TSTP Solution File: ITP091^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP091^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n005.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 : Thu Aug 31 03:18:09 EDT 2023
% Result : Theorem 0.56s 1.08s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.18/0.19 % Problem : ITP091^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.20 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n005.cluster.edu
% 0.20/0.41 % Model : x86_64 x86_64
% 0.20/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.41 % Memory : 8042.1875MB
% 0.20/0.41 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.41 % CPULimit : 300
% 0.20/0.41 % WCLimit : 300
% 0.20/0.41 % DateTime : Sun Aug 27 12:00:08 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.28/0.60 %----Proving TH0
% 0.28/0.61 %------------------------------------------------------------------------------
% 0.28/0.61 % File : ITP091^1 : TPTP v8.1.2. Released v7.5.0.
% 0.28/0.61 % Domain : Interactive Theorem Proving
% 0.28/0.61 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_460__3295970_1
% 0.28/0.61 % Version : Especial.
% 0.28/0.61 % English :
% 0.28/0.61
% 0.28/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.28/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.28/0.61 % Source : [Des21]
% 0.28/0.61 % Names : KnowledgeKeysSecrets/prob_460__3295970_1 [Des21]
% 0.28/0.61
% 0.28/0.61 % Status : Theorem
% 0.28/0.61 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.28/0.61 % Syntax : Number of formulae : 447 ( 176 unt; 91 typ; 0 def)
% 0.28/0.61 % Number of atoms : 1276 ( 456 equ; 0 cnn)
% 0.28/0.61 % Maximal formula atoms : 13 ( 3 avg)
% 0.28/0.61 % Number of connectives : 3881 ( 291 ~; 51 |; 125 &;2855 @)
% 0.28/0.61 % ( 0 <=>; 559 =>; 0 <=; 0 <~>)
% 0.28/0.61 % Maximal formula depth : 19 ( 7 avg)
% 0.28/0.61 % Number of types : 14 ( 13 usr)
% 0.28/0.61 % Number of type conns : 127 ( 127 >; 0 *; 0 +; 0 <<)
% 0.28/0.61 % Number of symbols : 79 ( 78 usr; 10 con; 0-3 aty)
% 0.28/0.61 % Number of variables : 999 ( 56 ^; 898 !; 45 ?; 999 :)
% 0.28/0.61 % SPC : TH0_THM_EQU_NAR
% 0.28/0.61
% 0.28/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:35:59.539
% 0.28/0.61 %------------------------------------------------------------------------------
% 0.28/0.61 % Could-be-implicit typings (13)
% 0.28/0.61 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.28/0.61 list_S529945141ession: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.28/0.61 set_Secrecy_Secrets: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.61 set_Secrecy_specID: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.61 set_Secrecy_chanID: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.28/0.61 set_Secrecy_Keys: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.28/0.61 set_Secrecy_KS: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.28/0.61 secrecy_Expression: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.28/0.61 secrecy_Secrets: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.28/0.61 secrecy_specID: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Secrecy____types__OchanID,type,
% 0.28/0.61 secrecy_chanID: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.28/0.61 secrecy_Keys: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.28/0.61 secrecy_KS: $tType ).
% 0.28/0.61
% 0.28/0.61 thf(ty_n_t__Nat__Onat,type,
% 0.28/0.61 nat: $tType ).
% 0.28/0.61
% 0.28/0.61 % Explicit typings (78)
% 0.28/0.61 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.28/0.61 localSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
% 0.28/0.61 knowle233900195orrect: secrecy_specID > secrecy_KS > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.28/0.61 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.28/0.61 sup_su1301156759ecy_KS: set_Secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.28/0.61 sup_su552545507y_Keys: set_Secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.28/0.61 sup_su1029080330ecrets: set_Secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.61 sup_su370684444chanID: set_Secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.61 sup_su1712599557specID: set_Secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
% 0.28/0.61 mem_Se1967555118ession: secrecy_Expression > list_S529945141ession > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKS_M_Eo_J,type,
% 0.28/0.61 bot_bot_Secrecy_KS_o: secrecy_KS > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OKeys_M_Eo_J,type,
% 0.28/0.61 bot_bo2072920570Keys_o: secrecy_Keys > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OSecrets_M_Eo_J,type,
% 0.28/0.61 bot_bo1909946299rets_o: secrecy_Secrets > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OchanID_M_Eo_J,type,
% 0.28/0.61 bot_bo1012329985anID_o: secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001_062_It__Secrecy____types__OspecID_M_Eo_J,type,
% 0.28/0.61 bot_bo1767780696ecID_o: secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.28/0.61 bot_bo1943466239ecy_KS: set_Secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.28/0.61 bot_bo701486667y_Keys: set_Secrecy_Keys ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.28/0.61 bot_bo1124690338ecrets: set_Secrecy_Secrets ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.61 bot_bo443197316chanID: set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Secrecy____types__OspecID_J,type,
% 0.28/0.61 bot_bo1785112429specID: set_Secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Secrecy____types__OchanID_J,type,
% 0.28/0.61 ord_le1802272080chanID: set_Secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.28/0.61 correctCompositionKS: secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_Oeout,type,
% 0.28/0.61 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OeoutM,type,
% 0.28/0.61 eoutM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OexprChannel,type,
% 0.28/0.61 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_Oine,type,
% 0.28/0.61 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OineM,type,
% 0.28/0.61 ineM: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.28/0.61 ine_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.28/0.61 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.28/0.61 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.28/0.61 out_exprChannelSet: secrecy_specID > set_Secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.28/0.61 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OspecKeys,type,
% 0.28/0.61 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.28/0.61 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.28/0.61 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.28/0.61 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.28/0.61 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.28/0.61 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.28/0.61 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.28/0.61 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.28/0.61 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.28/0.61 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.28/0.61 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OchanID,type,
% 0.28/0.61 collec625564175chanID: ( secrecy_chanID > $o ) > set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OspecID,type,
% 0.28/0.61 collec1545797240specID: ( secrecy_specID > $o ) > set_Secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKS,type,
% 0.28/0.61 insert_Secrecy_KS: secrecy_KS > set_Secrecy_KS > set_Secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OKeys,type,
% 0.28/0.61 insert_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > set_Secrecy_Keys ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OSecrets,type,
% 0.28/0.61 insert565337510ecrets: secrecy_Secrets > set_Secrecy_Secrets > set_Secrecy_Secrets ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OchanID,type,
% 0.28/0.61 insert751661162chanID: secrecy_chanID > set_Secrecy_chanID > set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Oinsert_001t__Secrecy____types__OspecID,type,
% 0.28/0.61 insert1671894227specID: secrecy_specID > set_Secrecy_specID > set_Secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OchanID,type,
% 0.28/0.61 is_emp928984296chanID: set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__empty_001t__Secrecy____types__OspecID,type,
% 0.28/0.61 is_emp1849217361specID: set_Secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKS,type,
% 0.28/0.61 is_sin1442426433ecy_KS: set_Secrecy_KS > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OKeys,type,
% 0.28/0.61 is_sin1096471309y_Keys: set_Secrecy_Keys > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OSecrets,type,
% 0.28/0.61 is_sin1002224330ecrets: set_Secrecy_Secrets > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OchanID,type,
% 0.28/0.61 is_sin581274182chanID: set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Ois__singleton_001t__Secrecy____types__OspecID,type,
% 0.28/0.61 is_sin1501507247specID: set_Secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OchanID,type,
% 0.28/0.61 the_el2054381829chanID: set_Secrecy_chanID > secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_Set_Othe__elem_001t__Secrecy____types__OspecID,type,
% 0.28/0.61 the_el827131246specID: set_Secrecy_specID > secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.28/0.61 correctCompositionIn: secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.28/0.61 correc965049635ionLoc: secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.28/0.61 correc990227761ionOut: secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_OinStream,type,
% 0.28/0.61 inStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_Oins,type,
% 0.28/0.61 ins: secrecy_specID > set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_Oloc,type,
% 0.28/0.61 loc: secrecy_specID > set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_OlocStream,type,
% 0.28/0.61 locStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_Oout,type,
% 0.28/0.61 out: secrecy_specID > set_Secrecy_chanID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_OoutStream,type,
% 0.28/0.61 outStream: secrecy_specID > set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_inout_Osubcomponents,type,
% 0.28/0.61 subcomponents: secrecy_specID > set_Secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.28/0.61 member_Secrecy_KS: secrecy_KS > set_Secrecy_KS > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.28/0.61 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.28/0.61 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_member_001t__Secrecy____types__OchanID,type,
% 0.28/0.61 member1967978193chanID: secrecy_chanID > set_Secrecy_chanID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_c_member_001t__Secrecy____types__OspecID,type,
% 0.28/0.61 member740727610specID: secrecy_specID > set_Secrecy_specID > $o ).
% 0.28/0.61
% 0.28/0.61 thf(sy_v_P,type,
% 0.28/0.61 p: secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_v_PQ,type,
% 0.28/0.61 pq: secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_v_Q,type,
% 0.28/0.61 q: secrecy_specID ).
% 0.28/0.61
% 0.28/0.61 thf(sy_v_m,type,
% 0.28/0.61 m: secrecy_KS ).
% 0.28/0.61
% 0.28/0.61 thf(sy_v_secret____,type,
% 0.28/0.61 secret: secrecy_Secrets ).
% 0.28/0.61
% 0.28/0.61 % Relevant facts (355)
% 0.28/0.61 thf(fact_0_not__knowQm,axiom,
% 0.28/0.61 ~ ( knowle945212990e_know @ q @ m ) ).
% 0.28/0.61
% 0.28/0.61 % not_knowQm
% 0.28/0.61 thf(fact_1_a2,axiom,
% 0.28/0.61 ( m
% 0.28/0.61 = ( secrecy_sKS @ secret ) ) ).
% 0.28/0.61
% 0.28/0.61 % a2
% 0.28/0.61 thf(fact_2_knowPQ,axiom,
% 0.28/0.61 knowle945212990e_know @ pq @ m ).
% 0.28/0.61
% 0.28/0.61 % knowPQ
% 0.28/0.61 thf(fact_3_sg5,axiom,
% 0.28/0.61 member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ).
% 0.28/0.61
% 0.28/0.61 % sg5
% 0.28/0.61 thf(fact_4_KS_Oinject_I2_J,axiom,
% 0.28/0.61 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.28/0.61 ( ( ( secrecy_sKS @ X2 )
% 0.28/0.61 = ( secrecy_sKS @ Y2 ) )
% 0.28/0.61 = ( X2 = Y2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS.inject(2)
% 0.28/0.61 thf(fact_5_sg6a,axiom,
% 0.28/0.61 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 0.28/0.61
% 0.28/0.61 % sg6a
% 0.28/0.61 thf(fact_6_cCompLoc,axiom,
% 0.28/0.61 correc965049635ionLoc @ pq ).
