%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP088^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.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 08:55:27 AM UTC 2026
% Result : Theorem 20.49s 4.13s
% Output : Refutation 20.49s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP088^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n028.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 08:25:57 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : ITP088^2 : TPTP v9.2.1. Released v7.5.0.
% 0.31/0.46 % Domain : Interactive Theorem Proving
% 0.31/0.46 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_351__3295008_1
% 0.31/0.46 % Version : Especial.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.31/0.46 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.31/0.46 % Source : [Des21]
% 0.31/0.46 % Names : KnowledgeKeysSecrets/prob_351__3295008_1 [Des21]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.33 v9.0.0, 0.00 v8.2.0, 0.33 v8.1.0, 0.25 v7.5.0
% 0.31/0.46 % Syntax : Number of formulae : 348 ( 115 unt; 67 typ; 0 def)
% 0.31/0.46 % Number of atoms : 1061 ( 289 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 13 ( 3 avg)
% 0.31/0.46 % Number of connectives : 4550 ( 216 ~; 34 |; 95 &;3653 @)
% 0.31/0.46 % ( 0 <=>; 552 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 20 ( 8 avg)
% 0.31/0.46 % Number of types : 8 ( 7 usr)
% 0.31/0.46 % Number of type conns : 167 ( 167 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 61 ( 60 usr; 4 con; 0-6 aty)
% 0.31/0.46 % Number of variables : 1012 ( 63 ^; 900 !; 29 ?;1012 :)
% 0.31/0.46 % ( 20 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.46 % SPC : TH1_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This file was generated by Sledgehammer 2021-02-23 16:20:08.449
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % Could-be-implicit typings (9)
% 0.31/0.46 thf(ty_t_Secrecy__types_OExpression,type,
% 0.31/0.46 secrecy_Expression: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Secrecy__types_OSecrets,type,
% 0.31/0.46 secrecy_Secrets: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Secrecy__types_OspecID,type,
% 0.31/0.46 secrecy_specID: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Secrecy__types_OchanID,type,
% 0.31/0.46 secrecy_chanID: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Secrecy__types_OKeys,type,
% 0.31/0.46 secrecy_Keys: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Secrecy__types_OKS,type,
% 0.31/0.46 secrecy_KS: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_List_Olist,type,
% 0.31/0.46 list: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Set_Oset,type,
% 0.31/0.46 set: $tType > $tType ).
% 0.31/0.46
% 0.31/0.46 thf(ty_t_Nat_Onat,type,
% 0.31/0.46 nat: $tType ).
% 0.31/0.46
% 0.31/0.46 % Explicit typings (58)
% 0.31/0.46 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.31/0.46 bounded_lattice:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_HOL_Otype,type,
% 0.31/0.46 type:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Obot,type,
% 0.31/0.46 bot:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Oord,type,
% 0.31/0.46 ord:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Oorder,type,
% 0.31/0.46 order:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Olinorder,type,
% 0.31/0.46 linorder:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Orderings_Opreorder,type,
% 0.31/0.46 preorder:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.31/0.46 bounde1808546759up_bot:
% 0.31/0.46 !>[A: $tType] : $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.31/0.46 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 0.31/0.46 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 0.31/0.46 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.31/0.46 sup_sup:
% 0.31/0.46 !>[A: $tType] : ( A > A > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_ListExtras_Omem,type,
% 0.31/0.46 mem:
% 0.31/0.46 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.31/0.46 bot_bot:
% 0.31/0.46 !>[A: $tType] : A ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.31/0.46 ord_less_eq:
% 0.31/0.46 !>[A: $tType] : ( A > A > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.31/0.46 correctCompositionKS: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oeout,type,
% 0.31/0.46 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OeoutM,type,
% 0.31/0.46 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OexprChannel,type,
% 0.31/0.46 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oine,type,
% 0.31/0.46 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OineM,type,
% 0.31/0.46 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.31/0.46 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.31/0.46 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.31/0.46 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.31/0.46 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.31/0.46 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OspecKeys,type,
% 0.31/0.46 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.31/0.46 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.31/0.46 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_Ocase__Expression,type,
% 0.31/0.46 secrec487562139ession:
% 0.31/0.46 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > ( nat > A ) > ( secrecy_specID > A ) > secrecy_Expression > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OdE,type,
% 0.31/0.46 secrecy_dE: nat > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OidE,type,
% 0.31/0.46 secrecy_idE: secrecy_specID > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.31/0.46 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_Orec__Expression,type,
% 0.31/0.46 secrec1231112373ession:
% 0.31/0.46 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > ( nat > A ) > ( secrecy_specID > A ) > secrecy_Expression > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.31/0.46 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.31/0.46 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.31/0.46 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.31/0.46 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_OCollect,type,
% 0.31/0.46 collect:
% 0.31/0.46 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Oinsert,type,
% 0.31/0.46 insert:
% 0.31/0.46 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__empty,type,
% 0.31/0.46 is_empty:
% 0.31/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Ois__singleton,type,
% 0.31/0.46 is_singleton:
% 0.31/0.46 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_Set_Othe__elem,type,
% 0.31/0.46 the_elem:
% 0.31/0.46 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.31/0.46 correctCompositionIn: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.31/0.46 correc965049635ionLoc: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.31/0.46 correc990227761ionOut: secrecy_specID > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OinStream,type,
% 0.31/0.46 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Oins,type,
% 0.31/0.46 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Oloc,type,
% 0.31/0.46 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OlocStream,type,
% 0.31/0.46 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Oout,type,
% 0.31/0.46 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_OoutStream,type,
% 0.31/0.46 outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_inout_Osubcomponents,type,
% 0.31/0.46 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_c_member,type,
% 0.31/0.46 member:
% 0.31/0.46 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_P,type,
% 0.31/0.46 p: secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_PQ,type,
% 0.31/0.46 pq: secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_Q,type,
% 0.31/0.46 q: secrecy_specID ).
% 0.31/0.46
% 0.31/0.46 thf(sy_v_key,type,
% 0.31/0.46 key: secrecy_Keys ).
% 0.31/0.46
% 0.31/0.46 % Relevant facts (256)
% 0.31/0.46 thf(fact_0_assms_I4_J,axiom,
% 0.31/0.46 correctCompositionIn @ pq ).
% 0.31/0.46
% 0.31/0.46 % assms(4)
% 0.31/0.46 thf(fact_1_assms_I2_J,axiom,
% 0.31/0.46 ~ ( knowle1437066798e_know @ q @ ( secrecy_kKS @ key ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(2)
% 0.31/0.46 thf(fact_2_assms_I1_J,axiom,
% 0.31/0.46 ~ ( knowle1437066798e_know @ p @ ( secrecy_kKS @ key ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(1)
% 0.31/0.46 thf(fact_3_assms_I3_J,axiom,
% 0.31/0.46 ( ( subcomponents @ pq )
% 0.31/0.46 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % assms(3)
% 0.31/0.46 thf(fact_4_Expression_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.31/0.46 ( ( ( secrecy_kE @ X1 )
% 0.31/0.46 = ( secrecy_kE @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(1)
% 0.31/0.46 thf(fact_5_not__know__k__not__ine,axiom,
% 0.31/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.46 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.31/0.46 => ~ ( ine @ A2 @ ( secrecy_kE @ M ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_know_k_not_ine
% 0.31/0.46 thf(fact_6_know_Osimps_I1_J,axiom,
% 0.31/0.46 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.31/0.46 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 0.31/0.46 | ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % know.simps(1)
% 0.31/0.46 thf(fact_7_Expression_Osimps_I21_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X1: secrecy_Keys] :
% 0.31/0.46 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_kE @ X1 ) )
% 0.31/0.46 = ( F1 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(21)
% 0.31/0.46 thf(fact_8_Expression_Osimps_I17_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X1: secrecy_Keys] :
% 0.31/0.46 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_kE @ X1 ) )
% 0.31/0.46 = ( F1 @ X1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(17)
% 0.31/0.46 thf(fact_9_Expression_Odistinct_I5_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrecy_kE @ X1 )
% 0.31/0.46 != ( secrecy_idE @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(5)
% 0.31/0.46 thf(fact_10_Expression_Odistinct_I3_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X3: nat] :
% 0.31/0.46 ( ( secrecy_kE @ X1 )
% 0.31/0.46 != ( secrecy_dE @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(3)
% 0.31/0.46 thf(fact_11_KS2Expression_Osimps_I1_J,axiom,
% 0.31/0.46 ! [M: secrecy_Keys] :
% 0.31/0.46 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.31/0.46 = ( secrecy_kE @ M ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS2Expression.simps(1)
% 0.31/0.46 thf(fact_12_ineM__ine,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.46 ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ine @ P @ E ) ) ).
% 0.31/0.46
% 0.31/0.46 % ineM_ine
% 0.31/0.46 thf(fact_13_not__ine__ineM,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 0.31/0.46 ( ~ ( ine @ P @ E )
% 0.31/0.46 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_ine_ineM
% 0.31/0.46 thf(fact_14_LocalSecretsComposition__exprChannel__k,axiom,
% 0.31/0.46 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.31/0.46 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_exprChannel_k
% 0.31/0.46 thf(fact_15_Expression_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.31/0.46 ( ( secrecy_kE @ X1 )
% 0.31/0.46 != ( secrecy_sE @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(1)
% 0.31/0.46 thf(fact_16_KS_Oinject_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.31/0.46 ( ( ( secrecy_kKS @ X1 )
% 0.31/0.46 = ( secrecy_kKS @ Y1 ) )
% 0.31/0.46 = ( X1 = Y1 ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS.inject(1)
% 0.31/0.46 thf(fact_17_Expression_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.31/0.46 ( ( ( secrecy_sE @ X2 )
% 0.31/0.46 = ( secrecy_sE @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(2)
% 0.31/0.46 thf(fact_18_Expression_Oinject_I4_J,axiom,
% 0.31/0.46 ! [X4: secrecy_specID,Y4: secrecy_specID] :
% 0.31/0.46 ( ( ( secrecy_idE @ X4 )
% 0.31/0.46 = ( secrecy_idE @ Y4 ) )
% 0.31/0.46 = ( X4 = Y4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(4)
% 0.31/0.46 thf(fact_19_Expression_Oinject_I3_J,axiom,
% 0.31/0.46 ! [X3: nat,Y3: nat] :
% 0.31/0.46 ( ( ( secrecy_dE @ X3 )
% 0.31/0.46 = ( secrecy_dE @ Y3 ) )
% 0.31/0.46 = ( X3 = Y3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.inject(3)
% 0.31/0.46 thf(fact_20_Expression_Osimps_I24_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_idE @ X4 ) )
% 0.31/0.46 = ( F4 @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(24)
% 0.31/0.46 thf(fact_21_Expression_Osimps_I23_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X3: nat] :
% 0.31/0.46 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_dE @ X3 ) )
% 0.31/0.46 = ( F3 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(23)
% 0.31/0.46 thf(fact_22_Expression_Osimps_I22_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X2: secrecy_Secrets] :
% 0.31/0.46 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_sE @ X2 ) )
% 0.31/0.46 = ( F2 @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(22)
% 0.31/0.46 thf(fact_23_Expression_Osimps_I20_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_idE @ X4 ) )
% 0.31/0.46 = ( F4 @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(20)
% 0.31/0.46 thf(fact_24_Expression_Osimps_I19_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X3: nat] :
% 0.31/0.46 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_dE @ X3 ) )
% 0.31/0.46 = ( F3 @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(19)
% 0.31/0.46 thf(fact_25_Expression_Osimps_I18_J,axiom,
% 0.31/0.46 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X2: secrecy_Secrets] :
% 0.31/0.46 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_sE @ X2 ) )
% 0.31/0.46 = ( F2 @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.simps(18)
% 0.31/0.46 thf(fact_26_Expression_Odistinct_I11_J,axiom,
% 0.31/0.46 ! [X3: nat,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrecy_dE @ X3 )
% 0.31/0.46 != ( secrecy_idE @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(11)
% 0.31/0.46 thf(fact_27_Expression_Odistinct_I9_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,X4: secrecy_specID] :
% 0.31/0.46 ( ( secrecy_sE @ X2 )
% 0.31/0.46 != ( secrecy_idE @ X4 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(9)
% 0.31/0.46 thf(fact_28_Expression_Odistinct_I7_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,X3: nat] :
% 0.31/0.46 ( ( secrecy_sE @ X2 )
% 0.31/0.46 != ( secrecy_dE @ X3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.distinct(7)
% 0.31/0.46 thf(fact_29_ineM__L1,axiom,
% 0.31/0.46 ! [Ch: secrecy_chanID,M2: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch @ M2 )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ E )
% 0.31/0.46 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ineM_L1
% 0.31/0.46 thf(fact_30_ine__def,axiom,
% 0.31/0.46 ( ine
% 0.31/0.46 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.31/0.46 ? [Ch2: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 0.31/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_def
% 0.31/0.46 thf(fact_31_ineM__def,axiom,
% 0.31/0.46 ( ineM
% 0.31/0.46 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.46 ? [Ch2: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 0.31/0.46 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 0.31/0.46 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ineM_def
% 0.31/0.46 thf(fact_32_TBlemma3b,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ~ ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ M2 )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBlemma3b
% 0.31/0.46 thf(fact_33_TBtheorem1b,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ineM @ PQ @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem1b
% 0.31/0.46 thf(fact_34_TBtheorem3b,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem3b
% 0.31/0.46 thf(fact_35_ine__ins__neg1,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 0.31/0.46 ( ~ ( ine @ P @ M )
% 0.31/0.46 => ( ( exprChannel @ X @ M )
% 0.31/0.46 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_ins_neg1
% 0.31/0.46 thf(fact_36_correctCompositionIn__L2,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionIn_L2
% 0.31/0.46 thf(fact_37_Expression_Oinduct,axiom,
% 0.31/0.46 ! [P: secrecy_Expression > $o,Expression: secrecy_Expression] :
% 0.31/0.46 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kE @ X5 ) )
% 0.31/0.46 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sE @ X5 ) )
% 0.31/0.46 => ( ! [X5: nat] : ( P @ ( secrecy_dE @ X5 ) )
% 0.31/0.46 => ( ! [X5: secrecy_specID] : ( P @ ( secrecy_idE @ X5 ) )
% 0.31/0.46 => ( P @ Expression ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.induct
% 0.31/0.46 thf(fact_38_Expression_Oexhaust,axiom,
% 0.31/0.46 ! [Y: secrecy_Expression] :
% 0.31/0.46 ( ! [X12: secrecy_Keys] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_kE @ X12 ) )
% 0.31/0.46 => ( ! [X22: secrecy_Secrets] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_sE @ X22 ) )
% 0.31/0.46 => ( ! [X32: nat] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_dE @ X32 ) )
% 0.31/0.46 => ~ ! [X42: secrecy_specID] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_idE @ X42 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Expression.exhaust
% 0.31/0.46 thf(fact_39_correctCompositionIn__prop1,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.31/0.46 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionIn_prop1
% 0.31/0.46 thf(fact_40_LocalSecretsComposition1,axiom,
% 0.31/0.46 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition1
% 0.31/0.46 thf(fact_41_LocalSecretsComposition__exprChannel__s,axiom,
% 0.31/0.46 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.31/0.46 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_exprChannel_s
% 0.31/0.46 thf(fact_42_TBtheorem3a,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( ine @ P @ E )
% 0.31/0.46 => ( ~ ( ine @ Q @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem3a
% 0.31/0.46 thf(fact_43_TBtheorem1a,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ine @ PQ @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ine @ P @ E )
% 0.31/0.46 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem1a
% 0.31/0.46 thf(fact_44_singletonI,axiom,
% 0.31/0.46 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonI
% 0.31/0.46 thf(fact_45_mem__Collect__eq,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,P: A > $o] :
% 0.31/0.46 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.31/0.46 = ( P @ A3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % mem_Collect_eq
% 0.31/0.46 thf(fact_46_Collect__mem__eq,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( collect @ A
% 0.31/0.46 @ ^ [X6: A] : ( member @ A @ X6 @ A2 ) )
% 0.31/0.46 = A2 ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_mem_eq
% 0.31/0.46 thf(fact_47_Collect__cong,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.46 ( ! [X5: A] :
% 0.31/0.46 ( ( P @ X5 )
% 0.31/0.46 = ( Q @ X5 ) )
% 0.31/0.46 => ( ( collect @ A @ P )
% 0.31/0.46 = ( collect @ A @ Q ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_cong
% 0.31/0.46 thf(fact_48_ext,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 0.31/0.46 ( ! [X5: A] :
% 0.31/0.46 ( ( F @ X5 )
% 0.31/0.46 = ( G @ X5 ) )
% 0.31/0.46 => ( F = G ) ) ).
% 0.31/0.46
% 0.31/0.46 % ext
% 0.31/0.46 thf(fact_49_LocalSecretsComposition__neg1__k,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg1_k
% 0.31/0.46 thf(fact_50_LocalSecretsComposition__ine2__k,axiom,
% 0.31/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_ine2_k
% 0.31/0.46 thf(fact_51_LocalSecretsComposition__ine1__k,axiom,
% 0.31/0.46 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_ine1_k
% 0.31/0.46 thf(fact_52_TBtheorem4b__P,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 0.31/0.46 & ( member @ secrecy_chanID @ Ch3 @ M2 ) )
% 0.31/0.46 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_P
% 0.31/0.46 thf(fact_53_TBtheorem4b__PQ,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 | ( ineM @ Q @ M2 @ E ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 0.31/0.46 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.31/0.46 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_PQ
% 0.31/0.46 thf(fact_54_TBtheorem4a__P,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( ine @ P @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_P
% 0.31/0.46 thf(fact_55_TBtheorem4a__PQ,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ( ine @ P @ E )
% 0.31/0.46 | ( ine @ Q @ E ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 0.31/0.46 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 0.31/0.46 & ( exprChannel @ Ch3 @ E )
% 0.31/0.46 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_PQ
% 0.31/0.46 thf(fact_56_insertCI,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 0.31/0.46 ( ( ~ ( member @ A @ A3 @ B2 )
% 0.31/0.46 => ( A3 = B3 ) )
% 0.31/0.46 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertCI
% 0.31/0.46 thf(fact_57_insert__iff,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 0.31/0.46 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 0.31/0.46 = ( ( A3 = B3 )
% 0.31/0.46 | ( member @ A @ A3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_iff
% 0.31/0.46 thf(fact_58_empty__Collect__eq,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o] :
% 0.31/0.46 ( ( ( bot_bot @ ( set @ A ) )
% 0.31/0.46 = ( collect @ A @ P ) )
% 0.31/0.46 = ( ! [X6: A] :
% 0.31/0.46 ~ ( P @ X6 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_Collect_eq
% 0.31/0.46 thf(fact_59_Collect__empty__eq,axiom,
% 0.31/0.46 ! [A: $tType,P: A > $o] :
% 0.31/0.46 ( ( ( collect @ A @ P )
% 0.31/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.46 = ( ! [X6: A] :
% 0.31/0.46 ~ ( P @ X6 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Collect_empty_eq
% 0.31/0.46 thf(fact_60_all__not__in__conv,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( ! [X6: A] :
% 0.31/0.46 ~ ( member @ A @ X6 @ A2 ) )
% 0.31/0.46 = ( A2
% 0.31/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % all_not_in_conv
% 0.31/0.46 thf(fact_61_empty__iff,axiom,
% 0.31/0.46 ! [A: $tType,C: A] :
% 0.31/0.46 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % empty_iff
% 0.31/0.46 thf(fact_62_insert__absorb2,axiom,
% 0.31/0.46 ! [A: $tType,X: A,A2: set @ A] :
% 0.31/0.46 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 0.31/0.46 = ( insert @ A @ X @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb2
% 0.31/0.46 thf(fact_63_TBtheorem4a__empty,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ( ine @ P @ E )
% 0.31/0.46 | ( ine @ Q @ E ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ( loc @ PQ )
% 0.31/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.31/0.46 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_empty
% 0.31/0.46 thf(fact_64_ex__in__conv,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( ? [X6: A] : ( member @ A @ X6 @ A2 ) )
% 0.31/0.46 = ( A2
% 0.31/0.46 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ex_in_conv
% 0.31/0.46 thf(fact_65_equals0I,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ! [Y5: A] :
% 0.31/0.46 ~ ( member @ A @ Y5 @ A2 )
% 0.31/0.46 => ( A2
% 0.31/0.46 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0I
% 0.31/0.46 thf(fact_66_equals0D,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A,A3: A] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.46 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % equals0D
% 0.31/0.46 thf(fact_67_emptyE,axiom,
% 0.31/0.46 ! [A: $tType,A3: A] :
% 0.31/0.46 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % emptyE
% 0.31/0.46 thf(fact_68_mk__disjoint__insert,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,A2: set @ A] :
% 0.31/0.46 ( ( member @ A @ A3 @ A2 )
% 0.31/0.46 => ? [B4: set @ A] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert @ A @ A3 @ B4 ) )
% 0.31/0.46 & ~ ( member @ A @ A3 @ B4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % mk_disjoint_insert
% 0.31/0.46 thf(fact_69_insert__commute,axiom,
% 0.31/0.46 ! [A: $tType,X: A,Y: A,A2: set @ A] :
% 0.31/0.46 ( ( insert @ A @ X @ ( insert @ A @ Y @ A2 ) )
% 0.31/0.46 = ( insert @ A @ Y @ ( insert @ A @ X @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_commute
% 0.31/0.46 thf(fact_70_insert__eq__iff,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,A2: set @ A,B3: A,B2: set @ A] :
% 0.31/0.46 ( ~ ( member @ A @ A3 @ A2 )
% 0.31/0.46 => ( ~ ( member @ A @ B3 @ B2 )
% 0.31/0.46 => ( ( ( insert @ A @ A3 @ A2 )
% 0.31/0.46 = ( insert @ A @ B3 @ B2 ) )
% 0.31/0.46 = ( ( ( A3 = B3 )
% 0.31/0.46 => ( A2 = B2 ) )
% 0.31/0.46 & ( ( A3 != B3 )
% 0.31/0.46 => ? [C2: set @ A] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert @ A @ B3 @ C2 ) )
% 0.31/0.46 & ~ ( member @ A @ B3 @ C2 )
% 0.31/0.46 & ( B2
% 0.31/0.46 = ( insert @ A @ A3 @ C2 ) )
% 0.31/0.46 & ~ ( member @ A @ A3 @ C2 ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_eq_iff
% 0.31/0.46 thf(fact_71_insert__absorb,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,A2: set @ A] :
% 0.31/0.46 ( ( member @ A @ A3 @ A2 )
% 0.31/0.46 => ( ( insert @ A @ A3 @ A2 )
% 0.31/0.46 = A2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_absorb
% 0.31/0.46 thf(fact_72_insert__ident,axiom,
% 0.31/0.46 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.31/0.46 ( ~ ( member @ A @ X @ A2 )
% 0.31/0.46 => ( ~ ( member @ A @ X @ B2 )
% 0.31/0.46 => ( ( ( insert @ A @ X @ A2 )
% 0.31/0.46 = ( insert @ A @ X @ B2 ) )
% 0.31/0.46 = ( A2 = B2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_ident
% 0.31/0.46 thf(fact_73_Set_Oset__insert,axiom,
% 0.31/0.46 ! [A: $tType,X: A,A2: set @ A] :
% 0.31/0.46 ( ( member @ A @ X @ A2 )
% 0.31/0.46 => ~ ! [B4: set @ A] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 = ( insert @ A @ X @ B4 ) )
% 0.31/0.46 => ( member @ A @ X @ B4 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % Set.set_insert
% 0.31/0.46 thf(fact_74_insertI2,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 0.31/0.46 ( ( member @ A @ A3 @ B2 )
% 0.31/0.46 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI2
% 0.31/0.46 thf(fact_75_insertI1,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B2: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertI1
% 0.31/0.46 thf(fact_76_insertE,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 0.31/0.46 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 0.31/0.46 => ( ( A3 != B3 )
% 0.31/0.46 => ( member @ A @ A3 @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insertE
% 0.31/0.46 thf(fact_77_correctCompositionIn__L1,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionIn_L1
% 0.31/0.46 thf(fact_78_singleton__inject,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B3: A] :
% 0.31/0.46 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.31/0.46 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.46 => ( A3 = B3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_inject
% 0.31/0.46 thf(fact_79_insert__not__empty,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,A2: set @ A] :
% 0.31/0.46 ( ( insert @ A @ A3 @ A2 )
% 0.31/0.46 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % insert_not_empty
% 0.31/0.46 thf(fact_80_doubleton__eq__iff,axiom,
% 0.31/0.46 ! [A: $tType,A3: A,B3: A,C: A,D: A] :
% 0.31/0.46 ( ( ( insert @ A @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.46 = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.31/0.46 = ( ( ( A3 = C )
% 0.31/0.46 & ( B3 = D ) )
% 0.31/0.46 | ( ( A3 = D )
% 0.31/0.46 & ( B3 = C ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % doubleton_eq_iff
% 0.31/0.46 thf(fact_81_singleton__iff,axiom,
% 0.31/0.46 ! [A: $tType,B3: A,A3: A] :
% 0.31/0.46 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.46 = ( B3 = A3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % singleton_iff
% 0.31/0.46 thf(fact_82_singletonD,axiom,
% 0.31/0.46 ! [A: $tType,B3: A,A3: A] :
% 0.31/0.46 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.46 => ( B3 = A3 ) ) ).
% 0.31/0.46
% 0.31/0.46 % singletonD
% 0.31/0.46 thf(fact_83_correctCompositionInLoc__exprChannel,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ M )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ( ins @ PQ ) )
% 0.31/0.46 => ~ ( exprChannel @ X5 @ M ) )
% 0.31/0.46 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionInLoc_exprChannel
% 0.31/0.46 thf(fact_84_subcomponents__loc,axiom,
% 0.31/0.46 ! [X: secrecy_specID] :
% 0.31/0.46 ( ( correc965049635ionLoc @ X )
% 0.31/0.46 => ( ( ( subcomponents @ X )
% 0.31/0.46 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 0.31/0.46 => ( ( loc @ X )
% 0.31/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % subcomponents_loc
% 0.31/0.46 thf(fact_85_TBtheorem4b__notP1,axiom,
% 0.31/0.46 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ineM @ P @ M2 @ E )
% 0.31/0.46 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.31/0.46 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.31/0.46 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_notP1
% 0.31/0.46 thf(fact_86_TBtheorem4a__notP1,axiom,
% 0.31/0.46 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ( ine @ P @ E )
% 0.31/0.46 => ( ~ ( ine @ Q @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.46 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 0.31/0.46 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_notP1
% 0.31/0.46 thf(fact_87_TBtheorem4b__notPQ,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 0.31/0.46 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 0.31/0.46 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_notPQ
% 0.31/0.46 thf(fact_88_TBtheorem4b__notP2,axiom,
% 0.31/0.46 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.31/0.46 ( ~ ( ineM @ Q @ M2 @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 0.31/0.46 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4b_notP2
% 0.31/0.46 thf(fact_89_TBtheorem4a__notPQ,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.46 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 0.31/0.46 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 0.31/0.46 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_notPQ
% 0.31/0.46 thf(fact_90_TBtheorem4a__notP2,axiom,
% 0.31/0.46 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.31/0.46 ( ~ ( ine @ Q @ E )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.46 => ( ! [X5: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 0.31/0.46 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.46 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % TBtheorem4a_notP2
% 0.31/0.46 thf(fact_91_ine__exprChannelSet__Single,axiom,
% 0.31/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.46 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.31/0.46 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_exprChannelSet_Single
% 0.31/0.46 thf(fact_92_ine__exprChannelSingle__Set,axiom,
% 0.31/0.46 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.46 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.31/0.46 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_exprChannelSingle_Set
% 0.31/0.46 thf(fact_93_ine__nonempty__exprChannelSet,axiom,
% 0.31/0.46 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.46 => ( ( ChSet
% 0.31/0.46 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.31/0.46 => ( ine @ P @ E ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_nonempty_exprChannelSet
% 0.31/0.46 thf(fact_94_ine__empty__exprChannelSet,axiom,
% 0.31/0.46 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.46 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.46 => ( ( ChSet
% 0.31/0.46 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.31/0.46 => ~ ( ine @ P @ E ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_empty_exprChannelSet
% 0.31/0.46 thf(fact_95_ine__exprChannelSet__def,axiom,
% 0.31/0.46 ( ine_exprChannelSet
% 0.31/0.46 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.46 ( ! [X6: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ X6 @ ( ins @ SP ) )
% 0.31/0.46 & ( exprChannel @ X6 @ E2 ) ) )
% 0.31/0.46 & ! [X6: secrecy_chanID] :
% 0.31/0.46 ( ( ~ ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 0.31/0.46 & ( member @ secrecy_chanID @ X6 @ ( ins @ SP ) ) )
% 0.31/0.46 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_exprChannelSet_def
% 0.31/0.46 thf(fact_96_ine__exprChannelSingle__def,axiom,
% 0.31/0.46 ( ine_ex1303305700Single
% 0.31/0.46 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 0.31/0.46 & ( exprChannel @ Ch2 @ E2 )
% 0.31/0.46 & ! [X6: secrecy_chanID,T: nat] :
% 0.31/0.46 ( ( ( member @ secrecy_chanID @ X6 @ ( ins @ SP ) )
% 0.31/0.46 & ( X6 != Ch2 ) )
% 0.31/0.46 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % ine_exprChannelSingle_def
% 0.31/0.46 thf(fact_97_LocalSecretsComposition__neg1,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ! [M4: secrecy_Keys] :
% 0.31/0.46 ( ( Ks
% 0.31/0.46 = ( secrecy_kKS @ M4 ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.31/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.31/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.31/0.46 ( ( Ks
% 0.31/0.46 = ( secrecy_sKS @ M4 ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.31/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg1
% 0.31/0.46 thf(fact_98_locStream__def,axiom,
% 0.31/0.46 ( locStream
% 0.31/0.46 = ( ^ [X6: secrecy_specID] :
% 0.31/0.46 ( ^ [Y6: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y6 = Z )
% 0.31/0.46 @ ( loc @ X6 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % locStream_def
% 0.31/0.46 thf(fact_99_inStream__def,axiom,
% 0.31/0.46 ( inStream
% 0.31/0.46 = ( ^ [X6: secrecy_specID] :
% 0.31/0.46 ( ^ [Y6: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y6 = Z )
% 0.31/0.46 @ ( ins @ X6 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % inStream_def
% 0.31/0.46 thf(fact_100_the__elem__eq,axiom,
% 0.31/0.46 ! [A: $tType,X: A] :
% 0.31/0.46 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.46 = X ) ).
% 0.31/0.46
% 0.31/0.46 % the_elem_eq
% 0.31/0.46 thf(fact_101_bot__apply,axiom,
% 0.31/0.46 ! [C3: $tType,D2: $tType] :
% 0.31/0.46 ( ( bot @ C3 )
% 0.31/0.46 => ( ( bot_bot @ ( D2 > C3 ) )
% 0.31/0.46 = ( ^ [X6: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_apply
% 0.31/0.46 thf(fact_102_LocalSecretsComposition__ine1__s,axiom,
% 0.31/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_ine1_s
% 0.31/0.46 thf(fact_103_KS_Oinject_I2_J,axiom,
% 0.31/0.46 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.31/0.46 ( ( ( secrecy_sKS @ X2 )
% 0.31/0.46 = ( secrecy_sKS @ Y2 ) )
% 0.31/0.46 = ( X2 = Y2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS.inject(2)
% 0.31/0.46 thf(fact_104_bot__set__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( bot_bot @ ( set @ A ) )
% 0.31/0.46 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_set_def
% 0.31/0.46 thf(fact_105_KS_Oexhaust,axiom,
% 0.31/0.46 ! [Y: secrecy_KS] :
% 0.31/0.46 ( ! [X12: secrecy_Keys] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_kKS @ X12 ) )
% 0.31/0.46 => ~ ! [X22: secrecy_Secrets] :
% 0.31/0.46 ( Y
% 0.31/0.46 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS.exhaust
% 0.31/0.46 thf(fact_106_KS_Oinduct,axiom,
% 0.31/0.46 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.31/0.46 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kKS @ X5 ) )
% 0.31/0.46 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X5 ) )
% 0.31/0.46 => ( P @ KS ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS.induct
% 0.31/0.46 thf(fact_107_KS_Odistinct_I1_J,axiom,
% 0.31/0.46 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.31/0.46 ( ( secrecy_kKS @ X1 )
% 0.31/0.46 != ( secrecy_sKS @ X2 ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS.distinct(1)
% 0.31/0.46 thf(fact_108_KS2Expression_Osimps_I2_J,axiom,
% 0.31/0.46 ! [M: secrecy_Secrets] :
% 0.31/0.46 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.31/0.46 = ( secrecy_sE @ M ) ) ).
% 0.31/0.46
% 0.31/0.46 % KS2Expression.simps(2)
% 0.31/0.46 thf(fact_109_bot__fun__def,axiom,
% 0.31/0.46 ! [B: $tType,A: $tType] :
% 0.31/0.46 ( ( bot @ B )
% 0.31/0.46 => ( ( bot_bot @ ( A > B ) )
% 0.31/0.46 = ( ^ [X6: A] : ( bot_bot @ B ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % bot_fun_def
% 0.31/0.46 thf(fact_110_not__know__s__not__ine,axiom,
% 0.31/0.46 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.46 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.31/0.46 => ~ ( ine @ A2 @ ( secrecy_sE @ M ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % not_know_s_not_ine
% 0.31/0.46 thf(fact_111_know_Osimps_I2_J,axiom,
% 0.31/0.46 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.46 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.31/0.46 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 0.31/0.46 | ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % know.simps(2)
% 0.31/0.46 thf(fact_112_LocalSecretsComposition__neg1__s,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.31/0.46 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg1_s
% 0.31/0.46 thf(fact_113_LocalSecretsComposition__ine2__s,axiom,
% 0.31/0.46 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.46 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.31/0.46 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_ine2_s
% 0.31/0.46 thf(fact_114_is__singleton__the__elem,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( is_singleton @ A )
% 0.31/0.46 = ( ^ [A4: set @ A] :
% 0.31/0.46 ( A4
% 0.31/0.46 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_the_elem
% 0.31/0.46 thf(fact_115_is__singletonI,axiom,
% 0.31/0.46 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI
% 0.31/0.46 thf(fact_116_LocalSecretsComposition__neg__loc__s,axiom,
% 0.31/0.46 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg_loc_s
% 0.31/0.46 thf(fact_117_LocalSecretsComposition__neg__loc__k,axiom,
% 0.31/0.46 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.31/0.46 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg_loc_k
% 0.31/0.46 thf(fact_118_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ? [Ch4: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_s_Qex
% 0.31/0.46 thf(fact_119_correctCompositionKS__PQ,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.46 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_PQ
% 0.31/0.46 thf(fact_120_correctCompositionKS__neg1,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_neg1
% 0.31/0.46 thf(fact_121_correctCompositionKS__negP,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_negP
% 0.31/0.46 thf(fact_122_correctCompositionKS__negQ,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_negQ
% 0.31/0.46 thf(fact_123_is__singletonI_H,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( A2
% 0.31/0.46 != ( bot_bot @ ( set @ A ) ) )
% 0.31/0.46 => ( ! [X5: A,Y5: A] :
% 0.31/0.46 ( ( member @ A @ X5 @ A2 )
% 0.31/0.46 => ( ( member @ A @ Y5 @ A2 )
% 0.31/0.46 => ( X5 = Y5 ) ) )
% 0.31/0.46 => ( is_singleton @ A @ A2 ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonI'
% 0.31/0.46 thf(fact_124_know__composition,axiom,
% 0.31/0.46 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.46 => ( ( ( knowle1437066798e_know @ P @ M )
% 0.31/0.46 | ( knowle1437066798e_know @ Q @ M ) )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % know_composition
% 0.31/0.46 thf(fact_125_know__composition1,axiom,
% 0.31/0.46 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.46 => ( ( knowle1437066798e_know @ P @ M )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % know_composition1
% 0.31/0.46 thf(fact_126_know__composition2,axiom,
% 0.31/0.46 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.46 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.31/0.46 => ( ( knowle1437066798e_know @ Q @ M )
% 0.31/0.46 => ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % know_composition2
% 0.31/0.46 thf(fact_127_is__singletonE,axiom,
% 0.31/0.46 ! [A: $tType,A2: set @ A] :
% 0.31/0.46 ( ( is_singleton @ A @ A2 )
% 0.31/0.46 => ~ ! [X5: A] :
% 0.31/0.46 ( A2
% 0.31/0.46 != ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singletonE
% 0.31/0.46 thf(fact_128_is__singleton__def,axiom,
% 0.31/0.46 ! [A: $tType] :
% 0.31/0.46 ( ( is_singleton @ A )
% 0.31/0.46 = ( ^ [A4: set @ A] :
% 0.31/0.46 ? [X6: A] :
% 0.31/0.46 ( A4
% 0.31/0.46 = ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % is_singleton_def
% 0.31/0.46 thf(fact_129_correctCompositionKS__exprChannel__k__P,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_k_P
% 0.31/0.46 thf(fact_130_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_k_Q
% 0.31/0.46 thf(fact_131_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ? [Ch4: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_k_Pex
% 0.31/0.46 thf(fact_132_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ? [Ch4: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_k_Qex
% 0.31/0.46 thf(fact_133_correctCompositionKS__exprChannel__s__P,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_s_P
% 0.31/0.46 thf(fact_134_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_s_Q
% 0.31/0.46 thf(fact_135_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.31/0.46 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.31/0.46 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.31/0.46 => ( ( correctCompositionIn @ PQ )
% 0.31/0.46 => ? [Ch4: secrecy_chanID] :
% 0.31/0.46 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.31/0.46 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % correctCompositionKS_exprChannel_s_Pex
% 0.31/0.46 thf(fact_136_LocalSecretsComposition__neg,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.31/0.46 => ( ! [M4: secrecy_Keys] :
% 0.31/0.46 ( ( Ks
% 0.31/0.46 = ( secrecy_kKS @ M4 ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.31/0.46 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.31/0.46 => ( ! [M4: secrecy_Secrets] :
% 0.31/0.46 ( ( Ks
% 0.31/0.46 = ( secrecy_sKS @ M4 ) )
% 0.31/0.46 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.31/0.46 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.46 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 % LocalSecretsComposition_neg
% 0.31/0.46 thf(fact_137_LocalSecretsComposition__neg__s,axiom,
% 0.31/0.46 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.46 ( ( ( subcomponents @ PQ )
% 0.31/0.46 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.46 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.46 => ( ( correctCompositionKS @ PQ )
% 0.31/0.46 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg_s
% 0.31/0.47 thf(fact_138_LocalSecretsComposition__neg__k,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc965049635ionLoc @ PQ )
% 0.31/0.47 => ( ( correctCompositionKS @ PQ )
% 0.31/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.31/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.31/0.47 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.31/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % LocalSecretsComposition_neg_k
% 0.31/0.47 thf(fact_139_bot__empty__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bot_bot @ ( A > $o ) )
% 0.31/0.47 = ( ^ [X6: A] : ( member @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_empty_eq
% 0.31/0.47 thf(fact_140_UnCI,axiom,
% 0.31/0.47 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 0.31/0.47 ( ( ~ ( member @ A @ C @ B2 )
% 0.31/0.47 => ( member @ A @ C @ A2 ) )
% 0.31/0.47 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnCI
% 0.31/0.47 thf(fact_141_Un__iff,axiom,
% 0.31/0.47 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 = ( ( member @ A @ C @ A2 )
% 0.31/0.47 | ( member @ A @ C @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_iff
% 0.31/0.47 thf(fact_142_Un__empty,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 = ( ( A2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty
% 0.31/0.47 thf(fact_143_Un__insert__right,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 0.31/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_right
% 0.31/0.47 thf(fact_144_Un__insert__left,axiom,
% 0.31/0.47 ! [A: $tType,A3: A,B2: set @ A,C4: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 0.31/0.47 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_insert_left
% 0.31/0.47 thf(fact_145_Un__empty__right,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_right
% 0.31/0.47 thf(fact_146_Un__empty__left,axiom,
% 0.31/0.47 ! [A: $tType,B2: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 0.31/0.47 = B2 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_empty_left
% 0.31/0.47 thf(fact_147_UnE,axiom,
% 0.31/0.47 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 => ( ~ ( member @ A @ C @ A2 )
% 0.31/0.47 => ( member @ A @ C @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnE
% 0.31/0.47 thf(fact_148_UnI1,axiom,
% 0.31/0.47 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( member @ A @ C @ A2 )
% 0.31/0.47 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI1
% 0.31/0.47 thf(fact_149_UnI2,axiom,
% 0.31/0.47 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 0.31/0.47 ( ( member @ A @ C @ B2 )
% 0.31/0.47 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % UnI2
% 0.31/0.47 thf(fact_150_bex__Un,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.31/0.47 ( ( ? [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 & ( P @ X6 ) ) )
% 0.31/0.47 = ( ? [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ A2 )
% 0.31/0.47 & ( P @ X6 ) )
% 0.31/0.47 | ? [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ B2 )
% 0.31/0.47 & ( P @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bex_Un
% 0.31/0.47 thf(fact_151_ball__Un,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 0.31/0.47 ( ( ! [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 => ( P @ X6 ) ) )
% 0.31/0.47 = ( ! [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ A2 )
% 0.31/0.47 => ( P @ X6 ) )
% 0.31/0.47 & ! [X6: A] :
% 0.31/0.47 ( ( member @ A @ X6 @ B2 )
% 0.31/0.47 => ( P @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ball_Un
% 0.31/0.47 thf(fact_152_Un__assoc,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.31/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_assoc
% 0.31/0.47 thf(fact_153_Un__absorb,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.31/0.47 = A2 ) ).
