSecrets @ q))),
% 3.04/1.69 file('/export/starexec/sandbox2/tmp/tmp.M5SM4yxb8e/DTF2THF_24271.p',conj_0)).
% 3.04/1.69 thf(f807,plain,(
% 3.04/1.69 ( ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) | ($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))) )),
% 3.04/1.69 inference(cnf_transformation,[status(thm)],[f799])).
% 3.04/1.69 thf(f799,plain,(
% 3.04/1.69 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ((ine @ X0 @ (secrecy_kE @ X1)) = $true) | ($true != (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))) & (($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) | (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) & ((ine @ X0 @ (secrecy_kE @ X1)) != $true))))),
% 3.04/1.69 inference(flattening,[status(thm)],[f798])).
% 3.04/1.69 thf(f798,plain,(
% 3.04/1.69 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ((ine @ X0 @ (secrecy_kE @ X1)) = $true)) | ($true != (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))) & (($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) | (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) & ((ine @ X0 @ (secrecy_kE @ X1)) != $true))))),
% 3.04/1.69 inference(nnf_transformation,[status(thm)],[f459])).
% 3.04/1.69 thf(f459,plain,(
% 3.04/1.69 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ((ine @ X0 @ (secrecy_kE @ X1)) = $true)) <=> ($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))))),
% 3.04/1.69 inference(fool_elimination,[status(thm)],[f458])).
% 3.04/1.69 thf(f458,plain,(
% 3.04/1.69 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) | (ine @ X0 @ (secrecy_kE @ X1)) = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))),
% 3.04/1.69 inference(rectify,[status(thm)],[f11])).
% 3.04/1.69 thf(f11,axiom,(
% 3.04/1.69 ! [X5 : secrecy_specID,X6 : secrecy_Keys] : ((member @ secrecy_KS @ (secrecy_kKS @ X6) @ (localSecrets @ X5)) | (ine @ X5 @ (secrecy_kE @ X6)) = (knowle1437066798e_know @ X5 @ (secrecy_kKS @ X6)))),
% 3.04/1.69 file('/export/starexec/sandbox2/tmp/tmp.M5SM4yxb8e/DTF2THF_24271.p',fact_10_know_Osimps_I1_J)).
% 3.04/1.69 % SZS output end Proof for DTF2THF_24271
% 3.04/1.69 % (24464)------------------------------
% 3.04/1.69 % (24464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.04/1.69 % (24464)Termination reason: Refutation
% 3.04/1.69
% 3.04/1.69 % (24464)Memory used [KB]: 6396
% 3.04/1.69 % (24464)Time elapsed: 0.020 s
% 3.04/1.69 % (24464)Instructions burned: 54 (million)
% 3.04/1.69 % (24464)------------------------------
% 3.04/1.69 % (24464)------------------------------
% 3.04/1.69 % (24439)Success in time 0.069 s
%------------------------------------------------------------------------------