% 0.28/0.61
% 0.28/0.61 % cCompLoc
% 0.28/0.61 thf(fact_7_a22,axiom,
% 0.28/0.61 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 0.28/0.61
% 0.28/0.61 % a22
% 0.28/0.61 thf(fact_8_know_Osimps_I2_J,axiom,
% 0.28/0.61 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.61 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.61 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.28/0.61 | ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % know.simps(2)
% 0.28/0.61 thf(fact_9_subPQ,axiom,
% 0.28/0.61 ( ( subcomponents @ pq )
% 0.28/0.61 = ( insert1671894227specID @ p @ ( insert1671894227specID @ q @ bot_bo1785112429specID ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % subPQ
% 0.28/0.61 thf(fact_10_cCompI,axiom,
% 0.28/0.61 correctCompositionIn @ pq ).
% 0.28/0.61
% 0.28/0.61 % cCompI
% 0.28/0.61 thf(fact_11_KS_Odistinct_I1_J,axiom,
% 0.28/0.61 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.28/0.61 ( ( secrecy_kKS @ X1 )
% 0.28/0.61 != ( secrecy_sKS @ X2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS.distinct(1)
% 0.28/0.61 thf(fact_12_KS_Oinduct,axiom,
% 0.28/0.61 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.28/0.61 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.28/0.61 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.28/0.61 => ( P @ KS ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS.induct
% 0.28/0.61 thf(fact_13_KS_Oinject_I1_J,axiom,
% 0.28/0.61 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.28/0.61 ( ( ( secrecy_kKS @ X1 )
% 0.28/0.61 = ( secrecy_kKS @ Y1 ) )
% 0.28/0.61 = ( X1 = Y1 ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS.inject(1)
% 0.28/0.61 thf(fact_14_Expression_Oinject_I2_J,axiom,
% 0.28/0.61 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.28/0.61 ( ( ( secrecy_sE @ X2 )
% 0.28/0.61 = ( secrecy_sE @ Y2 ) )
% 0.28/0.61 = ( X2 = Y2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % Expression.inject(2)
% 0.28/0.61 thf(fact_15_know__composition__neg1,axiom,
% 0.28/0.61 ! [P: secrecy_specID,M: secrecy_KS,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.61 ( ~ ( knowle945212990e_know @ P @ M )
% 0.28/0.61 => ( ~ ( knowle945212990e_know @ Q @ M )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ( correctCompositionIn @ PQ )
% 0.28/0.61 => ~ ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % know_composition_neg1
% 0.28/0.61 thf(fact_16_know__composition__neg__ine__s,axiom,
% 0.28/0.61 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.61 ( ~ ( knowle945212990e_know @ P @ ( secrecy_sKS @ Secret ) )
% 0.28/0.61 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correctCompositionIn @ PQ )
% 0.28/0.61 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % know_composition_neg_ine_s
% 0.28/0.61 thf(fact_17_not__know__s__not__ine,axiom,
% 0.28/0.61 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.61 ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.61 => ~ ( ine @ A @ ( secrecy_sE @ M ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % not_know_s_not_ine
% 0.28/0.61 thf(fact_18_KS_Oexhaust,axiom,
% 0.28/0.61 ! [Y: secrecy_KS] :
% 0.28/0.61 ( ! [X12: secrecy_Keys] :
% 0.28/0.61 ( Y
% 0.28/0.61 != ( secrecy_kKS @ X12 ) )
% 0.28/0.61 => ~ ! [X22: secrecy_Secrets] :
% 0.28/0.61 ( Y
% 0.28/0.61 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS.exhaust
% 0.28/0.61 thf(fact_19_LocalSecretsComposition__ine1__s,axiom,
% 0.28/0.61 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.61 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.28/0.61 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_ine1_s
% 0.28/0.61 thf(fact_20_LocalSecretsComposition__ine2__s,axiom,
% 0.28/0.61 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.61 ( ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.28/0.61 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_ine2_s
% 0.28/0.61 thf(fact_21_LocalSecretsComposition__neg1__s,axiom,
% 0.28/0.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.28/0.61 ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.28/0.61 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.28/0.61 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_neg1_s
% 0.28/0.61 thf(fact_22_TBtheorem1a,axiom,
% 0.28/0.61 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.61 ( ( ine @ PQ @ E )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correctCompositionIn @ PQ )
% 0.28/0.61 => ( ( ine @ P @ E )
% 0.28/0.61 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % TBtheorem1a
% 0.28/0.61 thf(fact_23_TBtheorem3a,axiom,
% 0.28/0.61 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.61 ( ~ ( ine @ P @ E )
% 0.28/0.61 => ( ~ ( ine @ Q @ E )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correctCompositionIn @ PQ )
% 0.28/0.61 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % TBtheorem3a
% 0.28/0.61 thf(fact_24_singletonI,axiom,
% 0.28/0.61 ! [A2: secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonI
% 0.28/0.61 thf(fact_25_singletonI,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonI
% 0.28/0.61 thf(fact_26_singletonI,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonI
% 0.28/0.61 thf(fact_27_singletonI,axiom,
% 0.28/0.61 ! [A2: secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonI
% 0.28/0.61 thf(fact_28_singletonI,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonI
% 0.28/0.61 thf(fact_29_LocalSecretsComposition1,axiom,
% 0.28/0.61 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.61 ( ( member_Secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( member_Secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition1
% 0.28/0.61 thf(fact_30_insertCI,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.28/0.61 ( ( ~ ( member_Secrecy_KS @ A2 @ B )
% 0.28/0.61 => ( A2 = B2 ) )
% 0.28/0.61 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertCI
% 0.28/0.61 thf(fact_31_insertCI,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.61 ( ( ~ ( member1967978193chanID @ A2 @ B )
% 0.28/0.61 => ( A2 = B2 ) )
% 0.28/0.61 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertCI
% 0.28/0.61 thf(fact_32_insertCI,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.61 ( ( ~ ( member740727610specID @ A2 @ B )
% 0.28/0.61 => ( A2 = B2 ) )
% 0.28/0.61 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertCI
% 0.28/0.61 thf(fact_33_insertCI,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.28/0.61 ( ( ~ ( member_Secrecy_Keys @ A2 @ B )
% 0.28/0.61 => ( A2 = B2 ) )
% 0.28/0.61 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertCI
% 0.28/0.61 thf(fact_34_insertCI,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.28/0.61 ( ( ~ ( member2138796287ecrets @ A2 @ B )
% 0.28/0.61 => ( A2 = B2 ) )
% 0.28/0.61 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertCI
% 0.28/0.61 thf(fact_35_insert__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.28/0.61 = ( ( A2 = B2 )
% 0.28/0.61 | ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_iff
% 0.28/0.61 thf(fact_36_insert__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.28/0.61 = ( ( A2 = B2 )
% 0.28/0.61 | ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_iff
% 0.28/0.61 thf(fact_37_insert__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.28/0.61 = ( ( A2 = B2 )
% 0.28/0.61 | ( member740727610specID @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_iff
% 0.28/0.61 thf(fact_38_insert__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.28/0.61 = ( ( A2 = B2 )
% 0.28/0.61 | ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_iff
% 0.28/0.61 thf(fact_39_insert__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.28/0.61 = ( ( A2 = B2 )
% 0.28/0.61 | ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_iff
% 0.28/0.61 thf(fact_40_insert__absorb2,axiom,
% 0.28/0.61 ! [X3: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ X3 @ A ) )
% 0.28/0.61 = ( insert1671894227specID @ X3 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb2
% 0.28/0.61 thf(fact_41_insert__absorb2,axiom,
% 0.28/0.61 ! [X3: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ X3 @ A ) )
% 0.28/0.61 = ( insert751661162chanID @ X3 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb2
% 0.28/0.61 thf(fact_42_empty__Collect__eq,axiom,
% 0.28/0.61 ! [P: secrecy_specID > $o] :
% 0.28/0.61 ( ( bot_bo1785112429specID
% 0.28/0.61 = ( collec1545797240specID @ P ) )
% 0.28/0.61 = ( ! [X4: secrecy_specID] :
% 0.28/0.61 ~ ( P @ X4 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % empty_Collect_eq
% 0.28/0.61 thf(fact_43_empty__Collect__eq,axiom,
% 0.28/0.61 ! [P: secrecy_chanID > $o] :
% 0.28/0.61 ( ( bot_bo443197316chanID
% 0.28/0.61 = ( collec625564175chanID @ P ) )
% 0.28/0.61 = ( ! [X4: secrecy_chanID] :
% 0.28/0.61 ~ ( P @ X4 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % empty_Collect_eq
% 0.28/0.61 thf(fact_44_Collect__empty__eq,axiom,
% 0.28/0.61 ! [P: secrecy_specID > $o] :
% 0.28/0.61 ( ( ( collec1545797240specID @ P )
% 0.28/0.61 = bot_bo1785112429specID )
% 0.28/0.61 = ( ! [X4: secrecy_specID] :
% 0.28/0.61 ~ ( P @ X4 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_empty_eq
% 0.28/0.61 thf(fact_45_Collect__empty__eq,axiom,
% 0.28/0.61 ! [P: secrecy_chanID > $o] :
% 0.28/0.61 ( ( ( collec625564175chanID @ P )
% 0.28/0.61 = bot_bo443197316chanID )
% 0.28/0.61 = ( ! [X4: secrecy_chanID] :
% 0.28/0.61 ~ ( P @ X4 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_empty_eq
% 0.28/0.61 thf(fact_46_all__not__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_KS] :
% 0.28/0.61 ( ( ! [X4: secrecy_KS] :
% 0.28/0.61 ~ ( member_Secrecy_KS @ X4 @ A ) )
% 0.28/0.61 = ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.28/0.61
% 0.28/0.61 % all_not_in_conv
% 0.28/0.61 thf(fact_47_all__not__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( ! [X4: secrecy_Keys] :
% 0.28/0.61 ~ ( member_Secrecy_Keys @ X4 @ A ) )
% 0.28/0.61 = ( A = bot_bo701486667y_Keys ) ) ).
% 0.28/0.61
% 0.28/0.61 % all_not_in_conv
% 0.28/0.61 thf(fact_48_all__not__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( ! [X4: secrecy_Secrets] :
% 0.28/0.61 ~ ( member2138796287ecrets @ X4 @ A ) )
% 0.28/0.61 = ( A = bot_bo1124690338ecrets ) ) ).
% 0.28/0.61
% 0.28/0.61 % all_not_in_conv
% 0.28/0.61 thf(fact_49_all__not__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_specID] :
% 0.28/0.61 ( ( ! [X4: secrecy_specID] :
% 0.28/0.61 ~ ( member740727610specID @ X4 @ A ) )
% 0.28/0.61 = ( A = bot_bo1785112429specID ) ) ).
% 0.28/0.61
% 0.28/0.61 % all_not_in_conv
% 0.28/0.61 thf(fact_50_all__not__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( ! [X4: secrecy_chanID] :
% 0.28/0.61 ~ ( member1967978193chanID @ X4 @ A ) )
% 0.28/0.61 = ( A = bot_bo443197316chanID ) ) ).
% 0.28/0.61
% 0.28/0.61 % all_not_in_conv
% 0.28/0.61 thf(fact_51_empty__iff,axiom,
% 0.28/0.61 ! [C: secrecy_KS] :
% 0.28/0.61 ~ ( member_Secrecy_KS @ C @ bot_bo1943466239ecy_KS ) ).
% 0.28/0.61
% 0.28/0.61 % empty_iff
% 0.28/0.61 thf(fact_52_empty__iff,axiom,
% 0.28/0.61 ! [C: secrecy_Keys] :
% 0.28/0.61 ~ ( member_Secrecy_Keys @ C @ bot_bo701486667y_Keys ) ).