% 0.31/0.47
% 0.31/0.47 % Un_absorb
% 0.31/0.47 thf(fact_154_Un__commute,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) )
% 0.31/0.47 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_commute
% 0.31/0.47 thf(fact_155_Un__left__absorb,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_absorb
% 0.31/0.47 thf(fact_156_Un__left__commute,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 0.31/0.47 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_left_commute
% 0.31/0.47 thf(fact_157_singleton__Un__iff,axiom,
% 0.31/0.47 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 = ( ( ( A2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.31/0.47 | ( ( A2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 | ( ( A2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_Un_iff
% 0.31/0.47 thf(fact_158_Un__singleton__iff,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 0.31/0.47 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 = ( ( ( A2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.31/0.47 | ( ( A2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 | ( ( A2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 & ( B2
% 0.31/0.47 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_singleton_iff
% 0.31/0.47 thf(fact_159_insert__is__Un,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( insert @ A )
% 0.31/0.47 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_is_Un
% 0.31/0.47 thf(fact_160_sup__bot_Oright__neutral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [A3: A] :
% 0.31/0.47 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 0.31/0.47 = A3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.right_neutral
% 0.31/0.47 thf(fact_161_sup__bot_Oneutr__eq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [A3: A,B3: A] :
% 0.31/0.47 ( ( ( bot_bot @ A )
% 0.31/0.47 = ( sup_sup @ A @ A3 @ B3 ) )
% 0.31/0.47 = ( ( A3
% 0.31/0.47 = ( bot_bot @ A ) )
% 0.31/0.47 & ( B3
% 0.31/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.neutr_eq_iff
% 0.31/0.47 thf(fact_162_sup__bot_Oleft__neutral,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [A3: A] :
% 0.31/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 0.31/0.47 = A3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.left_neutral
% 0.31/0.47 thf(fact_163_sup__bot_Oeq__neutr__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [A3: A,B3: A] :
% 0.31/0.47 ( ( ( sup_sup @ A @ A3 @ B3 )
% 0.31/0.47 = ( bot_bot @ A ) )
% 0.31/0.47 = ( ( A3
% 0.31/0.47 = ( bot_bot @ A ) )
% 0.31/0.47 & ( B3
% 0.31/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot.eq_neutr_iff
% 0.31/0.47 thf(fact_164_sup__bot__left,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_left
% 0.31/0.47 thf(fact_165_sup__bot__right,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [X: A] :
% 0.31/0.47 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.31/0.47 = X ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_bot_right
% 0.31/0.47 thf(fact_166_bot__eq__sup__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ( bot_bot @ A )
% 0.31/0.47 = ( sup_sup @ A @ X @ Y ) )
% 0.31/0.47 = ( ( X
% 0.31/0.47 = ( bot_bot @ A ) )
% 0.31/0.47 & ( Y
% 0.31/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % bot_eq_sup_iff
% 0.31/0.47 thf(fact_167_sup__eq__bot__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( bounde1808546759up_bot @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ( sup_sup @ A @ X @ Y )
% 0.31/0.47 = ( bot_bot @ A ) )
% 0.31/0.47 = ( ( X
% 0.31/0.47 = ( bot_bot @ A ) )
% 0.31/0.47 & ( Y
% 0.31/0.47 = ( bot_bot @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % sup_eq_bot_iff
% 0.31/0.47 thf(fact_168_ineM__Un1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,A2: set @ secrecy_chanID,E: secrecy_Expression,B2: set @ secrecy_chanID] :
% 0.31/0.47 ( ( ineM @ P @ A2 @ E )
% 0.31/0.47 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A2 @ B2 ) @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % ineM_Un1
% 0.31/0.47 thf(fact_169_Collect__empty__eq__bot,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o] :
% 0.31/0.47 ( ( ( collect @ A @ P )
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 = ( P
% 0.31/0.47 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_empty_eq_bot
% 0.31/0.47 thf(fact_170_notSpecKeysSecretsExpr__def,axiom,
% 0.31/0.47 ( notSpe1586871396tsExpr
% 0.31/0.47 = ( ^ [P2: secrecy_specID,E3: list @ secrecy_Expression] :
% 0.31/0.47 ( ! [X6: secrecy_Keys] :
% 0.31/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X6 ) @ E3 )
% 0.31/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X6 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.31/0.47 & ! [Y7: secrecy_Secrets] :
% 0.31/0.47 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y7 ) @ E3 )
% 0.31/0.47 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y7 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % notSpecKeysSecretsExpr_def
% 0.31/0.47 thf(fact_171_Set_Ois__empty__def,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( is_empty @ A )
% 0.31/0.47 = ( ^ [A4: set @ A] :
% 0.31/0.47 ( A4
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Set.is_empty_def
% 0.31/0.47 thf(fact_172_TBtheorem5a__empty,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( eout @ P @ E )
% 0.31/0.47 | ( eout @ Q @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( ( loc @ PQ )
% 0.31/0.47 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.31/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_empty
% 0.31/0.47 thf(fact_173_correctCompositionKS__subcomp1,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.31/0.47 ( ( correctCompositionKS @ C4 )
% 0.31/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.31/0.47 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 0.31/0.47 => ? [X5: secrecy_specID] :
% 0.31/0.47 ( ( member @ secrecy_specID @ X5 @ ( subcomponents @ C4 ) )
% 0.31/0.47 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X5 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp1
% 0.31/0.47 thf(fact_174_correctCompositionKS__subcomp2,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.31/0.47 ( ( correctCompositionKS @ C4 )
% 0.31/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.31/0.47 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 0.31/0.47 => ? [X5: secrecy_specID] :
% 0.31/0.47 ( ( member @ secrecy_specID @ X5 @ ( subcomponents @ C4 ) )
% 0.31/0.47 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X5 ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp2
% 0.31/0.47 thf(fact_175_TBtheorem2a,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eout @ PQ @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( eout @ P @ E )
% 0.31/0.47 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem2a
% 0.31/0.47 thf(fact_176_correctCompositionKS__subcomp4,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.31/0.47 ( ( correctCompositionKS @ C4 )
% 0.31/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.31/0.47 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 0.31/0.47 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp4
% 0.31/0.47 thf(fact_177_correctCompositionKS__subcomp3,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.31/0.47 ( ( correctCompositionKS @ C4 )
% 0.31/0.47 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.31/0.47 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.31/0.47 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionKS_subcomp3
% 0.31/0.47 thf(fact_178_TBtheorem5a__notP1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( eout @ P @ E )
% 0.31/0.47 => ( ~ ( eout @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.31/0.47 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_notP1
% 0.31/0.47 thf(fact_179_TBtheorem5a__notP2,axiom,
% 0.31/0.47 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.31/0.47 ( ~ ( eout @ Q @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 0.31/0.47 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_notP2
% 0.31/0.47 thf(fact_180_TBtheorem5a__notPQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 0.31/0.47 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 0.31/0.47 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_notPQ
% 0.31/0.47 thf(fact_181_out__exprChannelSingle__Set,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.31/0.47 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSingle_Set
% 0.31/0.47 thf(fact_182_out__exprChannelSet__Single,axiom,
% 0.31/0.47 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.31/0.47 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSet_Single
% 0.31/0.47 thf(fact_183_TBtheorem5b__notPQ,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.31/0.47 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.31/0.47 => ( ( M2
% 0.31/0.47 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 0.31/0.47 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 0.31/0.47 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_notPQ
% 0.31/0.47 thf(fact_184_eout__know__s,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 = ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 0.31/0.47 = ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 0.31/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_s
% 0.31/0.47 thf(fact_185_not__know__s__not__eout,axiom,
% 0.31/0.47 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 0.31/0.47 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 0.31/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ~ ( eout @ A2 @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_know_s_not_eout
% 0.31/0.47 thf(fact_186_eoutM__eout,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.31/0.47 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 => ( eout @ P @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutM_eout
% 0.31/0.47 thf(fact_187_not__eout__eoutM,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 0.31/0.47 ( ~ ( eout @ P @ E )
% 0.31/0.47 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_eout_eoutM
% 0.31/0.47 thf(fact_188_TBtheorem2b,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eoutM @ PQ @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem2b
% 0.31/0.47 thf(fact_189_TBtheorem5b__notP2,axiom,
% 0.31/0.47 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.31/0.47 ( ~ ( eoutM @ Q @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.31/0.47 => ( ! [X5: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 0.31/0.47 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_notP2
% 0.31/0.47 thf(fact_190_TBtheorem5b__notP1,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 => ( ~ ( eoutM @ Q @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 0.31/0.47 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.31/0.47 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_notP1
% 0.31/0.47 thf(fact_191_eout__know__nonKS__k,axiom,
% 0.31/0.47 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 0.31/0.47 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 0.31/0.47 => ( ( eout @ A2 @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_nonKS_k
% 0.31/0.47 thf(fact_192_eoutKnowCorrect__L1k,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 0.31/0.47 => ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 0.31/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutKnowCorrect_L1k
% 0.31/0.47 thf(fact_193_not__know__k__not__eout,axiom,
% 0.31/0.47 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 0.31/0.47 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 0.31/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 => ~ ( eout @ A2 @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % not_know_k_not_eout
% 0.31/0.47 thf(fact_194_eout__know__k,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 0.31/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 0.31/0.47 = ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 0.31/0.47 = ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 0.31/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_k
% 0.31/0.47 thf(fact_195_eout__know__nonKS__s,axiom,
% 0.31/0.47 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 0.31/0.47 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 0.31/0.47 => ( ( eout @ A2 @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_know_nonKS_s
% 0.31/0.47 thf(fact_196_eoutKnowCorrect__L1s,axiom,
% 0.31/0.47 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 0.31/0.47 => ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 0.31/0.47 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutKnowCorrect_L1s
% 0.31/0.47 thf(fact_197_TBtheore54b__P,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 0.31/0.47 & ( member @ secrecy_chanID @ Ch3 @ M2 ) )
% 0.31/0.47 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheore54b_P
% 0.31/0.47 thf(fact_198_TBtheorem5b__PQ,axiom,
% 0.31/0.47 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( eoutM @ P @ M2 @ E )
% 0.31/0.47 | ( eoutM @ Q @ M2 @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 0.31/0.47 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 0.31/0.47 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5b_PQ
% 0.31/0.47 thf(fact_199_TBtheorem45a__P,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.31/0.47 ( ( eout @ P @ E )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem45a_P
% 0.31/0.47 thf(fact_200_eout__def,axiom,
% 0.31/0.47 ( eout
% 0.31/0.47 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.31/0.47 ? [Ch2: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eout_def
% 0.31/0.47 thf(fact_201_eoutM__def,axiom,
% 0.31/0.47 ( eoutM
% 0.31/0.47 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ? [Ch2: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 0.31/0.47 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eoutM_def
% 0.31/0.47 thf(fact_202_out__exprChannelSet__def,axiom,
% 0.31/0.47 ( out_exprChannelSet
% 0.31/0.47 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ( ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 0.31/0.47 => ( ( member @ secrecy_chanID @ X6 @ ( out @ SP ) )
% 0.31/0.47 & ( exprChannel @ X6 @ E2 ) ) )
% 0.31/0.47 & ! [X6: secrecy_chanID] :
% 0.31/0.47 ( ( ~ ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 0.31/0.47 & ( member @ secrecy_chanID @ X6 @ ( out @ SP ) ) )
% 0.31/0.47 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSet_def
% 0.31/0.47 thf(fact_203_out__exprChannelSingle__def,axiom,
% 0.31/0.47 ( out_ex985543062Single
% 0.31/0.47 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 0.31/0.47 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 0.31/0.47 & ( exprChannel @ Ch2 @ E2 )
% 0.31/0.47 & ! [X6: secrecy_chanID,T: nat] :
% 0.31/0.47 ( ( ( member @ secrecy_chanID @ X6 @ ( out @ SP ) )
% 0.31/0.47 & ( X6 != Ch2 ) )
% 0.31/0.47 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % out_exprChannelSingle_def
% 0.31/0.47 thf(fact_204_correctCompositionOut__prop1,axiom,
% 0.31/0.47 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.31/0.47 ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 0.31/0.47 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 0.31/0.47 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % correctCompositionOut_prop1
% 0.31/0.47 thf(fact_205_TBtheorem5a__PQ,axiom,
% 0.31/0.47 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.31/0.47 ( ( ( eout @ P @ E )
% 0.31/0.47 | ( eout @ Q @ E ) )
% 0.31/0.47 => ( ( ( subcomponents @ PQ )
% 0.31/0.47 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.31/0.47 => ( ( correc990227761ionOut @ PQ )
% 0.31/0.47 => ( ? [Ch3: secrecy_chanID] :
% 0.31/0.47 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 0.31/0.47 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 0.31/0.47 & ( exprChannel @ Ch3 @ E )
% 0.31/0.47 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 0.31/0.47 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % TBtheorem5a_PQ
% 0.31/0.47 thf(fact_206_outStream__def,axiom,
% 0.31/0.47 ( outStream
% 0.31/0.47 = ( ^ [X6: secrecy_specID] :
% 0.31/0.47 ( ^ [Y6: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y6 = Z )
% 0.31/0.47 @ ( out @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % outStream_def
% 0.31/0.47 thf(fact_207_adv__not__know2,axiom,
% 0.31/0.47 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Secrets] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 0.31/0.47 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.31/0.47 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % adv_not_know2
% 0.31/0.47 thf(fact_208_order__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_refl
% 0.31/0.47 thf(fact_209_subset__antisym,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.31/0.47 => ( A2 = B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_antisym
% 0.31/0.47 thf(fact_210_subsetI,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ! [X5: A] :
% 0.31/0.47 ( ( member @ A @ X5 @ A2 )
% 0.31/0.47 => ( member @ A @ X5 @ B2 ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % subsetI
% 0.31/0.47 thf(fact_211_empty__subsetI,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 0.31/0.47
% 0.31/0.47 % empty_subsetI
% 0.31/0.47 thf(fact_212_subset__empty,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 = ( A2
% 0.31/0.47 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_empty
% 0.31/0.47 thf(fact_213_insert__subset,axiom,
% 0.31/0.47 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 0.31/0.47 = ( ( member @ A @ X @ B2 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % insert_subset
% 0.31/0.47 thf(fact_214_Un__subset__iff,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 0.31/0.47 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_subset_iff
% 0.31/0.47 thf(fact_215_singleton__insert__inj__eq,axiom,
% 0.31/0.47 ! [A: $tType,B3: A,A3: A,A2: set @ A] :
% 0.31/0.47 ( ( ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) )
% 0.31/0.47 = ( insert @ A @ A3 @ A2 ) )
% 0.31/0.47 = ( ( A3 = B3 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_insert_inj_eq
% 0.31/0.47 thf(fact_216_singleton__insert__inj__eq_H,axiom,
% 0.31/0.47 ! [A: $tType,A3: A,A2: set @ A,B3: A] :
% 0.31/0.47 ( ( ( insert @ A @ A3 @ A2 )
% 0.31/0.47 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.31/0.47 = ( ( A3 = B3 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % singleton_insert_inj_eq'
% 0.31/0.47 thf(fact_217_Un__mono,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,C4: set @ A,B2: set @ A,D3: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.31/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D3 )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_mono
% 0.31/0.47 thf(fact_218_Un__least,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,C4: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.31/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C4 )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_least
% 0.31/0.47 thf(fact_219_Un__upper1,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_upper1
% 0.31/0.47 thf(fact_220_Un__upper2,axiom,
% 0.31/0.47 ! [A: $tType,B2: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_upper2
% 0.31/0.47 thf(fact_221_Un__absorb1,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 = B2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_absorb1
% 0.31/0.47 thf(fact_222_Un__absorb2,axiom,
% 0.31/0.47 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 0.31/0.47 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 = A2 ) ) ).
% 0.31/0.47
% 0.31/0.47 % Un_absorb2
% 0.31/0.47 thf(fact_223_subset__UnE,axiom,
% 0.31/0.47 ! [A: $tType,C4: set @ A,A2: set @ A,B2: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 0.31/0.47 => ~ ! [A6: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 0.31/0.47 => ! [B6: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B2 )
% 0.31/0.47 => ( C4
% 0.31/0.47 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_UnE
% 0.31/0.47 thf(fact_224_subset__Un__eq,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) )
% 0.31/0.47 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.31/0.47 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.47 = B5 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_Un_eq
% 0.31/0.47 thf(fact_225_dual__order_Oantisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.47 => ( A3 = B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.antisym
% 0.31/0.47 thf(fact_226_dual__order_Oeq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.31/0.47 = ( ^ [A5: A,B7: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B7 @ A5 )
% 0.31/0.47 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.eq_iff
% 0.31/0.47 thf(fact_227_dual__order_Otrans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [B3: A,A3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ C @ B3 )
% 0.31/0.47 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.trans
% 0.31/0.47 thf(fact_228_linorder__wlog,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [P: A > A > $o,A3: A,B3: A] :
% 0.31/0.47 ( ! [A7: A,B8: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A7 @ B8 )
% 0.31/0.47 => ( P @ A7 @ B8 ) )
% 0.31/0.47 => ( ! [A7: A,B8: A] :
% 0.31/0.47 ( ( P @ B8 @ A7 )
% 0.31/0.47 => ( P @ A7 @ B8 ) )
% 0.31/0.47 => ( P @ A3 @ B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linorder_wlog
% 0.31/0.47 thf(fact_229_dual__order_Orefl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.31/0.47
% 0.31/0.47 % dual_order.refl
% 0.31/0.47 thf(fact_230_order__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z2: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.31/0.47 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_trans
% 0.31/0.47 thf(fact_231_order__class_Oorder_Oantisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A3: A,B3: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 0.31/0.47 => ( A3 = B3 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.antisym
% 0.31/0.47 thf(fact_232_ord__le__eq__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A3: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.47 => ( ( B3 = C )
% 0.31/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_trans
% 0.31/0.47 thf(fact_233_ord__eq__le__trans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ord @ A )
% 0.31/0.47 => ! [A3: A,B3: A,C: A] :
% 0.31/0.47 ( ( A3 = B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_trans
% 0.31/0.47 thf(fact_234_order__class_Oorder_Oeq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.31/0.47 = ( ^ [A5: A,B7: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A5 @ B7 )
% 0.31/0.47 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_class.order.eq_iff
% 0.31/0.47 thf(fact_235_antisym__conv,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [Y: A,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 = ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym_conv
% 0.31/0.47 thf(fact_236_le__cases3,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A,Z2: A] :
% 0.31/0.47 ( ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 0.31/0.47 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.31/0.47 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.31/0.47 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases3
% 0.31/0.47 thf(fact_237_order_Otrans,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [A3: A,B3: A,C: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ A @ B3 @ C )
% 0.31/0.47 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order.trans
% 0.31/0.47 thf(fact_238_le__cases,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ~ ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_cases
% 0.31/0.47 thf(fact_239_eq__refl,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( preorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( X = Y )
% 0.31/0.47 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_refl
% 0.31/0.47 thf(fact_240_linear,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( linorder @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % linear
% 0.31/0.47 thf(fact_241_antisym,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ! [X: A,Y: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X @ Y )
% 0.31/0.47 => ( ( ord_less_eq @ A @ Y @ X )
% 0.31/0.47 => ( X = Y ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % antisym
% 0.31/0.47 thf(fact_242_eq__iff,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( order @ A )
% 0.31/0.47 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 0.31/0.47 = ( ^ [X6: A,Y7: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X6 @ Y7 )
% 0.31/0.47 & ( ord_less_eq @ A @ Y7 @ X6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % eq_iff
% 0.31/0.47 thf(fact_243_ord__le__eq__subst,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( ord @ B )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A3: A,B3: A,F: A > B,C: B] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.47 => ( ( ( F @ B3 )
% 0.31/0.47 = C )
% 0.31/0.47 => ( ! [X5: A,Y5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_le_eq_subst
% 0.31/0.47 thf(fact_244_ord__eq__le__subst,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( ord @ B )
% 0.31/0.47 & ( ord @ A ) )
% 0.31/0.47 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( A3
% 0.31/0.47 = ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X5: B,Y5: B] :
% 0.31/0.47 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % ord_eq_le_subst
% 0.31/0.47 thf(fact_245_order__subst2,axiom,
% 0.31/0.47 ! [A: $tType,C3: $tType] :
% 0.31/0.47 ( ( ( order @ C3 )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A3: A,B3: A,F: A > C3,C: C3] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ B3 )
% 0.31/0.47 => ( ( ord_less_eq @ C3 @ ( F @ B3 ) @ C )
% 0.31/0.47 => ( ! [X5: A,Y5: A] :
% 0.31/0.47 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ C3 @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ C3 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst2
% 0.31/0.47 thf(fact_246_order__subst1,axiom,
% 0.31/0.47 ! [A: $tType,B: $tType] :
% 0.31/0.47 ( ( ( order @ B )
% 0.31/0.47 & ( order @ A ) )
% 0.31/0.47 => ! [A3: A,F: B > A,B3: B,C: B] :
% 0.31/0.47 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 0.31/0.47 => ( ( ord_less_eq @ B @ B3 @ C )
% 0.31/0.47 => ( ! [X5: B,Y5: B] :
% 0.31/0.47 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 0.31/0.47 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 0.31/0.47 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % order_subst1
% 0.31/0.47 thf(fact_247_le__fun__def,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ( ( ord_less_eq @ ( A > B ) )
% 0.31/0.47 = ( ^ [F5: A > B,G2: A > B] :
% 0.31/0.47 ! [X6: A] : ( ord_less_eq @ B @ ( F5 @ X6 ) @ ( G2 @ X6 ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_fun_def
% 0.31/0.47 thf(fact_248_le__funI,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ! [F: A > B,G: A > B] :
% 0.31/0.47 ( ! [X5: A] : ( ord_less_eq @ B @ ( F @ X5 ) @ ( G @ X5 ) )
% 0.31/0.47 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funI
% 0.31/0.47 thf(fact_249_le__funE,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funE
% 0.31/0.47 thf(fact_250_le__funD,axiom,
% 0.31/0.47 ! [B: $tType,A: $tType] :
% 0.31/0.47 ( ( ord @ B )
% 0.31/0.47 => ! [F: A > B,G: A > B,X: A] :
% 0.31/0.47 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 0.31/0.47 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % le_funD
% 0.31/0.47 thf(fact_251_Collect__mono__iff,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 0.31/0.47 = ( ! [X6: A] :
% 0.31/0.47 ( ( P @ X6 )
% 0.31/0.47 => ( Q @ X6 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono_iff
% 0.31/0.47 thf(fact_252_set__eq__subset,axiom,
% 0.31/0.47 ! [A: $tType] :
% 0.31/0.47 ( ( ^ [Y6: set @ A,Z: set @ A] : ( Y6 = Z ) )
% 0.31/0.47 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 0.31/0.47 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % set_eq_subset
% 0.31/0.47 thf(fact_253_subset__trans,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 0.31/0.47 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 0.31/0.47 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C4 )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % subset_trans
% 0.31/0.47 thf(fact_254_Collect__mono,axiom,
% 0.31/0.47 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.31/0.47 ( ! [X5: A] :
% 0.31/0.47 ( ( P @ X5 )
% 0.31/0.47 => ( Q @ X5 ) )
% 0.31/0.47 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 0.31/0.47
% 0.31/0.47 % Collect_mono
% 0.31/0.47 thf(fact_255_subset__refl,axiom,
% 0.31/0.47 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 0.31/0.47
% 0.31/0.47 % subset_refl
% 0.31/0.47
% 0.31/0.47 % Type constructors (24)
% 0.31/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.31/0.47 bounded_lattice @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.31/0.47 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.31/0.47 ! [A8: $tType,A9: $tType] :
% 0.31/0.47 ( ( bounded_lattice @ A9 )
% 0.31/0.47 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.31/0.47 ! [A8: $tType,A9: $tType] :
% 0.31/0.47 ( ( bounded_lattice @ A9 )
% 0.31/0.47 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.31/0.47 ! [A8: $tType,A9: $tType] :
% 0.31/0.47 ( ( preorder @ A9 )
% 0.31/0.47 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.31/0.47 ! [A8: $tType,A9: $tType] :
% 0.31/0.47 ( ( order @ A9 )
% 0.31/0.47 => ( order @ ( A8 > A9 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Oord,axiom,
% 0.31/0.47 ! [A8: $tType,A9: $tType] :
% 0.31/0.47 ( ( ord @ A9 )
% 0.31/0.47 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_fun___Orderings_Obot,axiom,
% 0.31/0.47 ! [A8: $tType,A9: $tType] :
% 0.31/0.47 ( ( bot @ A9 )
% 0.31/0.47 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 0.31/0.47 preorder @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.31/0.47 linorder @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 0.31/0.47 order @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 0.31/0.47 ord @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Nat_Onat___Orderings_Obot_6,axiom,
% 0.31/0.47 bot @ nat ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.31/0.47 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 0.31/0.47 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 0.31/0.47 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 0.31/0.47 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 0.31/0.47 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 0.31/0.47 bounde1808546759up_bot @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.31/0.47 preorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 0.31/0.47 linorder @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.31/0.47 order @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.31/0.47 ord @ $o ).
% 0.31/0.47
% 0.31/0.47 thf(tcon_HOL_Obool___Orderings_Obot_17,axiom,
% 0.31/0.47 bot @ $o ).
% 0.31/0.47
% 0.31/0.47 % Conjectures (1)
% 0.31/0.47 thf(conj_0,conjecture,
% 0.31/0.47 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 2.90/1.51 ---- Embedded in THF ---
% 2.90/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.90/1.51 %%% Generated on Tue Feb 24 08:25:58 EST 2026
% 2.90/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.90/1.51 %%% Logic specification used:
% 2.90/1.51 %%% thf(spec, logic, $$dhol).
% 2.90/1.51
% 2.90/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2DTF19196.p
% 2.90/1.51 thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 2.90/1.51 thf(ty_t_Secrecy__types_OSecrets, type, secrecy_Secrets: $tType).
% 2.90/1.51 thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 2.90/1.51 thf(ty_t_Secrecy__types_OchanID, type, secrecy_chanID: $tType).
% 2.90/1.51 thf(ty_t_Secrecy__types_OKeys, type, secrecy_Keys: $tType).
% 2.90/1.51 thf(ty_t_Secrecy__types_OKS, type, secrecy_KS: $tType).
% 2.90/1.51 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 2.90/1.51 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 2.90/1.51 thf(ty_t_Nat_Onat, type, nat: $tType).
% 2.90/1.51 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 2.90/1.51 thf(sy_c_CompLocalSecrets_OLocalSecrets, type, localSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.90/1.51 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect, type, knowle1667810483orrect: (secrecy_specID > (secrecy_KS > $o))).
% 2.90/1.51 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow, type, knowle1437066798e_know: (secrecy_specID > (secrecy_KS > $o))).
% 2.90/1.51 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 2.90/1.51 thf(sy_c_ListExtras_Omem, type, mem: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 2.90/1.51 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 2.90/1.51 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 2.90/1.51 thf(sy_c_Secrecy_OcorrectCompositionKS, type, correctCompositionKS: (secrecy_specID > $o)).
% 2.90/1.51 thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 2.90/1.51 thf(sy_c_Secrecy_OeoutM, type, eoutM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.90/1.51 thf(sy_c_Secrecy_OexprChannel, type, exprChannel: (secrecy_chanID > (secrecy_Expression > $o))).
% 2.90/1.51 thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 2.90/1.51 thf(sy_c_Secrecy_OineM, type, ineM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.90/1.51 thf(sy_c_Secrecy_Oine__exprChannelSet, type, ine_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.90/1.51 thf(sy_c_Secrecy_Oine__exprChannelSingle, type, ine_ex1303305700Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 2.90/1.51 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr, type, notSpe1586871396tsExpr: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 2.90/1.51 thf(sy_c_Secrecy_Oout__exprChannelSet, type, out_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 2.90/1.51 thf(sy_c_Secrecy_Oout__exprChannelSingle, type, out_ex985543062Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 2.90/1.51 thf(sy_c_Secrecy_OspecKeys, type, specKeys: (secrecy_specID > (set @ secrecy_Keys))).
% 2.90/1.51 thf(sy_c_Secrecy_OspecKeysSecrets, type, specKeysSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 2.90/1.51 thf(sy_c_Secrecy_OspecSecrets, type, specSecrets: (secrecy_specID > (set @ secrecy_Secrets))).
% 2.90/1.51 thf(sy_c_Secrecy__types_OExpression_Ocase__Expression, type, secrec487562139ession: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > ((nat > A) > ((secrecy_specID > A) > (secrecy_Expression > A)))))))).
% 2.90/1.51 thf(sy_c_Secrecy__types_OExpression_OdE, type, secrecy_dE: (nat > secrecy_Expression)).
% 2.90/1.51 thf(sy_c_Secrecy__types_OExpression_OidE, type, secrecy_idE: (secrecy_specID > secrecy_Expression)).
% 2.90/1.51 thf(sy_c_Secrecy__types_OExpression_OkE, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 2.90/1.51 thf(sy_c_Secrecy__types_OExpression_Orec__Expression, type, secrec1231112373ession: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > ((nat > A) > ((secrecy_specID > A) > (secrecy_Expression > A)))))))).
% 2.90/1.51 thf(sy_c_Secrecy__types_OExpression_OsE, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 2.90/1.51 thf(sy_c_Secrecy__types_OKS2Expression, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 2.90/1.51 thf(sy_c_Secrecy__types_OKS_OkKS, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 2.90/1.51 thf(sy_c_Secrecy__types_OKS_OsKS, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 2.90/1.51 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 2.90/1.51 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 2.90/1.51 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.90/1.51 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 2.90/1.51 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 2.90/1.51 thf(sy_c_inout_OcorrectCompositionIn, type, correctCompositionIn: (secrecy_specID > $o)).
% 2.90/1.51 thf(sy_c_inout_OcorrectCompositionLoc, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 2.90/1.51 thf(sy_c_inout_OcorrectCompositionOut, type, correc990227761ionOut: (secrecy_specID > $o)).
% 2.90/1.51 thf(sy_c_inout_OinStream, type, inStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 2.90/1.51 thf(sy_c_inout_Oins, type, ins: (secrecy_specID > (set @ secrecy_chanID))).
% 2.90/1.51 thf(sy_c_inout_Oloc, type, loc: (secrecy_specID > (set @ secrecy_chanID))).
% 2.90/1.51 thf(sy_c_inout_OlocStream, type, locStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 2.90/1.51 thf(sy_c_inout_Oout, type, out: (secrecy_specID > (set @ secrecy_chanID))).
% 2.90/1.51 thf(sy_c_inout_OoutStream, type, outStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 2.90/1.51 thf(sy_c_inout_Osubcomponents, type, subcomponents: (secrecy_specID > (set @ secrecy_specID))).
% 2.90/1.51 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 2.90/1.51 thf(sy_v_P, type, p: secrecy_specID).
% 2.90/1.51 thf(sy_v_PQ, type, pq: secrecy_specID).
% 2.90/1.51 thf(sy_v_Q, type, q: secrecy_specID).
% 2.90/1.51 thf(sy_v_key, type, key: secrecy_Keys).
% 2.90/1.51 thf(fact_0_assms_I4_J, axiom, (correctCompositionIn @ pq)).
% 2.90/1.51 thf(fact_1_assms_I2_J, axiom, (~ (((knowle1437066798e_know @ q) @ (secrecy_kKS @ key))))).
% 2.90/1.51 thf(fact_2_assms_I1_J, axiom, (~ (((knowle1437066798e_know @ p) @ (secrecy_kKS @ key))))).
% 2.90/1.51 thf(fact_3_assms_I3_J, axiom, ((subcomponents @ pq) = (((insert @ secrecy_specID) @ p) @ (((insert @ secrecy_specID) @ q) @ (bot_bot @ (set @ secrecy_specID)))))).
% 2.90/1.51 thf(fact_4_Expression_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kE @ X1) = (secrecy_kE @ Y1)) = (X1 = Y1))))).
% 2.90/1.51 thf(fact_5_not__know__k__not__ine, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: (((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (~ (((ine @ A2) @ (secrecy_kE @ M)))))))).
% 2.90/1.51 thf(fact_6_know_Osimps_I1_J, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: ((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)) = (((ine @ A2) @ (secrecy_kE @ M)) | (((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (localSecrets @ A2))))))).
% 2.90/1.51 thf(fact_7_Expression_Osimps_I21_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X1:secrecy_Keys]: ((((((((secrec1231112373ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_kE @ X1)) = (F1 @ X1))))).
% 2.90/1.51 thf(fact_8_Expression_Osimps_I17_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X1:secrecy_Keys]: ((((((((secrec487562139ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_kE @ X1)) = (F1 @ X1))))).
% 2.90/1.51 thf(fact_9_Expression_Odistinct_I5_J, axiom, (! [X1:secrecy_Keys,X4:secrecy_specID]: (((secrecy_kE @ X1) != (secrecy_idE @ X4))))).
% 2.90/1.51 thf(fact_10_Expression_Odistinct_I3_J, axiom, (! [X1:secrecy_Keys,X3:nat]: (((secrecy_kE @ X1) != (secrecy_dE @ X3))))).