% 0.28/0.61
% 0.28/0.61 % empty_iff
% 0.28/0.61 thf(fact_53_empty__iff,axiom,
% 0.28/0.61 ! [C: secrecy_Secrets] :
% 0.28/0.61 ~ ( member2138796287ecrets @ C @ bot_bo1124690338ecrets ) ).
% 0.28/0.61
% 0.28/0.61 % empty_iff
% 0.28/0.61 thf(fact_54_empty__iff,axiom,
% 0.28/0.61 ! [C: secrecy_specID] :
% 0.28/0.61 ~ ( member740727610specID @ C @ bot_bo1785112429specID ) ).
% 0.28/0.61
% 0.28/0.61 % empty_iff
% 0.28/0.61 thf(fact_55_empty__iff,axiom,
% 0.28/0.61 ! [C: secrecy_chanID] :
% 0.28/0.61 ~ ( member1967978193chanID @ C @ bot_bo443197316chanID ) ).
% 0.28/0.61
% 0.28/0.61 % empty_iff
% 0.28/0.61 thf(fact_56_ex__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_KS] :
% 0.28/0.61 ( ( ? [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ A ) )
% 0.28/0.61 = ( A != bot_bo1943466239ecy_KS ) ) ).
% 0.28/0.61
% 0.28/0.61 % ex_in_conv
% 0.28/0.61 thf(fact_57_ex__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( ? [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.28/0.61 = ( A != bot_bo701486667y_Keys ) ) ).
% 0.28/0.61
% 0.28/0.61 % ex_in_conv
% 0.28/0.61 thf(fact_58_ex__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( ? [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.28/0.61 = ( A != bot_bo1124690338ecrets ) ) ).
% 0.28/0.61
% 0.28/0.61 % ex_in_conv
% 0.28/0.61 thf(fact_59_ex__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_specID] :
% 0.28/0.61 ( ( ? [X4: secrecy_specID] : ( member740727610specID @ X4 @ A ) )
% 0.28/0.61 = ( A != bot_bo1785112429specID ) ) ).
% 0.28/0.61
% 0.28/0.61 % ex_in_conv
% 0.28/0.61 thf(fact_60_ex__in__conv,axiom,
% 0.28/0.61 ! [A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( ? [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ A ) )
% 0.28/0.61 = ( A != bot_bo443197316chanID ) ) ).
% 0.28/0.61
% 0.28/0.61 % ex_in_conv
% 0.28/0.61 thf(fact_61_equals0I,axiom,
% 0.28/0.61 ! [A: set_Secrecy_KS] :
% 0.28/0.61 ( ! [Y3: secrecy_KS] :
% 0.28/0.61 ~ ( member_Secrecy_KS @ Y3 @ A )
% 0.28/0.61 => ( A = bot_bo1943466239ecy_KS ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0I
% 0.28/0.61 thf(fact_62_equals0I,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Keys] :
% 0.28/0.61 ( ! [Y3: secrecy_Keys] :
% 0.28/0.61 ~ ( member_Secrecy_Keys @ Y3 @ A )
% 0.28/0.61 => ( A = bot_bo701486667y_Keys ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0I
% 0.28/0.61 thf(fact_63_equals0I,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ! [Y3: secrecy_Secrets] :
% 0.28/0.61 ~ ( member2138796287ecrets @ Y3 @ A )
% 0.28/0.61 => ( A = bot_bo1124690338ecrets ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0I
% 0.28/0.61 thf(fact_64_equals0I,axiom,
% 0.28/0.61 ! [A: set_Secrecy_specID] :
% 0.28/0.61 ( ! [Y3: secrecy_specID] :
% 0.28/0.61 ~ ( member740727610specID @ Y3 @ A )
% 0.28/0.61 => ( A = bot_bo1785112429specID ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0I
% 0.28/0.61 thf(fact_65_equals0I,axiom,
% 0.28/0.61 ! [A: set_Secrecy_chanID] :
% 0.28/0.61 ( ! [Y3: secrecy_chanID] :
% 0.28/0.61 ~ ( member1967978193chanID @ Y3 @ A )
% 0.28/0.61 => ( A = bot_bo443197316chanID ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0I
% 0.28/0.61 thf(fact_66_equals0D,axiom,
% 0.28/0.61 ! [A: set_Secrecy_KS,A2: secrecy_KS] :
% 0.28/0.61 ( ( A = bot_bo1943466239ecy_KS )
% 0.28/0.61 => ~ ( member_Secrecy_KS @ A2 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0D
% 0.28/0.61 thf(fact_67_equals0D,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Keys,A2: secrecy_Keys] :
% 0.28/0.61 ( ( A = bot_bo701486667y_Keys )
% 0.28/0.61 => ~ ( member_Secrecy_Keys @ A2 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0D
% 0.28/0.61 thf(fact_68_equals0D,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Secrets,A2: secrecy_Secrets] :
% 0.28/0.61 ( ( A = bot_bo1124690338ecrets )
% 0.28/0.61 => ~ ( member2138796287ecrets @ A2 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0D
% 0.28/0.61 thf(fact_69_equals0D,axiom,
% 0.28/0.61 ! [A: set_Secrecy_specID,A2: secrecy_specID] :
% 0.28/0.61 ( ( A = bot_bo1785112429specID )
% 0.28/0.61 => ~ ( member740727610specID @ A2 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0D
% 0.28/0.61 thf(fact_70_equals0D,axiom,
% 0.28/0.61 ! [A: set_Secrecy_chanID,A2: secrecy_chanID] :
% 0.28/0.61 ( ( A = bot_bo443197316chanID )
% 0.28/0.61 => ~ ( member1967978193chanID @ A2 @ A ) ) ).
% 0.28/0.61
% 0.28/0.61 % equals0D
% 0.28/0.61 thf(fact_71_emptyE,axiom,
% 0.28/0.61 ! [A2: secrecy_KS] :
% 0.28/0.61 ~ ( member_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) ).
% 0.28/0.61
% 0.28/0.61 % emptyE
% 0.28/0.61 thf(fact_72_emptyE,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys] :
% 0.28/0.61 ~ ( member_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) ).
% 0.28/0.61
% 0.28/0.61 % emptyE
% 0.28/0.61 thf(fact_73_emptyE,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets] :
% 0.28/0.61 ~ ( member2138796287ecrets @ A2 @ bot_bo1124690338ecrets ) ).
% 0.28/0.61
% 0.28/0.61 % emptyE
% 0.28/0.61 thf(fact_74_emptyE,axiom,
% 0.28/0.61 ! [A2: secrecy_specID] :
% 0.28/0.61 ~ ( member740727610specID @ A2 @ bot_bo1785112429specID ) ).
% 0.28/0.61
% 0.28/0.61 % emptyE
% 0.28/0.61 thf(fact_75_emptyE,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID] :
% 0.28/0.61 ~ ( member1967978193chanID @ A2 @ bot_bo443197316chanID ) ).
% 0.28/0.61
% 0.28/0.61 % emptyE
% 0.28/0.61 thf(fact_76_mk__disjoint__insert,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ A2 @ A )
% 0.28/0.61 => ? [B3: set_Secrecy_KS] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert_Secrecy_KS @ A2 @ B3 ) )
% 0.28/0.61 & ~ ( member_Secrecy_KS @ A2 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % mk_disjoint_insert
% 0.28/0.61 thf(fact_77_mk__disjoint__insert,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ A2 @ A )
% 0.28/0.61 => ? [B3: set_Secrecy_chanID] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert751661162chanID @ A2 @ B3 ) )
% 0.28/0.61 & ~ ( member1967978193chanID @ A2 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % mk_disjoint_insert
% 0.28/0.61 thf(fact_78_mk__disjoint__insert,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ A2 @ A )
% 0.28/0.61 => ? [B3: set_Secrecy_specID] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert1671894227specID @ A2 @ B3 ) )
% 0.28/0.61 & ~ ( member740727610specID @ A2 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % mk_disjoint_insert
% 0.28/0.61 thf(fact_79_mk__disjoint__insert,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.28/0.61 => ? [B3: set_Secrecy_Keys] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert_Secrecy_Keys @ A2 @ B3 ) )
% 0.28/0.61 & ~ ( member_Secrecy_Keys @ A2 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % mk_disjoint_insert
% 0.28/0.61 thf(fact_80_mk__disjoint__insert,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ A2 @ A )
% 0.28/0.61 => ? [B3: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert565337510ecrets @ A2 @ B3 ) )
% 0.28/0.61 & ~ ( member2138796287ecrets @ A2 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % mk_disjoint_insert
% 0.28/0.61 thf(fact_81_insert__commute,axiom,
% 0.28/0.61 ! [X3: secrecy_specID,Y: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( insert1671894227specID @ X3 @ ( insert1671894227specID @ Y @ A ) )
% 0.28/0.61 = ( insert1671894227specID @ Y @ ( insert1671894227specID @ X3 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_commute
% 0.28/0.61 thf(fact_82_insert__commute,axiom,
% 0.28/0.61 ! [X3: secrecy_chanID,Y: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( insert751661162chanID @ X3 @ ( insert751661162chanID @ Y @ A ) )
% 0.28/0.61 = ( insert751661162chanID @ Y @ ( insert751661162chanID @ X3 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_commute
% 0.28/0.61 thf(fact_83_insert__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,A: set_Secrecy_KS,B2: secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.61 ( ~ ( member_Secrecy_KS @ A2 @ A )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ B2 @ B )
% 0.28/0.61 => ( ( ( insert_Secrecy_KS @ A2 @ A )
% 0.28/0.61 = ( insert_Secrecy_KS @ B2 @ B ) )
% 0.28/0.61 = ( ( ( A2 = B2 )
% 0.28/0.61 => ( A = B ) )
% 0.28/0.61 & ( ( A2 != B2 )
% 0.28/0.61 => ? [C2: set_Secrecy_KS] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert_Secrecy_KS @ B2 @ C2 ) )
% 0.28/0.61 & ~ ( member_Secrecy_KS @ B2 @ C2 )
% 0.28/0.61 & ( B
% 0.28/0.61 = ( insert_Secrecy_KS @ A2 @ C2 ) )
% 0.28/0.61 & ~ ( member_Secrecy_KS @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_eq_iff
% 0.28/0.61 thf(fact_84_insert__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,A: set_Secrecy_chanID,B2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.61 ( ~ ( member1967978193chanID @ A2 @ A )
% 0.28/0.61 => ( ~ ( member1967978193chanID @ B2 @ B )
% 0.28/0.61 => ( ( ( insert751661162chanID @ A2 @ A )
% 0.28/0.61 = ( insert751661162chanID @ B2 @ B ) )
% 0.28/0.61 = ( ( ( A2 = B2 )
% 0.28/0.61 => ( A = B ) )
% 0.28/0.61 & ( ( A2 != B2 )
% 0.28/0.61 => ? [C2: set_Secrecy_chanID] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert751661162chanID @ B2 @ C2 ) )
% 0.28/0.61 & ~ ( member1967978193chanID @ B2 @ C2 )
% 0.28/0.61 & ( B
% 0.28/0.61 = ( insert751661162chanID @ A2 @ C2 ) )
% 0.28/0.61 & ~ ( member1967978193chanID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_eq_iff
% 0.28/0.61 thf(fact_85_insert__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,A: set_Secrecy_specID,B2: secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.61 ( ~ ( member740727610specID @ A2 @ A )
% 0.28/0.61 => ( ~ ( member740727610specID @ B2 @ B )
% 0.28/0.61 => ( ( ( insert1671894227specID @ A2 @ A )
% 0.28/0.61 = ( insert1671894227specID @ B2 @ B ) )
% 0.28/0.61 = ( ( ( A2 = B2 )
% 0.28/0.61 => ( A = B ) )
% 0.28/0.61 & ( ( A2 != B2 )
% 0.28/0.61 => ? [C2: set_Secrecy_specID] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert1671894227specID @ B2 @ C2 ) )
% 0.28/0.61 & ~ ( member740727610specID @ B2 @ C2 )
% 0.28/0.61 & ( B
% 0.28/0.61 = ( insert1671894227specID @ A2 @ C2 ) )
% 0.28/0.61 & ~ ( member740727610specID @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_eq_iff
% 0.28/0.61 thf(fact_86_insert__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,A: set_Secrecy_Keys,B2: secrecy_Keys,B: set_Secrecy_Keys] :