% 2.90/1.51 thf(fact_11_KS2Expression_Osimps_I1_J, axiom, (! [M:secrecy_Keys]: (((secrec1016742679ession @ (secrecy_kKS @ M)) = (secrecy_kE @ M))))).
% 2.90/1.51 thf(fact_12_ineM__ine, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ineM @ P) @ M2) @ E) => ((ine @ P) @ E))))).
% 2.90/1.51 thf(fact_13_not__ine__ineM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M2:(set @ secrecy_chanID)]: (((~ (((ine @ P) @ E))) => (~ ((((ineM @ P) @ M2) @ E))))))).
% 2.90/1.51 thf(fact_14_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))))))))))).
% 2.90/1.51 thf(fact_15_Expression_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X2:secrecy_Secrets]: (((secrecy_kE @ X1) != (secrecy_sE @ X2))))).
% 2.90/1.51 thf(fact_16_KS_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kKS @ X1) = (secrecy_kKS @ Y1)) = (X1 = Y1))))).
% 2.90/1.51 thf(fact_17_Expression_Oinject_I2_J, axiom, (! [X2:secrecy_Secrets,Y2:secrecy_Secrets]: ((((secrecy_sE @ X2) = (secrecy_sE @ Y2)) = (X2 = Y2))))).
% 2.90/1.51 thf(fact_18_Expression_Oinject_I4_J, axiom, (! [X4:secrecy_specID,Y4:secrecy_specID]: ((((secrecy_idE @ X4) = (secrecy_idE @ Y4)) = (X4 = Y4))))).
% 2.90/1.51 thf(fact_19_Expression_Oinject_I3_J, axiom, (! [X3:nat,Y3:nat]: ((((secrecy_dE @ X3) = (secrecy_dE @ Y3)) = (X3 = Y3))))).
% 2.90/1.51 thf(fact_20_Expression_Osimps_I24_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X4:secrecy_specID]: ((((((((secrec1231112373ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_idE @ X4)) = (F4 @ X4))))).
% 2.90/1.51 thf(fact_21_Expression_Osimps_I23_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X3:nat]: ((((((((secrec1231112373ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_dE @ X3)) = (F3 @ X3))))).
% 2.90/1.51 thf(fact_22_Expression_Osimps_I22_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X2:secrecy_Secrets]: ((((((((secrec1231112373ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_sE @ X2)) = (F2 @ X2))))).
% 2.90/1.51 thf(fact_23_Expression_Osimps_I20_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X4:secrecy_specID]: ((((((((secrec487562139ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_idE @ X4)) = (F4 @ X4))))).
% 2.90/1.51 thf(fact_24_Expression_Osimps_I19_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X3:nat]: ((((((((secrec487562139ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_dE @ X3)) = (F3 @ X3))))).
% 2.90/1.51 thf(fact_25_Expression_Osimps_I18_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),F3:(nat > A),F4:(secrecy_specID > A),X2:secrecy_Secrets]: ((((((((secrec487562139ession @ A) @ F1) @ F2) @ F3) @ F4) @ (secrecy_sE @ X2)) = (F2 @ X2))))).
% 2.90/1.51 thf(fact_26_Expression_Odistinct_I11_J, axiom, (! [X3:nat,X4:secrecy_specID]: (((secrecy_dE @ X3) != (secrecy_idE @ X4))))).
% 2.90/1.51 thf(fact_27_Expression_Odistinct_I9_J, axiom, (! [X2:secrecy_Secrets,X4:secrecy_specID]: (((secrecy_sE @ X2) != (secrecy_idE @ X4))))).
% 2.90/1.51 thf(fact_28_Expression_Odistinct_I7_J, axiom, (! [X2:secrecy_Secrets,X3:nat]: (((secrecy_sE @ X2) != (secrecy_dE @ X3))))).
% 2.90/1.51 thf(fact_29_ineM__L1, axiom, (! [Ch:secrecy_chanID,M2:(set @ secrecy_chanID),P:secrecy_specID,E:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch) @ M2) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ E) => (((ineM @ P) @ M2) @ E))))))).
% 2.90/1.51 thf(fact_30_ine__def, axiom, (ine = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ SP)) & ((exprChannel @ Ch2) @ E2)))))))).
% 2.90/1.51 thf(fact_31_ineM__def, axiom, (ineM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ SP)) & ((((member @ secrecy_chanID) @ Ch2) @ M3) & ((exprChannel @ Ch2) @ E2))))))))).
% 2.90/1.51 thf(fact_32_TBlemma3b, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((ineM @ P) @ M2) @ E))) => ((~ ((((ineM @ Q) @ M2) @ E))) => (((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) @ E)))))))))))).
% 2.90/1.51 thf(fact_33_TBtheorem1b, axiom, (! [PQ:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((ineM @ PQ) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ineM @ P) @ M2) @ E) | (((ineM @ Q) @ M2) @ E)))))))).
% 2.90/1.51 thf(fact_34_TBtheorem3b, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((ineM @ P) @ M2) @ E))) => ((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ ((((ineM @ PQ) @ M2) @ E)))))))))).
% 2.90/1.51 thf(fact_35_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))))))))).
% 2.90/1.51 thf(fact_36_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))))))))).
% 2.90/1.51 thf(fact_37_Expression_Oinduct, axiom, (! [P:(secrecy_Expression > $o),Expression:secrecy_Expression]: (((! [X5:secrecy_Keys]: ((P @ (secrecy_kE @ X5)))) => ((! [X5:secrecy_Secrets]: ((P @ (secrecy_sE @ X5)))) => ((! [X5:nat]: ((P @ (secrecy_dE @ X5)))) => ((! [X5:secrecy_specID]: ((P @ (secrecy_idE @ X5)))) => (P @ Expression)))))))).
% 2.90/1.51 thf(fact_38_Expression_Oexhaust, axiom, (! [Y:secrecy_Expression]: (((! [X12:secrecy_Keys]: ((Y != (secrecy_kE @ X12)))) => ((! [X22:secrecy_Secrets]: ((Y != (secrecy_sE @ X22)))) => ((! [X32:nat]: ((Y != (secrecy_dE @ X32)))) => (~ ((! [X42:secrecy_specID]: ((Y != (secrecy_idE @ X42)))))))))))).
% 2.90/1.51 thf(fact_39_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))))))))).
% 2.90/1.51 thf(fact_40_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))))))).
% 2.90/1.51 thf(fact_41_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))))))))))).
% 2.90/1.51 thf(fact_42_TBtheorem3a, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((ine @ P) @ E))) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ E)))))))))).
% 2.90/1.51 thf(fact_43_TBtheorem1a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((ine @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((ine @ P) @ E) | ((ine @ Q) @ E)))))))).
% 2.90/1.51 thf(fact_44_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 2.90/1.51 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 2.90/1.51 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X6:A]: ((((member @ A) @ X6) @ A2)))) = A2)))).
% 2.90/1.51 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) = (Q @ X5)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 2.90/1.51 thf(fact_48_ext, axiom, (! [B:$tType,A:$tType,F:(A > B),G:(A > B)]: (((! [X5:A]: (((F @ X5) = (G @ X5)))) => (F = G))))).
% 2.90/1.51 thf(fact_49_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))))))))))))).
% 2.90/1.51 thf(fact_50_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))))))))))).
% 2.90/1.51 thf(fact_51_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))))))))))).
% 2.90/1.51 thf(fact_52_TBtheorem4b__P, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((ineM @ P) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ Q)) & (((exprChannel @ Ch3) @ E) & ((~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch3) @ M2)))))) => (((ineM @ PQ) @ M2) @ E)))))))).
% 2.90/1.51 thf(fact_53_TBtheorem4b__PQ, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((ineM @ P) @ M2) @ E) | (((ineM @ Q) @ M2) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (ins @ Q))) & ((((member @ secrecy_chanID) @ Ch3) @ M2) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))))))) => (((ineM @ PQ) @ M2) @ E)))))))).
% 2.90/1.51 thf(fact_54_TBtheorem4a__P, axiom, (! [P:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((ine @ P) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ P)) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E)))))))).
% 2.90/1.51 thf(fact_55_TBtheorem4a__PQ, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E) | ((ine @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (ins @ Q))) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E)))))))).
% 2.90/1.51 thf(fact_56_insertCI, axiom, (! [A:$tType,A3:A,B2:(set @ A),B3:A]: ((((~ ((((member @ A) @ A3) @ B2))) => (A3 = B3)) => (((member @ A) @ A3) @ (((insert @ A) @ B3) @ B2)))))).
% 2.90/1.51 thf(fact_57_insert__iff, axiom, (! [A:$tType,A3:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B3) @ A2)) = ((A3 = B3) | (((member @ A) @ A3) @ A2)))))).
% 2.90/1.51 thf(fact_58_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X6:A]: ((~ ((P @ X6))))))))).
% 2.90/1.51 thf(fact_59_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X6:A]: ((~ ((P @ X6))))))))).
% 2.90/1.51 thf(fact_60_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X6:A]: ((~ ((((member @ A) @ X6) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.90/1.51 thf(fact_61_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 2.90/1.51 thf(fact_62_insert__absorb2, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A2)) = (((insert @ A) @ X) @ A2))))).
% 2.90/1.51 thf(fact_63_TBtheorem4a__empty, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E) | ((ine @ Q) @ E)) => (((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) @ E)))))))).
% 2.90/1.51 thf(fact_64_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X6:A]: ((((member @ A) @ X6) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 2.90/1.51 thf(fact_65_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y5:A]: ((~ ((((member @ A) @ Y5) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 2.90/1.51 thf(fact_66_equals0D, axiom, (! [A:$tType,A2:(set @ A),A3:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A2))))))).
% 2.90/1.51 thf(fact_67_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 2.90/1.51 thf(fact_68_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => (? [B4:(set @ A)]: (((A2 = (((insert @ A) @ A3) @ B4)) & (~ ((((member @ A) @ A3) @ B4)))))))))).
% 2.90/1.51 thf(fact_69_insert__commute, axiom, (! [A:$tType,X:A,Y:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y) @ A2)) = (((insert @ A) @ Y) @ (((insert @ A) @ X) @ A2)))))).
% 2.90/1.51 thf(fact_70_insert__eq__iff, axiom, (! [A:$tType,A3:A,A2:(set @ A),B3:A,B2:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((~ ((((member @ A) @ B3) @ B2))) => (((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B3) @ B2)) = (((A3 = B3) => (A2 = B2)) & ((A3 != B3) => (? [C2:(set @ A)]: (((A2 = (((insert @ A) @ B3) @ C2)) & ((~ ((((member @ A) @ B3) @ C2))) & ((B2 = (((insert @ A) @ A3) @ C2)) & (~ ((((member @ A) @ A3) @ C2)))))))))))))))).
% 2.90/1.51 thf(fact_71_insert__absorb, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ A2) = A2))))).
% 2.90/1.51 thf(fact_72_insert__ident, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((~ ((((member @ A) @ X) @ B2))) => (((((insert @ A) @ X) @ A2) = (((insert @ A) @ X) @ B2)) = (A2 = B2))))))).
% 2.90/1.51 thf(fact_73_Set_Oset__insert, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((member @ A) @ X) @ A2) => (~ ((! [B4:(set @ A)]: (((A2 = (((insert @ A) @ X) @ B4)) => (((member @ A) @ X) @ B4)))))))))).
% 2.90/1.51 thf(fact_74_insertI2, axiom, (! [A:$tType,A3:A,B2:(set @ A),B3:A]: (((((member @ A) @ A3) @ B2) => (((member @ A) @ A3) @ (((insert @ A) @ B3) @ B2)))))).
% 2.90/1.51 thf(fact_75_insertI1, axiom, (! [A:$tType,A3:A,B2:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B2))))).
% 2.90/1.51 thf(fact_76_insertE, axiom, (! [A:$tType,A3:A,B3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B3) @ A2)) => ((A3 != B3) => (((member @ A) @ A3) @ A2)))))).
% 2.90/1.51 thf(fact_77_correctCompositionIn__L1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((member @ secrecy_chanID) @ Ch) @ (ins @ PQ))))))))).
% 2.90/1.51 thf(fact_78_singleton__inject, axiom, (! [A:$tType,A3:A,B3:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) => (A3 = B3))))).
% 2.90/1.51 thf(fact_79_insert__not__empty, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ A2) != (bot_bot @ (set @ A)))))).
% 2.90/1.51 thf(fact_80_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B3:A,C:A,D:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A3 = C) & (B3 = D)) | ((A3 = D) & (B3 = C))))))).
% 2.90/1.51 thf(fact_81_singleton__iff, axiom, (! [A:$tType,B3:A,A3:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B3 = A3))))).
% 2.90/1.51 thf(fact_82_singletonD, axiom, (! [A:$tType,B3:A,A3:A]: (((((member @ A) @ B3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B3 = A3))))).
% 2.90/1.51 thf(fact_83_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) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ (ins @ PQ)) => (~ (((exprChannel @ X5) @ M)))))) => (((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))))))))).
% 2.90/1.51 thf(fact_84_subcomponents__loc, axiom, (! [X:secrecy_specID]: (((correc965049635ionLoc @ X) => (((subcomponents @ X) = (bot_bot @ (set @ secrecy_specID))) => ((loc @ X) = (bot_bot @ (set @ secrecy_chanID)))))))).
% 2.90/1.51 thf(fact_85_TBtheorem4b__notP1, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ineM @ P) @ M2) @ E) => ((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch3) @ E) & ((((member @ secrecy_chanID) @ Ch3) @ M2) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))) => (~ ((((ineM @ PQ) @ M2) @ E))))))))))).
% 2.90/1.51 thf(fact_86_TBtheorem4a__notP1, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((ine @ P) @ E) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch3:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch3) @ E) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E))))))))))).
% 2.90/1.51 thf(fact_87_TBtheorem4b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E: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) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetP) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetQ) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M2) @ E)))))))))))).
% 2.90/1.51 thf(fact_88_TBtheorem4b__notP2, axiom, (! [Q:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSet) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M2) @ E))))))))))).
% 2.90/1.51 thf(fact_89_TBtheorem4a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E: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) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetP) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetQ) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E)))))))))))).
% 2.90/1.51 thf(fact_90_TBtheorem4a__notP2, axiom, (! [Q:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSet) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E))))))))))).
% 2.90/1.51 thf(fact_91_ine__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E) => (((ine_ex1303305700Single @ P) @ Ch) @ E))))).
% 2.90/1.51 thf(fact_92_ine__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((ine_ex1303305700Single @ P) @ Ch) @ E) => (((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E))))).
% 2.90/1.51 thf(fact_93_ine__nonempty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((ChSet != (bot_bot @ (set @ secrecy_chanID))) => ((ine @ P) @ E)))))).
% 2.90/1.51 thf(fact_94_ine__empty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((ChSet = (bot_bot @ (set @ secrecy_chanID))) => (~ (((ine @ P) @ E)))))))).
% 2.90/1.51 thf(fact_95_ine__exprChannelSet__def, axiom, (ine_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X6:secrecy_chanID]: (((((member @ secrecy_chanID) @ X6) @ ChSet2) => ((((member @ secrecy_chanID) @ X6) @ (ins @ SP)) & ((exprChannel @ X6) @ E2))))) & (! [X6:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X6) @ ChSet2))) & (((member @ secrecy_chanID) @ X6) @ (ins @ SP))) => (~ (((exprChannel @ X6) @ E2))))))))))).
% 2.90/1.51 thf(fact_96_ine__exprChannelSingle__def, axiom, (ine_ex1303305700Single = (^ [SP:secrecy_specID,Ch2:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ SP)) & (((exprChannel @ Ch2) @ E2) & (! [X6:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X6) @ (ins @ SP)) & (X6 != Ch2)) => (~ (((exprChannel @ X6) @ E2)))))))))))).
% 2.90/1.51 thf(fact_97_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))))))))))))).
% 2.90/1.51 thf(fact_98_locStream__def, axiom, (locStream = (^ [X6:secrecy_specID]: (((^ [Y6:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y6 = Z))) @ (loc @ X6)))))).
% 2.90/1.51 thf(fact_99_inStream__def, axiom, (inStream = (^ [X6:secrecy_specID]: (((^ [Y6:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y6 = Z))) @ (ins @ X6)))))).
% 2.90/1.51 thf(fact_100_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 2.90/1.51 thf(fact_101_bot__apply, axiom, (! [C3:$tType,D2:$tType]: (((bot @ C3) => ((bot_bot @ (D2 > C3)) = (^ [X6:D2]: ((bot_bot @ C3)))))))).
% 2.90/1.51 thf(fact_102_LocalSecretsComposition__ine1__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_sE @ S))))))))))).
% 2.90/1.51 thf(fact_103_KS_Oinject_I2_J, axiom, (! [X2:secrecy_Secrets,Y2:secrecy_Secrets]: ((((secrecy_sKS @ X2) = (secrecy_sKS @ Y2)) = (X2 = Y2))))).
% 2.90/1.51 thf(fact_104_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 2.90/1.51 thf(fact_105_KS_Oexhaust, axiom, (! [Y:secrecy_KS]: (((! [X12:secrecy_Keys]: ((Y != (secrecy_kKS @ X12)))) => (~ ((! [X22:secrecy_Secrets]: ((Y != (secrecy_sKS @ X22)))))))))).
% 2.90/1.51 thf(fact_106_KS_Oinduct, axiom, (! [P:(secrecy_KS > $o),KS:secrecy_KS]: (((! [X5:secrecy_Keys]: ((P @ (secrecy_kKS @ X5)))) => ((! [X5:secrecy_Secrets]: ((P @ (secrecy_sKS @ X5)))) => (P @ KS)))))).
% 2.90/1.51 thf(fact_107_KS_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X2:secrecy_Secrets]: (((secrecy_kKS @ X1) != (secrecy_sKS @ X2))))).
% 2.90/1.51 thf(fact_108_KS2Expression_Osimps_I2_J, axiom, (! [M:secrecy_Secrets]: (((secrec1016742679ession @ (secrecy_sKS @ M)) = (secrecy_sE @ M))))).
% 2.90/1.51 thf(fact_109_bot__fun__def, axiom, (! [B:$tType,A:$tType]: (((bot @ B) => ((bot_bot @ (A > B)) = (^ [X6:A]: ((bot_bot @ B)))))))).
% 2.90/1.51 thf(fact_110_not__know__s__not__ine, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: (((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (~ (((ine @ A2) @ (secrecy_sE @ M)))))))).
% 2.90/1.51 thf(fact_111_know_Osimps_I2_J, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: ((((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)) = (((ine @ A2) @ (secrecy_sE @ M)) | (((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (localSecrets @ A2))))))).
% 2.90/1.51 thf(fact_112_LocalSecretsComposition__neg1__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,S:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ))))))))))))).
% 2.90/1.51 thf(fact_113_LocalSecretsComposition__ine2__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_sE @ S))))))))))).
% 2.90/1.51 thf(fact_114_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((A4 = (((insert @ A) @ ((the_elem @ A) @ A4)) @ (bot_bot @ (set @ A)))))))))).
% 2.90/1.51 thf(fact_115_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 2.90/1.51 thf(fact_116_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)))))))))).
% 2.90/1.51 thf(fact_117_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)))))))))).
% 2.90/1.51 thf(fact_118_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))))))))))))))).
% 2.90/1.51 thf(fact_119_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))))))))).
% 2.90/1.51 thf(fact_120_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))))))))))).
% 2.90/1.51 thf(fact_121_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)))))))))).
% 2.90/1.51 thf(fact_122_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)))))))))).
% 2.90/1.51 thf(fact_123_is__singletonI_H, axiom, (! [A:$tType,A2:(set @ A)]: (((A2 != (bot_bot @ (set @ A))) => ((! [X5:A,Y5:A]: (((((member @ A) @ X5) @ A2) => ((((member @ A) @ Y5) @ A2) => (X5 = Y5))))) => ((is_singleton @ A) @ A2)))))).
% 2.90/1.51 thf(fact_124_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)))))))))).
% 2.90/1.51 thf(fact_125_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)))))))))).
% 2.90/1.51 thf(fact_126_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)))))))))).
% 2.90/1.51 thf(fact_127_is__singletonE, axiom, (! [A:$tType,A2:(set @ A)]: ((((is_singleton @ A) @ A2) => (~ ((! [X5:A]: ((A2 != (((insert @ A) @ X5) @ (bot_bot @ (set @ A)))))))))))).
% 2.90/1.51 thf(fact_128_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((? [X6:A]: ((A4 = (((insert @ A) @ X6) @ (bot_bot @ (set @ A)))))))))))).
% 2.90/1.51 thf(fact_129_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))))))))))))).
% 2.90/1.51 thf(fact_130_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))))))))))))).
% 2.90/1.51 thf(fact_131_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))))))))))))))).
% 2.90/1.51 thf(fact_132_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))))))))))))))).
% 2.90/1.51 thf(fact_133_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))))))))))))).
% 2.90/1.51 thf(fact_134_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))))))))))))).
% 2.90/1.51 thf(fact_135_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))))))))))))))).
% 2.90/1.51 thf(fact_136_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))))))))))))))).
% 2.90/1.51 thf(fact_137_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))))))))))))))).
% 2.90/1.51 thf(fact_138_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))))))))))))))).
% 2.90/1.51 thf(fact_139_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X6:A]: ((((member @ A) @ X6) @ (bot_bot @ (set @ A))))))))).
% 2.90/1.51 thf(fact_140_UnCI, axiom, (! [A:$tType,C:A,B2:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C) @ B2))) => (((member @ A) @ C) @ A2)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.90/1.51 thf(fact_141_Un__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = ((((member @ A) @ C) @ A2) | (((member @ A) @ C) @ B2)))))).
% 2.90/1.51 thf(fact_142_Un__empty, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A2) @ B2) = (bot_bot @ (set @ A))) = ((A2 = (bot_bot @ (set @ A))) & (B2 = (bot_bot @ (set @ A)))))))).
% 2.90/1.51 thf(fact_143_Un__insert__right, axiom, (! [A:$tType,A2:(set @ A),A3:A,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B2)) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.90/1.51 thf(fact_144_Un__insert__left, axiom, (! [A:$tType,A3:A,B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A3) @ B2)) @ C4) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ B2) @ C4)))))).
% 2.90/1.51 thf(fact_145_Un__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 2.90/1.51 thf(fact_146_Un__empty__left, axiom, (! [A:$tType,B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B2) = B2)))).
% 2.90/1.51 thf(fact_147_UnE, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => ((~ ((((member @ A) @ C) @ A2))) => (((member @ A) @ C) @ B2)))))).
% 2.90/1.51 thf(fact_148_UnI1, axiom, (! [A:$tType,C:A,A2:(set @ A),B2:(set @ A)]: (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.90/1.51 thf(fact_149_UnI2, axiom, (! [A:$tType,C:A,B2:(set @ A),A2:(set @ A)]: (((((member @ A) @ C) @ B2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B2)))))).
% 2.90/1.51 thf(fact_150_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((? [X6:A]: (((((member @ A) @ X6) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) & (P @ X6)))) = ((? [X6:A]: (((((member @ A) @ X6) @ A2) & (P @ X6)))) | (? [X6:A]: (((((member @ A) @ X6) @ B2) & (P @ X6))))))))).
% 2.90/1.51 thf(fact_151_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),P:(A > $o)]: (((! [X6:A]: (((((member @ A) @ X6) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (P @ X6)))) = ((! [X6:A]: (((((member @ A) @ X6) @ A2) => (P @ X6)))) & (! [X6:A]: (((((member @ A) @ X6) @ B2) => (P @ X6))))))))).
% 2.90/1.51 thf(fact_152_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C4) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)))))).
% 2.90/1.51 thf(fact_153_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 2.90/1.51 thf(fact_154_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A4))))))).
% 2.90/1.51 thf(fact_155_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.90/1.51 thf(fact_156_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B2) @ C4)) = (((sup_sup @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ C4)))))).
% 2.90/1.51 thf(fact_157_singleton__Un__iff, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A2) @ B2)) = (((A2 = (bot_bot @ (set @ A))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.90/1.51 thf(fact_158_Un__singleton__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A2) @ B2) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A2 = (bot_bot @ (set @ A))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 2.90/1.51 thf(fact_159_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A5:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))))))))).
% 2.90/1.51 thf(fact_160_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ (bot_bot @ A)) = A3))))))).
% 2.90/1.51 thf(fact_161_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B3:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A3) @ B3)) = ((A3 = (bot_bot @ A)) & (B3 = (bot_bot @ A)))))))))).
% 2.90/1.51 thf(fact_162_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A3) = A3))))))).
% 2.90/1.51 thf(fact_163_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B3:A]: ((((((sup_sup @ A) @ A3) @ B3) = (bot_bot @ A)) = ((A3 = (bot_bot @ A)) & (B3 = (bot_bot @ A)))))))))).
% 2.90/1.51 thf(fact_164_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 2.90/1.51 thf(fact_165_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 2.90/1.51 thf(fact_166_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.90/1.51 thf(fact_167_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y:A]: ((((((sup_sup @ A) @ X) @ Y) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y = (bot_bot @ A)))))))))).
% 2.90/1.51 thf(fact_168_ineM__Un1, axiom, (! [P:secrecy_specID,A2:(set @ secrecy_chanID),E:secrecy_Expression,B2:(set @ secrecy_chanID)]: (((((ineM @ P) @ A2) @ E) => (((ineM @ P) @ (((sup_sup @ (set @ secrecy_chanID)) @ A2) @ B2)) @ E))))).
% 2.90/1.51 thf(fact_169_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 2.90/1.51 thf(fact_170_notSpecKeysSecretsExpr__def, axiom, (notSpe1586871396tsExpr = (^ [P2:secrecy_specID,E3:(list @ secrecy_Expression)]: (((! [X6:secrecy_Keys]: (((((mem @ secrecy_Expression) @ (secrecy_kE @ X6)) @ E3) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ X6)) @ (specKeysSecrets @ P2))))))) & (! [Y7:secrecy_Secrets]: (((((mem @ secrecy_Expression) @ (secrecy_sE @ Y7)) @ E3) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Y7)) @ (specKeysSecrets @ P2)))))))))))).
% 2.90/1.51 thf(fact_171_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A4:(set @ A)]: ((A4 = (bot_bot @ (set @ A))))))))).
% 2.90/1.51 thf(fact_172_TBtheorem5a__empty, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E) | ((eout @ Q) @ E)) => (((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) @ E)))))))).
% 2.90/1.51 thf(fact_173_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)) => (? [X5:secrecy_specID]: (((((member @ secrecy_specID) @ X5) @ (subcomponents @ C4)) & (((member @ secrecy_Keys) @ Xa) @ (specKeys @ X5))))))))))).
% 2.90/1.51 thf(fact_174_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)) => (? [X5:secrecy_specID]: (((((member @ secrecy_specID) @ X5) @ (subcomponents @ C4)) & (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X5))))))))))).
% 2.90/1.51 thf(fact_175_TBtheorem2a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((eout @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((eout @ P) @ E) | ((eout @ Q) @ E)))))))).
% 2.90/1.51 thf(fact_176_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)))))))).
% 2.90/1.51 thf(fact_177_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)))))))).
% 2.90/1.51 thf(fact_178_TBtheorem5a__notP1, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((eout @ P) @ E) => ((~ (((eout @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch3) @ E) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E))))))))))).
% 2.90/1.51 thf(fact_179_TBtheorem5a__notP2, axiom, (! [Q:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((eout @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSet) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E))))))))))).
% 2.90/1.51 thf(fact_180_TBtheorem5a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E: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) @ E) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetP) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetQ) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E)))))))))))).
% 2.90/1.51 thf(fact_181_out__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((out_ex985543062Single @ P) @ Ch) @ E) => (((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E))))).
% 2.90/1.51 thf(fact_182_out__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E) => (((out_ex985543062Single @ P) @ Ch) @ E))))).
% 2.90/1.51 thf(fact_183_TBtheorem5b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E: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) @ E) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E) => ((M2 = (((sup_sup @ (set @ secrecy_chanID)) @ ChSetP) @ ChSetQ)) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetP) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSetQ) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M2) @ E))))))))))))).
% 2.90/1.51 thf(fact_184_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)))))))).
% 2.90/1.51 thf(fact_185_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)))))))))).
% 2.90/1.51 thf(fact_186_eoutM__eout, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression]: (((((eoutM @ P) @ M2) @ E) => ((eout @ P) @ E))))).
% 2.90/1.51 thf(fact_187_not__eout__eoutM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M2:(set @ secrecy_chanID)]: (((~ (((eout @ P) @ E))) => (~ ((((eoutM @ P) @ M2) @ E))))))).
% 2.90/1.51 thf(fact_188_TBtheorem2b, axiom, (! [PQ:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ PQ) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((eoutM @ P) @ M2) @ E) | (((eoutM @ Q) @ M2) @ E)))))))).
% 2.90/1.51 thf(fact_189_TBtheorem5b__notP2, axiom, (! [Q:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((eoutM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E) => ((! [X5:secrecy_chanID]: (((((member @ secrecy_chanID) @ X5) @ ChSet) => (((member @ secrecy_chanID) @ X5) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M2) @ E))))))))))).
% 2.90/1.51 thf(fact_190_TBtheorem5b__notP1, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eoutM @ P) @ M2) @ E) => ((~ ((((eoutM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch3) @ E) & ((((member @ secrecy_chanID) @ Ch3) @ M2) & (((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))) => (~ ((((eoutM @ PQ) @ M2) @ E))))))))))).
% 2.90/1.51 thf(fact_191_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)))))))).
% 2.90/1.51 thf(fact_192_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)))))))).
% 2.90/1.51 thf(fact_193_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)))))))))).
% 2.90/1.51 thf(fact_194_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)))))))).
% 2.90/1.51 thf(fact_195_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)))))))).
% 2.90/1.51 thf(fact_196_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)))))))).
% 2.90/1.51 thf(fact_197_TBtheore54b__P, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ P) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ Q)) & (((exprChannel @ Ch3) @ E) & ((~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch3) @ M2)))))) => (((eoutM @ PQ) @ M2) @ E)))))))).
% 2.90/1.51 thf(fact_198_TBtheorem5b__PQ, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((eoutM @ P) @ M2) @ E) | (((eoutM @ Q) @ M2) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (out @ Q))) & ((((member @ secrecy_chanID) @ Ch3) @ M2) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ))))))))) => (((eoutM @ PQ) @ M2) @ E)))))))).
% 2.90/1.51 thf(fact_199_TBtheorem45a__P, axiom, (! [P:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((eout @ P) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ P)) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E)))))))).
% 2.90/1.51 thf(fact_200_eout__def, axiom, (eout = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ SP)) & ((exprChannel @ Ch2) @ E2)))))))).
% 2.90/1.51 thf(fact_201_eoutM__def, axiom, (eoutM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ SP)) & ((((member @ secrecy_chanID) @ Ch2) @ M3) & ((exprChannel @ Ch2) @ E2))))))))).
% 2.90/1.51 thf(fact_202_out__exprChannelSet__def, axiom, (out_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X6:secrecy_chanID]: (((((member @ secrecy_chanID) @ X6) @ ChSet2) => ((((member @ secrecy_chanID) @ X6) @ (out @ SP)) & ((exprChannel @ X6) @ E2))))) & (! [X6:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X6) @ ChSet2))) & (((member @ secrecy_chanID) @ X6) @ (out @ SP))) => (~ (((exprChannel @ X6) @ E2))))))))))).
% 2.90/1.51 thf(fact_203_out__exprChannelSingle__def, axiom, (out_ex985543062Single = (^ [SP:secrecy_specID,Ch2:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ SP)) & (((exprChannel @ Ch2) @ E2) & (! [X6:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X6) @ (out @ SP)) & (X6 != Ch2)) => (~ (((exprChannel @ X6) @ E2)))))))))))).
% 2.90/1.51 thf(fact_204_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))))))))).
% 2.90/1.51 thf(fact_205_TBtheorem5a__PQ, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E) | ((eout @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch3:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch3) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch3) @ (out @ Q))) & (((exprChannel @ Ch3) @ E) & (~ ((((member @ secrecy_chanID) @ Ch3) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E)))))))).
% 2.90/1.51 thf(fact_206_outStream__def, axiom, (outStream = (^ [X6:secrecy_specID]: (((^ [Y6:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y6 = Z))) @ (out @ X6)))))).
% 2.90/1.51 thf(fact_207_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))))))))).
% 2.90/1.51 thf(fact_208_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 2.90/1.51 thf(fact_209_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ A2) => (A2 = B2)))))).
% 2.90/1.51 thf(fact_210_subsetI, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((! [X5:A]: (((((member @ A) @ X5) @ A2) => (((member @ A) @ X5) @ B2)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B2))))).
% 2.90/1.51 thf(fact_211_empty__subsetI, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2)))).
% 2.90/1.51 thf(fact_212_subset__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ A))))))).
% 2.90/1.51 thf(fact_213_insert__subset, axiom, (! [A:$tType,X:A,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ B2) = ((((member @ A) @ X) @ B2) & (((ord_less_eq @ (set @ A)) @ A2) @ B2)))))).
% 2.90/1.51 thf(fact_214_Un__subset__iff, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A2) @ C4) & (((ord_less_eq @ (set @ A)) @ B2) @ C4)))))).
% 2.90/1.51 thf(fact_215_singleton__insert__inj__eq, axiom, (! [A:$tType,B3:A,A3:A,A2:(set @ A)]: ((((((insert @ A) @ B3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A2)) = ((A3 = B3) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))))))).
% 2.90/1.51 thf(fact_216_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A2:(set @ A),B3:A]: ((((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B3) @ (bot_bot @ (set @ A)))) = ((A3 = B3) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B3) @ (bot_bot @ (set @ A))))))))).
% 2.90/1.51 thf(fact_217_Un__mono, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B2:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ B2) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ (((sup_sup @ (set @ A)) @ C4) @ D3))))))).
% 2.90/1.51 thf(fact_218_Un__least, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ B2) @ C4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) @ C4)))))).
% 2.90/1.51 thf(fact_219_Un__upper1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.90/1.51 thf(fact_220_Un__upper2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B2) @ (((sup_sup @ (set @ A)) @ A2) @ B2))))).
% 2.90/1.51 thf(fact_221_Un__absorb1, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((sup_sup @ (set @ A)) @ A2) @ B2) = B2))))).
% 2.90/1.51 thf(fact_222_Un__absorb2, axiom, (! [A:$tType,B2:(set @ A),A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B2) @ A2) => ((((sup_sup @ (set @ A)) @ A2) @ B2) = A2))))).
% 2.90/1.51 thf(fact_223_subset__UnE, axiom, (! [A:$tType,C4:(set @ A),A2:(set @ A),B2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((sup_sup @ (set @ A)) @ A2) @ B2)) => (~ ((! [A6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ A2) => (! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ B2) => (C4 != (((sup_sup @ (set @ A)) @ A6) @ B6)))))))))))))).
% 2.90/1.51 thf(fact_224_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ B5) = B5))))))).
% 2.90/1.51 thf(fact_225_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ A3) @ B3) => (A3 = B3))))))))).
% 2.90/1.51 thf(fact_226_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y6:A,Z:A]: ((Y6 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ B7) @ A5) & (((ord_less_eq @ A) @ A5) @ B7))))))))).
% 2.90/1.51 thf(fact_227_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B3:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B3) @ A3) => ((((ord_less_eq @ A) @ C) @ B3) => (((ord_less_eq @ A) @ C) @ A3))))))))).
% 2.90/1.51 thf(fact_228_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B3:A]: (((! [A7:A,B8:A]: (((((ord_less_eq @ A) @ A7) @ B8) => ((P @ A7) @ B8)))) => ((! [A7:A,B8:A]: ((((P @ B8) @ A7) => ((P @ A7) @ B8)))) => ((P @ A3) @ B3))))))))).
% 2.90/1.51 thf(fact_229_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 2.90/1.51 thf(fact_230_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 2.90/1.51 thf(fact_231_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ A3) => (A3 = B3))))))))).
% 2.90/1.51 thf(fact_232_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((B3 = C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.90/1.51 thf(fact_233_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B3:A,C:A]: (((A3 = B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.90/1.51 thf(fact_234_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y6:A,Z:A]: ((Y6 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ A5) @ B7) & (((ord_less_eq @ A) @ B7) @ A5))))))))).
% 2.90/1.51 thf(fact_235_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y:A,X:A]: (((((ord_less_eq @ A) @ Y) @ X) => ((((ord_less_eq @ A) @ X) @ Y) = (X = Y))))))))).
% 2.90/1.51 thf(fact_236_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ Z2)))) => (((((ord_less_eq @ A) @ Y) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y)))) => (((((ord_less_eq @ A) @ Z2) @ Y) => (~ ((((ord_less_eq @ A) @ Y) @ X)))) => (((((ord_less_eq @ A) @ Y) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y))))))))))))))))).
% 2.90/1.51 thf(fact_237_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B3:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ A) @ B3) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 2.90/1.51 thf(fact_238_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y))) => (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.90/1.51 thf(fact_239_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y:A]: (((X = Y) => (((ord_less_eq @ A) @ X) @ Y)))))))).
% 2.90/1.51 thf(fact_240_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) | (((ord_less_eq @ A) @ Y) @ X)))))))).
% 2.90/1.51 thf(fact_241_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y:A]: (((((ord_less_eq @ A) @ X) @ Y) => ((((ord_less_eq @ A) @ Y) @ X) => (X = Y))))))))).
% 2.90/1.51 thf(fact_242_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y6:A,Z:A]: ((Y6 = Z))) = (^ [X6:A,Y7:A]: (((((ord_less_eq @ A) @ X6) @ Y7) & (((ord_less_eq @ A) @ Y7) @ X6))))))))).