% 0.28/0.61 ( ~ ( member_Secrecy_Keys @ A2 @ A )
% 0.28/0.61 => ( ~ ( member_Secrecy_Keys @ B2 @ B )
% 0.28/0.61 => ( ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.28/0.61 = ( insert_Secrecy_Keys @ B2 @ B ) )
% 0.28/0.61 = ( ( ( A2 = B2 )
% 0.28/0.61 => ( A = B ) )
% 0.28/0.61 & ( ( A2 != B2 )
% 0.28/0.61 => ? [C2: set_Secrecy_Keys] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert_Secrecy_Keys @ B2 @ C2 ) )
% 0.28/0.61 & ~ ( member_Secrecy_Keys @ B2 @ C2 )
% 0.28/0.61 & ( B
% 0.28/0.61 = ( insert_Secrecy_Keys @ A2 @ C2 ) )
% 0.28/0.61 & ~ ( member_Secrecy_Keys @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_eq_iff
% 0.28/0.61 thf(fact_87_insert__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets,B2: secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.28/0.61 ( ~ ( member2138796287ecrets @ A2 @ A )
% 0.28/0.61 => ( ~ ( member2138796287ecrets @ B2 @ B )
% 0.28/0.61 => ( ( ( insert565337510ecrets @ A2 @ A )
% 0.28/0.61 = ( insert565337510ecrets @ B2 @ B ) )
% 0.28/0.61 = ( ( ( A2 = B2 )
% 0.28/0.61 => ( A = B ) )
% 0.28/0.61 & ( ( A2 != B2 )
% 0.28/0.61 => ? [C2: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert565337510ecrets @ B2 @ C2 ) )
% 0.28/0.61 & ~ ( member2138796287ecrets @ B2 @ C2 )
% 0.28/0.61 & ( B
% 0.28/0.61 = ( insert565337510ecrets @ A2 @ C2 ) )
% 0.28/0.61 & ~ ( member2138796287ecrets @ A2 @ C2 ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_eq_iff
% 0.28/0.61 thf(fact_88_insert__absorb,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ A2 @ A )
% 0.28/0.61 => ( ( insert_Secrecy_KS @ A2 @ A )
% 0.28/0.61 = A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb
% 0.28/0.61 thf(fact_89_insert__absorb,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ A2 @ A )
% 0.28/0.61 => ( ( insert751661162chanID @ A2 @ A )
% 0.28/0.61 = A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb
% 0.28/0.61 thf(fact_90_insert__absorb,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ A2 @ A )
% 0.28/0.61 => ( ( insert1671894227specID @ A2 @ A )
% 0.28/0.61 = A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb
% 0.28/0.61 thf(fact_91_insert__absorb,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ A2 @ A )
% 0.28/0.61 => ( ( insert_Secrecy_Keys @ A2 @ A )
% 0.28/0.61 = A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb
% 0.28/0.61 thf(fact_92_insert__absorb,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ A2 @ A )
% 0.28/0.61 => ( ( insert565337510ecrets @ A2 @ A )
% 0.28/0.61 = A ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_absorb
% 0.28/0.61 thf(fact_93_mem__Collect__eq,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,P: secrecy_KS > $o] :
% 0.28/0.61 ( ( member_Secrecy_KS @ A2 @ ( collect_Secrecy_KS @ P ) )
% 0.28/0.61 = ( P @ A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % mem_Collect_eq
% 0.28/0.61 thf(fact_94_mem__Collect__eq,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,P: secrecy_chanID > $o] :
% 0.28/0.61 ( ( member1967978193chanID @ A2 @ ( collec625564175chanID @ P ) )
% 0.28/0.61 = ( P @ A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % mem_Collect_eq
% 0.28/0.61 thf(fact_95_mem__Collect__eq,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,P: secrecy_specID > $o] :
% 0.28/0.61 ( ( member740727610specID @ A2 @ ( collec1545797240specID @ P ) )
% 0.28/0.61 = ( P @ A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % mem_Collect_eq
% 0.28/0.61 thf(fact_96_mem__Collect__eq,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ A2 @ ( collect_Secrecy_Keys @ P ) )
% 0.28/0.61 = ( P @ A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % mem_Collect_eq
% 0.28/0.61 thf(fact_97_mem__Collect__eq,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.28/0.61 ( ( member2138796287ecrets @ A2 @ ( collec836099393ecrets @ P ) )
% 0.28/0.61 = ( P @ A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % mem_Collect_eq
% 0.28/0.61 thf(fact_98_Collect__mem__eq,axiom,
% 0.28/0.61 ! [A: set_Secrecy_KS] :
% 0.28/0.61 ( ( collect_Secrecy_KS
% 0.28/0.61 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ A ) )
% 0.28/0.61 = A ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_mem_eq
% 0.28/0.61 thf(fact_99_Collect__mem__eq,axiom,
% 0.28/0.61 ! [A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( collec625564175chanID
% 0.28/0.61 @ ^ [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ A ) )
% 0.28/0.61 = A ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_mem_eq
% 0.28/0.61 thf(fact_100_Collect__mem__eq,axiom,
% 0.28/0.61 ! [A: set_Secrecy_specID] :
% 0.28/0.61 ( ( collec1545797240specID
% 0.28/0.61 @ ^ [X4: secrecy_specID] : ( member740727610specID @ X4 @ A ) )
% 0.28/0.61 = A ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_mem_eq
% 0.28/0.61 thf(fact_101_Collect__mem__eq,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( collect_Secrecy_Keys
% 0.28/0.61 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.28/0.61 = A ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_mem_eq
% 0.28/0.61 thf(fact_102_Collect__mem__eq,axiom,
% 0.28/0.61 ! [A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( collec836099393ecrets
% 0.28/0.61 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.28/0.61 = A ) ).
% 0.28/0.61
% 0.28/0.61 % Collect_mem_eq
% 0.28/0.61 thf(fact_103_insert__ident,axiom,
% 0.28/0.61 ! [X3: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.61 ( ~ ( member_Secrecy_KS @ X3 @ A )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ X3 @ B )
% 0.28/0.61 => ( ( ( insert_Secrecy_KS @ X3 @ A )
% 0.28/0.61 = ( insert_Secrecy_KS @ X3 @ B ) )
% 0.28/0.61 = ( A = B ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_ident
% 0.28/0.61 thf(fact_104_insert__ident,axiom,
% 0.28/0.61 ! [X3: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.61 ( ~ ( member1967978193chanID @ X3 @ A )
% 0.28/0.61 => ( ~ ( member1967978193chanID @ X3 @ B )
% 0.28/0.61 => ( ( ( insert751661162chanID @ X3 @ A )
% 0.28/0.61 = ( insert751661162chanID @ X3 @ B ) )
% 0.28/0.61 = ( A = B ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_ident
% 0.28/0.61 thf(fact_105_insert__ident,axiom,
% 0.28/0.61 ! [X3: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.61 ( ~ ( member740727610specID @ X3 @ A )
% 0.28/0.61 => ( ~ ( member740727610specID @ X3 @ B )
% 0.28/0.61 => ( ( ( insert1671894227specID @ X3 @ A )
% 0.28/0.61 = ( insert1671894227specID @ X3 @ B ) )
% 0.28/0.61 = ( A = B ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_ident
% 0.28/0.61 thf(fact_106_insert__ident,axiom,
% 0.28/0.61 ! [X3: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.28/0.61 ( ~ ( member_Secrecy_Keys @ X3 @ A )
% 0.28/0.61 => ( ~ ( member_Secrecy_Keys @ X3 @ B )
% 0.28/0.61 => ( ( ( insert_Secrecy_Keys @ X3 @ A )
% 0.28/0.61 = ( insert_Secrecy_Keys @ X3 @ B ) )
% 0.28/0.61 = ( A = B ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_ident
% 0.28/0.61 thf(fact_107_insert__ident,axiom,
% 0.28/0.61 ! [X3: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.28/0.61 ( ~ ( member2138796287ecrets @ X3 @ A )
% 0.28/0.61 => ( ~ ( member2138796287ecrets @ X3 @ B )
% 0.28/0.61 => ( ( ( insert565337510ecrets @ X3 @ A )
% 0.28/0.61 = ( insert565337510ecrets @ X3 @ B ) )
% 0.28/0.61 = ( A = B ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insert_ident
% 0.28/0.61 thf(fact_108_Set_Oset__insert,axiom,
% 0.28/0.61 ! [X3: secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ X3 @ A )
% 0.28/0.61 => ~ ! [B3: set_Secrecy_KS] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert_Secrecy_KS @ X3 @ B3 ) )
% 0.28/0.61 => ( member_Secrecy_KS @ X3 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Set.set_insert
% 0.28/0.61 thf(fact_109_Set_Oset__insert,axiom,
% 0.28/0.61 ! [X3: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ X3 @ A )
% 0.28/0.61 => ~ ! [B3: set_Secrecy_chanID] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert751661162chanID @ X3 @ B3 ) )
% 0.28/0.61 => ( member1967978193chanID @ X3 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Set.set_insert
% 0.28/0.61 thf(fact_110_Set_Oset__insert,axiom,
% 0.28/0.61 ! [X3: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ X3 @ A )
% 0.28/0.61 => ~ ! [B3: set_Secrecy_specID] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert1671894227specID @ X3 @ B3 ) )
% 0.28/0.61 => ( member740727610specID @ X3 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Set.set_insert
% 0.28/0.61 thf(fact_111_Set_Oset__insert,axiom,
% 0.28/0.61 ! [X3: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ X3 @ A )
% 0.28/0.61 => ~ ! [B3: set_Secrecy_Keys] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert_Secrecy_Keys @ X3 @ B3 ) )
% 0.28/0.61 => ( member_Secrecy_Keys @ X3 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Set.set_insert
% 0.28/0.61 thf(fact_112_Set_Oset__insert,axiom,
% 0.28/0.61 ! [X3: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ X3 @ A )
% 0.28/0.61 => ~ ! [B3: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( A
% 0.28/0.61 = ( insert565337510ecrets @ X3 @ B3 ) )
% 0.28/0.61 => ( member2138796287ecrets @ X3 @ B3 ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % Set.set_insert
% 0.28/0.61 thf(fact_113_insertI2,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,B: set_Secrecy_KS,B2: secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ A2 @ B )
% 0.28/0.61 => ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI2
% 0.28/0.61 thf(fact_114_insertI2,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ A2 @ B )
% 0.28/0.61 => ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI2
% 0.28/0.61 thf(fact_115_insertI2,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B: set_Secrecy_specID,B2: secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ A2 @ B )
% 0.28/0.61 => ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI2
% 0.28/0.61 thf(fact_116_insertI2,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,B: set_Secrecy_Keys,B2: secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ A2 @ B )
% 0.28/0.61 => ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI2
% 0.28/0.61 thf(fact_117_insertI2,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets,B2: secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ A2 @ B )
% 0.28/0.61 => ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ B ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI2
% 0.28/0.61 thf(fact_118_insertI1,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,B: set_Secrecy_KS] : ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ A2 @ B ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI1
% 0.28/0.61 thf(fact_119_insertI1,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B: set_Secrecy_chanID] : ( member1967978193chanID @ A2 @ ( insert751661162chanID @ A2 @ B ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI1
% 0.28/0.61 thf(fact_120_insertI1,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B: set_Secrecy_specID] : ( member740727610specID @ A2 @ ( insert1671894227specID @ A2 @ B ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI1
% 0.28/0.61 thf(fact_121_insertI1,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,B: set_Secrecy_Keys] : ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ A2 @ B ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI1
% 0.28/0.61 thf(fact_122_insertI1,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,B: set_Secrecy_Secrets] : ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ A2 @ B ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertI1
% 0.28/0.61 thf(fact_123_insertE,axiom,
% 0.28/0.61 ! [A2: secrecy_KS,B2: secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ A2 @ ( insert_Secrecy_KS @ B2 @ A ) )
% 0.28/0.61 => ( ( A2 != B2 )
% 0.28/0.61 => ( member_Secrecy_KS @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertE
% 0.28/0.61 thf(fact_124_insertE,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ A2 @ ( insert751661162chanID @ B2 @ A ) )
% 0.28/0.61 => ( ( A2 != B2 )
% 0.28/0.61 => ( member1967978193chanID @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertE
% 0.28/0.61 thf(fact_125_insertE,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B2: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ A2 @ ( insert1671894227specID @ B2 @ A ) )
% 0.28/0.61 => ( ( A2 != B2 )
% 0.28/0.61 => ( member740727610specID @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertE
% 0.28/0.61 thf(fact_126_insertE,axiom,
% 0.28/0.61 ! [A2: secrecy_Keys,B2: secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ A2 @ ( insert_Secrecy_Keys @ B2 @ A ) )
% 0.28/0.61 => ( ( A2 != B2 )
% 0.28/0.61 => ( member_Secrecy_Keys @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertE
% 0.28/0.61 thf(fact_127_insertE,axiom,
% 0.28/0.61 ! [A2: secrecy_Secrets,B2: secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ A2 @ ( insert565337510ecrets @ B2 @ A ) )
% 0.28/0.61 => ( ( A2 != B2 )
% 0.28/0.61 => ( member2138796287ecrets @ A2 @ A ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % insertE
% 0.28/0.61 thf(fact_128_singleton__inject,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B2: secrecy_specID] :
% 0.28/0.61 ( ( ( insert1671894227specID @ A2 @ bot_bo1785112429specID )
% 0.28/0.61 = ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.28/0.61 => ( A2 = B2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_inject
% 0.28/0.61 thf(fact_129_singleton__inject,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B2: secrecy_chanID] :
% 0.28/0.61 ( ( ( insert751661162chanID @ A2 @ bot_bo443197316chanID )
% 0.28/0.61 = ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.28/0.61 => ( A2 = B2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_inject
% 0.28/0.61 thf(fact_130_insert__not__empty,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.61 ( ( insert1671894227specID @ A2 @ A )
% 0.28/0.61 != bot_bo1785112429specID ) ).
% 0.28/0.61
% 0.28/0.61 % insert_not_empty
% 0.28/0.61 thf(fact_131_insert__not__empty,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.61 ( ( insert751661162chanID @ A2 @ A )
% 0.28/0.61 != bot_bo443197316chanID ) ).
% 0.28/0.61
% 0.28/0.61 % insert_not_empty
% 0.28/0.61 thf(fact_132_doubleton__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_specID,B2: secrecy_specID,C: secrecy_specID,D: secrecy_specID] :
% 0.28/0.61 ( ( ( insert1671894227specID @ A2 @ ( insert1671894227specID @ B2 @ bot_bo1785112429specID ) )
% 0.28/0.61 = ( insert1671894227specID @ C @ ( insert1671894227specID @ D @ bot_bo1785112429specID ) ) )
% 0.28/0.61 = ( ( ( A2 = C )
% 0.28/0.61 & ( B2 = D ) )
% 0.28/0.61 | ( ( A2 = D )
% 0.28/0.61 & ( B2 = C ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % doubleton_eq_iff
% 0.28/0.61 thf(fact_133_doubleton__eq__iff,axiom,
% 0.28/0.61 ! [A2: secrecy_chanID,B2: secrecy_chanID,C: secrecy_chanID,D: secrecy_chanID] :
% 0.28/0.61 ( ( ( insert751661162chanID @ A2 @ ( insert751661162chanID @ B2 @ bot_bo443197316chanID ) )
% 0.28/0.61 = ( insert751661162chanID @ C @ ( insert751661162chanID @ D @ bot_bo443197316chanID ) ) )
% 0.28/0.61 = ( ( ( A2 = C )
% 0.28/0.61 & ( B2 = D ) )
% 0.28/0.61 | ( ( A2 = D )
% 0.28/0.61 & ( B2 = C ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % doubleton_eq_iff
% 0.28/0.61 thf(fact_134_singleton__iff,axiom,
% 0.28/0.61 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.61 = ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_iff
% 0.28/0.61 thf(fact_135_singleton__iff,axiom,
% 0.28/0.61 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.28/0.61 = ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_iff
% 0.28/0.61 thf(fact_136_singleton__iff,axiom,
% 0.28/0.61 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.28/0.61 = ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_iff
% 0.28/0.61 thf(fact_137_singleton__iff,axiom,
% 0.28/0.61 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.28/0.61 = ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_iff
% 0.28/0.61 thf(fact_138_singleton__iff,axiom,
% 0.28/0.61 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.28/0.61 = ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singleton_iff
% 0.28/0.61 thf(fact_139_singletonD,axiom,
% 0.28/0.61 ! [B2: secrecy_KS,A2: secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ B2 @ ( insert_Secrecy_KS @ A2 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.61 => ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonD
% 0.28/0.61 thf(fact_140_singletonD,axiom,
% 0.28/0.61 ! [B2: secrecy_Keys,A2: secrecy_Keys] :
% 0.28/0.61 ( ( member_Secrecy_Keys @ B2 @ ( insert_Secrecy_Keys @ A2 @ bot_bo701486667y_Keys ) )
% 0.28/0.61 => ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonD
% 0.28/0.61 thf(fact_141_singletonD,axiom,
% 0.28/0.61 ! [B2: secrecy_Secrets,A2: secrecy_Secrets] :
% 0.28/0.61 ( ( member2138796287ecrets @ B2 @ ( insert565337510ecrets @ A2 @ bot_bo1124690338ecrets ) )
% 0.28/0.61 => ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonD
% 0.28/0.61 thf(fact_142_singletonD,axiom,
% 0.28/0.61 ! [B2: secrecy_specID,A2: secrecy_specID] :
% 0.28/0.61 ( ( member740727610specID @ B2 @ ( insert1671894227specID @ A2 @ bot_bo1785112429specID ) )
% 0.28/0.61 => ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonD
% 0.28/0.61 thf(fact_143_singletonD,axiom,
% 0.28/0.61 ! [B2: secrecy_chanID,A2: secrecy_chanID] :
% 0.28/0.61 ( ( member1967978193chanID @ B2 @ ( insert751661162chanID @ A2 @ bot_bo443197316chanID ) )
% 0.28/0.61 => ( B2 = A2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % singletonD
% 0.28/0.61 thf(fact_144_LocalSecretsComposition__neg1,axiom,
% 0.28/0.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.28/0.61 ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ! [M2: secrecy_Keys] :
% 0.28/0.61 ( ( Ks
% 0.28/0.61 = ( secrecy_kKS @ M2 ) )
% 0.28/0.61 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 0.28/0.61 & ~ ( ine @ Q @ ( secrecy_kE @ M2 ) ) ) )
% 0.28/0.61 => ( ! [M2: secrecy_Secrets] :
% 0.28/0.61 ( ( Ks
% 0.28/0.61 = ( secrecy_sKS @ M2 ) )
% 0.28/0.61 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 0.28/0.61 & ~ ( ine @ Q @ ( secrecy_sE @ M2 ) ) ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.28/0.61 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_neg1
% 0.28/0.61 thf(fact_145_the__elem__eq,axiom,
% 0.28/0.61 ! [X3: secrecy_specID] :
% 0.28/0.61 ( ( the_el827131246specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.61 = X3 ) ).
% 0.28/0.61
% 0.28/0.61 % the_elem_eq
% 0.28/0.61 thf(fact_146_the__elem__eq,axiom,
% 0.28/0.61 ! [X3: secrecy_chanID] :
% 0.28/0.61 ( ( the_el2054381829chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.61 = X3 ) ).
% 0.28/0.61
% 0.28/0.61 % the_elem_eq
% 0.28/0.61 thf(fact_147_LocalSecretsComposition__neg1__k,axiom,
% 0.28/0.61 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.28/0.61 ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.28/0.61 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.28/0.61 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_neg1_k
% 0.28/0.61 thf(fact_148_LocalSecretsComposition__ine2__k,axiom,
% 0.28/0.61 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.61 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.28/0.61 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_ine2_k
% 0.28/0.61 thf(fact_149_LocalSecretsComposition__ine1__k,axiom,
% 0.28/0.61 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.61 ( ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.61 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.28/0.61 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.28/0.61 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % LocalSecretsComposition_ine1_k
% 0.28/0.61 thf(fact_150_know__composition__neg__ine__k,axiom,
% 0.28/0.61 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.61 ( ~ ( knowle945212990e_know @ P @ ( secrecy_kKS @ Key ) )
% 0.28/0.61 => ( ~ ( knowle945212990e_know @ Q @ ( secrecy_kKS @ Key ) )
% 0.28/0.61 => ( ( ( subcomponents @ PQ )
% 0.28/0.61 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.61 => ( ( correctCompositionIn @ PQ )
% 0.28/0.61 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % know_composition_neg_ine_k
% 0.28/0.61 thf(fact_151_is__singletonI,axiom,
% 0.28/0.61 ! [X3: secrecy_specID] : ( is_sin1501507247specID @ ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ).
% 0.28/0.61
% 0.28/0.61 % is_singletonI
% 0.28/0.61 thf(fact_152_is__singletonI,axiom,
% 0.28/0.61 ! [X3: secrecy_chanID] : ( is_sin581274182chanID @ ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ).