% 2.90/1.51 thf(fact_243_ord__le__eq__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,B3:A,F:(A > B),C:B]: (((((ord_less_eq @ A) @ A3) @ B3) => (((F @ B3) = C) => ((! [X5:A,Y5:A]: (((((ord_less_eq @ A) @ X5) @ Y5) => (((ord_less_eq @ B) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ B) @ (F @ A3)) @ C)))))))))).
% 2.90/1.51 thf(fact_244_ord__eq__le__subst, axiom, (! [A:$tType,B:$tType]: ((((ord @ B) & (ord @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((A3 = (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X5:B,Y5:B]: (((((ord_less_eq @ B) @ X5) @ Y5) => (((ord_less_eq @ A) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A3) @ (F @ C))))))))))).
% 2.90/1.51 thf(fact_245_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A3:A,B3:A,F:(A > C3),C:C3]: (((((ord_less_eq @ A) @ A3) @ B3) => ((((ord_less_eq @ C3) @ (F @ B3)) @ C) => ((! [X5:A,Y5:A]: (((((ord_less_eq @ A) @ X5) @ Y5) => (((ord_less_eq @ C3) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ C3) @ (F @ A3)) @ C)))))))))).
% 2.90/1.51 thf(fact_246_order__subst1, axiom, (! [A:$tType,B:$tType]: ((((order @ B) & (order @ A)) => (! [A3:A,F:(B > A),B3:B,C:B]: (((((ord_less_eq @ A) @ A3) @ (F @ B3)) => ((((ord_less_eq @ B) @ B3) @ C) => ((! [X5:B,Y5:B]: (((((ord_less_eq @ B) @ X5) @ Y5) => (((ord_less_eq @ A) @ (F @ X5)) @ (F @ Y5))))) => (((ord_less_eq @ A) @ A3) @ (F @ C))))))))))).
% 2.90/1.51 thf(fact_247_le__fun__def, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => ((ord_less_eq @ (A > B)) = (^ [F5:(A > B),G2:(A > B)]: ((! [X6:A]: ((((ord_less_eq @ B) @ (F5 @ X6)) @ (G2 @ X6))))))))))).
% 2.90/1.51 thf(fact_248_le__funI, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B)]: (((! [X5:A]: ((((ord_less_eq @ B) @ (F @ X5)) @ (G @ X5)))) => (((ord_less_eq @ (A > B)) @ F) @ G)))))))).
% 2.90/1.51 thf(fact_249_le__funE, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.90/1.51 thf(fact_250_le__funD, axiom, (! [B:$tType,A:$tType]: (((ord @ B) => (! [F:(A > B),G:(A > B),X:A]: (((((ord_less_eq @ (A > B)) @ F) @ G) => (((ord_less_eq @ B) @ (F @ X)) @ (G @ X))))))))).
% 2.90/1.51 thf(fact_251_Collect__mono__iff, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)) = (! [X6:A]: (((P @ X6) => (Q @ X6)))))))).
% 2.90/1.51 thf(fact_252_set__eq__subset, axiom, (! [A:$tType]: (((^ [Y6:(set @ A),Z:(set @ A)]: ((Y6 = Z))) = (^ [A4:(set @ A),B5:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A4) @ B5) & (((ord_less_eq @ (set @ A)) @ B5) @ A4)))))))).
% 2.90/1.51 thf(fact_253_subset__trans, axiom, (! [A:$tType,A2:(set @ A),B2:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B2) => ((((ord_less_eq @ (set @ A)) @ B2) @ C4) => (((ord_less_eq @ (set @ A)) @ A2) @ C4)))))).
% 2.90/1.51 thf(fact_254_Collect__mono, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X5:A]: (((P @ X5) => (Q @ X5)))) => (((ord_less_eq @ (set @ A)) @ ((collect @ A) @ P)) @ ((collect @ A) @ Q)))))).
% 2.90/1.51 thf(fact_255_subset__refl, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ A2)))).
% 2.90/1.51 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 2.90/1.51 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 2.90/1.51 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 2.90/1.51 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounde1808546759up_bot @ (A8 > A9)))))).
% 2.90/1.51 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 2.90/1.51 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 2.90/1.51 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 2.90/1.51 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 2.90/1.51 thf(tcon_Nat_Onat___Orderings_Opreorder_3, axiom, (preorder @ nat)).
% 2.90/1.51 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 2.90/1.51 thf(tcon_Nat_Onat___Orderings_Oorder_4, axiom, (order @ nat)).
% 2.90/1.51 thf(tcon_Nat_Onat___Orderings_Oord_5, axiom, (ord @ nat)).
% 2.90/1.51 thf(tcon_Nat_Onat___Orderings_Obot_6, axiom, (bot @ nat)).
% 2.90/1.51 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, axiom, (! [A8:$tType]: ((bounde1808546759up_bot @ (set @ A8))))).
% 2.90/1.51 thf(tcon_Set_Oset___Orderings_Opreorder_8, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 2.90/1.51 thf(tcon_Set_Oset___Orderings_Oorder_9, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 2.90/1.51 thf(tcon_Set_Oset___Orderings_Oord_10, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 2.90/1.51 thf(tcon_Set_Oset___Orderings_Obot_11, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 2.90/1.51 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, axiom, (bounde1808546759up_bot @ $o)).
% 2.90/1.51 thf(tcon_HOL_Obool___Orderings_Opreorder_13, axiom, (preorder @ $o)).
% 2.90/1.51 thf(tcon_HOL_Obool___Orderings_Olinorder_14, axiom, (linorder @ $o)).
% 2.90/1.51 thf(tcon_HOL_Obool___Orderings_Oorder_15, axiom, (order @ $o)).
% 2.90/1.51 thf(tcon_HOL_Obool___Orderings_Oord_16, axiom, (ord @ $o)).
% 2.90/1.51 thf(tcon_HOL_Obool___Orderings_Obot_17, axiom, (bot @ $o)).
% 2.90/1.51 thf(conj_0, conjecture, (~ (((ine @ pq) @ (secrecy_kE @ key))))).
% 2.90/1.51 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2DTF19196.p
% 2.90/1.51 ------------------------
% 2.90/1.57 ---- Cleaned THF ---
% 2.90/1.57 thf(ty_t_Secrecy__types_OExpression,type,
% 2.90/1.57 secrecy_Expression: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Secrecy__types_OSecrets,type,
% 2.90/1.57 secrecy_Secrets: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Secrecy__types_OspecID,type,
% 2.90/1.57 secrecy_specID: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Secrecy__types_OchanID,type,
% 2.90/1.57 secrecy_chanID: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Secrecy__types_OKeys,type,
% 2.90/1.57 secrecy_Keys: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Secrecy__types_OKS,type,
% 2.90/1.57 secrecy_KS: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_List_Olist,type,
% 2.90/1.57 list: $tType > $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Set_Oset,type,
% 2.90/1.57 set: $tType > $tType ).
% 2.90/1.57
% 2.90/1.57 thf(ty_t_Nat_Onat,type,
% 2.90/1.57 nat: $tType ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Lattices_Obounded__lattice,type,
% 2.90/1.57 bounded_lattice:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_HOL_Otype,type,
% 2.90/1.57 type:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Orderings_Obot,type,
% 2.90/1.57 bot:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Orderings_Oord,type,
% 2.90/1.57 ord:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Orderings_Oorder,type,
% 2.90/1.57 order:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Orderings_Olinorder,type,
% 2.90/1.57 linorder:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Orderings_Opreorder,type,
% 2.90/1.57 preorder:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 2.90/1.57 bounde1808546759up_bot:
% 2.90/1.57 !>[A: $tType] : $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 2.90/1.57 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 2.90/1.57 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 2.90/1.57 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Lattices_Osup__class_Osup,type,
% 2.90/1.57 sup_sup:
% 2.90/1.57 !>[A: $tType] : ( A > A > A ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_ListExtras_Omem,type,
% 2.90/1.57 mem:
% 2.90/1.57 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Orderings_Obot__class_Obot,type,
% 2.90/1.57 bot_bot:
% 2.90/1.57 !>[A: $tType] : A ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 2.90/1.57 ord_less_eq:
% 2.90/1.57 !>[A: $tType] : ( A > A > $o ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 2.90/1.57 correctCompositionKS: secrecy_specID > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_Oeout,type,
% 2.90/1.57 eout: secrecy_specID > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OeoutM,type,
% 2.90/1.57 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OexprChannel,type,
% 2.90/1.57 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_Oine,type,
% 2.90/1.57 ine: secrecy_specID > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OineM,type,
% 2.90/1.57 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 2.90/1.57 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 2.90/1.57 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 2.90/1.57 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 2.90/1.57 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 2.90/1.57 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OspecKeys,type,
% 2.90/1.57 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 2.90/1.57 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy_OspecSecrets,type,
% 2.90/1.57 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OExpression_Ocase__Expression,type,
% 2.90/1.57 secrec487562139ession:
% 2.90/1.57 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > ( nat > A ) > ( secrecy_specID > A ) > secrecy_Expression > A ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OExpression_OdE,type,
% 2.90/1.57 secrecy_dE: nat > secrecy_Expression ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OExpression_OidE,type,
% 2.90/1.57 secrecy_idE: secrecy_specID > secrecy_Expression ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 2.90/1.57 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OExpression_Orec__Expression,type,
% 2.90/1.57 secrec1231112373ession:
% 2.90/1.57 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > ( nat > A ) > ( secrecy_specID > A ) > secrecy_Expression > A ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 2.90/1.57 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 2.90/1.57 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 2.90/1.57 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 2.90/1.57 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Set_OCollect,type,
% 2.90/1.57 collect:
% 2.90/1.57 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Set_Oinsert,type,
% 2.90/1.57 insert:
% 2.90/1.57 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Set_Ois__empty,type,
% 2.90/1.57 is_empty:
% 2.90/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Set_Ois__singleton,type,
% 2.90/1.57 is_singleton:
% 2.90/1.57 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_Set_Othe__elem,type,
% 2.90/1.57 the_elem:
% 2.90/1.57 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_OcorrectCompositionIn,type,
% 2.90/1.57 correctCompositionIn: secrecy_specID > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 2.90/1.57 correc965049635ionLoc: secrecy_specID > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_OcorrectCompositionOut,type,
% 2.90/1.57 correc990227761ionOut: secrecy_specID > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_OinStream,type,
% 2.90/1.57 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_Oins,type,
% 2.90/1.57 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_Oloc,type,
% 2.90/1.57 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_OlocStream,type,
% 2.90/1.57 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_Oout,type,
% 2.90/1.57 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_OoutStream,type,
% 2.90/1.57 outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_inout_Osubcomponents,type,
% 2.90/1.57 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_c_member,type,
% 2.90/1.57 member:
% 2.90/1.57 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 2.90/1.57
% 2.90/1.57 thf(sy_v_P,type,
% 2.90/1.57 p: secrecy_specID ).
% 2.90/1.57
% 2.90/1.57 thf(sy_v_PQ,type,
% 2.90/1.57 pq: secrecy_specID ).
% 2.90/1.57
% 2.90/1.57 thf(sy_v_Q,type,
% 2.90/1.57 q: secrecy_specID ).
% 2.90/1.57
% 2.90/1.57 thf(sy_v_key,type,
% 2.90/1.57 key: secrecy_Keys ).
% 2.90/1.57
% 2.90/1.57 thf(fact_0_assms_I4_J,axiom,
% 2.90/1.57 correctCompositionIn @ pq ).
% 2.90/1.57
% 2.90/1.57 thf(fact_1_assms_I2_J,axiom,
% 2.90/1.57 ~ ( knowle1437066798e_know @ q @ ( secrecy_kKS @ key ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_2_assms_I1_J,axiom,
% 2.90/1.57 ~ ( knowle1437066798e_know @ p @ ( secrecy_kKS @ key ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_3_assms_I3_J,axiom,
% 2.90/1.57 ( ( subcomponents @ pq )
% 2.90/1.57 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_4_Expression_Oinject_I1_J,axiom,
% 2.90/1.57 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.90/1.57 ( ( ( secrecy_kE @ X1 )
% 2.90/1.57 = ( secrecy_kE @ Y1 ) )
% 2.90/1.57 = ( X1 = Y1 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_5_not__know__k__not__ine,axiom,
% 2.90/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.90/1.57 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 => ~ ( ine @ A2 @ ( secrecy_kE @ M ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_6_know_Osimps_I1_J,axiom,
% 2.90/1.57 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 2.90/1.57 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 2.90/1.57 | ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_7_Expression_Osimps_I21_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X1: secrecy_Keys] :
% 2.90/1.57 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_kE @ X1 ) )
% 2.90/1.57 = ( F1 @ X1 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_8_Expression_Osimps_I17_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X1: secrecy_Keys] :
% 2.90/1.57 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_kE @ X1 ) )
% 2.90/1.57 = ( F1 @ X1 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_9_Expression_Odistinct_I5_J,axiom,
% 2.90/1.57 ! [X1: secrecy_Keys,X4: secrecy_specID] :
% 2.90/1.57 ( ( secrecy_kE @ X1 )
% 2.90/1.57 != ( secrecy_idE @ X4 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_10_Expression_Odistinct_I3_J,axiom,
% 2.90/1.57 ! [X1: secrecy_Keys,X3: nat] :
% 2.90/1.57 ( ( secrecy_kE @ X1 )
% 2.90/1.57 != ( secrecy_dE @ X3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_11_KS2Expression_Osimps_I1_J,axiom,
% 2.90/1.57 ! [M: secrecy_Keys] :
% 2.90/1.57 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 2.90/1.57 = ( secrecy_kE @ M ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_12_ineM__ine,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( ineM @ P @ M2 @ E )
% 2.90/1.57 => ( ine @ P @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_13_not__ine__ineM,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 2.90/1.57 ( ~ ( ine @ P @ E )
% 2.90/1.57 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_14_LocalSecretsComposition__exprChannel__k,axiom,
% 2.90/1.57 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_15_Expression_Odistinct_I1_J,axiom,
% 2.90/1.57 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.90/1.57 ( ( secrecy_kE @ X1 )
% 2.90/1.57 != ( secrecy_sE @ X2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_16_KS_Oinject_I1_J,axiom,
% 2.90/1.57 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 2.90/1.57 ( ( ( secrecy_kKS @ X1 )
% 2.90/1.57 = ( secrecy_kKS @ Y1 ) )
% 2.90/1.57 = ( X1 = Y1 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_17_Expression_Oinject_I2_J,axiom,
% 2.90/1.57 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.90/1.57 ( ( ( secrecy_sE @ X2 )
% 2.90/1.57 = ( secrecy_sE @ Y2 ) )
% 2.90/1.57 = ( X2 = Y2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_18_Expression_Oinject_I4_J,axiom,
% 2.90/1.57 ! [X4: secrecy_specID,Y4: secrecy_specID] :
% 2.90/1.57 ( ( ( secrecy_idE @ X4 )
% 2.90/1.57 = ( secrecy_idE @ Y4 ) )
% 2.90/1.57 = ( X4 = Y4 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_19_Expression_Oinject_I3_J,axiom,
% 2.90/1.57 ! [X3: nat,Y3: nat] :
% 2.90/1.57 ( ( ( secrecy_dE @ X3 )
% 2.90/1.57 = ( secrecy_dE @ Y3 ) )
% 2.90/1.57 = ( X3 = Y3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_20_Expression_Osimps_I24_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X4: secrecy_specID] :
% 2.90/1.57 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_idE @ X4 ) )
% 2.90/1.57 = ( F4 @ X4 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_21_Expression_Osimps_I23_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X3: nat] :
% 2.90/1.57 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_dE @ X3 ) )
% 2.90/1.57 = ( F3 @ X3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_22_Expression_Osimps_I22_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X2: secrecy_Secrets] :
% 2.90/1.57 ( ( secrec1231112373ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_sE @ X2 ) )
% 2.90/1.57 = ( F2 @ X2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_23_Expression_Osimps_I20_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X4: secrecy_specID] :
% 2.90/1.57 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_idE @ X4 ) )
% 2.90/1.57 = ( F4 @ X4 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_24_Expression_Osimps_I19_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X3: nat] :
% 2.90/1.57 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_dE @ X3 ) )
% 2.90/1.57 = ( F3 @ X3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_25_Expression_Osimps_I18_J,axiom,
% 2.90/1.57 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,F3: nat > A,F4: secrecy_specID > A,X2: secrecy_Secrets] :
% 2.90/1.57 ( ( secrec487562139ession @ A @ F1 @ F2 @ F3 @ F4 @ ( secrecy_sE @ X2 ) )
% 2.90/1.57 = ( F2 @ X2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_26_Expression_Odistinct_I11_J,axiom,
% 2.90/1.57 ! [X3: nat,X4: secrecy_specID] :
% 2.90/1.57 ( ( secrecy_dE @ X3 )
% 2.90/1.57 != ( secrecy_idE @ X4 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_27_Expression_Odistinct_I9_J,axiom,
% 2.90/1.57 ! [X2: secrecy_Secrets,X4: secrecy_specID] :
% 2.90/1.57 ( ( secrecy_sE @ X2 )
% 2.90/1.57 != ( secrecy_idE @ X4 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_28_Expression_Odistinct_I7_J,axiom,
% 2.90/1.57 ! [X2: secrecy_Secrets,X3: nat] :
% 2.90/1.57 ( ( secrecy_sE @ X2 )
% 2.90/1.57 != ( secrecy_dE @ X3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_29_ineM__L1,axiom,
% 2.90/1.57 ! [Ch: secrecy_chanID,M2: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch @ M2 )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ E )
% 2.90/1.57 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_30_ine__def,axiom,
% 2.90/1.57 ( ine
% 2.90/1.57 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.90/1.57 ? [Ch2: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 2.90/1.57 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_31_ineM__def,axiom,
% 2.90/1.57 ( ineM
% 2.90/1.57 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 2.90/1.57 ? [Ch2: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 2.90/1.57 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_32_TBlemma3b,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 2.90/1.57 ( ~ ( ineM @ P @ M2 @ E )
% 2.90/1.57 => ( ~ ( ineM @ Q @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ M2 )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 2.90/1.57 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_33_TBtheorem1b,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( ineM @ PQ @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ineM @ P @ M2 @ E )
% 2.90/1.57 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_34_TBtheorem3b,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ~ ( ineM @ P @ M2 @ E )
% 2.90/1.57 => ( ~ ( ineM @ Q @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_35_ine__ins__neg1,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 2.90/1.57 ( ~ ( ine @ P @ M )
% 2.90/1.57 => ( ( exprChannel @ X @ M )
% 2.90/1.57 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_36_correctCompositionIn__L2,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_37_Expression_Oinduct,axiom,
% 2.90/1.57 ! [P: secrecy_Expression > $o,Expression: secrecy_Expression] :
% 2.90/1.57 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kE @ X5 ) )
% 2.90/1.57 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sE @ X5 ) )
% 2.90/1.57 => ( ! [X5: nat] : ( P @ ( secrecy_dE @ X5 ) )
% 2.90/1.57 => ( ! [X5: secrecy_specID] : ( P @ ( secrecy_idE @ X5 ) )
% 2.90/1.57 => ( P @ Expression ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_38_Expression_Oexhaust,axiom,
% 2.90/1.57 ! [Y: secrecy_Expression] :
% 2.90/1.57 ( ! [X12: secrecy_Keys] :
% 2.90/1.57 ( Y
% 2.90/1.57 != ( secrecy_kE @ X12 ) )
% 2.90/1.57 => ( ! [X22: secrecy_Secrets] :
% 2.90/1.57 ( Y
% 2.90/1.57 != ( secrecy_sE @ X22 ) )
% 2.90/1.57 => ( ! [X32: nat] :
% 2.90/1.57 ( Y
% 2.90/1.57 != ( secrecy_dE @ X32 ) )
% 2.90/1.57 => ~ ! [X42: secrecy_specID] :
% 2.90/1.57 ( Y
% 2.90/1.57 != ( secrecy_idE @ X42 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_39_correctCompositionIn__prop1,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_40_LocalSecretsComposition1,axiom,
% 2.90/1.57 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_41_LocalSecretsComposition__exprChannel__s,axiom,
% 2.90/1.57 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_42_TBtheorem3a,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ~ ( ine @ P @ E )
% 2.90/1.57 => ( ~ ( ine @ Q @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_43_TBtheorem1a,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( ine @ PQ @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ine @ P @ E )
% 2.90/1.57 | ( ine @ Q @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_44_singletonI,axiom,
% 2.90/1.57 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_45_mem__Collect__eq,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,P: A > $o] :
% 2.90/1.57 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 2.90/1.57 = ( P @ A3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_46_Collect__mem__eq,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( collect @ A
% 2.90/1.57 @ ^ [X6: A] : ( member @ A @ X6 @ A2 ) )
% 2.90/1.57 = A2 ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_47_Collect__cong,axiom,
% 2.90/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.90/1.57 ( ! [X5: A] :
% 2.90/1.57 ( ( P @ X5 )
% 2.90/1.57 = ( Q @ X5 ) )
% 2.90/1.57 => ( ( collect @ A @ P )
% 2.90/1.57 = ( collect @ A @ Q ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_48_ext,axiom,
% 2.90/1.57 ! [B: $tType,A: $tType,F: A > B,G: A > B] :
% 2.90/1.57 ( ! [X5: A] :
% 2.90/1.57 ( ( F @ X5 )
% 2.90/1.57 = ( G @ X5 ) )
% 2.90/1.57 => ( F = G ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_49_LocalSecretsComposition__neg1__k,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_50_LocalSecretsComposition__ine2__k,axiom,
% 2.90/1.57 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.90/1.57 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_51_LocalSecretsComposition__ine1__k,axiom,
% 2.90/1.57 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 2.90/1.57 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_52_TBtheorem4b__P,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( ineM @ P @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ M2 ) )
% 2.90/1.57 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_53_TBtheorem4b__PQ,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ( ineM @ P @ M2 @ E )
% 2.90/1.57 | ( ineM @ Q @ M2 @ E ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_54_TBtheorem4a__P,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( ine @ P @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_55_TBtheorem4a__PQ,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ( ine @ P @ E )
% 2.90/1.57 | ( ine @ Q @ E ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ Ch3 @ ( ins @ Q ) ) )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_56_insertCI,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 2.90/1.57 ( ( ~ ( member @ A @ A3 @ B2 )
% 2.90/1.57 => ( A3 = B3 ) )
% 2.90/1.57 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_57_insert__iff,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 2.90/1.57 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 2.90/1.57 = ( ( A3 = B3 )
% 2.90/1.57 | ( member @ A @ A3 @ A2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_58_empty__Collect__eq,axiom,
% 2.90/1.57 ! [A: $tType,P: A > $o] :
% 2.90/1.57 ( ( ( bot_bot @ ( set @ A ) )
% 2.90/1.57 = ( collect @ A @ P ) )
% 2.90/1.57 = ( ! [X6: A] :
% 2.90/1.57 ~ ( P @ X6 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_59_Collect__empty__eq,axiom,
% 2.90/1.57 ! [A: $tType,P: A > $o] :
% 2.90/1.57 ( ( ( collect @ A @ P )
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( ! [X6: A] :
% 2.90/1.57 ~ ( P @ X6 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_60_all__not__in__conv,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( ! [X6: A] :
% 2.90/1.57 ~ ( member @ A @ X6 @ A2 ) )
% 2.90/1.57 = ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_61_empty__iff,axiom,
% 2.90/1.57 ! [A: $tType,C: A] :
% 2.90/1.57 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_62_insert__absorb2,axiom,
% 2.90/1.57 ! [A: $tType,X: A,A2: set @ A] :
% 2.90/1.57 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 2.90/1.57 = ( insert @ A @ X @ A2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_63_TBtheorem4a__empty,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ( ine @ P @ E )
% 2.90/1.57 | ( ine @ Q @ E ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ( loc @ PQ )
% 2.90/1.57 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 2.90/1.57 => ( ine @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_64_ex__in__conv,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( ? [X6: A] : ( member @ A @ X6 @ A2 ) )
% 2.90/1.57 = ( A2
% 2.90/1.57 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_65_equals0I,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ! [Y5: A] :
% 2.90/1.57 ~ ( member @ A @ Y5 @ A2 )
% 2.90/1.57 => ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_66_equals0D,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,A3: A] :
% 2.90/1.57 ( ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_67_emptyE,axiom,
% 2.90/1.57 ! [A: $tType,A3: A] :
% 2.90/1.57 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_68_mk__disjoint__insert,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.90/1.57 ( ( member @ A @ A3 @ A2 )
% 2.90/1.57 => ? [B4: set @ A] :
% 2.90/1.57 ( ( A2
% 2.90/1.57 = ( insert @ A @ A3 @ B4 ) )
% 2.90/1.57 & ~ ( member @ A @ A3 @ B4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_69_insert__commute,axiom,
% 2.90/1.57 ! [A: $tType,X: A,Y: A,A2: set @ A] :
% 2.90/1.57 ( ( insert @ A @ X @ ( insert @ A @ Y @ A2 ) )
% 2.90/1.57 = ( insert @ A @ Y @ ( insert @ A @ X @ A2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_70_insert__eq__iff,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,A2: set @ A,B3: A,B2: set @ A] :
% 2.90/1.57 ( ~ ( member @ A @ A3 @ A2 )
% 2.90/1.57 => ( ~ ( member @ A @ B3 @ B2 )
% 2.90/1.57 => ( ( ( insert @ A @ A3 @ A2 )
% 2.90/1.57 = ( insert @ A @ B3 @ B2 ) )
% 2.90/1.57 = ( ( ( A3 = B3 )
% 2.90/1.57 => ( A2 = B2 ) )
% 2.90/1.57 & ( ( A3 != B3 )
% 2.90/1.57 => ? [C2: set @ A] :
% 2.90/1.57 ( ( A2
% 2.90/1.57 = ( insert @ A @ B3 @ C2 ) )
% 2.90/1.57 & ~ ( member @ A @ B3 @ C2 )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( insert @ A @ A3 @ C2 ) )
% 2.90/1.57 & ~ ( member @ A @ A3 @ C2 ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_71_insert__absorb,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.90/1.57 ( ( member @ A @ A3 @ A2 )
% 2.90/1.57 => ( ( insert @ A @ A3 @ A2 )
% 2.90/1.57 = A2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_72_insert__ident,axiom,
% 2.90/1.57 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ~ ( member @ A @ X @ A2 )
% 2.90/1.57 => ( ~ ( member @ A @ X @ B2 )
% 2.90/1.57 => ( ( ( insert @ A @ X @ A2 )
% 2.90/1.57 = ( insert @ A @ X @ B2 ) )
% 2.90/1.57 = ( A2 = B2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_73_Set_Oset__insert,axiom,
% 2.90/1.57 ! [A: $tType,X: A,A2: set @ A] :
% 2.90/1.57 ( ( member @ A @ X @ A2 )
% 2.90/1.57 => ~ ! [B4: set @ A] :
% 2.90/1.57 ( ( A2
% 2.90/1.57 = ( insert @ A @ X @ B4 ) )
% 2.90/1.57 => ( member @ A @ X @ B4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_74_insertI2,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B2: set @ A,B3: A] :
% 2.90/1.57 ( ( member @ A @ A3 @ B2 )
% 2.90/1.57 => ( member @ A @ A3 @ ( insert @ A @ B3 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_75_insertI1,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B2: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_76_insertE,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B3: A,A2: set @ A] :
% 2.90/1.57 ( ( member @ A @ A3 @ ( insert @ A @ B3 @ A2 ) )
% 2.90/1.57 => ( ( A3 != B3 )
% 2.90/1.57 => ( member @ A @ A3 @ A2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_77_correctCompositionIn__L1,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_78_singleton__inject,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B3: A] :
% 2.90/1.57 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 => ( A3 = B3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_79_insert__not__empty,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,A2: set @ A] :
% 2.90/1.57 ( ( insert @ A @ A3 @ A2 )
% 2.90/1.57 != ( bot_bot @ ( set @ A ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_80_doubleton__eq__iff,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B3: A,C: A,D: A] :
% 2.90/1.57 ( ( ( insert @ A @ A3 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.90/1.57 = ( ( ( A3 = C )
% 2.90/1.57 & ( B3 = D ) )
% 2.90/1.57 | ( ( A3 = D )
% 2.90/1.57 & ( B3 = C ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_81_singleton__iff,axiom,
% 2.90/1.57 ! [A: $tType,B3: A,A3: A] :
% 2.90/1.57 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 = ( B3 = A3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_82_singletonD,axiom,
% 2.90/1.57 ! [A: $tType,B3: A,A3: A] :
% 2.90/1.57 ( ( member @ A @ B3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 => ( B3 = A3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_83_correctCompositionInLoc__exprChannel,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ M )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ( ins @ PQ ) )
% 2.90/1.57 => ~ ( exprChannel @ X5 @ M ) )
% 2.90/1.57 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_84_subcomponents__loc,axiom,
% 2.90/1.57 ! [X: secrecy_specID] :
% 2.90/1.57 ( ( correc965049635ionLoc @ X )
% 2.90/1.57 => ( ( ( subcomponents @ X )
% 2.90/1.57 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 2.90/1.57 => ( ( loc @ X )
% 2.90/1.57 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_85_TBtheorem4b__notP1,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ineM @ P @ M2 @ E )
% 2.90/1.57 => ( ~ ( ineM @ Q @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_86_TBtheorem4a__notP1,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ine @ P @ E )
% 2.90/1.57 => ( ~ ( ine @ Q @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( ine_ex1303305700Single @ P @ Ch3 @ E )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_87_TBtheorem4b__notPQ,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.90/1.57 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_88_TBtheorem4b__notP2,axiom,
% 2.90/1.57 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 2.90/1.57 ( ~ ( ineM @ Q @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_89_TBtheorem4a__notPQ,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 2.90/1.57 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_90_TBtheorem4a__notP2,axiom,
% 2.90/1.57 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 2.90/1.57 ( ~ ( ine @ Q @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_91_ine__exprChannelSet__Single,axiom,
% 2.90/1.57 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 2.90/1.57 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_92_ine__exprChannelSingle__Set,axiom,
% 2.90/1.57 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 2.90/1.57 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_93_ine__nonempty__exprChannelSet,axiom,
% 2.90/1.57 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.90/1.57 => ( ( ChSet
% 2.90/1.57 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 2.90/1.57 => ( ine @ P @ E ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_94_ine__empty__exprChannelSet,axiom,
% 2.90/1.57 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 2.90/1.57 => ( ( ChSet
% 2.90/1.57 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 2.90/1.57 => ~ ( ine @ P @ E ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_95_ine__exprChannelSet__def,axiom,
% 2.90/1.57 ( ine_exprChannelSet
% 2.90/1.57 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 2.90/1.57 ( ! [X6: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ X6 @ ( ins @ SP ) )
% 2.90/1.57 & ( exprChannel @ X6 @ E2 ) ) )
% 2.90/1.57 & ! [X6: secrecy_chanID] :
% 2.90/1.57 ( ( ~ ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 2.90/1.57 & ( member @ secrecy_chanID @ X6 @ ( ins @ SP ) ) )
% 2.90/1.57 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_96_ine__exprChannelSingle__def,axiom,
% 2.90/1.57 ( ine_ex1303305700Single
% 2.90/1.57 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ SP ) )
% 2.90/1.57 & ( exprChannel @ Ch2 @ E2 )
% 2.90/1.57 & ! [X6: secrecy_chanID,T: nat] :
% 2.90/1.57 ( ( ( member @ secrecy_chanID @ X6 @ ( ins @ SP ) )
% 2.90/1.57 & ( X6 != Ch2 ) )
% 2.90/1.57 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_97_LocalSecretsComposition__neg1,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ! [M4: secrecy_Keys] :
% 2.90/1.57 ( ( Ks
% 2.90/1.57 = ( secrecy_kKS @ M4 ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 2.90/1.57 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 2.90/1.57 => ( ! [M4: secrecy_Secrets] :
% 2.90/1.57 ( ( Ks
% 2.90/1.57 = ( secrecy_sKS @ M4 ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 2.90/1.57 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_98_locStream__def,axiom,
% 2.90/1.57 ( locStream
% 2.90/1.57 = ( ^ [X6: secrecy_specID] :
% 2.90/1.57 ( ^ [Y6: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y6 = Z )
% 2.90/1.57 @ ( loc @ X6 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_99_inStream__def,axiom,
% 2.90/1.57 ( inStream
% 2.90/1.57 = ( ^ [X6: secrecy_specID] :
% 2.90/1.57 ( ^ [Y6: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y6 = Z )
% 2.90/1.57 @ ( ins @ X6 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_100_the__elem__eq,axiom,
% 2.90/1.57 ! [A: $tType,X: A] :
% 2.90/1.57 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 = X ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_101_bot__apply,axiom,
% 2.90/1.57 ! [C3: $tType,D2: $tType] :
% 2.90/1.57 ( ( bot @ C3 )
% 2.90/1.57 => ( ( bot_bot @ ( D2 > C3 ) )
% 2.90/1.57 = ( ^ [X6: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_102_LocalSecretsComposition__ine1__s,axiom,
% 2.90/1.57 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.90/1.57 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_103_KS_Oinject_I2_J,axiom,
% 2.90/1.57 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 2.90/1.57 ( ( ( secrecy_sKS @ X2 )
% 2.90/1.57 = ( secrecy_sKS @ Y2 ) )
% 2.90/1.57 = ( X2 = Y2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_104_bot__set__def,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bot_bot @ ( set @ A ) )
% 2.90/1.57 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_105_KS_Oexhaust,axiom,
% 2.90/1.57 ! [Y: secrecy_KS] :
% 2.90/1.57 ( ! [X12: secrecy_Keys] :
% 2.90/1.57 ( Y
% 2.90/1.57 != ( secrecy_kKS @ X12 ) )
% 2.90/1.57 => ~ ! [X22: secrecy_Secrets] :
% 2.90/1.57 ( Y
% 2.90/1.57 != ( secrecy_sKS @ X22 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_106_KS_Oinduct,axiom,
% 2.90/1.57 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 2.90/1.57 ( ! [X5: secrecy_Keys] : ( P @ ( secrecy_kKS @ X5 ) )
% 2.90/1.57 => ( ! [X5: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X5 ) )
% 2.90/1.57 => ( P @ KS ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_107_KS_Odistinct_I1_J,axiom,
% 2.90/1.57 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 2.90/1.57 ( ( secrecy_kKS @ X1 )
% 2.90/1.57 != ( secrecy_sKS @ X2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_108_KS2Expression_Osimps_I2_J,axiom,
% 2.90/1.57 ! [M: secrecy_Secrets] :
% 2.90/1.57 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 2.90/1.57 = ( secrecy_sE @ M ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_109_bot__fun__def,axiom,
% 2.90/1.57 ! [B: $tType,A: $tType] :
% 2.90/1.57 ( ( bot @ B )
% 2.90/1.57 => ( ( bot_bot @ ( A > B ) )
% 2.90/1.57 = ( ^ [X6: A] : ( bot_bot @ B ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_110_not__know__s__not__ine,axiom,
% 2.90/1.57 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 2.90/1.57 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 => ~ ( ine @ A2 @ ( secrecy_sE @ M ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_111_know_Osimps_I2_J,axiom,
% 2.90/1.57 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 2.90/1.57 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 2.90/1.57 | ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_112_LocalSecretsComposition__neg1__s,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_113_LocalSecretsComposition__ine2__s,axiom,
% 2.90/1.57 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 2.90/1.57 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_114_is__singleton__the__elem,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( is_singleton @ A )
% 2.90/1.57 = ( ^ [A4: set @ A] :
% 2.90/1.57 ( A4
% 2.90/1.57 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_115_is__singletonI,axiom,
% 2.90/1.57 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_116_LocalSecretsComposition__neg__loc__s,axiom,
% 2.90/1.57 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.90/1.57 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_117_LocalSecretsComposition__neg__loc__k,axiom,
% 2.90/1.57 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 2.90/1.57 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_118_correctCompositionKS__exprChannel__s__Qex,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ? [Ch4: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_119_correctCompositionKS__PQ,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.90/1.57 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_120_correctCompositionKS__neg1,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_121_correctCompositionKS__negP,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_122_correctCompositionKS__negQ,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_123_is__singletonI_H,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( A2
% 2.90/1.57 != ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 => ( ! [X5: A,Y5: A] :
% 2.90/1.57 ( ( member @ A @ X5 @ A2 )
% 2.90/1.57 => ( ( member @ A @ Y5 @ A2 )
% 2.90/1.57 => ( X5 = Y5 ) ) )
% 2.90/1.57 => ( is_singleton @ A @ A2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_124_know__composition,axiom,
% 2.90/1.57 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ( ( ( knowle1437066798e_know @ P @ M )
% 2.90/1.57 | ( knowle1437066798e_know @ Q @ M ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_125_know__composition1,axiom,
% 2.90/1.57 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ( ( knowle1437066798e_know @ P @ M )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_126_know__composition2,axiom,
% 2.90/1.57 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ( ( knowle1437066798e_know @ Q @ M )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_127_is__singletonE,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( is_singleton @ A @ A2 )
% 2.90/1.57 => ~ ! [X5: A] :
% 2.90/1.57 ( A2
% 2.90/1.57 != ( insert @ A @ X5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_128_is__singleton__def,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( is_singleton @ A )
% 2.90/1.57 = ( ^ [A4: set @ A] :
% 2.90/1.57 ? [X6: A] :
% 2.90/1.57 ( A4
% 2.90/1.57 = ( insert @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_129_correctCompositionKS__exprChannel__k__P,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_130_correctCompositionKS__exprChannel__k__Q,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_131_correctCompositionKS__exprChannel__k__Pex,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ? [Ch4: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_132_correctCompositionKS__exprChannel__k__Qex,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ? [Ch4: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_133_correctCompositionKS__exprChannel__s__P,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_134_correctCompositionKS__exprChannel__s__Q,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_135_correctCompositionKS__exprChannel__s__Pex,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 2.90/1.57 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 2.90/1.57 => ( ( correctCompositionIn @ PQ )
% 2.90/1.57 => ? [Ch4: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 2.90/1.57 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_136_LocalSecretsComposition__neg,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ( ! [M4: secrecy_Keys] :
% 2.90/1.57 ( ( Ks