% 0.28/0.61
% 0.28/0.61 % is_singletonI
% 0.28/0.61 thf(fact_153_KS2Expression_Osimps_I2_J,axiom,
% 0.28/0.61 ! [M: secrecy_Secrets] :
% 0.28/0.61 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.28/0.61 = ( secrecy_sE @ M ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS2Expression.simps(2)
% 0.28/0.61 thf(fact_154_Expression_Oinject_I1_J,axiom,
% 0.28/0.61 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.28/0.61 ( ( ( secrecy_kE @ X1 )
% 0.28/0.61 = ( secrecy_kE @ Y1 ) )
% 0.28/0.61 = ( X1 = Y1 ) ) ).
% 0.28/0.61
% 0.28/0.61 % Expression.inject(1)
% 0.28/0.61 thf(fact_155_KS2Expression_Osimps_I1_J,axiom,
% 0.28/0.61 ! [M: secrecy_Keys] :
% 0.28/0.61 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.28/0.61 = ( secrecy_kE @ M ) ) ).
% 0.28/0.61
% 0.28/0.61 % KS2Expression.simps(1)
% 0.28/0.61 thf(fact_156_bot__set__def,axiom,
% 0.28/0.61 ( bot_bo1785112429specID
% 0.28/0.61 = ( collec1545797240specID @ bot_bo1767780696ecID_o ) ) ).
% 0.28/0.61
% 0.28/0.61 % bot_set_def
% 0.28/0.61 thf(fact_157_bot__set__def,axiom,
% 0.28/0.61 ( bot_bo443197316chanID
% 0.28/0.61 = ( collec625564175chanID @ bot_bo1012329985anID_o ) ) ).
% 0.28/0.61
% 0.28/0.61 % bot_set_def
% 0.28/0.61 thf(fact_158_Expression_Odistinct_I1_J,axiom,
% 0.28/0.61 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.28/0.61 ( ( secrecy_kE @ X1 )
% 0.28/0.61 != ( secrecy_sE @ X2 ) ) ).
% 0.28/0.61
% 0.28/0.61 % Expression.distinct(1)
% 0.28/0.61 thf(fact_159_is__singleton__the__elem,axiom,
% 0.28/0.61 ( is_sin1501507247specID
% 0.28/0.61 = ( ^ [A3: set_Secrecy_specID] :
% 0.28/0.61 ( A3
% 0.28/0.61 = ( insert1671894227specID @ ( the_el827131246specID @ A3 ) @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % is_singleton_the_elem
% 0.28/0.61 thf(fact_160_is__singleton__the__elem,axiom,
% 0.28/0.61 ( is_sin581274182chanID
% 0.28/0.61 = ( ^ [A3: set_Secrecy_chanID] :
% 0.28/0.61 ( A3
% 0.28/0.61 = ( insert751661162chanID @ ( the_el2054381829chanID @ A3 ) @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.61
% 0.28/0.61 % is_singleton_the_elem
% 0.28/0.61 thf(fact_161_is__singletonI_H,axiom,
% 0.28/0.61 ! [A: set_Secrecy_KS] :
% 0.28/0.61 ( ( A != bot_bo1943466239ecy_KS )
% 0.28/0.61 => ( ! [X: secrecy_KS,Y3: secrecy_KS] :
% 0.28/0.61 ( ( member_Secrecy_KS @ X @ A )
% 0.28/0.61 => ( ( member_Secrecy_KS @ Y3 @ A )
% 0.28/0.61 => ( X = Y3 ) ) )
% 0.28/0.61 => ( is_sin1442426433ecy_KS @ A ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonI'
% 0.28/0.62 thf(fact_162_is__singletonI_H,axiom,
% 0.28/0.62 ! [A: set_Secrecy_Keys] :
% 0.28/0.62 ( ( A != bot_bo701486667y_Keys )
% 0.28/0.62 => ( ! [X: secrecy_Keys,Y3: secrecy_Keys] :
% 0.28/0.62 ( ( member_Secrecy_Keys @ X @ A )
% 0.28/0.62 => ( ( member_Secrecy_Keys @ Y3 @ A )
% 0.28/0.62 => ( X = Y3 ) ) )
% 0.28/0.62 => ( is_sin1096471309y_Keys @ A ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonI'
% 0.28/0.62 thf(fact_163_is__singletonI_H,axiom,
% 0.28/0.62 ! [A: set_Secrecy_Secrets] :
% 0.28/0.62 ( ( A != bot_bo1124690338ecrets )
% 0.28/0.62 => ( ! [X: secrecy_Secrets,Y3: secrecy_Secrets] :
% 0.28/0.62 ( ( member2138796287ecrets @ X @ A )
% 0.28/0.62 => ( ( member2138796287ecrets @ Y3 @ A )
% 0.28/0.62 => ( X = Y3 ) ) )
% 0.28/0.62 => ( is_sin1002224330ecrets @ A ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonI'
% 0.28/0.62 thf(fact_164_is__singletonI_H,axiom,
% 0.28/0.62 ! [A: set_Secrecy_specID] :
% 0.28/0.62 ( ( A != bot_bo1785112429specID )
% 0.28/0.62 => ( ! [X: secrecy_specID,Y3: secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ X @ A )
% 0.28/0.62 => ( ( member740727610specID @ Y3 @ A )
% 0.28/0.62 => ( X = Y3 ) ) )
% 0.28/0.62 => ( is_sin1501507247specID @ A ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonI'
% 0.28/0.62 thf(fact_165_is__singletonI_H,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID] :
% 0.28/0.62 ( ( A != bot_bo443197316chanID )
% 0.28/0.62 => ( ! [X: secrecy_chanID,Y3: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ A )
% 0.28/0.62 => ( ( member1967978193chanID @ Y3 @ A )
% 0.28/0.62 => ( X = Y3 ) ) )
% 0.28/0.62 => ( is_sin581274182chanID @ A ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonI'
% 0.28/0.62 thf(fact_166_not__know__k__not__ine,axiom,
% 0.28/0.62 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.62 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.62 => ~ ( ine @ A @ ( secrecy_kE @ M ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % not_know_k_not_ine
% 0.28/0.62 thf(fact_167_is__singletonE,axiom,
% 0.28/0.62 ! [A: set_Secrecy_specID] :
% 0.28/0.62 ( ( is_sin1501507247specID @ A )
% 0.28/0.62 => ~ ! [X: secrecy_specID] :
% 0.28/0.62 ( A
% 0.28/0.62 != ( insert1671894227specID @ X @ bot_bo1785112429specID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonE
% 0.28/0.62 thf(fact_168_is__singletonE,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID] :
% 0.28/0.62 ( ( is_sin581274182chanID @ A )
% 0.28/0.62 => ~ ! [X: secrecy_chanID] :
% 0.28/0.62 ( A
% 0.28/0.62 != ( insert751661162chanID @ X @ bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singletonE
% 0.28/0.62 thf(fact_169_is__singleton__def,axiom,
% 0.28/0.62 ( is_sin1501507247specID
% 0.28/0.62 = ( ^ [A3: set_Secrecy_specID] :
% 0.28/0.62 ? [X4: secrecy_specID] :
% 0.28/0.62 ( A3
% 0.28/0.62 = ( insert1671894227specID @ X4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singleton_def
% 0.28/0.62 thf(fact_170_is__singleton__def,axiom,
% 0.28/0.62 ( is_sin581274182chanID
% 0.28/0.62 = ( ^ [A3: set_Secrecy_chanID] :
% 0.28/0.62 ? [X4: secrecy_chanID] :
% 0.28/0.62 ( A3
% 0.28/0.62 = ( insert751661162chanID @ X4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % is_singleton_def
% 0.28/0.62 thf(fact_171_know_Osimps_I1_J,axiom,
% 0.28/0.62 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.62 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.62 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.28/0.62 | ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % know.simps(1)
% 0.28/0.62 thf(fact_172_TBtheorem4a__empty,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ( ine @ P @ E )
% 0.28/0.62 | ( ine @ Q @ E ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( ( loc @ PQ )
% 0.28/0.62 = bot_bo443197316chanID )
% 0.28/0.62 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4a_empty
% 0.28/0.62 thf(fact_173_TBtheorem1b,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( ineM @ PQ @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( ineM @ P @ M3 @ E )
% 0.28/0.62 | ( ineM @ Q @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem1b
% 0.28/0.62 thf(fact_174_TBtheorem3b,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ~ ( ineM @ P @ M3 @ E )
% 0.28/0.62 => ( ~ ( ineM @ Q @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem3b
% 0.28/0.62 thf(fact_175_Set_Ois__empty__def,axiom,
% 0.28/0.62 ( is_emp1849217361specID
% 0.28/0.62 = ( ^ [A3: set_Secrecy_specID] : ( A3 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Set.is_empty_def
% 0.28/0.62 thf(fact_176_Set_Ois__empty__def,axiom,
% 0.28/0.62 ( is_emp928984296chanID
% 0.28/0.62 = ( ^ [A3: set_Secrecy_chanID] : ( A3 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Set.is_empty_def
% 0.28/0.62 thf(fact_177_correctCompositionIn__L2,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionIn_L2
% 0.28/0.62 thf(fact_178_correctCompositionIn__prop1,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ X3 @ ( ins @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionIn_prop1
% 0.28/0.62 thf(fact_179_TBtheorem4a__notP1,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ine @ P @ E )
% 0.28/0.62 => ( ~ ( ine @ Q @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4a_notP1
% 0.28/0.62 thf(fact_180_not__ine__ineM,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,M3: set_Secrecy_chanID] :
% 0.28/0.62 ( ~ ( ine @ P @ E )
% 0.28/0.62 => ~ ( ineM @ P @ M3 @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % not_ine_ineM
% 0.28/0.62 thf(fact_181_ineM__ine,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( ineM @ P @ M3 @ E )
% 0.28/0.62 => ( ine @ P @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % ineM_ine
% 0.28/0.62 thf(fact_182_TBtheorem4b__notP1,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ineM @ P @ M3 @ E )
% 0.28/0.62 => ( ~ ( ineM @ Q @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4b_notP1
% 0.28/0.62 thf(fact_183_correctCompositionIn__L1,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ~ ( member1967978193chanID @ Ch @ ( loc @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( member1967978193chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionIn_L1
% 0.28/0.62 thf(fact_184_subcomponents__loc,axiom,
% 0.28/0.62 ! [X3: secrecy_specID] :
% 0.28/0.62 ( ( correc965049635ionLoc @ X3 )
% 0.28/0.62 => ( ( ( subcomponents @ X3 )
% 0.28/0.62 = bot_bo1785112429specID )
% 0.28/0.62 => ( ( loc @ X3 )
% 0.28/0.62 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % subcomponents_loc
% 0.28/0.62 thf(fact_185_TBtheorem4b__notPQ,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.62 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetP )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4b_notPQ
% 0.28/0.62 thf(fact_186_TBtheorem4b__notP2,axiom,
% 0.28/0.62 ! [Q: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.62 ( ~ ( ineM @ Q @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSet )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( ineM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4b_notP2
% 0.28/0.62 thf(fact_187_TBtheorem4a__notPQ,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.62 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetP )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4a_notPQ
% 0.28/0.62 thf(fact_188_TBtheorem4a__notP2,axiom,
% 0.28/0.62 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.62 ( ~ ( ine @ Q @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSet )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4a_notP2
% 0.28/0.62 thf(fact_189_TBtheorem4b__PQ,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ( ineM @ P @ M3 @ E )
% 0.28/0.62 | ( ineM @ Q @ M3 @ E ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4b_PQ
% 0.28/0.62 thf(fact_190_ine__exprChannelSet__def,axiom,
% 0.28/0.62 ( ine_exprChannelSet
% 0.28/0.62 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.62 ( ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ ChSet2 )
% 0.28/0.62 => ( ( member1967978193chanID @ X4 @ ( ins @ SP ) )
% 0.28/0.62 & ( exprChannel @ X4 @ E2 ) ) )
% 0.28/0.62 & ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( ~ ( member1967978193chanID @ X4 @ ChSet2 )
% 0.28/0.62 & ( member1967978193chanID @ X4 @ ( ins @ SP ) ) )
% 0.28/0.62 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_exprChannelSet_def
% 0.28/0.62 thf(fact_191_ine__def,axiom,
% 0.28/0.62 ( ine
% 0.28/0.62 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.28/0.62 ? [Ch3: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.28/0.62 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_def