% 2.90/1.57 = ( secrecy_kKS @ M4 ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 2.90/1.57 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 2.90/1.57 => ( ! [M4: secrecy_Secrets] :
% 2.90/1.57 ( ( Ks
% 2.90/1.57 = ( secrecy_sKS @ M4 ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 2.90/1.57 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_137_LocalSecretsComposition__neg__s,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_138_LocalSecretsComposition__neg__k,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc965049635ionLoc @ PQ )
% 2.90/1.57 => ( ( correctCompositionKS @ PQ )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 2.90/1.57 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 2.90/1.57 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 2.90/1.57 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_139_bot__empty__eq,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bot_bot @ ( A > $o ) )
% 2.90/1.57 = ( ^ [X6: A] : ( member @ A @ X6 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_140_UnCI,axiom,
% 2.90/1.57 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 2.90/1.57 ( ( ~ ( member @ A @ C @ B2 )
% 2.90/1.57 => ( member @ A @ C @ A2 ) )
% 2.90/1.57 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_141_Un__iff,axiom,
% 2.90/1.57 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 = ( ( member @ A @ C @ A2 )
% 2.90/1.57 | ( member @ A @ C @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_142_Un__empty,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_143_Un__insert__right,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,A3: A,B2: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B2 ) )
% 2.90/1.57 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_144_Un__insert__left,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,B2: set @ A,C4: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B2 ) @ C4 )
% 2.90/1.57 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_145_Un__empty__right,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = A2 ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_146_Un__empty__left,axiom,
% 2.90/1.57 ! [A: $tType,B2: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B2 )
% 2.90/1.57 = B2 ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_147_UnE,axiom,
% 2.90/1.57 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 => ( ~ ( member @ A @ C @ A2 )
% 2.90/1.57 => ( member @ A @ C @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_148_UnI1,axiom,
% 2.90/1.57 ! [A: $tType,C: A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( member @ A @ C @ A2 )
% 2.90/1.57 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_149_UnI2,axiom,
% 2.90/1.57 ! [A: $tType,C: A,B2: set @ A,A2: set @ A] :
% 2.90/1.57 ( ( member @ A @ C @ B2 )
% 2.90/1.57 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_150_bex__Un,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.90/1.57 ( ( ? [X6: A] :
% 2.90/1.57 ( ( member @ A @ X6 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 & ( P @ X6 ) ) )
% 2.90/1.57 = ( ? [X6: A] :
% 2.90/1.57 ( ( member @ A @ X6 @ A2 )
% 2.90/1.57 & ( P @ X6 ) )
% 2.90/1.57 | ? [X6: A] :
% 2.90/1.57 ( ( member @ A @ X6 @ B2 )
% 2.90/1.57 & ( P @ X6 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_151_ball__Un,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,P: A > $o] :
% 2.90/1.57 ( ( ! [X6: A] :
% 2.90/1.57 ( ( member @ A @ X6 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 => ( P @ X6 ) ) )
% 2.90/1.57 = ( ! [X6: A] :
% 2.90/1.57 ( ( member @ A @ X6 @ A2 )
% 2.90/1.57 => ( P @ X6 ) )
% 2.90/1.57 & ! [X6: A] :
% 2.90/1.57 ( ( member @ A @ X6 @ B2 )
% 2.90/1.57 => ( P @ X6 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_152_Un__assoc,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.90/1.57 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_153_Un__absorb,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 2.90/1.57 = A2 ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_154_Un__commute,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) )
% 2.90/1.57 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_155_Un__left__absorb,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_156_Un__left__commute,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B2 @ C4 ) )
% 2.90/1.57 = ( sup_sup @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_157_singleton__Un__iff,axiom,
% 2.90/1.57 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 = ( ( ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.90/1.57 | ( ( A2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 | ( ( A2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_158_Un__singleton__iff,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,X: A] :
% 2.90/1.57 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 = ( ( ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 2.90/1.57 | ( ( A2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 | ( ( A2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 & ( B2
% 2.90/1.57 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_159_insert__is__Un,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( insert @ A )
% 2.90/1.57 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_160_sup__bot_Oright__neutral,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [A3: A] :
% 2.90/1.57 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 2.90/1.57 = A3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_161_sup__bot_Oneutr__eq__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [A3: A,B3: A] :
% 2.90/1.57 ( ( ( bot_bot @ A )
% 2.90/1.57 = ( sup_sup @ A @ A3 @ B3 ) )
% 2.90/1.57 = ( ( A3
% 2.90/1.57 = ( bot_bot @ A ) )
% 2.90/1.57 & ( B3
% 2.90/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_162_sup__bot_Oleft__neutral,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [A3: A] :
% 2.90/1.57 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 2.90/1.57 = A3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_163_sup__bot_Oeq__neutr__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [A3: A,B3: A] :
% 2.90/1.57 ( ( ( sup_sup @ A @ A3 @ B3 )
% 2.90/1.57 = ( bot_bot @ A ) )
% 2.90/1.57 = ( ( A3
% 2.90/1.57 = ( bot_bot @ A ) )
% 2.90/1.57 & ( B3
% 2.90/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_164_sup__bot__left,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [X: A] :
% 2.90/1.57 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 2.90/1.57 = X ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_165_sup__bot__right,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [X: A] :
% 2.90/1.57 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 2.90/1.57 = X ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_166_bot__eq__sup__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [X: A,Y: A] :
% 2.90/1.57 ( ( ( bot_bot @ A )
% 2.90/1.57 = ( sup_sup @ A @ X @ Y ) )
% 2.90/1.57 = ( ( X
% 2.90/1.57 = ( bot_bot @ A ) )
% 2.90/1.57 & ( Y
% 2.90/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_167_sup__eq__bot__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( bounde1808546759up_bot @ A )
% 2.90/1.57 => ! [X: A,Y: A] :
% 2.90/1.57 ( ( ( sup_sup @ A @ X @ Y )
% 2.90/1.57 = ( bot_bot @ A ) )
% 2.90/1.57 = ( ( X
% 2.90/1.57 = ( bot_bot @ A ) )
% 2.90/1.57 & ( Y
% 2.90/1.57 = ( bot_bot @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_168_ineM__Un1,axiom,
% 2.90/1.57 ! [P: secrecy_specID,A2: set @ secrecy_chanID,E: secrecy_Expression,B2: set @ secrecy_chanID] :
% 2.90/1.57 ( ( ineM @ P @ A2 @ E )
% 2.90/1.57 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A2 @ B2 ) @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_169_Collect__empty__eq__bot,axiom,
% 2.90/1.57 ! [A: $tType,P: A > $o] :
% 2.90/1.57 ( ( ( collect @ A @ P )
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( P
% 2.90/1.57 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_170_notSpecKeysSecretsExpr__def,axiom,
% 2.90/1.57 ( notSpe1586871396tsExpr
% 2.90/1.57 = ( ^ [P2: secrecy_specID,E3: list @ secrecy_Expression] :
% 2.90/1.57 ( ! [X6: secrecy_Keys] :
% 2.90/1.57 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X6 ) @ E3 )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X6 ) @ ( specKeysSecrets @ P2 ) ) )
% 2.90/1.57 & ! [Y7: secrecy_Secrets] :
% 2.90/1.57 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y7 ) @ E3 )
% 2.90/1.57 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y7 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_171_Set_Ois__empty__def,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( is_empty @ A )
% 2.90/1.57 = ( ^ [A4: set @ A] :
% 2.90/1.57 ( A4
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_172_TBtheorem5a__empty,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ( eout @ P @ E )
% 2.90/1.57 | ( eout @ Q @ E ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( ( loc @ PQ )
% 2.90/1.57 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 2.90/1.57 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_173_correctCompositionKS__subcomp1,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 2.90/1.57 ( ( correctCompositionKS @ C4 )
% 2.90/1.57 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 2.90/1.57 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 2.90/1.57 => ? [X5: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_specID @ X5 @ ( subcomponents @ C4 ) )
% 2.90/1.57 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X5 ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_174_correctCompositionKS__subcomp2,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 2.90/1.57 ( ( correctCompositionKS @ C4 )
% 2.90/1.57 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 2.90/1.57 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 2.90/1.57 => ? [X5: secrecy_specID] :
% 2.90/1.57 ( ( member @ secrecy_specID @ X5 @ ( subcomponents @ C4 ) )
% 2.90/1.57 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X5 ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_175_TBtheorem2a,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( eout @ PQ @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( eout @ P @ E )
% 2.90/1.57 | ( eout @ Q @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_176_correctCompositionKS__subcomp4,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 2.90/1.57 ( ( correctCompositionKS @ C4 )
% 2.90/1.57 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 2.90/1.57 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 2.90/1.57 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_177_correctCompositionKS__subcomp3,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 2.90/1.57 ( ( correctCompositionKS @ C4 )
% 2.90/1.57 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 2.90/1.57 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 2.90/1.57 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_178_TBtheorem5a__notP1,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( eout @ P @ E )
% 2.90/1.57 => ( ~ ( eout @ Q @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_179_TBtheorem5a__notP2,axiom,
% 2.90/1.57 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 2.90/1.57 ( ~ ( eout @ Q @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_180_TBtheorem5a__notPQ,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.90/1.57 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_181_out__exprChannelSingle__Set,axiom,
% 2.90/1.57 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( out_ex985543062Single @ P @ Ch @ E )
% 2.90/1.57 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_182_out__exprChannelSet__Single,axiom,
% 2.90/1.57 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 2.90/1.57 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_183_TBtheorem5b__notPQ,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 2.90/1.57 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 2.90/1.57 => ( ( M2
% 2.90/1.57 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetP )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSetQ )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_184_eout__know__s,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 2.90/1.57 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 = ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 2.90/1.57 = ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 2.90/1.57 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_185_not__know__s__not__eout,axiom,
% 2.90/1.57 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 2.90/1.57 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 => ~ ( eout @ A2 @ ( secrecy_sE @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_186_eoutM__eout,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 2.90/1.57 ( ( eoutM @ P @ M2 @ E )
% 2.90/1.57 => ( eout @ P @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_187_not__eout__eoutM,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 2.90/1.57 ( ~ ( eout @ P @ E )
% 2.90/1.57 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_188_TBtheorem2b,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( eoutM @ PQ @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( eoutM @ P @ M2 @ E )
% 2.90/1.57 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_189_TBtheorem5b__notP2,axiom,
% 2.90/1.57 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 2.90/1.57 ( ~ ( eoutM @ Q @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 2.90/1.57 => ( ! [X5: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X5 @ ChSet )
% 2.90/1.57 => ( member @ secrecy_chanID @ X5 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_190_TBtheorem5b__notP1,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( eoutM @ P @ M2 @ E )
% 2.90/1.57 => ( ~ ( eoutM @ Q @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( out_ex985543062Single @ P @ Ch3 @ E )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_191_eout__know__nonKS__k,axiom,
% 2.90/1.57 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 2.90/1.57 => ( ( eout @ A2 @ ( secrecy_kE @ M ) )
% 2.90/1.57 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_192_eoutKnowCorrect__L1k,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 2.90/1.57 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 => ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 2.90/1.57 => ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 2.90/1.57 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_193_not__know__k__not__eout,axiom,
% 2.90/1.57 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 2.90/1.57 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 => ~ ( eout @ A2 @ ( secrecy_kE @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_194_eout__know__k,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 2.90/1.57 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 2.90/1.57 = ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 2.90/1.57 = ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 2.90/1.57 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_195_eout__know__nonKS__s,axiom,
% 2.90/1.57 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 2.90/1.57 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 2.90/1.57 => ( ( eout @ A2 @ ( secrecy_sE @ M ) )
% 2.90/1.57 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 => ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_196_eoutKnowCorrect__L1s,axiom,
% 2.90/1.57 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 2.90/1.57 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 => ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 2.90/1.57 => ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 2.90/1.57 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_197_TBtheore54b__P,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( eoutM @ P @ M2 @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ M2 ) )
% 2.90/1.57 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_198_TBtheorem5b__PQ,axiom,
% 2.90/1.57 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ( eoutM @ P @ M2 @ E )
% 2.90/1.57 | ( eoutM @ Q @ M2 @ E ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch3 @ M2 )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_199_TBtheorem45a__P,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 2.90/1.57 ( ( eout @ P @ E )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_200_eout__def,axiom,
% 2.90/1.57 ( eout
% 2.90/1.57 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 2.90/1.57 ? [Ch2: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 2.90/1.57 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_201_eoutM__def,axiom,
% 2.90/1.57 ( eoutM
% 2.90/1.57 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 2.90/1.57 ? [Ch2: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 2.90/1.57 & ( member @ secrecy_chanID @ Ch2 @ M3 )
% 2.90/1.57 & ( exprChannel @ Ch2 @ E2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_202_out__exprChannelSet__def,axiom,
% 2.90/1.57 ( out_exprChannelSet
% 2.90/1.57 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 2.90/1.57 ( ! [X6: secrecy_chanID] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ X6 @ ( out @ SP ) )
% 2.90/1.57 & ( exprChannel @ X6 @ E2 ) ) )
% 2.90/1.57 & ! [X6: secrecy_chanID] :
% 2.90/1.57 ( ( ~ ( member @ secrecy_chanID @ X6 @ ChSet2 )
% 2.90/1.57 & ( member @ secrecy_chanID @ X6 @ ( out @ SP ) ) )
% 2.90/1.57 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_203_out__exprChannelSingle__def,axiom,
% 2.90/1.57 ( out_ex985543062Single
% 2.90/1.57 = ( ^ [SP: secrecy_specID,Ch2: secrecy_chanID,E2: secrecy_Expression] :
% 2.90/1.57 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ SP ) )
% 2.90/1.57 & ( exprChannel @ Ch2 @ E2 )
% 2.90/1.57 & ! [X6: secrecy_chanID,T: nat] :
% 2.90/1.57 ( ( ( member @ secrecy_chanID @ X6 @ ( out @ SP ) )
% 2.90/1.57 & ( X6 != Ch2 ) )
% 2.90/1.57 => ~ ( exprChannel @ X6 @ E2 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_204_correctCompositionOut__prop1,axiom,
% 2.90/1.57 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 2.90/1.57 ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 2.90/1.57 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_205_TBtheorem5a__PQ,axiom,
% 2.90/1.57 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 2.90/1.57 ( ( ( eout @ P @ E )
% 2.90/1.57 | ( eout @ Q @ E ) )
% 2.90/1.57 => ( ( ( subcomponents @ PQ )
% 2.90/1.57 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 2.90/1.57 => ( ( correc990227761ionOut @ PQ )
% 2.90/1.57 => ( ? [Ch3: secrecy_chanID] :
% 2.90/1.57 ( ( ( member @ secrecy_chanID @ Ch3 @ ( out @ P ) )
% 2.90/1.57 | ( member @ secrecy_chanID @ Ch3 @ ( out @ Q ) ) )
% 2.90/1.57 & ( exprChannel @ Ch3 @ E )
% 2.90/1.57 & ~ ( member @ secrecy_chanID @ Ch3 @ ( loc @ PQ ) ) )
% 2.90/1.57 => ( eout @ PQ @ E ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_206_outStream__def,axiom,
% 2.90/1.57 ( outStream
% 2.90/1.57 = ( ^ [X6: secrecy_specID] :
% 2.90/1.57 ( ^ [Y6: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y6 = Z )
% 2.90/1.57 @ ( out @ X6 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_207_adv__not__know2,axiom,
% 2.90/1.57 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Secrets] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 2.90/1.57 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 2.90/1.57 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_208_order__refl,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( preorder @ A )
% 2.90/1.57 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_209_subset__antisym,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 2.90/1.57 => ( A2 = B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_210_subsetI,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ! [X5: A] :
% 2.90/1.57 ( ( member @ A @ X5 @ A2 )
% 2.90/1.57 => ( member @ A @ X5 @ B2 ) )
% 2.90/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_211_empty__subsetI,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_212_subset__empty,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( A2
% 2.90/1.57 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_213_insert__subset,axiom,
% 2.90/1.57 ! [A: $tType,X: A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B2 )
% 2.90/1.57 = ( ( member @ A @ X @ B2 )
% 2.90/1.57 & ( ord_less_eq @ ( set @ A ) @ A2 @ B2 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_214_Un__subset__iff,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 )
% 2.90/1.57 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 2.90/1.57 & ( ord_less_eq @ ( set @ A ) @ B2 @ C4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_215_singleton__insert__inj__eq,axiom,
% 2.90/1.57 ! [A: $tType,B3: A,A3: A,A2: set @ A] :
% 2.90/1.57 ( ( ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) )
% 2.90/1.57 = ( insert @ A @ A3 @ A2 ) )
% 2.90/1.57 = ( ( A3 = B3 )
% 2.90/1.57 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_216_singleton__insert__inj__eq_H,axiom,
% 2.90/1.57 ! [A: $tType,A3: A,A2: set @ A,B3: A] :
% 2.90/1.57 ( ( ( insert @ A @ A3 @ A2 )
% 2.90/1.57 = ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) )
% 2.90/1.57 = ( ( A3 = B3 )
% 2.90/1.57 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_217_Un__mono,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,C4: set @ A,B2: set @ A,D3: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 2.90/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ D3 )
% 2.90/1.57 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_218_Un__least,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,C4: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 2.90/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C4 )
% 2.90/1.57 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) @ C4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_219_Un__upper1,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_220_Un__upper2,axiom,
% 2.90/1.57 ! [A: $tType,B2: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B2 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_221_Un__absorb1,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 = B2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_222_Un__absorb2,axiom,
% 2.90/1.57 ! [A: $tType,B2: set @ A,A2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ B2 @ A2 )
% 2.90/1.57 => ( ( sup_sup @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 = A2 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_223_subset__UnE,axiom,
% 2.90/1.57 ! [A: $tType,C4: set @ A,A2: set @ A,B2: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A2 @ B2 ) )
% 2.90/1.57 => ~ ! [A6: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 2.90/1.57 => ! [B6: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B2 )
% 2.90/1.57 => ( C4
% 2.90/1.57 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_224_subset__Un__eq,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) )
% 2.90/1.57 = ( ^ [A4: set @ A,B5: set @ A] :
% 2.90/1.57 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 2.90/1.57 = B5 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_225_dual__order_Oantisym,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [B3: A,A3: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.90/1.57 => ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.90/1.57 => ( A3 = B3 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_226_dual__order_Oeq__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 2.90/1.57 = ( ^ [A5: A,B7: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ B7 @ A5 )
% 2.90/1.57 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_227_dual__order_Otrans,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [B3: A,A3: A,C: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.90/1.57 => ( ( ord_less_eq @ A @ C @ B3 )
% 2.90/1.57 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_228_linorder__wlog,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( linorder @ A )
% 2.90/1.57 => ! [P: A > A > $o,A3: A,B3: A] :
% 2.90/1.57 ( ! [A7: A,B8: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A7 @ B8 )
% 2.90/1.57 => ( P @ A7 @ B8 ) )
% 2.90/1.57 => ( ! [A7: A,B8: A] :
% 2.90/1.57 ( ( P @ B8 @ A7 )
% 2.90/1.57 => ( P @ A7 @ B8 ) )
% 2.90/1.57 => ( P @ A3 @ B3 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_229_dual__order_Orefl,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_230_order__trans,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( preorder @ A )
% 2.90/1.57 => ! [X: A,Y: A,Z2: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ X @ Y )
% 2.90/1.57 => ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.90/1.57 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_231_order__class_Oorder_Oantisym,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [A3: A,B3: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.90/1.57 => ( ( ord_less_eq @ A @ B3 @ A3 )
% 2.90/1.57 => ( A3 = B3 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_232_ord__le__eq__trans,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( ord @ A )
% 2.90/1.57 => ! [A3: A,B3: A,C: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.90/1.57 => ( ( B3 = C )
% 2.90/1.57 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_233_ord__eq__le__trans,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( ord @ A )
% 2.90/1.57 => ! [A3: A,B3: A,C: A] :
% 2.90/1.57 ( ( A3 = B3 )
% 2.90/1.57 => ( ( ord_less_eq @ A @ B3 @ C )
% 2.90/1.57 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_234_order__class_Oorder_Oeq__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 2.90/1.57 = ( ^ [A5: A,B7: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A5 @ B7 )
% 2.90/1.57 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_235_antisym__conv,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [Y: A,X: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ Y @ X )
% 2.90/1.57 => ( ( ord_less_eq @ A @ X @ Y )
% 2.90/1.57 = ( X = Y ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_236_le__cases3,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( linorder @ A )
% 2.90/1.57 => ! [X: A,Y: A,Z2: A] :
% 2.90/1.57 ( ( ( ord_less_eq @ A @ X @ Y )
% 2.90/1.57 => ~ ( ord_less_eq @ A @ Y @ Z2 ) )
% 2.90/1.57 => ( ( ( ord_less_eq @ A @ Y @ X )
% 2.90/1.57 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 2.90/1.57 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 2.90/1.57 => ~ ( ord_less_eq @ A @ Z2 @ Y ) )
% 2.90/1.57 => ( ( ( ord_less_eq @ A @ Z2 @ Y )
% 2.90/1.57 => ~ ( ord_less_eq @ A @ Y @ X ) )
% 2.90/1.57 => ( ( ( ord_less_eq @ A @ Y @ Z2 )
% 2.90/1.57 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 2.90/1.57 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 2.90/1.57 => ~ ( ord_less_eq @ A @ X @ Y ) ) ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_237_order_Otrans,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [A3: A,B3: A,C: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.90/1.57 => ( ( ord_less_eq @ A @ B3 @ C )
% 2.90/1.57 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_238_le__cases,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( linorder @ A )
% 2.90/1.57 => ! [X: A,Y: A] :
% 2.90/1.57 ( ~ ( ord_less_eq @ A @ X @ Y )
% 2.90/1.57 => ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_239_eq__refl,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( preorder @ A )
% 2.90/1.57 => ! [X: A,Y: A] :
% 2.90/1.57 ( ( X = Y )
% 2.90/1.57 => ( ord_less_eq @ A @ X @ Y ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_240_linear,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( linorder @ A )
% 2.90/1.57 => ! [X: A,Y: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ X @ Y )
% 2.90/1.57 | ( ord_less_eq @ A @ Y @ X ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_241_antisym,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ! [X: A,Y: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ X @ Y )
% 2.90/1.57 => ( ( ord_less_eq @ A @ Y @ X )
% 2.90/1.57 => ( X = Y ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_242_eq__iff,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( order @ A )
% 2.90/1.57 => ( ( ^ [Y6: A,Z: A] : ( Y6 = Z ) )
% 2.90/1.57 = ( ^ [X6: A,Y7: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ X6 @ Y7 )
% 2.90/1.57 & ( ord_less_eq @ A @ Y7 @ X6 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_243_ord__le__eq__subst,axiom,
% 2.90/1.57 ! [A: $tType,B: $tType] :
% 2.90/1.57 ( ( ( ord @ B )
% 2.90/1.57 & ( ord @ A ) )
% 2.90/1.57 => ! [A3: A,B3: A,F: A > B,C: B] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.90/1.57 => ( ( ( F @ B3 )
% 2.90/1.57 = C )
% 2.90/1.57 => ( ! [X5: A,Y5: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 2.90/1.57 => ( ord_less_eq @ B @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 2.90/1.57 => ( ord_less_eq @ B @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_244_ord__eq__le__subst,axiom,
% 2.90/1.57 ! [A: $tType,B: $tType] :
% 2.90/1.57 ( ( ( ord @ B )
% 2.90/1.57 & ( ord @ A ) )
% 2.90/1.57 => ! [A3: A,F: B > A,B3: B,C: B] :
% 2.90/1.57 ( ( A3
% 2.90/1.57 = ( F @ B3 ) )
% 2.90/1.57 => ( ( ord_less_eq @ B @ B3 @ C )
% 2.90/1.57 => ( ! [X5: B,Y5: B] :
% 2.90/1.57 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 2.90/1.57 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 2.90/1.57 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_245_order__subst2,axiom,
% 2.90/1.57 ! [A: $tType,C3: $tType] :
% 2.90/1.57 ( ( ( order @ C3 )
% 2.90/1.57 & ( order @ A ) )
% 2.90/1.57 => ! [A3: A,B3: A,F: A > C3,C: C3] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A3 @ B3 )
% 2.90/1.57 => ( ( ord_less_eq @ C3 @ ( F @ B3 ) @ C )
% 2.90/1.57 => ( ! [X5: A,Y5: A] :
% 2.90/1.57 ( ( ord_less_eq @ A @ X5 @ Y5 )
% 2.90/1.57 => ( ord_less_eq @ C3 @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 2.90/1.57 => ( ord_less_eq @ C3 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_246_order__subst1,axiom,
% 2.90/1.57 ! [A: $tType,B: $tType] :
% 2.90/1.57 ( ( ( order @ B )
% 2.90/1.57 & ( order @ A ) )
% 2.90/1.57 => ! [A3: A,F: B > A,B3: B,C: B] :
% 2.90/1.57 ( ( ord_less_eq @ A @ A3 @ ( F @ B3 ) )
% 2.90/1.57 => ( ( ord_less_eq @ B @ B3 @ C )
% 2.90/1.57 => ( ! [X5: B,Y5: B] :
% 2.90/1.57 ( ( ord_less_eq @ B @ X5 @ Y5 )
% 2.90/1.57 => ( ord_less_eq @ A @ ( F @ X5 ) @ ( F @ Y5 ) ) )
% 2.90/1.57 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_247_le__fun__def,axiom,
% 2.90/1.57 ! [B: $tType,A: $tType] :
% 2.90/1.57 ( ( ord @ B )
% 2.90/1.57 => ( ( ord_less_eq @ ( A > B ) )
% 2.90/1.57 = ( ^ [F5: A > B,G2: A > B] :
% 2.90/1.57 ! [X6: A] : ( ord_less_eq @ B @ ( F5 @ X6 ) @ ( G2 @ X6 ) ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_248_le__funI,axiom,
% 2.90/1.57 ! [B: $tType,A: $tType] :
% 2.90/1.57 ( ( ord @ B )
% 2.90/1.57 => ! [F: A > B,G: A > B] :
% 2.90/1.57 ( ! [X5: A] : ( ord_less_eq @ B @ ( F @ X5 ) @ ( G @ X5 ) )
% 2.90/1.57 => ( ord_less_eq @ ( A > B ) @ F @ G ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_249_le__funE,axiom,
% 2.90/1.57 ! [B: $tType,A: $tType] :
% 2.90/1.57 ( ( ord @ B )
% 2.90/1.57 => ! [F: A > B,G: A > B,X: A] :
% 2.90/1.57 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.90/1.57 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_250_le__funD,axiom,
% 2.90/1.57 ! [B: $tType,A: $tType] :
% 2.90/1.57 ( ( ord @ B )
% 2.90/1.57 => ! [F: A > B,G: A > B,X: A] :
% 2.90/1.57 ( ( ord_less_eq @ ( A > B ) @ F @ G )
% 2.90/1.57 => ( ord_less_eq @ B @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_251_Collect__mono__iff,axiom,
% 2.90/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) )
% 2.90/1.57 = ( ! [X6: A] :
% 2.90/1.57 ( ( P @ X6 )
% 2.90/1.57 => ( Q @ X6 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_252_set__eq__subset,axiom,
% 2.90/1.57 ! [A: $tType] :
% 2.90/1.57 ( ( ^ [Y6: set @ A,Z: set @ A] : ( Y6 = Z ) )
% 2.90/1.57 = ( ^ [A4: set @ A,B5: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A4 @ B5 )
% 2.90/1.57 & ( ord_less_eq @ ( set @ A ) @ B5 @ A4 ) ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_253_subset__trans,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A,B2: set @ A,C4: set @ A] :
% 2.90/1.57 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B2 )
% 2.90/1.57 => ( ( ord_less_eq @ ( set @ A ) @ B2 @ C4 )
% 2.90/1.57 => ( ord_less_eq @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_254_Collect__mono,axiom,
% 2.90/1.57 ! [A: $tType,P: A > $o,Q: A > $o] :
% 2.90/1.57 ( ! [X5: A] :
% 2.90/1.57 ( ( P @ X5 )
% 2.90/1.57 => ( Q @ X5 ) )
% 2.90/1.57 => ( ord_less_eq @ ( set @ A ) @ ( collect @ A @ P ) @ ( collect @ A @ Q ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(fact_255_subset__refl,axiom,
% 2.90/1.57 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ A2 ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 2.90/1.57 bounded_lattice @ $o ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 2.90/1.57 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 2.90/1.57 ! [A8: $tType,A9: $tType] :
% 2.90/1.57 ( ( bounded_lattice @ A9 )
% 2.90/1.57 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 2.90/1.57 ! [A8: $tType,A9: $tType] :
% 2.90/1.57 ( ( bounded_lattice @ A9 )
% 2.90/1.57 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_fun___Orderings_Opreorder,axiom,
% 2.90/1.57 ! [A8: $tType,A9: $tType] :
% 2.90/1.57 ( ( preorder @ A9 )
% 2.90/1.57 => ( preorder @ ( A8 > A9 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_fun___Orderings_Oorder,axiom,
% 2.90/1.57 ! [A8: $tType,A9: $tType] :
% 2.90/1.57 ( ( order @ A9 )
% 2.90/1.57 => ( order @ ( A8 > A9 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_fun___Orderings_Oord,axiom,
% 2.90/1.57 ! [A8: $tType,A9: $tType] :
% 2.90/1.57 ( ( ord @ A9 )
% 2.90/1.57 => ( ord @ ( A8 > A9 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_fun___Orderings_Obot,axiom,
% 2.90/1.57 ! [A8: $tType,A9: $tType] :
% 2.90/1.57 ( ( bot @ A9 )
% 2.90/1.57 => ( bot @ ( A8 > A9 ) ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 2.90/1.57 preorder @ nat ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 2.90/1.57 linorder @ nat ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 2.90/1.57 order @ nat ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 2.90/1.57 ord @ nat ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Nat_Onat___Orderings_Obot_6,axiom,
% 2.90/1.57 bot @ nat ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 2.90/1.57 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 2.90/1.57 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 2.90/1.57 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 2.90/1.57 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 2.90/1.57 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 2.90/1.57 bounde1808546759up_bot @ $o ).
% 2.90/1.57
% 2.90/1.57 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 2.90/1.57 preorder @ $o ).
% 2.90/1.58
% 2.90/1.58 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 2.90/1.58 linorder @ $o ).
% 2.90/1.58
% 2.90/1.58 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 2.90/1.58 order @ $o ).
% 2.90/1.58
% 2.90/1.58 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 2.90/1.58 ord @ $o ).
% 2.90/1.58
% 2.90/1.58 thf(tcon_HOL_Obool___Orderings_Obot_17,axiom,
% 2.90/1.58 bot @ $o ).
% 2.90/1.58
% 2.90/1.58 thf(conj_0,conjecture,
% 2.90/1.58 ~ ( ine @ pq @ ( secrecy_kE @ key ) ) ).
% 2.90/1.58 ------------------------
% 2.97/1.61 % (19510)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_19196 for (2999ds/2Mi)
% 2.97/1.61 % (19512)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/18Mi)
% 2.97/1.61 % (19510)Instruction limit reached!
% 2.97/1.61 % (19510)------------------------------
% 2.97/1.61 % (19510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.61 % (19510)Termination reason: Unknown
% 2.97/1.61 % (19510)Termination phase: shuffling
% 2.97/1.61
% 2.97/1.61 % (19510)Memory used [KB]: 1407
% 2.97/1.61 % (19510)Time elapsed: 0.003 s
% 2.97/1.61 % (19510)Instructions burned: 4 (million)
% 2.97/1.61 % (19510)------------------------------
% 2.97/1.61 % (19510)------------------------------
% 2.97/1.62 % (19512)Instruction limit reached!
% 2.97/1.62 % (19512)------------------------------
% 2.97/1.62 % (19512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (19512)Termination reason: Unknown
% 2.97/1.62 % (19512)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (19506)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/183Mi)
% 2.97/1.62 % (19512)Memory used [KB]: 1663
% 2.97/1.62 % (19512)Time elapsed: 0.008 s
% 2.97/1.62 % (19512)Instructions burned: 19 (million)
% 2.97/1.62 % (19512)------------------------------
% 2.97/1.62 % (19512)------------------------------
% 2.97/1.62 % (19507)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_19196 for (2999ds/4Mi)
% 2.97/1.62 % (19508)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_19196 for (2999ds/27Mi)
% 2.97/1.62 % (19509)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/2Mi)
% 2.97/1.62 % (19511)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_19196 for (2999ds/275Mi)
% 2.97/1.62 % (19509)Instruction limit reached!
% 2.97/1.62 % (19509)------------------------------
% 2.97/1.62 % (19509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (19509)Termination reason: Unknown
% 2.97/1.62 % (19509)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (19509)Memory used [KB]: 1407
% 2.97/1.62 % (19509)Time elapsed: 0.004 s
% 2.97/1.62 % (19509)Instructions burned: 3 (million)
% 2.97/1.62 % (19509)------------------------------
% 2.97/1.62 % (19509)------------------------------
% 2.97/1.62 % (19507)Instruction limit reached!
% 2.97/1.62 % (19507)------------------------------
% 2.97/1.62 % (19507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (19507)Termination reason: Unknown
% 2.97/1.62 % (19507)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (19507)Memory used [KB]: 1407
% 2.97/1.62 % (19507)Time elapsed: 0.005 s
% 2.97/1.62 % (19507)Instructions burned: 5 (million)
% 2.97/1.62 % (19507)------------------------------
% 2.97/1.62 % (19507)------------------------------
% 2.97/1.62 % (19513)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/3Mi)
% 2.97/1.62 % (19513)Instruction limit reached!
% 2.97/1.62 % (19513)------------------------------
% 2.97/1.62 % (19513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.62 % (19513)Termination reason: Unknown
% 2.97/1.62 % (19513)Termination phase: shuffling
% 2.97/1.62
% 2.97/1.62 % (19513)Memory used [KB]: 1407
% 2.97/1.62 % (19513)Time elapsed: 0.003 s
% 2.97/1.62 % (19513)Instructions burned: 5 (million)
% 2.97/1.62 % (19513)------------------------------
% 2.97/1.62 % (19513)------------------------------
% 2.97/1.63 % (19514)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_19196 for (2999ds/37Mi)
% 2.97/1.63 % (19517)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_19196 for (2999ds/1041Mi)
% 2.97/1.63 % (19508)Instruction limit reached!
% 2.97/1.63 % (19508)------------------------------
% 2.97/1.63 % (19508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.63 % (19508)Termination reason: Unknown
% 2.97/1.63 % (19508)Termination phase: shuffling
% 2.97/1.63
% 2.97/1.63 % (19508)Memory used [KB]: 1791
% 2.97/1.63 % (19508)Time elapsed: 0.019 s
% 2.97/1.63 % (19508)Instructions burned: 27 (million)
% 2.97/1.63 % (19508)------------------------------
% 2.97/1.63 % (19508)------------------------------
% 2.97/1.63 % (19515)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_19196 for (2999ds/15Mi)
% 2.97/1.64 % (19516)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_19196 for (2999ds/3Mi)
% 2.97/1.64 % (19514)Instruction limit reached!
% 2.97/1.64 % (19514)------------------------------
% 2.97/1.64 % (19514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (19514)Termination reason: Unknown
% 2.97/1.64 % (19514)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (19514)Memory used [KB]: 2046
% 2.97/1.64 % (19514)Time elapsed: 0.012 s
% 2.97/1.64 % (19514)Instructions burned: 37 (million)
% 2.97/1.64 % (19514)------------------------------
% 2.97/1.64 % (19514)------------------------------
% 2.97/1.64 % (19516)Instruction limit reached!
% 2.97/1.64 % (19516)------------------------------
% 2.97/1.64 % (19516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (19516)Termination reason: Unknown
% 2.97/1.64 % (19516)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (19516)Memory used [KB]: 1407
% 2.97/1.64 % (19516)Time elapsed: 0.004 s
% 2.97/1.64 % (19516)Instructions burned: 3 (million)
% 2.97/1.64 % (19516)------------------------------
% 2.97/1.64 % (19516)------------------------------
% 2.97/1.64 % (19511)Refutation not found, incomplete strategy
% 2.97/1.64 % (19511)------------------------------
% 2.97/1.64 % (19511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (19511)Termination reason: Refutation not found, incomplete strategy
% 2.97/1.64
% 2.97/1.64
% 2.97/1.64 % (19511)Memory used [KB]: 6524
% 2.97/1.64 % (19511)Time elapsed: 0.027 s
% 2.97/1.64 % (19511)Instructions burned: 60 (million)
% 2.97/1.64 % (19511)------------------------------
% 2.97/1.64 % (19511)------------------------------
% 2.97/1.64 % (19518)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/7Mi)
% 2.97/1.64 % (19515)Instruction limit reached!