% 0.28/0.62 thf(fact_192_ine__ins__neg1,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M: secrecy_Expression,X3: secrecy_chanID] :
% 0.28/0.62 ( ~ ( ine @ P @ M )
% 0.28/0.62 => ( ( exprChannel @ X3 @ M )
% 0.28/0.62 => ~ ( member1967978193chanID @ X3 @ ( ins @ P ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_ins_neg1
% 0.28/0.62 thf(fact_193_ineM__def,axiom,
% 0.28/0.62 ( ineM
% 0.28/0.62 = ( ^ [SP: secrecy_specID,M4: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.62 ? [Ch3: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.28/0.62 & ( member1967978193chanID @ Ch3 @ M4 )
% 0.28/0.62 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ineM_def
% 0.28/0.62 thf(fact_194_ineM__L1,axiom,
% 0.28/0.62 ! [Ch: secrecy_chanID,M3: set_Secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch @ M3 )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ E )
% 0.28/0.62 => ( ineM @ P @ M3 @ E ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ineM_L1
% 0.28/0.62 thf(fact_195_ine__exprChannelSingle__def,axiom,
% 0.28/0.62 ( ine_ex1303305700Single
% 0.28/0.62 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch3 @ ( ins @ SP ) )
% 0.28/0.62 & ( exprChannel @ Ch3 @ E2 )
% 0.28/0.62 & ! [X4: secrecy_chanID,T: nat] :
% 0.28/0.62 ( ( ( member1967978193chanID @ X4 @ ( ins @ SP ) )
% 0.28/0.62 & ( X4 != Ch3 ) )
% 0.28/0.62 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_exprChannelSingle_def
% 0.28/0.62 thf(fact_196_LocalSecretsComposition__exprChannel__s,axiom,
% 0.28/0.62 ! [X3: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( exprChannel @ X3 @ ( secrecy_sE @ Secrets ) )
% 0.28/0.62 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.28/0.62 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.28/0.62 => ( ~ ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.28/0.62 & ~ ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_exprChannel_s
% 0.28/0.62 thf(fact_197_LocalSecretsComposition__exprChannel__k,axiom,
% 0.28/0.62 ! [X3: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( exprChannel @ X3 @ ( secrecy_kE @ Keys ) )
% 0.28/0.62 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.28/0.62 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.28/0.62 => ( ~ ( member1967978193chanID @ X3 @ ( ins @ P ) )
% 0.28/0.62 & ~ ( member1967978193chanID @ X3 @ ( ins @ Q ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_exprChannel_k
% 0.28/0.62 thf(fact_198_ine__nonempty__exprChannelSet,axiom,
% 0.28/0.62 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.62 => ( ( ChSet != bot_bo443197316chanID )
% 0.28/0.62 => ( ine @ P @ E ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_nonempty_exprChannelSet
% 0.28/0.62 thf(fact_199_ine__empty__exprChannelSet,axiom,
% 0.28/0.62 ! [P: secrecy_specID,ChSet: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.62 => ( ( ChSet = bot_bo443197316chanID )
% 0.28/0.62 => ~ ( ine @ P @ E ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_empty_exprChannelSet
% 0.28/0.62 thf(fact_200_ine__exprChannelSingle__Set,axiom,
% 0.28/0.62 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.28/0.62 => ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_exprChannelSingle_Set
% 0.28/0.62 thf(fact_201_ine__exprChannelSet__Single,axiom,
% 0.28/0.62 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( ine_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.28/0.62 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % ine_exprChannelSet_Single
% 0.28/0.62 thf(fact_202_correctCompositionInLoc__exprChannel,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ M )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ( ins @ PQ ) )
% 0.28/0.62 => ~ ( exprChannel @ X @ M ) )
% 0.28/0.62 => ( member1967978193chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionInLoc_exprChannel
% 0.28/0.62 thf(fact_203_TBlemma3b,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.62 ( ~ ( ineM @ P @ M3 @ E )
% 0.28/0.62 => ( ~ ( ineM @ Q @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ M3 )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.62 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBlemma3b
% 0.28/0.62 thf(fact_204_TBtheorem4a__P,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( ine @ P @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4a_P
% 0.28/0.62 thf(fact_205_TBtheorem4a__PQ,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ( ine @ P @ E )
% 0.28/0.62 | ( ine @ Q @ E ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( ( member1967978193chanID @ Ch2 @ ( ins @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4a_PQ
% 0.28/0.62 thf(fact_206_TBtheorem4b__P,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( ineM @ P @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch2 @ ( ins @ Q ) )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ M3 ) )
% 0.28/0.62 => ( ineM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem4b_P
% 0.28/0.62 thf(fact_207_locStream__def,axiom,
% 0.28/0.62 ( locStream
% 0.28/0.62 = ( ^ [X4: secrecy_specID] :
% 0.28/0.62 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.28/0.62 @ ( loc @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % locStream_def
% 0.28/0.62 thf(fact_208_inStream__def,axiom,
% 0.28/0.62 ( inStream
% 0.28/0.62 = ( ^ [X4: secrecy_specID] :
% 0.28/0.62 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.28/0.62 @ ( ins @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % inStream_def
% 0.28/0.62 thf(fact_209_Collect__empty__eq__bot,axiom,
% 0.28/0.62 ! [P: secrecy_specID > $o] :
% 0.28/0.62 ( ( ( collec1545797240specID @ P )
% 0.28/0.62 = bot_bo1785112429specID )
% 0.28/0.62 = ( P = bot_bo1767780696ecID_o ) ) ).
% 0.28/0.62
% 0.28/0.62 % Collect_empty_eq_bot
% 0.28/0.62 thf(fact_210_Collect__empty__eq__bot,axiom,
% 0.28/0.62 ! [P: secrecy_chanID > $o] :
% 0.28/0.62 ( ( ( collec625564175chanID @ P )
% 0.28/0.62 = bot_bo443197316chanID )
% 0.28/0.62 = ( P = bot_bo1012329985anID_o ) ) ).
% 0.28/0.62
% 0.28/0.62 % Collect_empty_eq_bot
% 0.28/0.62 thf(fact_211_bot__empty__eq,axiom,
% 0.28/0.62 ( bot_bot_Secrecy_KS_o
% 0.28/0.62 = ( ^ [X4: secrecy_KS] : ( member_Secrecy_KS @ X4 @ bot_bo1943466239ecy_KS ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bot_empty_eq
% 0.28/0.62 thf(fact_212_bot__empty__eq,axiom,
% 0.28/0.62 ( bot_bo2072920570Keys_o
% 0.28/0.62 = ( ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ bot_bo701486667y_Keys ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bot_empty_eq
% 0.28/0.62 thf(fact_213_bot__empty__eq,axiom,
% 0.28/0.62 ( bot_bo1909946299rets_o
% 0.28/0.62 = ( ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ bot_bo1124690338ecrets ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bot_empty_eq
% 0.28/0.62 thf(fact_214_bot__empty__eq,axiom,
% 0.28/0.62 ( bot_bo1767780696ecID_o
% 0.28/0.62 = ( ^ [X4: secrecy_specID] : ( member740727610specID @ X4 @ bot_bo1785112429specID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bot_empty_eq
% 0.28/0.62 thf(fact_215_bot__empty__eq,axiom,
% 0.28/0.62 ( bot_bo1012329985anID_o
% 0.28/0.62 = ( ^ [X4: secrecy_chanID] : ( member1967978193chanID @ X4 @ bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bot_empty_eq
% 0.28/0.62 thf(fact_216_LocalSecretsComposition__neg__loc__s,axiom,
% 0.28/0.62 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.62 ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_neg_loc_s
% 0.28/0.62 thf(fact_217_LocalSecretsComposition__neg__loc__k,axiom,
% 0.28/0.62 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.28/0.62 ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ~ ( member1967978193chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_neg_loc_k
% 0.28/0.62 thf(fact_218_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ? [Ch4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_s_Qex
% 0.28/0.62 thf(fact_219_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ? [Ch4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_s_Pex
% 0.28/0.62 thf(fact_220_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_s_Q
% 0.28/0.62 thf(fact_221_correctCompositionKS__exprChannel__s__P,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_s_P
% 0.28/0.62 thf(fact_222_correctCompositionKS__PQ,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.28/0.62 | ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_PQ
% 0.28/0.62 thf(fact_223_correctCompositionKS__neg1,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_neg1
% 0.28/0.62 thf(fact_224_correctCompositionKS__negP,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_negP
% 0.28/0.62 thf(fact_225_correctCompositionKS__negQ,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_negQ
% 0.28/0.62 thf(fact_226_know__composition,axiom,
% 0.28/0.62 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ( ( ( knowle945212990e_know @ P @ M )
% 0.28/0.62 | ( knowle945212990e_know @ Q @ M ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % know_composition
% 0.28/0.62 thf(fact_227_know__composition1,axiom,
% 0.28/0.62 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ( ( knowle945212990e_know @ P @ M )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % know_composition1
% 0.28/0.62 thf(fact_228_know__composition2,axiom,
% 0.28/0.62 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ( ( knowle945212990e_know @ Q @ M )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( knowle945212990e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % know_composition2
% 0.28/0.62 thf(fact_229_correctCompositionKS__exprChannel__k__P,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_k_P
% 0.28/0.62 thf(fact_230_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_k_Q
% 0.28/0.62 thf(fact_231_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ P ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ? [Ch4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_k_Pex
% 0.28/0.62 thf(fact_232_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ Ch @ ( ins @ Q ) )
% 0.28/0.62 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.28/0.62 => ( ( correctCompositionIn @ PQ )
% 0.28/0.62 => ? [Ch4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch4 @ ( ins @ PQ ) )
% 0.28/0.62 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_exprChannel_k_Qex
% 0.28/0.62 thf(fact_233_LocalSecretsComposition__neg,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ( ! [M2: secrecy_Keys] :
% 0.28/0.62 ( ( Ks
% 0.28/0.62 = ( secrecy_kKS @ M2 ) )
% 0.28/0.62 => ( ~ ( ine @ P @ ( secrecy_kE @ M2 ) )
% 0.28/0.62 & ~ ( ine @ Q @ ( secrecy_kE @ M2 ) ) ) )
% 0.28/0.62 => ( ! [M2: secrecy_Secrets] :
% 0.28/0.62 ( ( Ks
% 0.28/0.62 = ( secrecy_sKS @ M2 ) )
% 0.28/0.62 => ( ~ ( ine @ P @ ( secrecy_sE @ M2 ) )
% 0.28/0.62 & ~ ( ine @ Q @ ( secrecy_sE @ M2 ) ) ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ Ks @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_neg