% 2.97/1.64 % (19515)------------------------------
% 2.97/1.64 % (19515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.64 % (19515)Termination reason: Unknown
% 2.97/1.64 % (19515)Termination phase: shuffling
% 2.97/1.64
% 2.97/1.64 % (19515)Memory used [KB]: 1663
% 2.97/1.64 % (19515)Time elapsed: 0.012 s
% 2.97/1.64 % (19515)Instructions burned: 16 (million)
% 2.97/1.64 % (19515)------------------------------
% 2.97/1.64 % (19515)------------------------------
% 2.97/1.65 % (19518)Instruction limit reached!
% 2.97/1.65 % (19518)------------------------------
% 2.97/1.65 % (19518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.65 % (19518)Termination reason: Unknown
% 2.97/1.65 % (19518)Termination phase: shuffling
% 2.97/1.65
% 2.97/1.65 % (19518)Memory used [KB]: 1535
% 2.97/1.65 % (19518)Time elapsed: 0.005 s
% 2.97/1.65 % (19518)Instructions burned: 9 (million)
% 2.97/1.65 % (19518)------------------------------
% 2.97/1.65 % (19518)------------------------------
% 2.97/1.65 % (19519)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/16Mi)
% 2.97/1.65 % (19521)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_19196 for (2999ds/3Mi)
% 2.97/1.65 % (19521)Instruction limit reached!
% 2.97/1.65 % (19521)------------------------------
% 2.97/1.65 % (19521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.65 % (19521)Termination reason: Unknown
% 2.97/1.65 % (19521)Termination phase: shuffling
% 2.97/1.65
% 2.97/1.65 % (19521)Memory used [KB]: 1407
% 2.97/1.65 % (19521)Time elapsed: 0.003 s
% 2.97/1.65 % (19521)Instructions burned: 4 (million)
% 2.97/1.65 % (19521)------------------------------
% 2.97/1.65 % (19521)------------------------------
% 2.97/1.65 % (19519)Instruction limit reached!
% 2.97/1.65 % (19519)------------------------------
% 2.97/1.65 % (19519)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.65 % (19519)Termination reason: Unknown
% 2.97/1.65 % (19519)Termination phase: shuffling
% 2.97/1.65
% 2.97/1.65 % (19519)Memory used [KB]: 1663
% 2.97/1.65 % (19519)Time elapsed: 0.008 s
% 2.97/1.65 % (19519)Instructions burned: 18 (million)
% 2.97/1.65 % (19519)------------------------------
% 2.97/1.65 % (19519)------------------------------
% 2.97/1.66 % (19520)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_19196 for (2999ds/3Mi)
% 2.97/1.66 % (19523)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/3Mi)
% 2.97/1.66 % (19520)Instruction limit reached!
% 2.97/1.66 % (19520)------------------------------
% 2.97/1.66 % (19520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (19520)Termination reason: Unknown
% 2.97/1.66 % (19520)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (19520)Memory used [KB]: 1407
% 2.97/1.66 % (19520)Time elapsed: 0.004 s
% 2.97/1.66 % (19520)Instructions burned: 3 (million)
% 2.97/1.66 % (19520)------------------------------
% 2.97/1.66 % (19520)------------------------------
% 2.97/1.66 % (19523)Instruction limit reached!
% 2.97/1.66 % (19523)------------------------------
% 2.97/1.66 % (19523)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (19523)Termination reason: Unknown
% 2.97/1.66 % (19523)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (19523)Memory used [KB]: 1407
% 2.97/1.66 % (19523)Time elapsed: 0.003 s
% 2.97/1.66 % (19523)Instructions burned: 4 (million)
% 2.97/1.66 % (19523)------------------------------
% 2.97/1.66 % (19523)------------------------------
% 2.97/1.66 % (19522)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/7Mi)
% 2.97/1.66 % (19524)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/4Mi)
% 2.97/1.66 % (19525)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/18Mi)
% 2.97/1.66 % (19524)Instruction limit reached!
% 2.97/1.66 % (19524)------------------------------
% 2.97/1.66 % (19524)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.66 % (19524)Termination reason: Unknown
% 2.97/1.66 % (19524)Termination phase: shuffling
% 2.97/1.66
% 2.97/1.66 % (19524)Memory used [KB]: 1407
% 2.97/1.66 % (19524)Time elapsed: 0.003 s
% 2.97/1.66 % (19524)Instructions burned: 4 (million)
% 2.97/1.66 % (19524)------------------------------
% 2.97/1.66 % (19524)------------------------------
% 2.97/1.67 % (19522)Instruction limit reached!
% 2.97/1.67 % (19522)------------------------------
% 2.97/1.67 % (19522)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (19522)Termination reason: Unknown
% 2.97/1.67 % (19522)Termination phase: shuffling
% 2.97/1.67
% 2.97/1.67 % (19522)Memory used [KB]: 1535
% 2.97/1.67 % (19522)Time elapsed: 0.006 s
% 2.97/1.67 % (19522)Instructions burned: 8 (million)
% 2.97/1.67 % (19522)------------------------------
% 2.97/1.67 % (19522)------------------------------
% 2.97/1.67 % (19527)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/6Mi)
% 2.97/1.67 % (19525)Instruction limit reached!
% 2.97/1.67 % (19525)------------------------------
% 2.97/1.67 % (19525)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (19525)Termination reason: Unknown
% 2.97/1.67 % (19525)Termination phase: shuffling
% 2.97/1.67
% 2.97/1.67 % (19525)Memory used [KB]: 1663
% 2.97/1.67 % (19525)Time elapsed: 0.008 s
% 2.97/1.67 % (19525)Instructions burned: 18 (million)
% 2.97/1.67 % (19525)------------------------------
% 2.97/1.67 % (19525)------------------------------
% 2.97/1.67 % (19527)Instruction limit reached!
% 2.97/1.67 % (19527)------------------------------
% 2.97/1.67 % (19527)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.67 % (19527)Termination reason: Unknown
% 2.97/1.67 % (19527)Termination phase: shuffling
% 2.97/1.67
% 2.97/1.67 % (19527)Memory used [KB]: 1407
% 2.97/1.67 % (19527)Time elapsed: 0.004 s
% 2.97/1.67 % (19527)Instructions burned: 6 (million)
% 2.97/1.67 % (19527)------------------------------
% 2.97/1.67 % (19527)------------------------------
% 2.97/1.67 % (19528)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_19196 for (2999ds/902Mi)
% 2.97/1.67 % (19526)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/710Mi)
% 2.97/1.68 % (19530)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/5Mi)
% 2.97/1.68 % (19531)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_19196 for (2999ds/6Mi)
% 2.97/1.68 % (19529)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_19196 for (2999ds/21Mi)
% 2.97/1.68 % (19530)Instruction limit reached!
% 2.97/1.68 % (19530)------------------------------
% 2.97/1.68 % (19530)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.68 % (19530)Termination reason: Unknown
% 2.97/1.68 % (19530)Termination phase: shuffling
% 2.97/1.68
% 2.97/1.68 % (19530)Memory used [KB]: 1407
% 2.97/1.68 % (19530)Time elapsed: 0.004 s
% 2.97/1.68 % (19530)Instructions burned: 7 (million)
% 2.97/1.68 % (19530)------------------------------
% 2.97/1.68 % (19530)------------------------------
% 2.97/1.68 % (19531)Instruction limit reached!
% 2.97/1.68 % (19531)------------------------------
% 2.97/1.68 % (19531)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.68 % (19531)Termination reason: Unknown
% 2.97/1.68 % (19531)Termination phase: shuffling
% 2.97/1.68
% 2.97/1.68 % (19531)Memory used [KB]: 1407
% 2.97/1.68 % (19531)Time elapsed: 0.004 s
% 2.97/1.68 % (19531)Instructions burned: 7 (million)
% 2.97/1.68 % (19531)------------------------------
% 2.97/1.68 % (19531)------------------------------
% 2.97/1.69 % (19529)Instruction limit reached!
% 2.97/1.69 % (19529)------------------------------
% 2.97/1.69 % (19529)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.69 % (19529)Termination reason: Unknown
% 2.97/1.69 % (19529)Termination phase: shuffling
% 2.97/1.69
% 2.97/1.69 % (19529)Memory used [KB]: 1663
% 2.97/1.69 % (19529)Time elapsed: 0.011 s
% 2.97/1.69 % (19529)Instructions burned: 23 (million)
% 2.97/1.69 % (19529)------------------------------
% 2.97/1.69 % (19529)------------------------------
% 2.97/1.69 % (19532)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/377Mi)
% 2.97/1.69 % (19533)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_19196 for (2999ds/779Mi)
% 2.97/1.70 % (19534)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_19196 for (2998ds/19Mi)
% 2.97/1.71 % (19534)Instruction limit reached!
% 2.97/1.71 % (19534)------------------------------
% 2.97/1.71 % (19534)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (19534)Termination reason: Unknown
% 2.97/1.71 % (19534)Termination phase: shuffling
% 2.97/1.71
% 2.97/1.71 % (19534)Memory used [KB]: 1663
% 2.97/1.71 % (19534)Time elapsed: 0.008 s
% 2.97/1.71 % (19534)Instructions burned: 20 (million)
% 2.97/1.71 % (19534)------------------------------
% 2.97/1.71 % (19534)------------------------------
% 2.97/1.71 % (19506)Instruction limit reached!
% 2.97/1.71 % (19506)------------------------------
% 2.97/1.71 % (19506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.71 % (19506)Termination reason: Unknown
% 2.97/1.71 % (19506)Termination phase: Saturation
% 2.97/1.71
% 2.97/1.71 % (19506)Memory used [KB]: 7164
% 2.97/1.71 % (19506)Time elapsed: 0.097 s
% 2.97/1.71 % (19506)Instructions burned: 184 (million)
% 2.97/1.71 % (19506)------------------------------
% 2.97/1.71 % (19506)------------------------------
% 2.97/1.72 % (19535)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19196 for (2998ds/879Mi)
% 2.97/1.72 % (19536)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19196 for (2998ds/17Mi)
% 2.97/1.73 % (19536)Instruction limit reached!
% 2.97/1.73 % (19536)------------------------------
% 2.97/1.73 % (19536)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.73 % (19536)Termination reason: Unknown
% 2.97/1.73 % (19536)Termination phase: shuffling
% 2.97/1.73
% 2.97/1.73 % (19536)Memory used [KB]: 1663
% 2.97/1.73 % (19536)Time elapsed: 0.008 s
% 2.97/1.73 % (19536)Instructions burned: 17 (million)
% 2.97/1.73 % (19536)------------------------------
% 2.97/1.73 % (19536)------------------------------
% 2.97/1.74 % (19537)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19196 for (2998ds/3Mi)
% 2.97/1.74 % (19537)Instruction limit reached!
% 2.97/1.74 % (19537)------------------------------
% 2.97/1.74 % (19537)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.74 % (19537)Termination reason: Unknown
% 2.97/1.74 % (19537)Termination phase: shuffling
% 2.97/1.74
% 2.97/1.74 % (19537)Memory used [KB]: 1407
% 2.97/1.74 % (19537)Time elapsed: 0.003 s
% 2.97/1.74 % (19537)Instructions burned: 4 (million)
% 2.97/1.74 % (19537)------------------------------
% 2.97/1.74 % (19537)------------------------------
% 2.97/1.75 % (19538)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19196 for (2998ds/30Mi)
% 2.97/1.76 % (19538)Instruction limit reached!
% 2.97/1.76 % (19538)------------------------------
% 2.97/1.76 % (19538)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.76 % (19538)Termination reason: Unknown
% 2.97/1.76 % (19538)Termination phase: shuffling
% 2.97/1.76
% 2.97/1.76 % (19538)Memory used [KB]: 1918
% 2.97/1.76 % (19538)Time elapsed: 0.013 s
% 2.97/1.76 % (19538)Instructions burned: 32 (million)
% 2.97/1.76 % (19538)------------------------------
% 2.97/1.76 % (19538)------------------------------
% 2.97/1.77 % (19539)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19196 for (2998ds/127Mi)
% 2.97/1.80 % (19532)Instruction limit reached!
% 2.97/1.80 % (19532)------------------------------
% 2.97/1.80 % (19532)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.80 % (19532)Termination reason: Unknown
% 2.97/1.80 % (19532)Termination phase: Saturation
% 2.97/1.80
% 2.97/1.80 % (19532)Memory used [KB]: 7803
% 2.97/1.80 % (19532)Time elapsed: 0.107 s
% 2.97/1.80 % (19532)Instructions burned: 377 (million)
% 2.97/1.80 % (19532)------------------------------
% 2.97/1.80 % (19532)------------------------------
% 2.97/1.81 % (19540)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19196 for (2997ds/100Mi)
% 2.97/1.81 % (19539)Instruction limit reached!
% 2.97/1.81 % (19539)------------------------------
% 2.97/1.81 % (19539)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.81 % (19539)Termination reason: Unknown
% 2.97/1.81 % (19539)Termination phase: Property scanning
% 2.97/1.81
% 2.97/1.81 % (19539)Memory used [KB]: 2302
% 2.97/1.81 % (19539)Time elapsed: 0.040 s
% 2.97/1.81 % (19539)Instructions burned: 128 (million)
% 2.97/1.81 % (19539)------------------------------
% 2.97/1.81 % (19539)------------------------------
% 2.97/1.82 % (19541)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_19196 for (2997ds/3Mi)
% 2.97/1.82 % (19541)Instruction limit reached!
% 2.97/1.82 % (19541)------------------------------
% 2.97/1.82 % (19541)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.82 % (19541)Termination reason: Unknown
% 2.97/1.82 % (19541)Termination phase: shuffling
% 2.97/1.82
% 2.97/1.82 % (19541)Memory used [KB]: 1407
% 2.97/1.82 % (19541)Time elapsed: 0.003 s
% 2.97/1.82 % (19541)Instructions burned: 4 (million)
% 2.97/1.82 % (19541)------------------------------
% 2.97/1.82 % (19541)------------------------------
% 2.97/1.83 % (19542)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_19196 for (2997ds/20Mi)
% 2.97/1.83 % (19540)Instruction limit reached!
% 2.97/1.83 % (19540)------------------------------
% 2.97/1.83 % (19540)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.83 % (19540)Termination reason: Unknown
% 2.97/1.83 % (19540)Termination phase: Property scanning
% 2.97/1.83
% 2.97/1.83 % (19540)Memory used [KB]: 2302
% 2.97/1.83 % (19540)Time elapsed: 0.028 s
% 2.97/1.83 % (19540)Instructions burned: 101 (million)
% 2.97/1.83 % (19540)------------------------------
% 2.97/1.83 % (19540)------------------------------
% 2.97/1.84 % (19542)Instruction limit reached!
% 2.97/1.84 % (19542)------------------------------
% 2.97/1.84 % (19542)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.84 % (19542)Termination reason: Unknown
% 2.97/1.84 % (19542)Termination phase: shuffling
% 2.97/1.84
% 2.97/1.84 % (19542)Memory used [KB]: 1663
% 2.97/1.84 % (19542)Time elapsed: 0.009 s
% 2.97/1.84 % (19542)Instructions burned: 20 (million)
% 2.97/1.84 % (19542)------------------------------
% 2.97/1.84 % (19542)------------------------------
% 2.97/1.84 % (19543)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_19196 for (2997ds/86Mi)
% 2.97/1.85 % (19544)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_19196 for (2997ds/107Mi)
% 2.97/1.87 % (19543)Instruction limit reached!
% 2.97/1.87 % (19543)------------------------------
% 2.97/1.87 % (19543)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.87 % (19543)Termination reason: Unknown
% 2.97/1.87 % (19543)Termination phase: Function definition elimination
% 2.97/1.87
% 2.97/1.87 % (19543)Memory used [KB]: 2302
% 2.97/1.87 % (19543)Time elapsed: 0.026 s
% 2.97/1.87 % (19543)Instructions burned: 88 (million)
% 2.97/1.87 % (19543)------------------------------
% 2.97/1.87 % (19543)------------------------------
% 2.97/1.88 % (19545)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_19196 for (2997ds/39Mi)
% 2.97/1.88 % (19544)Instruction limit reached!
% 2.97/1.88 % (19544)------------------------------
% 2.97/1.88 % (19544)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.88 % (19544)Termination reason: Unknown
% 2.97/1.88 % (19544)Termination phase: Property scanning
% 2.97/1.88
% 2.97/1.88 % (19544)Memory used [KB]: 2302
% 2.97/1.88 % (19544)Time elapsed: 0.035 s
% 2.97/1.88 % (19544)Instructions burned: 109 (million)
% 2.97/1.88 % (19544)------------------------------
% 2.97/1.88 % (19544)------------------------------
% 2.97/1.89 % (19545)Instruction limit reached!
% 2.97/1.89 % (19545)------------------------------
% 2.97/1.89 % (19545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.89 % (19545)Termination reason: Unknown
% 2.97/1.89 % (19545)Termination phase: shuffling
% 2.97/1.89
% 2.97/1.89 % (19545)Memory used [KB]: 2174
% 2.97/1.89 % (19545)Time elapsed: 0.012 s
% 2.97/1.89 % (19545)Instructions burned: 41 (million)
% 2.97/1.89 % (19545)------------------------------
% 2.97/1.89 % (19545)------------------------------
% 2.97/1.89 % (19546)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/448Mi)
% 2.97/1.90 % (19547)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/46Mi)
% 2.97/1.91 % (19535)Refutation not found, non-redundant clauses discarded% (19535)------------------------------
% 2.97/1.91 % (19535)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.91 % (19535)Termination reason: Refutation not found, non-redundant clauses discarded
% 2.97/1.91
% 2.97/1.91 % (19535)Memory used [KB]: 7675
% 2.97/1.91 % (19535)Time elapsed: 0.194 s
% 2.97/1.91 % (19535)Instructions burned: 600 (million)
% 2.97/1.91 % (19535)------------------------------
% 2.97/1.91 % (19535)------------------------------
% 2.97/1.91 % (19526)Instruction limit reached!
% 2.97/1.91 % (19526)------------------------------
% 2.97/1.91 % (19526)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.91 % (19526)Termination reason: Unknown
% 2.97/1.91 % (19526)Termination phase: Saturation
% 2.97/1.91
% 2.97/1.91 % (19526)Memory used [KB]: 7931
% 2.97/1.91 % (19526)Time elapsed: 0.238 s
% 2.97/1.91 % (19526)Instructions burned: 710 (million)
% 2.97/1.91 % (19526)------------------------------
% 2.97/1.91 % (19526)------------------------------
% 2.97/1.91 % (19547)Instruction limit reached!
% 2.97/1.91 % (19547)------------------------------
% 2.97/1.91 % (19547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.91 % (19547)Termination reason: Unknown
% 2.97/1.91 % (19547)Termination phase: SInE selection
% 2.97/1.91
% 2.97/1.91 % (19547)Memory used [KB]: 1918
% 2.97/1.91 % (19547)Time elapsed: 0.016 s
% 2.97/1.91 % (19547)Instructions burned: 47 (million)
% 2.97/1.91 % (19547)------------------------------
% 2.97/1.91 % (19547)------------------------------
% 2.97/1.92 % (19548)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/98Mi)
% 2.97/1.92 % (19549)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/507Mi)
% 2.97/1.92 % (19550)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/149Mi)
% 2.97/1.94 % (19517)Instruction limit reached!
% 2.97/1.94 % (19517)------------------------------
% 2.97/1.94 % (19517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.94 % (19517)Termination reason: Unknown
% 2.97/1.94 % (19517)Termination phase: Saturation
% 2.97/1.94
% 2.97/1.94 % (19517)Memory used [KB]: 9850
% 2.97/1.94 % (19517)Time elapsed: 0.315 s
% 2.97/1.94 % (19517)Instructions burned: 1043 (million)
% 2.97/1.94 % (19517)------------------------------
% 2.97/1.94 % (19517)------------------------------
% 2.97/1.94 % (19528)Instruction limit reached!
% 2.97/1.94 % (19528)------------------------------
% 2.97/1.94 % (19528)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.94 % (19528)Termination reason: Unknown
% 2.97/1.94 % (19528)Termination phase: Saturation
% 2.97/1.94
% 2.97/1.94 % (19528)Memory used [KB]: 8059
% 2.97/1.94 % (19528)Time elapsed: 0.272 s
% 2.97/1.94 % (19528)Instructions burned: 903 (million)
% 2.97/1.94 % (19528)------------------------------
% 2.97/1.94 % (19528)------------------------------
% 2.97/1.95 % (19533)Instruction limit reached!
% 2.97/1.95 % (19533)------------------------------
% 2.97/1.95 % (19533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.95 % (19533)Termination reason: Unknown
% 2.97/1.95 % (19533)Termination phase: Saturation
% 2.97/1.95
% 2.97/1.95 % (19533)Memory used [KB]: 8059
% 2.97/1.95 % (19533)Time elapsed: 0.278 s
% 2.97/1.95 % (19533)Instructions burned: 780 (million)
% 2.97/1.95 % (19533)------------------------------
% 2.97/1.95 % (19533)------------------------------
% 2.97/1.95 % (19548)Instruction limit reached!
% 2.97/1.95 % (19548)------------------------------
% 2.97/1.95 % (19548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.95 % (19548)Termination reason: Unknown
% 2.97/1.95 % (19548)Termination phase: Property scanning
% 2.97/1.95
% 2.97/1.95 % (19548)Memory used [KB]: 2302
% 2.97/1.95 % (19548)Time elapsed: 0.030 s
% 2.97/1.95 % (19548)Instructions burned: 99 (million)
% 2.97/1.95 % (19548)------------------------------
% 2.97/1.95 % (19548)------------------------------
% 2.97/1.95 % (19552)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/6Mi)
% 2.97/1.96 % (19552)Instruction limit reached!
% 2.97/1.96 % (19552)------------------------------
% 2.97/1.96 % (19552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.96 % (19552)Termination reason: Unknown
% 2.97/1.96 % (19552)Termination phase: shuffling
% 2.97/1.96
% 2.97/1.96 % (19552)Memory used [KB]: 1407
% 2.97/1.96 % (19552)Time elapsed: 0.003 s
% 2.97/1.96 % (19552)Instructions burned: 7 (million)
% 2.97/1.96 % (19552)------------------------------
% 2.97/1.96 % (19552)------------------------------
% 2.97/1.96 % (19553)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/1087Mi)
% 2.97/1.96 % (19554)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/47Mi)
% 2.97/1.96 % (19551)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/39Mi)
% 2.97/1.96 % (19550)Instruction limit reached!
% 2.97/1.96 % (19550)------------------------------
% 2.97/1.96 % (19550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.96 % (19550)Termination reason: Unknown
% 2.97/1.96 % (19550)Termination phase: Saturation
% 2.97/1.96
% 2.97/1.96 % (19550)Memory used [KB]: 6908
% 2.97/1.96 % (19550)Time elapsed: 0.042 s
% 2.97/1.96 % (19550)Instructions burned: 152 (million)
% 2.97/1.96 % (19550)------------------------------
% 2.97/1.96 % (19550)------------------------------
% 2.97/1.97 % (19555)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/44Mi)
% 2.97/1.97 % (19556)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/432Mi)
% 2.97/1.97 % (19554)Instruction limit reached!
% 2.97/1.97 % (19554)------------------------------
% 2.97/1.97 % (19554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.97 % (19554)Termination reason: Unknown
% 2.97/1.97 % (19554)Termination phase: Preprocessing 1
% 2.97/1.97
% 2.97/1.97 % (19554)Memory used [KB]: 1918
% 2.97/1.97 % (19554)Time elapsed: 0.017 s
% 2.97/1.97 % (19554)Instructions burned: 47 (million)
% 2.97/1.97 % (19554)------------------------------
% 2.97/1.97 % (19554)------------------------------
% 2.97/1.98 % (19555)Instruction limit reached!
% 2.97/1.98 % (19555)------------------------------
% 2.97/1.98 % (19555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.98 % (19555)Termination reason: Unknown
% 2.97/1.98 % (19555)Termination phase: shuffling
% 2.97/1.98
% 2.97/1.98 % (19555)Memory used [KB]: 2174
% 2.97/1.98 % (19555)Time elapsed: 0.013 s
% 2.97/1.98 % (19555)Instructions burned: 44 (million)
% 2.97/1.98 % (19555)------------------------------
% 2.97/1.98 % (19555)------------------------------
% 2.97/1.98 % (19557)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_19196 for (2996ds/62Mi)
% 2.97/1.99 % (19551)Instruction limit reached!
% 2.97/1.99 % (19551)------------------------------
% 2.97/1.99 % (19551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/1.99 % (19551)Termination reason: Unknown
% 2.97/1.99 % (19551)Termination phase: Property scanning
% 2.97/1.99
% 2.97/1.99 % (19551)Memory used [KB]: 1918
% 2.97/1.99 % (19551)Time elapsed: 0.026 s
% 2.97/1.99 % (19551)Instructions burned: 41 (million)
% 2.97/1.99 % (19551)------------------------------
% 2.97/1.99 % (19551)------------------------------
% 2.97/1.99 % (19558)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/31Mi)
% 2.97/2.00 % (19558)Instruction limit reached!
% 2.97/2.00 % (19558)------------------------------
% 2.97/2.00 % (19558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.00 % (19558)Termination reason: Unknown
% 2.97/2.00 % (19558)Termination phase: Property scanning
% 2.97/2.00
% 2.97/2.00 % (19558)Memory used [KB]: 1918
% 2.97/2.00 % (19558)Time elapsed: 0.012 s
% 2.97/2.00 % (19558)Instructions burned: 34 (million)
% 2.97/2.00 % (19558)------------------------------
% 2.97/2.00 % (19558)------------------------------
% 2.97/2.00 % (19557)Instruction limit reached!
% 2.97/2.00 % (19557)------------------------------
% 2.97/2.00 % (19557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.97/2.00 % (19557)Termination reason: Unknown
% 2.97/2.00 % (19557)Termination phase: Property scanning
% 2.97/2.00
% 2.97/2.00 % (19557)Memory used [KB]: 2302
% 2.97/2.00 % (19557)Time elapsed: 0.020 s
% 2.97/2.00 % (19557)Instructions burned: 63 (million)
% 2.97/2.00 % (19557)------------------------------
% 2.97/2.00 % (19557)------------------------------
% 2.97/2.00 % (19559)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/96Mi)
% 2.97/2.01 % (19560)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/453Mi)
% 5.83/2.01 % (19561)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/71Mi)
% 5.83/2.03 % (19546)Instruction limit reached!
% 5.83/2.03 % (19546)------------------------------
% 5.83/2.03 % (19546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.03 % (19546)Termination reason: Unknown
% 5.83/2.03 % (19546)Termination phase: Saturation
% 5.83/2.03
% 5.83/2.03 % (19546)Memory used [KB]: 7803
% 5.83/2.03 % (19546)Time elapsed: 0.142 s
% 5.83/2.03 % (19546)Instructions burned: 448 (million)
% 5.83/2.03 % (19546)------------------------------
% 5.83/2.03 % (19546)------------------------------
% 5.83/2.04 % (19561)Instruction limit reached!
% 5.83/2.04 % (19561)------------------------------
% 5.83/2.04 % (19561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.04 % (19561)Termination reason: Unknown
% 5.83/2.04 % (19561)Termination phase: Property scanning
% 5.83/2.04
% 5.83/2.04 % (19561)Memory used [KB]: 2302
% 5.83/2.04 % (19561)Time elapsed: 0.025 s
% 5.83/2.04 % (19561)Instructions burned: 72 (million)
% 5.83/2.04 % (19561)------------------------------
% 5.83/2.04 % (19561)------------------------------
% 5.83/2.04 % (19562)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/83Mi)
% 5.83/2.05 % (19563)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/11Mi)
% 5.83/2.05 % (19563)Instruction limit reached!
% 5.83/2.05 % (19563)------------------------------
% 5.83/2.05 % (19563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.05 % (19563)Termination reason: Unknown
% 5.83/2.05 % (19563)Termination phase: shuffling
% 5.83/2.05
% 5.83/2.05 % (19563)Memory used [KB]: 1663
% 5.83/2.05 % (19563)Time elapsed: 0.005 s
% 5.83/2.05 % (19563)Instructions burned: 12 (million)
% 5.83/2.05 % (19563)------------------------------
% 5.83/2.05 % (19563)------------------------------
% 5.83/2.05 % (19559)Instruction limit reached!
% 5.83/2.05 % (19559)------------------------------
% 5.83/2.05 % (19559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.05 % (19559)Termination reason: Unknown
% 5.83/2.05 % (19559)Termination phase: Property scanning
% 5.83/2.05
% 5.83/2.05 % (19559)Memory used [KB]: 2302
% 5.83/2.05 % (19559)Time elapsed: 0.050 s
% 5.83/2.05 % (19559)Instructions burned: 96 (million)
% 5.83/2.05 % (19559)------------------------------
% 5.83/2.05 % (19559)------------------------------
% 5.83/2.06 % (19564)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/41Mi)
% 5.83/2.06 % (19565)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/6Mi)
% 5.83/2.06 % (19565)Instruction limit reached!
% 5.83/2.06 % (19565)------------------------------
% 5.83/2.06 % (19565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.06 % (19565)Termination reason: Unknown
% 5.83/2.06 % (19565)Termination phase: shuffling
% 5.83/2.06
% 5.83/2.06 % (19565)Memory used [KB]: 1407
% 5.83/2.06 % (19565)Time elapsed: 0.004 s
% 5.83/2.06 % (19565)Instructions burned: 7 (million)
% 5.83/2.06 % (19565)------------------------------
% 5.83/2.06 % (19565)------------------------------
% 5.83/2.07 % (19562)Instruction limit reached!
% 5.83/2.07 % (19562)------------------------------
% 5.83/2.07 % (19562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.07 % (19562)Termination reason: Unknown
% 5.83/2.07 % (19562)Termination phase: Saturation
% 5.83/2.07
% 5.83/2.07 % (19562)Memory used [KB]: 6524
% 5.83/2.07 % (19562)Time elapsed: 0.030 s
% 5.83/2.07 % (19562)Instructions burned: 83 (million)
% 5.83/2.07 % (19562)------------------------------
% 5.83/2.07 % (19562)------------------------------
% 5.83/2.07 % (19564)Instruction limit reached!
% 5.83/2.07 % (19564)------------------------------
% 5.83/2.07 % (19564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.07 % (19564)Termination reason: Unknown
% 5.83/2.07 % (19564)Termination phase: shuffling
% 5.83/2.07
% 5.83/2.07 % (19564)Memory used [KB]: 2174
% 5.83/2.07 % (19564)Time elapsed: 0.013 s
% 5.83/2.07 % (19564)Instructions burned: 43 (million)
% 5.83/2.07 % (19564)------------------------------
% 5.83/2.07 % (19564)------------------------------
% 5.83/2.07 % (19566)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/150Mi)
% 5.83/2.08 % (19567)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/343Mi)
% 5.83/2.08 % (19568)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_19196 for (2995ds/109Mi)
% 5.83/2.09 % (19549)Instruction limit reached!
% 5.83/2.09 % (19549)------------------------------
% 5.83/2.09 % (19549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.09 % (19549)Termination reason: Unknown
% 5.83/2.09 % (19549)Termination phase: Saturation
% 5.83/2.09
% 5.83/2.09 % (19549)Memory used [KB]: 7931
% 5.83/2.09 % (19549)Time elapsed: 0.166 s
% 5.83/2.09 % (19549)Instructions burned: 510 (million)
% 5.83/2.09 % (19549)------------------------------
% 5.83/2.09 % (19549)------------------------------
% 5.83/2.10 % (19569)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/253Mi)
% 5.83/2.10 % (19556)Instruction limit reached!
% 5.83/2.10 % (19556)------------------------------
% 5.83/2.10 % (19556)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.83/2.10 % (19556)Termination reason: Unknown
% 5.83/2.10 % (19556)Termination phase: Saturation
% 5.83/2.10
% 5.83/2.10 % (19556)Memory used [KB]: 3709
% 5.83/2.10 % (19556)Time elapsed: 0.128 s
% 5.83/2.10 % (19556)Instructions burned: 433 (million)
% 5.83/2.10 % (19556)------------------------------
% 5.83/2.10 % (19556)------------------------------
% 5.83/2.11 % (19570)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/140Mi)
% 6.30/2.11 % (19568)Instruction limit reached!
% 6.30/2.11 % (19568)------------------------------
% 6.30/2.11 % (19568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.11 % (19568)Termination reason: Unknown
% 6.30/2.11 % (19568)Termination phase: Property scanning
% 6.30/2.11
% 6.30/2.11 % (19568)Memory used [KB]: 2302
% 6.30/2.11 % (19568)Time elapsed: 0.033 s
% 6.30/2.11 % (19568)Instructions burned: 111 (million)
% 6.30/2.11 % (19568)------------------------------
% 6.30/2.11 % (19568)------------------------------
% 6.30/2.12 % (19566)Instruction limit reached!
% 6.30/2.12 % (19566)------------------------------
% 6.30/2.12 % (19566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.12 % (19566)Termination reason: Unknown
% 6.30/2.12 % (19566)Termination phase: Saturation
% 6.30/2.12
% 6.30/2.12 % (19566)Memory used [KB]: 7036
% 6.30/2.12 % (19566)Time elapsed: 0.046 s
% 6.30/2.12 % (19566)Instructions burned: 150 (million)
% 6.30/2.12 % (19566)------------------------------
% 6.30/2.12 % (19566)------------------------------
% 6.30/2.12 % (19571)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/614Mi)
% 6.30/2.13 % (19572)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/202Mi)
% 6.30/2.13 % (19560)Instruction limit reached!
% 6.30/2.13 % (19560)------------------------------
% 6.30/2.13 % (19560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.13 % (19560)Termination reason: Unknown
% 6.30/2.13 % (19560)Termination phase: Saturation
% 6.30/2.13
% 6.30/2.13 % (19560)Memory used [KB]: 7803
% 6.30/2.13 % (19560)Time elapsed: 0.124 s
% 6.30/2.13 % (19560)Instructions burned: 453 (million)
% 6.30/2.13 % (19560)------------------------------
% 6.30/2.13 % (19560)------------------------------
% 6.30/2.14 % (19573)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/339Mi)
% 6.30/2.15 % (19572)Refutation not found, incomplete strategy
% 6.30/2.15 % (19572)------------------------------
% 6.30/2.15 % (19572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.15 % (19572)Termination reason: Refutation not found, incomplete strategy
% 6.30/2.15
% 6.30/2.15
% 6.30/2.15 % (19572)Memory used [KB]: 6524
% 6.30/2.15 % (19572)Time elapsed: 0.024 s
% 6.30/2.15 % (19572)Instructions burned: 66 (million)
% 6.30/2.15 % (19572)------------------------------
% 6.30/2.15 % (19572)------------------------------
% 6.30/2.15 % (19570)Instruction limit reached!
% 6.30/2.15 % (19570)------------------------------
% 6.30/2.15 % (19570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.15 % (19570)Termination reason: Unknown
% 6.30/2.15 % (19570)Termination phase: Saturation
% 6.30/2.15
% 6.30/2.15 % (19570)Memory used [KB]: 6780
% 6.30/2.15 % (19570)Time elapsed: 0.046 s
% 6.30/2.15 % (19570)Instructions burned: 141 (million)
% 6.30/2.15 % (19570)------------------------------
% 6.30/2.15 % (19570)------------------------------
% 6.30/2.16 % (19574)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/283Mi)
% 6.30/2.16 % (19575)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_19196 for (2994ds/134Mi)
% 6.30/2.17 % (19569)Instruction limit reached!
% 6.30/2.17 % (19569)------------------------------
% 6.30/2.17 % (19569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.17 % (19569)Termination reason: Unknown
% 6.30/2.17 % (19569)Termination phase: Saturation
% 6.30/2.17
% 6.30/2.17 % (19569)Memory used [KB]: 6780
% 6.30/2.17 % (19569)Time elapsed: 0.081 s
% 6.30/2.17 % (19569)Instructions burned: 254 (million)
% 6.30/2.17 % (19569)------------------------------
% 6.30/2.17 % (19569)------------------------------
% 6.30/2.18 % (19576)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/298Mi)
% 6.30/2.19 % (19567)Instruction limit reached!
% 6.30/2.19 % (19567)------------------------------
% 6.30/2.19 % (19567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.30/2.19 % (19567)Termination reason: Unknown
% 6.30/2.19 % (19567)Termination phase: Saturation
% 6.30/2.19
% 6.30/2.19 % (19567)Memory used [KB]: 7419
% 6.30/2.19 % (19567)Time elapsed: 0.110 s
% 6.30/2.19 % (19567)Instructions burned: 346 (million)
% 6.30/2.19 % (19567)------------------------------
% 6.30/2.19 % (19567)------------------------------
% 6.91/2.20 % (19577)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/192Mi)
% 6.91/2.20 % (19575)Instruction limit reached!
% 6.91/2.20 % (19575)------------------------------
% 6.91/2.20 % (19575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.20 % (19575)Termination reason: Unknown
% 6.91/2.20 % (19575)Termination phase: Property scanning
% 6.91/2.20
% 6.91/2.20 % (19575)Memory used [KB]: 2302
% 6.91/2.20 % (19575)Time elapsed: 0.038 s
% 6.91/2.20 % (19575)Instructions burned: 134 (million)
% 6.91/2.20 % (19575)------------------------------
% 6.91/2.20 % (19575)------------------------------
% 6.91/2.21 % (19578)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/258Mi)
% 6.91/2.24 % (19573)Instruction limit reached!
% 6.91/2.24 % (19573)------------------------------
% 6.91/2.24 % (19573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.24 % (19573)Termination reason: Unknown
% 6.91/2.24 % (19573)Termination phase: Saturation
% 6.91/2.24
% 6.91/2.24 % (19573)Memory used [KB]: 7419
% 6.91/2.24 % (19573)Time elapsed: 0.099 s
% 6.91/2.24 % (19573)Instructions burned: 339 (million)
% 6.91/2.24 % (19573)------------------------------
% 6.91/2.24 % (19573)------------------------------
% 6.91/2.25 % (19574)Instruction limit reached!
% 6.91/2.25 % (19574)------------------------------
% 6.91/2.25 % (19574)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.25 % (19574)Termination reason: Unknown
% 6.91/2.25 % (19574)Termination phase: Saturation
% 6.91/2.25
% 6.91/2.25 % (19574)Memory used [KB]: 7547
% 6.91/2.25 % (19574)Time elapsed: 0.107 s
% 6.91/2.25 % (19574)Instructions burned: 283 (million)
% 6.91/2.25 % (19574)------------------------------
% 6.91/2.25 % (19574)------------------------------
% 6.91/2.25 % (19579)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/90Mi)
% 6.91/2.25 % (19577)Instruction limit reached!
% 6.91/2.25 % (19577)------------------------------
% 6.91/2.25 % (19577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.25 % (19577)Termination reason: Unknown
% 6.91/2.25 % (19577)Termination phase: Saturation
% 6.91/2.25
% 6.91/2.25 % (19577)Memory used [KB]: 3070
% 6.91/2.25 % (19577)Time elapsed: 0.056 s
% 6.91/2.25 % (19577)Instructions burned: 193 (million)
% 6.91/2.25 % (19577)------------------------------
% 6.91/2.25 % (19577)------------------------------
% 6.91/2.26 % (19580)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/231Mi)
% 6.91/2.26 % (19576)Instruction limit reached!
% 6.91/2.26 % (19576)------------------------------
% 6.91/2.26 % (19576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.26 % (19576)Termination reason: Unknown
% 6.91/2.26 % (19576)Termination phase: Saturation
% 6.91/2.26
% 6.91/2.26 % (19576)Memory used [KB]: 7419
% 6.91/2.26 % (19576)Time elapsed: 0.079 s
% 6.91/2.26 % (19576)Instructions burned: 298 (million)
% 6.91/2.26 % (19576)------------------------------
% 6.91/2.26 % (19576)------------------------------
% 6.91/2.26 % (19581)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/458Mi)
% 6.91/2.27 % (19582)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19196 for (2993ds/31Mi)
% 6.91/2.27 % (19579)Instruction limit reached!
% 6.91/2.27 % (19579)------------------------------
% 6.91/2.27 % (19579)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.27 % (19579)Termination reason: Unknown
% 6.91/2.27 % (19579)Termination phase: Function definition elimination
% 6.91/2.27
% 6.91/2.27 % (19579)Memory used [KB]: 2302
% 6.91/2.27 % (19579)Time elapsed: 0.028 s
% 6.91/2.27 % (19579)Instructions burned: 91 (million)
% 6.91/2.27 % (19579)------------------------------
% 6.91/2.27 % (19579)------------------------------
% 6.91/2.28 % (19582)Instruction limit reached!
% 6.91/2.28 % (19582)------------------------------
% 6.91/2.28 % (19582)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.28 % (19582)Termination reason: Unknown
% 6.91/2.28 % (19582)Termination phase: Property scanning
% 6.91/2.28
% 6.91/2.28 % (19582)Memory used [KB]: 1918
% 6.91/2.28 % (19582)Time elapsed: 0.012 s
% 6.91/2.28 % (19582)Instructions burned: 32 (million)
% 6.91/2.28 % (19582)------------------------------
% 6.91/2.28 % (19582)------------------------------
% 6.91/2.28 % (19583)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/297Mi)
% 6.91/2.29 % (19578)Instruction limit reached!
% 6.91/2.29 % (19578)------------------------------
% 6.91/2.29 % (19578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.29 % (19578)Termination reason: Unknown
% 6.91/2.29 % (19578)Termination phase: Saturation
% 6.91/2.29
% 6.91/2.29 % (19578)Memory used [KB]: 7675
% 6.91/2.29 % (19578)Time elapsed: 0.076 s
% 6.91/2.29 % (19578)Instructions burned: 260 (million)
% 6.91/2.29 % (19578)------------------------------
% 6.91/2.29 % (19578)------------------------------
% 6.91/2.29 % (19584)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/987Mi)
% 6.91/2.29 % (19571)Instruction limit reached!
% 6.91/2.29 % (19571)------------------------------
% 6.91/2.29 % (19571)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.91/2.29 % (19571)Termination reason: Unknown
% 6.91/2.29 % (19571)Termination phase: Saturation
% 6.91/2.29
% 6.91/2.29 % (19571)Memory used [KB]: 8571
% 6.91/2.29 % (19571)Time elapsed: 0.172 s
% 6.91/2.29 % (19571)Instructions burned: 616 (million)
% 6.91/2.29 % (19571)------------------------------
% 6.91/2.29 % (19571)------------------------------
% 6.91/2.29 % (19585)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/182Mi)
% 7.73/2.30 % (19586)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/182Mi)
% 7.73/2.31 % (19553)Instruction limit reached!
% 7.73/2.31 % (19553)------------------------------
% 7.73/2.31 % (19553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.31 % (19553)Termination reason: Unknown
% 7.73/2.31 % (19553)Termination phase: Saturation
% 7.73/2.31
% 7.73/2.31 % (19553)Memory used [KB]: 7675
% 7.73/2.31 % (19553)Time elapsed: 0.354 s
% 7.73/2.31 % (19553)Instructions burned: 1089 (million)
% 7.73/2.31 % (19553)------------------------------
% 7.73/2.31 % (19553)------------------------------
% 7.73/2.32 % (19587)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/154Mi)
% 7.73/2.32 % (19580)Instruction limit reached!
% 7.73/2.32 % (19580)------------------------------
% 7.73/2.32 % (19580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.32 % (19580)Termination reason: Unknown
% 7.73/2.32 % (19580)Termination phase: Saturation
% 7.73/2.32
% 7.73/2.32 % (19580)Memory used [KB]: 7164
% 7.73/2.32 % (19580)Time elapsed: 0.066 s
% 7.73/2.32 % (19580)Instructions burned: 232 (million)
% 7.73/2.32 % (19580)------------------------------
% 7.73/2.32 % (19580)------------------------------
% 7.73/2.33 % (19588)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/79Mi)
% 7.73/2.34 % (19585)Instruction limit reached!
% 7.73/2.34 % (19585)------------------------------
% 7.73/2.34 % (19585)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.34 % (19585)Termination reason: Unknown
% 7.73/2.34 % (19585)Termination phase: Saturation
% 7.73/2.34
% 7.73/2.34 % (19585)Memory used [KB]: 7164
% 7.73/2.34 % (19585)Time elapsed: 0.051 s
% 7.73/2.34 % (19585)Instructions burned: 184 (million)
% 7.73/2.34 % (19585)------------------------------
% 7.73/2.34 % (19585)------------------------------
% 7.73/2.35 % (19589)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/216Mi)
% 7.73/2.36 % (19586)Instruction limit reached!
% 7.73/2.36 % (19586)------------------------------
% 7.73/2.36 % (19586)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.36 % (19586)Termination reason: Unknown
% 7.73/2.36 % (19586)Termination phase: Saturation
% 7.73/2.36
% 7.73/2.36 % (19586)Memory used [KB]: 7164
% 7.73/2.36 % (19586)Time elapsed: 0.055 s
% 7.73/2.36 % (19586)Instructions burned: 183 (million)
% 7.73/2.36 % (19586)------------------------------
% 7.73/2.36 % (19586)------------------------------
% 7.73/2.36 % (19588)Instruction limit reached!
% 7.73/2.36 % (19588)------------------------------
% 7.73/2.36 % (19588)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.36 % (19588)Termination reason: Unknown
% 7.73/2.36 % (19588)Termination phase: Property scanning
% 7.73/2.36
% 7.73/2.36 % (19588)Memory used [KB]: 2302
% 7.73/2.36 % (19588)Time elapsed: 0.027 s
% 7.73/2.36 % (19588)Instructions burned: 79 (million)
% 7.73/2.36 % (19588)------------------------------
% 7.73/2.36 % (19588)------------------------------
% 7.73/2.36 % (19587)Instruction limit reached!
% 7.73/2.36 % (19587)------------------------------
% 7.73/2.36 % (19587)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.36 % (19587)Termination reason: Unknown
% 7.73/2.36 % (19587)Termination phase: Property scanning
% 7.73/2.36
% 7.73/2.36 % (19587)Memory used [KB]: 2430
% 7.73/2.36 % (19587)Time elapsed: 0.041 s
% 7.73/2.36 % (19587)Instructions burned: 157 (million)
% 7.73/2.36 % (19587)------------------------------
% 7.73/2.36 % (19587)------------------------------
% 7.73/2.37 % (19590)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/114Mi)
% 7.73/2.37 % (19591)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/922Mi)
% 7.73/2.37 % (19592)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/182Mi)
% 7.73/2.37 % (19583)Instruction limit reached!
% 7.73/2.37 % (19583)------------------------------
% 7.73/2.37 % (19583)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.37 % (19583)Termination reason: Unknown
% 7.73/2.37 % (19583)Termination phase: Saturation
% 7.73/2.37
% 7.73/2.37 % (19583)Memory used [KB]: 7419
% 7.73/2.37 % (19583)Time elapsed: 0.090 s
% 7.73/2.37 % (19583)Instructions burned: 300 (million)
% 7.73/2.37 % (19583)------------------------------
% 7.73/2.37 % (19583)------------------------------
% 7.73/2.38 % (19593)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_19196 for (2992ds/164Mi)
% 7.73/2.39 % (19581)Instruction limit reached!
% 7.73/2.39 % (19581)------------------------------
% 7.73/2.39 % (19581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.73/2.39 % (19581)Termination reason: Unknown
% 7.73/2.39 % (19581)Termination phase: Saturation
% 7.73/2.39
% 7.73/2.39 % (19581)Memory used [KB]: 8187
% 7.73/2.39 % (19581)Time elapsed: 0.129 s
% 7.73/2.39 % (19581)Instructions burned: 458 (million)
% 7.73/2.39 % (19581)------------------------------
% 7.73/2.39 % (19581)------------------------------
% 8.27/2.40 % (19590)Instruction limit reached!
% 8.27/2.40 % (19590)------------------------------
% 8.27/2.40 % (19590)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.40 % (19590)Termination reason: Unknown
% 8.27/2.40 % (19590)Termination phase: Property scanning
% 8.27/2.40
% 8.27/2.40 % (19590)Memory used [KB]: 2302
% 8.27/2.40 % (19590)Time elapsed: 0.033 s
% 8.27/2.40 % (19590)Instructions burned: 115 (million)
% 8.27/2.40 % (19590)------------------------------
% 8.27/2.40 % (19590)------------------------------
% 8.27/2.40 % (19594)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/50Mi)
% 8.27/2.41 % (19595)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/368Mi)
% 8.27/2.41 % (19589)Instruction limit reached!
% 8.27/2.41 % (19589)------------------------------
% 8.27/2.41 % (19589)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.41 % (19589)Termination reason: Unknown
% 8.27/2.41 % (19589)Termination phase: Saturation
% 8.27/2.41
% 8.27/2.41 % (19589)Memory used [KB]: 7291
% 8.27/2.41 % (19589)Time elapsed: 0.059 s
% 8.27/2.41 % (19589)Instructions burned: 219 (million)
% 8.27/2.41 % (19589)------------------------------
% 8.27/2.41 % (19589)------------------------------
% 8.27/2.41 % (19594)Instruction limit reached!
% 8.27/2.41 % (19594)------------------------------
% 8.27/2.41 % (19594)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.41 % (19594)Termination reason: Unknown
% 8.27/2.41 % (19594)Termination phase: shuffling
% 8.27/2.41
% 8.27/2.41 % (19594)Memory used [KB]: 2302
% 8.27/2.41 % (19594)Time elapsed: 0.015 s
% 8.27/2.41 % (19594)Instructions burned: 51 (million)
% 8.27/2.41 % (19594)------------------------------
% 8.27/2.41 % (19594)------------------------------
% 8.27/2.41 % (19592)Instruction limit reached!
% 8.27/2.41 % (19592)------------------------------
% 8.27/2.41 % (19592)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.41 % (19592)Termination reason: Unknown
% 8.27/2.41 % (19592)Termination phase: Saturation
% 8.27/2.41
% 8.27/2.41 % (19592)Memory used [KB]: 7164
% 8.27/2.41 % (19592)Time elapsed: 0.048 s
% 8.27/2.41 % (19592)Instructions burned: 185 (million)
% 8.27/2.41 % (19592)------------------------------
% 8.27/2.41 % (19592)------------------------------
% 8.27/2.42 % (19596)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/1021Mi)
% 8.27/2.42 % (19597)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/267Mi)
% 8.27/2.42 % (19598)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/204Mi)
% 8.27/2.43 % (19593)Instruction limit reached!
% 8.27/2.43 % (19593)------------------------------
% 8.27/2.43 % (19593)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.43 % (19593)Termination reason: Unknown
% 8.27/2.43 % (19593)Termination phase: Saturation
% 8.27/2.43
% 8.27/2.43 % (19593)Memory used [KB]: 2558
% 8.27/2.43 % (19593)Time elapsed: 0.047 s
% 8.27/2.43 % (19593)Instructions burned: 166 (million)
% 8.27/2.43 % (19593)------------------------------
% 8.27/2.43 % (19593)------------------------------
% 8.27/2.44 % (19599)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/26Mi)
% 8.27/2.45 % (19599)Instruction limit reached!
% 8.27/2.45 % (19599)------------------------------
% 8.27/2.45 % (19599)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.45 % (19599)Termination reason: Unknown
% 8.27/2.45 % (19599)Termination phase: shuffling
% 8.27/2.45
% 8.27/2.45 % (19599)Memory used [KB]: 1918
% 8.27/2.45 % (19599)Time elapsed: 0.009 s
% 8.27/2.45 % (19599)Instructions burned: 27 (million)
% 8.27/2.45 % (19599)------------------------------
% 8.27/2.45 % (19599)------------------------------
% 8.27/2.46 % (19600)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/53Mi)
% 8.27/2.47 % (19600)Instruction limit reached!
% 8.27/2.47 % (19600)------------------------------
% 8.27/2.47 % (19600)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.47 % (19600)Termination reason: Unknown
% 8.27/2.47 % (19600)Termination phase: Property scanning
% 8.27/2.47
% 8.27/2.47 % (19600)Memory used [KB]: 2302
% 8.27/2.47 % (19600)Time elapsed: 0.016 s
% 8.27/2.47 % (19600)Instructions burned: 56 (million)
% 8.27/2.47 % (19600)------------------------------
% 8.27/2.47 % (19600)------------------------------
% 8.27/2.48 % (19601)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_19196 for (2991ds/4436Mi)
% 8.27/2.48 % (19598)Instruction limit reached!
% 8.27/2.48 % (19598)------------------------------
% 8.27/2.48 % (19598)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.27/2.48 % (19598)Termination reason: Unknown
% 8.27/2.48 % (19598)Termination phase: Saturation
% 8.27/2.48
% 8.27/2.48 % (19598)Memory used [KB]: 7036
% 8.27/2.48 % (19598)Time elapsed: 0.058 s
% 8.27/2.48 % (19598)Instructions burned: 205 (million)
% 8.27/2.48 % (19598)------------------------------
% 8.27/2.48 % (19598)------------------------------
% 8.27/2.49 % (19602)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_19196 for (2990ds/1539Mi)
% 8.62/2.50 % (19597)Instruction limit reached!
% 8.62/2.50 % (19597)------------------------------
% 8.62/2.50 % (19597)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.50 % (19597)Termination reason: Unknown
% 8.62/2.50 % (19597)Termination phase: Saturation
% 8.62/2.50
% 8.62/2.50 % (19597)Memory used [KB]: 7419
% 8.62/2.50 % (19597)Time elapsed: 0.073 s
% 8.62/2.50 % (19597)Instructions burned: 267 (million)
% 8.62/2.50 % (19597)------------------------------
% 8.62/2.50 % (19597)------------------------------
% 8.62/2.51 % (19603)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_19196 for (2990ds/408Mi)
% 8.62/2.51 % (19595)Instruction limit reached!
% 8.62/2.51 % (19595)------------------------------
% 8.62/2.51 % (19595)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.51 % (19595)Termination reason: Unknown
% 8.62/2.51 % (19595)Termination phase: Saturation
% 8.62/2.51
% 8.62/2.51 % (19595)Memory used [KB]: 7675
% 8.62/2.51 % (19595)Time elapsed: 0.103 s
% 8.62/2.51 % (19595)Instructions burned: 368 (million)
% 8.62/2.51 % (19595)------------------------------
% 8.62/2.51 % (19595)------------------------------
% 8.62/2.52 % (19604)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_19196 for (2990ds/5205Mi)
% 8.62/2.59 % (19584)Instruction limit reached!
% 8.62/2.59 % (19584)------------------------------
% 8.62/2.59 % (19584)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.62/2.59 % (19584)Termination reason: Unknown
% 8.62/2.59 % (19584)Termination phase: Saturation
% 8.62/2.59
% 8.62/2.59 % (19584)Memory used [KB]: 9850
% 8.62/2.59 % (19584)Time elapsed: 0.299 s
% 8.62/2.59 % (19584)Instructions burned: 987 (million)
% 8.62/2.59 % (19584)------------------------------
% 8.62/2.59 % (19584)------------------------------
% 9.12/2.60 % (19605)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_19196 for (2989ds/1913Mi)
% 9.12/2.63 % (19603)Instruction limit reached!
% 9.12/2.63 % (19603)------------------------------
% 9.12/2.63 % (19603)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.63 % (19603)Termination reason: Unknown
% 9.12/2.63 % (19603)Termination phase: Saturation
% 9.12/2.63
% 9.12/2.63 % (19603)Memory used [KB]: 8187
% 9.12/2.63 % (19603)Time elapsed: 0.126 s
% 9.12/2.63 % (19603)Instructions burned: 410 (million)
% 9.12/2.63 % (19603)------------------------------
% 9.12/2.63 % (19603)------------------------------
% 9.12/2.64 % (19606)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_19196 for (2989ds/4350Mi)
% 9.12/2.66 % (19606)Refutation not found, incomplete strategy
% 9.12/2.66 % (19606)------------------------------
% 9.12/2.66 % (19606)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.66 % (19606)Termination reason: Refutation not found, incomplete strategy
% 9.12/2.66
% 9.12/2.66
% 9.12/2.66 % (19606)Memory used [KB]: 6524
% 9.12/2.66 % (19606)Time elapsed: 0.018 s
% 9.12/2.66 % (19606)Instructions burned: 55 (million)
% 9.12/2.66 % (19606)------------------------------
% 9.12/2.66 % (19606)------------------------------
% 9.12/2.66 % (19591)Instruction limit reached!
% 9.12/2.66 % (19591)------------------------------
% 9.12/2.66 % (19591)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.66 % (19591)Termination reason: Unknown
% 9.12/2.66 % (19591)Termination phase: Saturation
% 9.12/2.66
% 9.12/2.66 % (19591)Memory used [KB]: 7547
% 9.12/2.66 % (19591)Time elapsed: 0.294 s
% 9.12/2.66 % (19591)Instructions burned: 922 (million)
% 9.12/2.66 % (19591)------------------------------
% 9.12/2.66 % (19591)------------------------------
% 9.12/2.67 % (19607)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_19196 for (2989ds/68Mi)
% 9.12/2.67 % (19608)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_19196 for (2989ds/358Mi)
% 9.12/2.69 % (19607)Instruction limit reached!
% 9.12/2.69 % (19607)------------------------------
% 9.12/2.69 % (19607)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.12/2.69 % (19607)Termination reason: Unknown
% 9.12/2.69 % (19607)Termination phase: Preprocessing 3
% 9.12/2.69
% 9.12/2.69 % (19607)Memory used [KB]: 2174
% 9.12/2.69 % (19607)Time elapsed: 0.022 s
% 9.12/2.69 % (19607)Instructions burned: 70 (million)
% 9.12/2.69 % (19607)------------------------------
% 9.12/2.69 % (19607)------------------------------
% 9.62/2.70 % (19609)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_19196 for (2988ds/31Mi)
% 9.62/2.71 % (19609)Instruction limit reached!
% 9.62/2.71 % (19609)------------------------------
% 9.62/2.71 % (19609)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.71 % (19609)Termination reason: Unknown
% 9.62/2.71 % (19609)Termination phase: Property scanning
% 9.62/2.71
% 9.62/2.71 % (19609)Memory used [KB]: 1918
% 9.62/2.71 % (19609)Time elapsed: 0.012 s
% 9.62/2.71 % (19609)Instructions burned: 31 (million)
% 9.62/2.71 % (19609)------------------------------
% 9.62/2.71 % (19609)------------------------------
% 9.62/2.72 % (19610)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_19196 for (2988ds/279Mi)
% 9.62/2.72 % (19596)Instruction limit reached!
% 9.62/2.72 % (19596)------------------------------
% 9.62/2.72 % (19596)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.72 % (19596)Termination reason: Unknown
% 9.62/2.72 % (19596)Termination phase: Saturation
% 9.62/2.72
% 9.62/2.72 % (19596)Memory used [KB]: 9338
% 9.62/2.72 % (19596)Time elapsed: 0.303 s
% 9.62/2.72 % (19596)Instructions burned: 1021 (million)
% 9.62/2.72 % (19596)------------------------------
% 9.62/2.72 % (19596)------------------------------
% 9.62/2.73 % (19611)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_19196 for (2988ds/258Mi)
% 9.62/2.76 % (19610)Refutation not found, incomplete strategy
% 9.62/2.76 % (19610)------------------------------
% 9.62/2.76 % (19610)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.76 % (19610)Termination reason: Refutation not found, incomplete strategy
% 9.62/2.76
% 9.62/2.76
% 9.62/2.76 % (19610)Memory used [KB]: 7036
% 9.62/2.76 % (19610)Time elapsed: 0.044 s
% 9.62/2.76 % (19610)Instructions burned: 161 (million)
% 9.62/2.76 % (19610)------------------------------
% 9.62/2.76 % (19610)------------------------------
% 9.62/2.77 % (19608)Instruction limit reached!
% 9.62/2.77 % (19608)------------------------------
% 9.62/2.77 % (19608)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.77 % (19608)Termination reason: Unknown
% 9.62/2.77 % (19608)Termination phase: Saturation
% 9.62/2.77
% 9.62/2.77 % (19608)Memory used [KB]: 7547
% 9.62/2.77 % (19608)Time elapsed: 0.100 s
% 9.62/2.77 % (19608)Instructions burned: 359 (million)
% 9.62/2.77 % (19608)------------------------------
% 9.62/2.77 % (19608)------------------------------
% 9.62/2.77 % (19612)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_19196 for (2988ds/26Mi)
% 9.62/2.78 % (19613)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_19196 for (2988ds/995Mi)
% 9.62/2.78 % (19612)Instruction limit reached!
% 9.62/2.78 % (19612)------------------------------
% 9.62/2.78 % (19612)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.62/2.78 % (19612)Termination reason: Unknown
% 9.62/2.78 % (19612)Termination phase: shuffling
% 9.62/2.78
% 9.62/2.78 % (19612)Memory used [KB]: 1791
% 9.62/2.78 % (19612)Time elapsed: 0.008 s
% 9.62/2.78 % (19612)Instructions burned: 26 (million)
% 9.62/2.78 % (19612)------------------------------
% 9.62/2.78 % (19612)------------------------------
% 9.62/2.79 % (19614)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_19196 for (2988ds/373Mi)
% 10.14/2.81 % (19611)Instruction limit reached!
% 10.14/2.81 % (19611)------------------------------
% 10.14/2.81 % (19611)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.81 % (19611)Termination reason: Unknown
% 10.14/2.81 % (19611)Termination phase: Saturation
% 10.14/2.81
% 10.14/2.81 % (19611)Memory used [KB]: 7547
% 10.14/2.81 % (19611)Time elapsed: 0.078 s
% 10.14/2.81 % (19611)Instructions burned: 260 (million)
% 10.14/2.81 % (19611)------------------------------
% 10.14/2.81 % (19611)------------------------------
% 10.14/2.82 % (19615)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_19196 for (2987ds/253Mi)
% 10.14/2.89 % (19615)Instruction limit reached!
% 10.14/2.89 % (19615)------------------------------
% 10.14/2.89 % (19615)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.89 % (19615)Termination reason: Unknown
% 10.14/2.89 % (19615)Termination phase: Saturation
% 10.14/2.89
% 10.14/2.89 % (19615)Memory used [KB]: 7419
% 10.14/2.89 % (19615)Time elapsed: 0.069 s
% 10.14/2.89 % (19615)Instructions burned: 254 (million)
% 10.14/2.89 % (19615)------------------------------
% 10.14/2.89 % (19615)------------------------------
% 10.14/2.89 % (19614)Instruction limit reached!
% 10.14/2.89 % (19614)------------------------------
% 10.14/2.89 % (19614)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.14/2.89 % (19614)Termination reason: Unknown
% 10.14/2.89 % (19614)Termination phase: Saturation
% 10.14/2.89
% 10.14/2.89 % (19614)Memory used [KB]: 7803
% 10.14/2.89 % (19614)Time elapsed: 0.108 s
% 10.14/2.89 % (19614)Instructions burned: 374 (million)
% 10.14/2.89 % (19614)------------------------------
% 10.14/2.89 % (19614)------------------------------
% 10.41/2.90 % (19616)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_19196 for (2986ds/832Mi)
% 10.41/2.90 % (19617)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_19196 for (2986ds/668Mi)
% 10.41/2.95 % (19602)Instruction limit reached!
% 10.41/2.95 % (19602)------------------------------
% 10.41/2.95 % (19602)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.41/2.95 % (19602)Termination reason: Unknown
% 10.41/2.95 % (19602)Termination phase: Saturation
% 10.41/2.95
% 10.41/2.95 % (19602)Memory used [KB]: 11129
% 10.41/2.95 % (19602)Time elapsed: 0.462 s
% 10.41/2.95 % (19602)Instructions burned: 1539 (million)
% 10.41/2.95 % (19602)------------------------------
% 10.41/2.95 % (19602)------------------------------
% 10.41/2.96 % (19618)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_19196 for (2986ds/40Mi)
% 10.41/2.97 % (19618)Instruction limit reached!
% 10.41/2.97 % (19618)------------------------------
% 10.41/2.97 % (19618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.41/2.97 % (19618)Termination reason: Unknown
% 10.41/2.97 % (19618)Termination phase: shuffling
% 10.41/2.97
% 10.41/2.97 % (19618)Memory used [KB]: 2174
% 10.41/2.97 % (19618)Time elapsed: 0.013 s
% 10.41/2.97 % (19618)Instructions burned: 43 (million)
% 10.41/2.97 % (19618)------------------------------
% 10.41/2.97 % (19618)------------------------------
% 10.41/2.98 % (19619)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_19196 for (2985ds/294Mi)
% 12.83/3.02 % (19619)Refutation not found, incomplete strategy
% 12.83/3.02 % (19619)------------------------------
% 12.83/3.02 % (19619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.02 % (19619)Termination reason: Refutation not found, incomplete strategy
% 12.83/3.02
% 12.83/3.02
% 12.83/3.02 % (19619)Memory used [KB]: 6908
% 12.83/3.02 % (19619)Time elapsed: 0.037 s
% 12.83/3.02 % (19619)Instructions burned: 138 (million)
% 12.83/3.02 % (19619)------------------------------
% 12.83/3.02 % (19619)------------------------------
% 12.83/3.03 % (19620)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_19196 for (2985ds/187Mi)
% 12.83/3.05 % (19613)Instruction limit reached!
% 12.83/3.05 % (19613)------------------------------
% 12.83/3.05 % (19613)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.05 % (19613)Termination reason: Unknown
% 12.83/3.05 % (19613)Termination phase: Saturation
% 12.83/3.05
% 12.83/3.05 % (19613)Memory used [KB]: 7931
% 12.83/3.05 % (19613)Time elapsed: 0.275 s
% 12.83/3.05 % (19613)Instructions burned: 997 (million)
% 12.83/3.05 % (19613)------------------------------
% 12.83/3.05 % (19613)------------------------------
% 12.83/3.06 % (19621)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_19196 for (2985ds/371Mi)
% 12.83/3.08 % (19620)Instruction limit reached!
% 12.83/3.08 % (19620)------------------------------
% 12.83/3.08 % (19620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.08 % (19620)Termination reason: Unknown
% 12.83/3.08 % (19620)Termination phase: Saturation
% 12.83/3.08
% 12.83/3.08 % (19620)Memory used [KB]: 6908
% 12.83/3.08 % (19620)Time elapsed: 0.052 s
% 12.83/3.08 % (19620)Instructions burned: 187 (million)
% 12.83/3.08 % (19620)------------------------------
% 12.83/3.08 % (19620)------------------------------
% 12.83/3.09 % (19622)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_19196 for (2984ds/1827Mi)
% 13.47/3.15 % (19617)Instruction limit reached!
% 13.47/3.15 % (19617)------------------------------
% 13.47/3.15 % (19617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.15 % (19617)Termination reason: Unknown
% 13.47/3.15 % (19617)Termination phase: Saturation
% 13.47/3.15
% 13.47/3.15 % (19617)Memory used [KB]: 13048
% 13.47/3.15 % (19617)Time elapsed: 0.243 s
% 13.47/3.15 % (19617)Instructions burned: 668 (million)
% 13.47/3.15 % (19617)------------------------------
% 13.47/3.15 % (19617)------------------------------
% 13.47/3.15 % (19616)Instruction limit reached!
% 13.47/3.15 % (19616)------------------------------
% 13.47/3.15 % (19616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.15 % (19616)Termination reason: Unknown
% 13.47/3.15 % (19616)Termination phase: Saturation
% 13.47/3.15
% 13.47/3.15 % (19616)Memory used [KB]: 8187
% 13.47/3.15 % (19616)Time elapsed: 0.280 s
% 13.47/3.15 % (19616)Instructions burned: 832 (million)
% 13.47/3.15 % (19616)------------------------------
% 13.47/3.15 % (19616)------------------------------
% 13.47/3.16 % (19623)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_19196 for (2984ds/70Mi)
% 13.47/3.16 % (19624)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_19196 for (2984ds/316Mi)
% 13.47/3.17 % (19605)Instruction limit reached!
% 13.47/3.17 % (19605)------------------------------
% 13.47/3.17 % (19605)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.17 % (19605)Termination reason: Unknown
% 13.47/3.17 % (19605)Termination phase: Saturation
% 13.47/3.17
% 13.47/3.17 % (19605)Memory used [KB]: 6012
% 13.47/3.17 % (19605)Time elapsed: 0.571 s
% 13.47/3.17 % (19605)Instructions burned: 1913 (million)
% 13.47/3.17 % (19605)------------------------------
% 13.47/3.17 % (19605)------------------------------
% 13.47/3.18 % (19623)Instruction limit reached!
% 13.47/3.18 % (19623)------------------------------
% 13.47/3.18 % (19623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.18 % (19623)Termination reason: Unknown
% 13.47/3.18 % (19623)Termination phase: Property scanning
% 13.47/3.18
% 13.47/3.18 % (19623)Memory used [KB]: 2302
% 13.47/3.18 % (19623)Time elapsed: 0.022 s
% 13.47/3.18 % (19623)Instructions burned: 70 (million)
% 13.47/3.18 % (19623)------------------------------
% 13.47/3.18 % (19623)------------------------------
% 13.47/3.18 % (19625)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_19196 for (2984ds/932Mi)
% 13.47/3.18 % (19621)Instruction limit reached!
% 13.47/3.18 % (19621)------------------------------
% 13.47/3.18 % (19621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.47/3.18 % (19621)Termination reason: Unknown
% 13.47/3.18 % (19621)Termination phase: Saturation
% 13.47/3.18
% 13.47/3.18 % (19621)Memory used [KB]: 7036
% 13.47/3.18 % (19621)Time elapsed: 0.121 s
% 13.47/3.18 % (19621)Instructions burned: 374 (million)
% 13.47/3.18 % (19621)------------------------------
% 13.47/3.18 % (19621)------------------------------
% 13.47/3.19 % (19626)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_19196 for (2984ds/4714Mi)
% 13.47/3.19 % (19627)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_19196 for (2984ds/8250Mi)
% 13.96/3.23 % (19624)Refutation not found, incomplete strategy
% 13.96/3.23 % (19624)------------------------------
% 13.96/3.23 % (19624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.23 % (19624)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.23
% 13.96/3.23
% 13.96/3.23 % (19624)Memory used [KB]: 7547
% 13.96/3.23 % (19624)Time elapsed: 0.070 s
% 13.96/3.23 % (19624)Instructions burned: 263 (million)
% 13.96/3.23 % (19624)------------------------------
% 13.96/3.23 % (19624)------------------------------
% 13.96/3.24 % (19628)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_19196 for (2983ds/770Mi)
% 13.96/3.26 % (19628)Refutation not found, incomplete strategy
% 13.96/3.26 % (19628)------------------------------
% 13.96/3.26 % (19628)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.26 % (19628)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.26
% 13.96/3.26
% 13.96/3.26 % (19628)Memory used [KB]: 6524
% 13.96/3.26 % (19628)Time elapsed: 0.018 s
% 13.96/3.26 % (19628)Instructions burned: 54 (million)
% 13.96/3.26 % (19628)------------------------------
% 13.96/3.26 % (19628)------------------------------
% 13.96/3.27 % (19626)Refutation not found, incomplete strategy
% 13.96/3.27 % (19626)------------------------------
% 13.96/3.27 % (19626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.96/3.27 % (19626)Termination reason: Refutation not found, incomplete strategy
% 13.96/3.27
% 13.96/3.27
% 13.96/3.27 % (19626)Memory used [KB]: 7675
% 13.96/3.27 % (19626)Time elapsed: 0.082 s
% 13.96/3.27 % (19626)Instructions burned: 280 (million)
% 13.96/3.27 % (19626)------------------------------
% 13.96/3.27 % (19626)------------------------------
% 13.96/3.27 % (19629)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_19196 for (2983ds/794Mi)
% 13.96/3.28 % (19630)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_19196 for (2983ds/464Mi)
% 14.56/3.41 % (19630)Instruction limit reached!
% 14.56/3.41 % (19630)------------------------------
% 14.56/3.41 % (19630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.56/3.41 % (19630)Termination reason: Unknown
% 14.56/3.41 % (19630)Termination phase: Saturation
% 14.56/3.41
% 14.56/3.41 % (19630)Memory used [KB]: 7803
% 14.56/3.41 % (19630)Time elapsed: 0.138 s
% 14.56/3.41 % (19630)Instructions burned: 464 (million)
% 14.56/3.41 % (19630)------------------------------
% 14.56/3.41 % (19630)------------------------------
% 14.56/3.43 % (19632)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_19196 for (2981ds/1376Mi)
% 14.56/3.45 % (19625)Instruction limit reached!
% 14.56/3.45 % (19625)------------------------------
% 14.56/3.45 % (19625)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.56/3.45 % (19625)Termination reason: Unknown
% 14.56/3.45 % (19625)Termination phase: Saturation
% 14.56/3.45
% 14.56/3.45 % (19625)Memory used [KB]: 9722
% 14.56/3.45 % (19625)Time elapsed: 0.271 s
% 14.56/3.45 % (19625)Instructions burned: 933 (million)
% 14.56/3.45 % (19625)------------------------------
% 14.56/3.45 % (19625)------------------------------
% 14.56/3.46 % (19633)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_19196 for (2981ds/906Mi)
% 15.19/3.50 % (19622)Instruction limit reached!
% 15.19/3.50 % (19622)------------------------------
% 15.19/3.50 % (19622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.50 % (19622)Termination reason: Unknown
% 15.19/3.50 % (19622)Termination phase: Saturation
% 15.19/3.50
% 15.19/3.50 % (19622)Memory used [KB]: 7931
% 15.19/3.50 % (19622)Time elapsed: 0.408 s
% 15.19/3.50 % (19622)Instructions burned: 1831 (million)
% 15.19/3.50 % (19622)------------------------------
% 15.19/3.50 % (19622)------------------------------
% 15.19/3.51 % (19634)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_19196 for (2980ds/434Mi)
% 15.19/3.51 % (19629)Instruction limit reached!
% 15.19/3.51 % (19629)------------------------------
% 15.19/3.51 % (19629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.51 % (19629)Termination reason: Unknown
% 15.19/3.51 % (19629)Termination phase: Saturation
% 15.19/3.51
% 15.19/3.51 % (19629)Memory used [KB]: 5245
% 15.19/3.51 % (19629)Time elapsed: 0.237 s
% 15.19/3.51 % (19629)Instructions burned: 797 (million)
% 15.19/3.51 % (19629)------------------------------
% 15.19/3.51 % (19629)------------------------------
% 15.19/3.52 % (19635)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_19196 for (2980ds/865Mi)
% 15.19/3.53 % (19634)Refutation not found, incomplete strategy
% 15.19/3.53 % (19634)------------------------------
% 15.19/3.53 % (19634)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 15.19/3.53 % (19634)Termination reason: Refutation not found, incomplete strategy
% 15.19/3.53
% 15.19/3.53
% 15.19/3.53 % (19634)Memory used [KB]: 6524
% 15.19/3.53 % (19634)Time elapsed: 0.020 s
% 15.19/3.53 % (19634)Instructions burned: 60 (million)
% 15.19/3.53 % (19634)------------------------------
% 15.19/3.53 % (19634)------------------------------
% 15.19/3.54 % (19636)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_19196 for (2980ds/593Mi)
% 16.29/3.70 % (19636)Instruction limit reached!
% 16.29/3.70 % (19636)------------------------------
% 16.29/3.70 % (19636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.70 % (19636)Termination reason: Unknown
% 16.29/3.70 % (19636)Termination phase: Saturation
% 16.29/3.70
% 16.29/3.70 % (19636)Memory used [KB]: 7803
% 16.29/3.70 % (19636)Time elapsed: 0.167 s
% 16.29/3.70 % (19636)Instructions burned: 594 (million)
% 16.29/3.70 % (19636)------------------------------
% 16.29/3.70 % (19636)------------------------------
% 16.29/3.71 % (19637)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_19196 for (2978ds/443Mi)
% 16.29/3.76 % (19633)Instruction limit reached!
% 16.29/3.76 % (19633)------------------------------
% 16.29/3.76 % (19633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.76 % (19633)Termination reason: Unknown
% 16.29/3.76 % (19633)Termination phase: Saturation
% 16.29/3.76
% 16.29/3.76 % (19633)Memory used [KB]: 12281
% 16.29/3.76 % (19633)Time elapsed: 0.303 s
% 16.29/3.76 % (19633)Instructions burned: 907 (million)
% 16.29/3.76 % (19633)------------------------------
% 16.29/3.76 % (19633)------------------------------
% 16.29/3.77 % (19638)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_19196 for (2978ds/594Mi)
% 16.29/3.78 % (19635)Instruction limit reached!
% 16.29/3.78 % (19635)------------------------------
% 16.29/3.78 % (19635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 16.29/3.78 % (19635)Termination reason: Unknown
% 16.29/3.78 % (19635)Termination phase: Saturation
% 16.29/3.78
% 16.29/3.78 % (19635)Memory used [KB]: 8315
% 16.29/3.78 % (19635)Time elapsed: 0.262 s
% 16.29/3.78 % (19635)Instructions burned: 868 (million)
% 16.29/3.78 % (19635)------------------------------
% 16.29/3.78 % (19635)------------------------------
% 16.29/3.79 % (19639)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_19196 for (2978ds/327Mi)
% 17.24/3.84 % (19637)Instruction limit reached!
% 17.24/3.84 % (19637)------------------------------
% 17.24/3.84 % (19637)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.84 % (19637)Termination reason: Unknown
% 17.24/3.84 % (19637)Termination phase: Saturation
% 17.24/3.84
% 17.24/3.84 % (19637)Memory used [KB]: 7803
% 17.24/3.84 % (19637)Time elapsed: 0.126 s
% 17.24/3.84 % (19637)Instructions burned: 445 (million)
% 17.24/3.84 % (19637)------------------------------
% 17.24/3.84 % (19637)------------------------------
% 17.24/3.84 % (19632)Instruction limit reached!
% 17.24/3.84 % (19632)------------------------------
% 17.24/3.84 % (19632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.84 % (19632)Termination reason: Unknown
% 17.24/3.84 % (19632)Termination phase: Saturation
% 17.24/3.84
% 17.24/3.84 % (19632)Memory used [KB]: 13944
% 17.24/3.84 % (19632)Time elapsed: 0.418 s
% 17.24/3.84 % (19632)Instructions burned: 1378 (million)
% 17.24/3.84 % (19632)------------------------------
% 17.24/3.84 % (19632)------------------------------
% 17.24/3.85 % (19640)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_19196 for (2977ds/5411Mi)
% 17.24/3.85 % (19641)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_19196 for (2977ds/1762Mi)
% 17.24/3.86 % (19601)Instruction limit reached!
% 17.24/3.86 % (19601)------------------------------
% 17.24/3.86 % (19601)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.86 % (19601)Termination reason: Unknown
% 17.24/3.86 % (19601)Termination phase: Saturation
% 17.24/3.86
% 17.24/3.86 % (19601)Memory used [KB]: 9466
% 17.24/3.86 % (19601)Time elapsed: 1.384 s
% 17.24/3.86 % (19601)Instructions burned: 4436 (million)
% 17.24/3.86 % (19601)------------------------------
% 17.24/3.86 % (19601)------------------------------
% 17.24/3.87 % (19640)Refutation not found, incomplete strategy
% 17.24/3.87 % (19640)------------------------------
% 17.24/3.87 % (19640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.87 % (19640)Termination reason: Refutation not found, incomplete strategy
% 17.24/3.87
% 17.24/3.87
% 17.24/3.87 % (19640)Memory used [KB]: 6524
% 17.24/3.87 % (19640)Time elapsed: 0.019 s
% 17.24/3.87 % (19640)Instructions burned: 59 (million)
% 17.24/3.87 % (19640)------------------------------
% 17.24/3.87 % (19640)------------------------------
% 17.24/3.87 % (19642)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_19196 for (2977ds/96Mi)
% 17.24/3.88 % (19643)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_19196 for (2977ds/503Mi)
% 17.24/3.88 % (19639)Instruction limit reached!
% 17.24/3.88 % (19639)------------------------------
% 17.24/3.88 % (19639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.88 % (19639)Termination reason: Unknown
% 17.24/3.88 % (19639)Termination phase: Saturation
% 17.24/3.88
% 17.24/3.88 % (19639)Memory used [KB]: 7419
% 17.24/3.88 % (19639)Time elapsed: 0.098 s
% 17.24/3.88 % (19639)Instructions burned: 327 (million)
% 17.24/3.88 % (19639)------------------------------
% 17.24/3.88 % (19639)------------------------------
% 17.24/3.89 % (19643)Refutation not found, incomplete strategy
% 17.24/3.89 % (19643)------------------------------
% 17.24/3.89 % (19643)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.24/3.89 % (19643)Termination reason: Refutation not found, incomplete strategy
% 17.24/3.89
% 17.24/3.89
% 17.24/3.89 % (19643)Memory used [KB]: 6524
% 17.24/3.89 % (19643)Time elapsed: 0.019 s
% 17.24/3.89 % (19643)Instructions burned: 59 (million)
% 17.24/3.89 % (19643)------------------------------
% 17.24/3.89 % (19643)------------------------------
% 17.24/3.89 % (19644)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_19196 for (2976ds/90Mi)
% 18.14/3.90 % (19642)Instruction limit reached!
% 18.14/3.90 % (19642)------------------------------
% 18.14/3.90 % (19642)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.90 % (19642)Termination reason: Unknown
% 18.14/3.90 % (19642)Termination phase: Property scanning
% 18.14/3.90
% 18.14/3.90 % (19642)Memory used [KB]: 2302
% 18.14/3.90 % (19642)Time elapsed: 0.027 s
% 18.14/3.90 % (19642)Instructions burned: 98 (million)
% 18.14/3.90 % (19642)------------------------------
% 18.14/3.90 % (19642)------------------------------
% 18.14/3.90 % (19645)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_19196 for (2976ds/593Mi)
% 18.14/3.91 % (19646)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_19196 for (2976ds/1512Mi)
% 18.14/3.92 % (19644)Instruction limit reached!
% 18.14/3.92 % (19644)------------------------------
% 18.14/3.92 % (19644)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.92 % (19644)Termination reason: Unknown
% 18.14/3.92 % (19644)Termination phase: Function definition elimination
% 18.14/3.92
% 18.14/3.92 % (19644)Memory used [KB]: 2302
% 18.14/3.92 % (19644)Time elapsed: 0.028 s
% 18.14/3.92 % (19644)Instructions burned: 91 (million)
% 18.14/3.92 % (19644)------------------------------
% 18.14/3.92 % (19644)------------------------------
% 18.14/3.93 % (19647)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_19196 for (2976ds/569Mi)
% 18.14/3.95 % (19638)Instruction limit reached!
% 18.14/3.95 % (19638)------------------------------
% 18.14/3.95 % (19638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.14/3.95 % (19638)Termination reason: Unknown
% 18.14/3.95 % (19638)Termination phase: Saturation
% 18.14/3.95
% 18.14/3.95 % (19638)Memory used [KB]: 7803
% 18.14/3.95 % (19638)Time elapsed: 0.199 s
% 18.14/3.95 % (19638)Instructions burned: 594 (million)
% 18.14/3.95 % (19638)------------------------------
% 18.14/3.95 % (19638)------------------------------
% 18.14/3.96 % (19648)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_19196 for (2976ds/501Mi)
% 19.92/4.03 % (19604)Instruction limit reached!
% 19.92/4.03 % (19604)------------------------------
% 19.92/4.03 % (19604)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.92/4.03 % (19604)Termination reason: Unknown
% 19.92/4.03 % (19604)Termination phase: Saturation
% 19.92/4.03
% 19.92/4.03 % (19604)Memory used [KB]: 15863
% 19.92/4.03 % (19604)Time elapsed: 1.514 s
% 19.92/4.03 % (19604)Instructions burned: 5207 (million)
% 19.92/4.03 % (19604)------------------------------
% 19.92/4.03 % (19604)------------------------------
% 19.92/4.04 % (19649)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_19196 for (2975ds/562Mi)
% 19.92/4.07 % (19645)Instruction limit reached!
% 19.92/4.07 % (19645)------------------------------
% 19.92/4.07 % (19645)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.92/4.07 % (19645)Termination reason: Unknown
% 19.92/4.07 % (19645)Termination phase: Saturation
% 19.92/4.07
% 19.92/4.07 % (19645)Memory used [KB]: 8571
% 19.92/4.07 % (19645)Time elapsed: 0.164 s
% 19.92/4.07 % (19645)Instructions burned: 593 (million)
% 19.92/4.07 % (19645)------------------------------
% 19.92/4.07 % (19645)------------------------------
% 19.92/4.08 % (19650)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_19196 for (2975ds/406Mi)
% 19.92/4.09 % (19647)Instruction limit reached!
% 19.92/4.09 % (19647)------------------------------
% 19.92/4.09 % (19647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.92/4.09 % (19647)Termination reason: Unknown
% 19.92/4.09 % (19647)Termination phase: Saturation
% 19.92/4.09
% 19.92/4.09 % (19647)Memory used [KB]: 7931
% 19.92/4.09 % (19647)Time elapsed: 0.159 s
% 19.92/4.09 % (19647)Instructions burned: 570 (million)
% 19.92/4.09 % (19647)------------------------------
% 19.92/4.09 % (19647)------------------------------
% 19.92/4.10 % (19651)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_19196 for (2974ds/582Mi)
% 19.92/4.11 % (19648)Instruction limit reached!
% 19.92/4.11 % (19648)------------------------------
% 19.92/4.11 % (19648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.92/4.11 % (19648)Termination reason: Unknown
% 19.92/4.11 % (19648)Termination phase: Saturation
% 19.92/4.11
% 19.92/4.11 % (19648)Memory used [KB]: 8315
% 19.92/4.11 % (19648)Time elapsed: 0.150 s
% 19.92/4.11 % (19648)Instructions burned: 502 (million)
% 19.92/4.11 % (19648)------------------------------
% 19.92/4.11 % (19648)------------------------------
% 19.92/4.12 % (19652)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_19196 for (2974ds/456Mi)
% 19.92/4.12 % (19627)First to succeed.
% 20.49/4.13 % (19627)Refutation found. Thanks to Tanya!
% 20.49/4.13 % SZS status Theorem for DTF2THF_19196
% 20.49/4.13 % SZS output start Proof for DTF2THF_19196
% 20.49/4.13 thf(type_def_5, type, secrecy_specID: $tType).
% 20.49/4.13 thf(type_def_6, type, secrecy_KS: $tType).
% 20.49/4.13 thf(type_def_7, type, set: ($tType) > $tType).
% 20.49/4.13 thf(type_def_9, type, list: ($tType) > $tType).
% 20.49/4.13 thf(type_def_10, type, secrecy_Expression: $tType).
% 20.49/4.13 thf(type_def_11, type, secrecy_chanID: $tType).
% 20.49/4.13 thf(type_def_12, type, secrecy_Keys: $tType).
% 20.49/4.13 thf(type_def_13, type, secrecy_Secrets: $tType).
% 20.49/4.13 thf(type_def_14, type, nat: $tType).
% 20.49/4.13 thf(func_def_0, type, secrecy_Expression: $tType).
% 20.49/4.13 thf(func_def_1, type, secrecy_Secrets: $tType).
% 20.49/4.13 thf(func_def_2, type, secrecy_specID: $tType).
% 20.49/4.13 thf(func_def_3, type, secrecy_chanID: $tType).
% 20.49/4.13 thf(func_def_4, type, secrecy_Keys: $tType).
% 20.49/4.13 thf(func_def_5, type, secrecy_KS: $tType).
% 20.49/4.13 thf(func_def_6, type, list: ($tType) > $tType).
% 20.49/4.13 thf(func_def_7, type, set: ($tType) > $tType).
% 20.49/4.13 thf(func_def_8, type, nat: $tType).
% 20.49/4.13 thf(func_def_9, type, bounded_lattice: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_12, type, ord: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_16, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 20.49/4.13 thf(func_def_17, type, localSecrets: secrecy_specID > set @ secrecy_KS).
% 20.49/4.13 thf(func_def_18, type, knowle1667810483orrect: secrecy_specID > secrecy_KS > $o).
% 20.49/4.13 thf(func_def_19, type, knowle1437066798e_know: secrecy_specID > secrecy_KS > $o).
% 20.49/4.13 thf(func_def_20, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 20.49/4.13 thf(func_def_21, type, mem: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 20.49/4.13 thf(func_def_22, type, bot_bot: !>[X0: $tType]:(X0)).
% 20.49/4.13 thf(func_def_23, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 20.49/4.13 thf(func_def_24, type, correctCompositionKS: secrecy_specID > $o).
% 20.49/4.13 thf(func_def_25, type, eout: secrecy_specID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_26, type, eoutM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_27, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_28, type, ine: secrecy_specID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_29, type, ineM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_30, type, ine_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_31, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_32, type, notSpe1586871396tsExpr: secrecy_specID > list @ secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_33, type, out_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_34, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 20.49/4.13 thf(func_def_35, type, specKeys: secrecy_specID > set @ secrecy_Keys).
% 20.49/4.13 thf(func_def_36, type, specKeysSecrets: secrecy_specID > set @ secrecy_KS).
% 20.49/4.13 thf(func_def_37, type, specSecrets: secrecy_specID > set @ secrecy_Secrets).
% 20.49/4.13 thf(func_def_38, type, secrec487562139ession: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > (nat > X0) > (secrecy_specID > X0) > secrecy_Expression > X0)).
% 20.49/4.13 thf(func_def_39, type, secrecy_dE: nat > secrecy_Expression).
% 20.49/4.13 thf(func_def_40, type, secrecy_idE: secrecy_specID > secrecy_Expression).
% 20.49/4.13 thf(func_def_41, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 20.49/4.13 thf(func_def_42, type, secrec1231112373ession: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > (nat > X0) > (secrecy_specID > X0) > secrecy_Expression > X0)).
% 20.49/4.13 thf(func_def_43, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 20.49/4.13 thf(func_def_44, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 20.49/4.13 thf(func_def_45, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 20.49/4.13 thf(func_def_46, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 20.49/4.13 thf(func_def_47, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 20.49/4.13 thf(func_def_48, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 20.49/4.13 thf(func_def_49, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 20.49/4.13 thf(func_def_50, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 20.49/4.13 thf(func_def_51, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_52, type, correctCompositionIn: secrecy_specID > $o).
% 20.49/4.13 thf(func_def_53, type, correc965049635ionLoc: secrecy_specID > $o).
% 20.49/4.13 thf(func_def_54, type, correc990227761ionOut: secrecy_specID > $o).
% 20.49/4.13 thf(func_def_55, type, inStream: secrecy_specID > set @ secrecy_chanID > $o).
% 20.49/4.13 thf(func_def_56, type, ins: secrecy_specID > set @ secrecy_chanID).
% 20.49/4.13 thf(func_def_57, type, loc: secrecy_specID > set @ secrecy_chanID).
% 20.49/4.13 thf(func_def_58, type, locStream: secrecy_specID > set @ secrecy_chanID > $o).
% 20.49/4.13 thf(func_def_59, type, out: secrecy_specID > set @ secrecy_chanID).
% 20.49/4.13 thf(func_def_60, type, outStream: secrecy_specID > set @ secrecy_chanID > $o).
% 20.49/4.13 thf(func_def_61, type, subcomponents: secrecy_specID > set @ secrecy_specID).
% 20.49/4.13 thf(func_def_62, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 20.49/4.13 thf(func_def_63, type, p: secrecy_specID).
% 20.49/4.13 thf(func_def_64, type, pq: secrecy_specID).
% 20.49/4.13 thf(func_def_65, type, q: secrecy_specID).
% 20.49/4.13 thf(func_def_66, type, key: secrecy_Keys).
% 20.49/4.13 thf(func_def_81, type, sP0: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > $o)).
% 20.49/4.13 thf(func_def_82, type, sP1: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > $o)).
% 20.49/4.13 thf(func_def_83, type, sP2: !>[X0: $tType]:(X0 > set @ X0 > set @ X0 > $o)).
% 20.49/4.13 thf(func_def_84, type, sP3: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 20.49/4.13 thf(func_def_85, type, sP4: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 20.49/4.13 thf(func_def_86, type, sP5: !>[X0: $tType]:(X0 > X0 > X0 > $o)).
% 20.49/4.13 thf(func_def_87, type, sP6: !>[X0: $tType]:(set @ X0 > X0 > set @ X0 > $o)).
% 20.49/4.13 thf(func_def_88, type, sK7: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.49/4.13 thf(func_def_89, type, sK8: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.49/4.13 thf(func_def_90, type, sK9: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_91, type, sK10: !>[X0: $tType]:((X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_92, type, sK11: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_93, type, sK12: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_94, type, sK13: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_95, type, sK14: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_96, type, sK15: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_97, type, sK16: !>[X0: $tType]:(set @ X0 > set @ X0 > X0 > X0 > set @ X0)).
% 20.49/4.13 thf(func_def_98, type, sK17: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 20.49/4.13 thf(func_def_99, type, sK18: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_100, type, sK19: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_101, type, sK20: secrecy_Secrets > secrecy_specID > secrecy_specID).
% 20.49/4.13 thf(func_def_102, type, sK21: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_103, type, sK22: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 20.49/4.13 thf(func_def_104, type, sK23: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_105, type, sK24: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_106, type, sK25: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_107, type, sK26: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_108, type, sK27: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_109, type, sK28: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_110, type, sK29: secrecy_Keys > secrecy_specID > secrecy_specID).
% 20.49/4.13 thf(func_def_111, type, sK30: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_112, type, sK31: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_113, type, sK32: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_114, type, sK33: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_115, type, sK34: !>[X0: $tType]:((X0 > $o) > set @ X0 > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_116, type, sK35: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_117, type, sK36: !>[X0: $tType]:((X0 > $o) > set @ X0 > X0)).
% 20.49/4.13 thf(func_def_118, type, sK37: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_119, type, sK38: secrecy_KS > secrecy_Keys).
% 20.49/4.13 thf(func_def_120, type, sK39: secrecy_KS > secrecy_Secrets).
% 20.49/4.13 thf(func_def_121, type, sK40: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 20.49/4.13 thf(func_def_122, type, sK41: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 20.49/4.13 thf(func_def_123, type, sK42: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 20.49/4.13 thf(func_def_124, type, sK43: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 20.49/4.13 thf(func_def_125, type, sK44: !>[X0: $tType]:(set @ X0 > X0)).
% 20.49/4.13 thf(func_def_126, type, sK45: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_127, type, sK46: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_128, type, sK47: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_129, type, sK48: !>[X0: $tType]:((X0 > X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_130, type, sK49: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.49/4.13 thf(func_def_131, type, sK50: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.49/4.13 thf(func_def_132, type, sK51: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_133, type, sK52: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_134, type, sK53: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 20.49/4.13 thf(func_def_135, type, sK54: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_136, type, sK55: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_137, type, sK56: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_138, type, sK57: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.49/4.13 thf(func_def_139, type, sK58: !>[X0: $tType, X1: $tType]:((X1 > X0) > X1)).
% 20.49/4.13 thf(func_def_140, type, sK59: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.49/4.13 thf(func_def_141, type, sK60: !>[X0: $tType, X1: $tType]:((X0 > X1) > X0)).
% 20.49/4.13 thf(func_def_142, type, sK61: (secrecy_KS > $o) > secrecy_Keys).
% 20.49/4.13 thf(func_def_143, type, sK62: (secrecy_KS > $o) > secrecy_Secrets).
% 20.49/4.13 thf(func_def_144, type, sK63: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_145, type, sK64: !>[X0: $tType]:((X0 > $o) > X0)).
% 20.49/4.13 thf(func_def_146, type, sK65: (secrecy_Expression > $o) > secrecy_Keys).
% 20.49/4.13 thf(func_def_147, type, sK66: (secrecy_Expression > $o) > secrecy_specID).
% 20.49/4.13 thf(func_def_148, type, sK67: (secrecy_Expression > $o) > secrecy_Secrets).
% 20.49/4.13 thf(func_def_149, type, sK68: (secrecy_Expression > $o) > nat).
% 20.49/4.13 thf(func_def_150, type, sK69: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_151, type, sK70: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 20.49/4.13 thf(func_def_152, type, sK71: secrecy_Expression > nat).
% 20.49/4.13 thf(func_def_153, type, sK72: secrecy_Expression > secrecy_Keys).
% 20.49/4.13 thf(func_def_154, type, sK73: secrecy_Expression > secrecy_specID).
% 20.49/4.13 thf(func_def_155, type, sK74: secrecy_Expression > secrecy_Secrets).
% 20.49/4.13 thf(func_def_156, type, sK75: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_157, type, sK76: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 20.49/4.13 thf(func_def_158, type, sK77: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 20.49/4.13 thf(func_def_159, type, sK78: set @ secrecy_chanID > secrecy_specID > secrecy_chanID).
% 20.49/4.13 thf(func_def_161, type, ph80: !>[X0: $tType]:(X0)).
% 20.49/4.13 thf(f5903,plain,(
% 20.49/4.13 $false),
% 20.49/4.13 inference(avatar_sat_refutation,[status(thm)],[f5831,f5858,f5902])).
% 20.49/4.13 thf(f5902,plain,(
% 20.49/4.13 ~spl79_60),
% 20.49/4.13 inference(avatar_contradiction_clause,[status(thm)],[f5901])).
% 20.49/4.13 thf(f5901,plain,(
% 20.49/4.13 $false | ~spl79_60),
% 20.49/4.13 inference(subsumption_resolution,[status(thm)],[f5900,f1678])).
% 20.49/4.13 thf(f1678,plain,(
% 20.49/4.13 ((knowle1437066798e_know @ p @ (secrecy_kKS @ key)) != $true)),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f801])).
% 20.49/4.13 thf(f801,plain,(
% 20.49/4.13 ((knowle1437066798e_know @ p @ (secrecy_kKS @ key)) != $true)),
% 20.49/4.13 inference(flattening,[status(thm)],[f405])).
% 20.49/4.13 thf(f405,plain,(
% 20.49/4.13 ~((knowle1437066798e_know @ p @ (secrecy_kKS @ key)) = $true)),
% 20.49/4.13 inference(fool_elimination,[status(thm)],[f404])).
% 20.49/4.13 thf(f404,plain,(
% 20.49/4.13 ~(knowle1437066798e_know @ p @ (secrecy_kKS @ key))),
% 20.49/4.13 inference(rectify,[status(thm)],[f3])).
% 20.49/4.13 thf(f3,axiom,(
% 20.49/4.13 ~(knowle1437066798e_know @ p @ (secrecy_kKS @ key))),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',fact_2_assms_I1_J)).
% 20.49/4.13 thf(f5900,plain,(
% 20.49/4.13 ((knowle1437066798e_know @ p @ (secrecy_kKS @ key)) = $true) | ~spl79_60),
% 20.49/4.13 inference(trivial_inequality_removal,[status(thm)],[f5889])).
% 20.49/4.13 thf(f5889,plain,(
% 20.49/4.13 ($true != $true) | ((knowle1437066798e_know @ p @ (secrecy_kKS @ key)) = $true) | ~spl79_60),
% 20.49/4.13 inference(superposition,[status(thm)],[f1402,f5830])).
% 20.49/4.13 thf(f5830,plain,(
% 20.49/4.13 ($true = (ine @ p @ (secrecy_kE @ key))) | ~spl79_60),
% 20.49/4.13 inference(avatar_component_clause,[status(thm)],[f5828])).
% 20.49/4.13 thf(f5828,definition,(
% 20.49/4.13 spl79_60 <=> ($true = (ine @ p @ (secrecy_kE @ key)))),
% 20.49/4.13 introduced(definition,[new_symbols(naming,[spl79_60])],[avatar_definition])).
% 20.49/4.13 thf(f1402,plain,(
% 20.49/4.13 ( ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (($true != (ine @ X0 @ (secrecy_kE @ X1))) | ($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))) )),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f1195])).
% 20.49/4.13 thf(f1195,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) | (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) & ($true != (ine @ X0 @ (secrecy_kE @ X1))))) & (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ($true = (ine @ X0 @ (secrecy_kE @ X1))) | ($true != (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))))),
% 20.49/4.13 inference(flattening,[status(thm)],[f1194])).
% 20.49/4.13 thf(f1194,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) | (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) != $true) & ($true != (ine @ X0 @ (secrecy_kE @ X1))))) & ((((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ($true = (ine @ X0 @ (secrecy_kE @ X1)))) | ($true != (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)))))),
% 20.49/4.13 inference(nnf_transformation,[status(thm)],[f433])).
% 20.49/4.13 thf(f433,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : (($true = (knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1))) <=> (((member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) = $true) | ($true = (ine @ X0 @ (secrecy_kE @ X1)))))),
% 20.49/4.13 inference(fool_elimination,[status(thm)],[f432])).
% 20.49/4.13 thf(f432,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Keys] : ((knowle1437066798e_know @ X0 @ (secrecy_kKS @ X1)) = (member @ secrecy_KS @ (secrecy_kKS @ X1) @ (localSecrets @ X0)) | (ine @ X0 @ (secrecy_kE @ X1)))),
% 20.49/4.13 inference(rectify,[status(thm)],[f7])).
% 20.49/4.13 thf(f7,axiom,(
% 20.49/4.13 ! [X3 : secrecy_specID,X4 : secrecy_Keys] : ((knowle1437066798e_know @ X3 @ (secrecy_kKS @ X4)) = (member @ secrecy_KS @ (secrecy_kKS @ X4) @ (localSecrets @ X3)) | (ine @ X3 @ (secrecy_kE @ X4)))),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',fact_6_know_Osimps_I1_J)).
% 20.49/4.13 thf(f5858,plain,(
% 20.49/4.13 ~spl79_59),
% 20.49/4.13 inference(avatar_contradiction_clause,[status(thm)],[f5857])).
% 20.49/4.13 thf(f5857,plain,(
% 20.49/4.13 $false | ~spl79_59),
% 20.49/4.13 inference(subsumption_resolution,[status(thm)],[f5848,f1456])).
% 20.49/4.13 thf(f1456,plain,(
% 20.49/4.13 ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) != $true)),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f827])).
% 20.49/4.13 thf(f827,plain,(
% 20.49/4.13 ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) != $true)),
% 20.49/4.13 inference(flattening,[status(thm)],[f497])).
% 20.49/4.13 thf(f497,plain,(
% 20.49/4.13 ~((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) = $true)),
% 20.49/4.13 inference(fool_elimination,[status(thm)],[f496])).
% 20.49/4.13 thf(f496,plain,(
% 20.49/4.13 ~(knowle1437066798e_know @ q @ (secrecy_kKS @ key))),
% 20.49/4.13 inference(rectify,[status(thm)],[f2])).
% 20.49/4.13 thf(f2,axiom,(
% 20.49/4.13 ~(knowle1437066798e_know @ q @ (secrecy_kKS @ key))),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',fact_1_assms_I2_J)).
% 20.49/4.13 thf(f5848,plain,(
% 20.49/4.13 ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) = $true) | ~spl79_59),
% 20.49/4.13 inference(trivial_inequality_removal,[status(thm)],[f5845])).
% 20.49/4.13 thf(f5845,plain,(
% 20.49/4.13 ($true != $true) | ((knowle1437066798e_know @ q @ (secrecy_kKS @ key)) = $true) | ~spl79_59),
% 20.49/4.13 inference(superposition,[status(thm)],[f1402,f5826])).
% 20.49/4.13 thf(f5826,plain,(
% 20.49/4.13 ($true = (ine @ q @ (secrecy_kE @ key))) | ~spl79_59),
% 20.49/4.13 inference(avatar_component_clause,[status(thm)],[f5824])).
% 20.49/4.13 thf(f5824,definition,(
% 20.49/4.13 spl79_59 <=> ($true = (ine @ q @ (secrecy_kE @ key)))),
% 20.49/4.13 introduced(definition,[new_symbols(naming,[spl79_59])],[avatar_definition])).
% 20.49/4.13 thf(f5831,plain,(
% 20.49/4.13 spl79_59 | spl79_60),
% 20.49/4.13 inference(avatar_split_clause,[status(thm)],[f5819,f5828,f5824])).
% 20.49/4.13 thf(f5819,plain,(
% 20.49/4.13 ($true = (ine @ p @ (secrecy_kE @ key))) | ($true = (ine @ q @ (secrecy_kE @ key)))),
% 20.49/4.13 inference(trivial_inequality_removal,[status(thm)],[f5805])).
% 20.49/4.13 thf(f5805,plain,(
% 20.49/4.13 ($true = (ine @ p @ (secrecy_kE @ key))) | ($true != $true) | ($true = (ine @ q @ (secrecy_kE @ key)))),
% 20.49/4.13 inference(superposition,[status(thm)],[f2705,f1688])).
% 20.49/4.13 thf(f1688,plain,(
% 20.49/4.13 ((ine @ pq @ (secrecy_kE @ key)) = $true)),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f843])).
% 20.49/4.13 thf(f843,plain,(
% 20.49/4.13 ((ine @ pq @ (secrecy_kE @ key)) = $true)),
% 20.49/4.13 inference(flattening,[status(thm)],[f565])).
% 20.49/4.13 thf(f565,plain,(
% 20.49/4.13 ~~((ine @ pq @ (secrecy_kE @ key)) = $true)),
% 20.49/4.13 inference(fool_elimination,[status(thm)],[f564])).
% 20.49/4.13 thf(f564,plain,(
% 20.49/4.13 ~~(ine @ pq @ (secrecy_kE @ key))),
% 20.49/4.13 inference(rectify,[status(thm)],[f282])).
% 20.49/4.13 thf(f282,negated_conjecture,(
% 20.49/4.13 ~~(ine @ pq @ (secrecy_kE @ key))),
% 20.49/4.13 inference(negated_conjecture,[status(cth)],[f281])).
% 20.49/4.13 thf(f281,conjecture,(
% 20.49/4.13 ~(ine @ pq @ (secrecy_kE @ key))),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',conj_0)).
% 20.49/4.13 thf(f2705,plain,(
% 20.49/4.13 ( ! [X0 : secrecy_Expression] : (($true != (ine @ pq @ X0)) | ($true = (ine @ p @ X0)) | ($true = (ine @ q @ X0))) )),
% 20.49/4.13 inference(subsumption_resolution,[status(thm)],[f2704,f1578])).
% 20.49/4.13 thf(f1578,plain,(
% 20.49/4.13 ((correctCompositionIn @ pq) = $true)),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f491])).
% 20.49/4.13 thf(f491,plain,(
% 20.49/4.13 ((correctCompositionIn @ pq) = $true)),
% 20.49/4.13 inference(fool_elimination,[status(thm)],[f490])).
% 20.49/4.13 thf(f490,plain,(
% 20.49/4.13 (correctCompositionIn @ pq)),
% 20.49/4.13 inference(rectify,[status(thm)],[f1])).
% 20.49/4.13 thf(f1,axiom,(
% 20.49/4.13 (correctCompositionIn @ pq)),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',fact_0_assms_I4_J)).
% 20.49/4.13 thf(f2704,plain,(
% 20.49/4.13 ( ! [X0 : secrecy_Expression] : (($true = (ine @ p @ X0)) | ($true != (ine @ pq @ X0)) | ((correctCompositionIn @ pq) != $true) | ($true = (ine @ q @ X0))) )),
% 20.49/4.13 inference(equality_resolution,[status(thm)],[f2004])).
% 20.49/4.13 thf(f2004,plain,(
% 20.49/4.13 ( ! [X0 : secrecy_specID,X1 : secrecy_Expression] : (((subcomponents @ pq) != (subcomponents @ X0)) | ($true != (ine @ X0 @ X1)) | ($true = (ine @ p @ X1)) | ($true = (ine @ q @ X1)) | ($true != (correctCompositionIn @ X0))) )),
% 20.49/4.13 inference(superposition,[status(thm)],[f1677,f1833])).
% 20.49/4.13 thf(f1833,plain,(
% 20.49/4.13 ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f4])).
% 20.49/4.13 thf(f4,axiom,(
% 20.49/4.13 ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',fact_3_assms_I3_J)).
% 20.49/4.13 thf(f1677,plain,(
% 20.49/4.13 ( ! [X2 : secrecy_specID,X3 : secrecy_specID,X0 : secrecy_specID,X1 : secrecy_Expression] : (((subcomponents @ X0) != (insert @ secrecy_specID @ X2 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) | ($true = (ine @ X2 @ X1)) | ((ine @ X3 @ X1) = $true) | ($true != (ine @ X0 @ X1)) | ($true != (correctCompositionIn @ X0))) )),
% 20.49/4.13 inference(cnf_transformation,[status(thm)],[f976])).
% 20.49/4.13 thf(f976,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Expression,X2 : secrecy_specID,X3 : secrecy_specID] : (($true = (ine @ X2 @ X1)) | ((subcomponents @ X0) != (insert @ secrecy_specID @ X2 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) | ($true != (correctCompositionIn @ X0)) | ($true != (ine @ X0 @ X1)) | ((ine @ X3 @ X1) = $true))),
% 20.49/4.13 inference(flattening,[status(thm)],[f975])).
% 20.49/4.13 thf(f975,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Expression,X2 : secrecy_specID,X3 : secrecy_specID] : ((((($true = (ine @ X2 @ X1)) | ((ine @ X3 @ X1) = $true)) | ($true != (correctCompositionIn @ X0))) | ((subcomponents @ X0) != (insert @ secrecy_specID @ X2 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID)))) | ($true != (ine @ X0 @ X1)))),
% 20.49/4.13 inference(ennf_transformation,[status(thm)],[f651])).
% 20.49/4.13 thf(f651,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Expression,X2 : secrecy_specID,X3 : secrecy_specID] : (($true = (ine @ X0 @ X1)) => (((subcomponents @ X0) = (insert @ secrecy_specID @ X2 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) => (($true = (correctCompositionIn @ X0)) => (($true = (ine @ X2 @ X1)) | ((ine @ X3 @ X1) = $true)))))),
% 20.49/4.13 inference(fool_elimination,[status(thm)],[f650])).
% 20.49/4.13 thf(f650,plain,(
% 20.49/4.13 ! [X0 : secrecy_specID,X1 : secrecy_Expression,X2 : secrecy_specID,X3 : secrecy_specID] : ((ine @ X0 @ X1) => (((subcomponents @ X0) = (insert @ secrecy_specID @ X2 @ (insert @ secrecy_specID @ X3 @ bot_bot @ set @ secrecy_specID))) => ((correctCompositionIn @ X0) => ((ine @ X3 @ X1) | (ine @ X2 @ X1)))))),
% 20.49/4.13 inference(rectify,[status(thm)],[f44])).
% 20.49/4.13 thf(f44,axiom,(
% 20.49/4.13 ! [X26 : secrecy_specID,X13 : secrecy_Expression,X11 : secrecy_specID,X16 : secrecy_specID] : ((ine @ X26 @ X13) => (((subcomponents @ X26) = (insert @ secrecy_specID @ X11 @ (insert @ secrecy_specID @ X16 @ bot_bot @ set @ secrecy_specID))) => ((correctCompositionIn @ X26) => ((ine @ X16 @ X13) | (ine @ X11 @ X13)))))),
% 20.49/4.13 file('/export/starexec/sandbox/tmp/tmp.yyEKwnUdJr/DTF2THF_19196.p',fact_43_TBtheorem1a)).
% 20.49/4.13 % SZS output end Proof for DTF2THF_19196
% 20.49/4.13 % (19627)------------------------------
% 20.49/4.13 % (19627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.49/4.13 % (19627)Termination reason: Refutation
% 20.49/4.13
% 20.49/4.13 % (19627)Memory used [KB]: 9594
% 20.49/4.13 % (19627)Time elapsed: 0.935 s
% 20.49/4.13 % (19627)Instructions burned: 2975 (million)
% 20.49/4.13 % (19627)------------------------------
% 20.49/4.13 % (19627)------------------------------
% 20.49/4.13 % (19505)Success in time 2.56 s
%------------------------------------------------------------------------------