% 0.28/0.62 thf(fact_234_LocalSecretsComposition__neg__s,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.28/0.62 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_neg_s
% 0.28/0.62 thf(fact_235_LocalSecretsComposition__neg__k,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc965049635ionLoc @ PQ )
% 0.28/0.62 => ( ( correctCompositionKS @ PQ )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.28/0.62 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.28/0.62 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_su1301156759ecy_KS @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % LocalSecretsComposition_neg_k
% 0.28/0.62 thf(fact_236_notSpecKeysSecretsExpr__def,axiom,
% 0.28/0.62 ( notSpe1586871396tsExpr
% 0.28/0.62 = ( ^ [P2: secrecy_specID,E3: list_S529945141ession] :
% 0.28/0.62 ( ! [X4: secrecy_Keys] :
% 0.28/0.62 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E3 )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.28/0.62 & ! [Y5: secrecy_Secrets] :
% 0.28/0.62 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y5 ) @ E3 )
% 0.28/0.62 => ~ ( member_Secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % notSpecKeysSecretsExpr_def
% 0.28/0.62 thf(fact_237_UnCI,axiom,
% 0.28/0.62 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.62 ( ( ~ ( member740727610specID @ C @ B )
% 0.28/0.62 => ( member740727610specID @ C @ A ) )
% 0.28/0.62 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnCI
% 0.28/0.62 thf(fact_238_UnCI,axiom,
% 0.28/0.62 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.62 ( ( ~ ( member_Secrecy_Keys @ C @ B )
% 0.28/0.62 => ( member_Secrecy_Keys @ C @ A ) )
% 0.28/0.62 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnCI
% 0.28/0.62 thf(fact_239_UnCI,axiom,
% 0.28/0.62 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.62 ( ( ~ ( member2138796287ecrets @ C @ B )
% 0.28/0.62 => ( member2138796287ecrets @ C @ A ) )
% 0.28/0.62 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnCI
% 0.28/0.62 thf(fact_240_UnCI,axiom,
% 0.28/0.62 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.62 ( ( ~ ( member_Secrecy_KS @ C @ B )
% 0.28/0.62 => ( member_Secrecy_KS @ C @ A ) )
% 0.28/0.62 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnCI
% 0.28/0.62 thf(fact_241_UnCI,axiom,
% 0.28/0.62 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ~ ( member1967978193chanID @ C @ B )
% 0.28/0.62 => ( member1967978193chanID @ C @ A ) )
% 0.28/0.62 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnCI
% 0.28/0.62 thf(fact_242_Un__iff,axiom,
% 0.28/0.62 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.28/0.62 = ( ( member740727610specID @ C @ A )
% 0.28/0.62 | ( member740727610specID @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_iff
% 0.28/0.62 thf(fact_243_Un__iff,axiom,
% 0.28/0.62 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.28/0.62 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.28/0.62 = ( ( member_Secrecy_Keys @ C @ A )
% 0.28/0.62 | ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_iff
% 0.28/0.62 thf(fact_244_Un__iff,axiom,
% 0.28/0.62 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.28/0.62 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.28/0.62 = ( ( member2138796287ecrets @ C @ A )
% 0.28/0.62 | ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_iff
% 0.28/0.62 thf(fact_245_Un__iff,axiom,
% 0.28/0.62 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.28/0.62 = ( ( member_Secrecy_KS @ C @ A )
% 0.28/0.62 | ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_iff
% 0.28/0.62 thf(fact_246_Un__iff,axiom,
% 0.28/0.62 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.28/0.62 = ( ( member1967978193chanID @ C @ A )
% 0.28/0.62 | ( member1967978193chanID @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_iff
% 0.28/0.62 thf(fact_247_Un__empty,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.28/0.62 = bot_bo1943466239ecy_KS )
% 0.28/0.62 = ( ( A = bot_bo1943466239ecy_KS )
% 0.28/0.62 & ( B = bot_bo1943466239ecy_KS ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty
% 0.28/0.62 thf(fact_248_Un__empty,axiom,
% 0.28/0.62 ! [A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.62 ( ( ( sup_su1712599557specID @ A @ B )
% 0.28/0.62 = bot_bo1785112429specID )
% 0.28/0.62 = ( ( A = bot_bo1785112429specID )
% 0.28/0.62 & ( B = bot_bo1785112429specID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty
% 0.28/0.62 thf(fact_249_Un__empty,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( sup_su370684444chanID @ A @ B )
% 0.28/0.62 = bot_bo443197316chanID )
% 0.28/0.62 = ( ( A = bot_bo443197316chanID )
% 0.28/0.62 & ( B = bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty
% 0.28/0.62 thf(fact_250_Un__insert__right,axiom,
% 0.28/0.62 ! [A: set_Secrecy_specID,A2: secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ A @ ( insert1671894227specID @ A2 @ B ) )
% 0.28/0.62 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_insert_right
% 0.28/0.62 thf(fact_251_Un__insert__right,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,A2: secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ A @ ( insert_Secrecy_KS @ A2 @ B ) )
% 0.28/0.62 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_insert_right
% 0.28/0.62 thf(fact_252_Un__insert__right,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,A2: secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ A @ ( insert751661162chanID @ A2 @ B ) )
% 0.28/0.62 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_insert_right
% 0.28/0.62 thf(fact_253_Un__insert__left,axiom,
% 0.28/0.62 ! [A2: secrecy_specID,B: set_Secrecy_specID,C3: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ ( insert1671894227specID @ A2 @ B ) @ C3 )
% 0.28/0.62 = ( insert1671894227specID @ A2 @ ( sup_su1712599557specID @ B @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_insert_left
% 0.28/0.62 thf(fact_254_Un__insert__left,axiom,
% 0.28/0.62 ! [A2: secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A2 @ B ) @ C3 )
% 0.28/0.62 = ( insert_Secrecy_KS @ A2 @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_insert_left
% 0.28/0.62 thf(fact_255_Un__insert__left,axiom,
% 0.28/0.62 ! [A2: secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ ( insert751661162chanID @ A2 @ B ) @ C3 )
% 0.28/0.62 = ( insert751661162chanID @ A2 @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_insert_left
% 0.28/0.62 thf(fact_256_UnE,axiom,
% 0.28/0.62 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) )
% 0.28/0.62 => ( ~ ( member740727610specID @ C @ A )
% 0.28/0.62 => ( member740727610specID @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnE
% 0.28/0.62 thf(fact_257_UnE,axiom,
% 0.28/0.62 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.28/0.62 ( ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_Keys @ C @ A )
% 0.28/0.62 => ( member_Secrecy_Keys @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnE
% 0.28/0.62 thf(fact_258_UnE,axiom,
% 0.28/0.62 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.28/0.62 ( ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) )
% 0.28/0.62 => ( ~ ( member2138796287ecrets @ C @ A )
% 0.28/0.62 => ( member2138796287ecrets @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnE
% 0.28/0.62 thf(fact_259_UnE,axiom,
% 0.28/0.62 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.28/0.62 => ( ~ ( member_Secrecy_KS @ C @ A )
% 0.28/0.62 => ( member_Secrecy_KS @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnE
% 0.28/0.62 thf(fact_260_UnE,axiom,
% 0.28/0.62 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) )
% 0.28/0.62 => ( ~ ( member1967978193chanID @ C @ A )
% 0.28/0.62 => ( member1967978193chanID @ C @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnE
% 0.28/0.62 thf(fact_261_UnI1,axiom,
% 0.28/0.62 ! [C: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ C @ A )
% 0.28/0.62 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI1
% 0.28/0.62 thf(fact_262_UnI1,axiom,
% 0.28/0.62 ! [C: secrecy_Keys,A: set_Secrecy_Keys,B: set_Secrecy_Keys] :
% 0.28/0.62 ( ( member_Secrecy_Keys @ C @ A )
% 0.28/0.62 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI1
% 0.28/0.62 thf(fact_263_UnI1,axiom,
% 0.28/0.62 ! [C: secrecy_Secrets,A: set_Secrecy_Secrets,B: set_Secrecy_Secrets] :
% 0.28/0.62 ( ( member2138796287ecrets @ C @ A )
% 0.28/0.62 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI1
% 0.28/0.62 thf(fact_264_UnI1,axiom,
% 0.28/0.62 ! [C: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ C @ A )
% 0.28/0.62 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI1
% 0.28/0.62 thf(fact_265_UnI1,axiom,
% 0.28/0.62 ! [C: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ C @ A )
% 0.28/0.62 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI1
% 0.28/0.62 thf(fact_266_UnI2,axiom,
% 0.28/0.62 ! [C: secrecy_specID,B: set_Secrecy_specID,A: set_Secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ C @ B )
% 0.28/0.62 => ( member740727610specID @ C @ ( sup_su1712599557specID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI2
% 0.28/0.62 thf(fact_267_UnI2,axiom,
% 0.28/0.62 ! [C: secrecy_Keys,B: set_Secrecy_Keys,A: set_Secrecy_Keys] :
% 0.28/0.62 ( ( member_Secrecy_Keys @ C @ B )
% 0.28/0.62 => ( member_Secrecy_Keys @ C @ ( sup_su552545507y_Keys @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI2
% 0.28/0.62 thf(fact_268_UnI2,axiom,
% 0.28/0.62 ! [C: secrecy_Secrets,B: set_Secrecy_Secrets,A: set_Secrecy_Secrets] :
% 0.28/0.62 ( ( member2138796287ecrets @ C @ B )
% 0.28/0.62 => ( member2138796287ecrets @ C @ ( sup_su1029080330ecrets @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI2
% 0.28/0.62 thf(fact_269_UnI2,axiom,
% 0.28/0.62 ! [C: secrecy_KS,B: set_Secrecy_KS,A: set_Secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ C @ B )
% 0.28/0.62 => ( member_Secrecy_KS @ C @ ( sup_su1301156759ecy_KS @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI2
% 0.28/0.62 thf(fact_270_UnI2,axiom,
% 0.28/0.62 ! [C: secrecy_chanID,B: set_Secrecy_chanID,A: set_Secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ C @ B )
% 0.28/0.62 => ( member1967978193chanID @ C @ ( sup_su370684444chanID @ A @ B ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % UnI2
% 0.28/0.62 thf(fact_271_bex__Un,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.28/0.62 ( ( ? [X4: secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ X4 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.28/0.62 & ( P @ X4 ) ) )
% 0.28/0.62 = ( ? [X4: secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ X4 @ A )
% 0.28/0.62 & ( P @ X4 ) )
% 0.28/0.62 | ? [X4: secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ X4 @ B )
% 0.28/0.62 & ( P @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bex_Un
% 0.28/0.62 thf(fact_272_bex__Un,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.28/0.62 ( ( ? [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ ( sup_su370684444chanID @ A @ B ) )
% 0.28/0.62 & ( P @ X4 ) ) )
% 0.28/0.62 = ( ? [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ A )
% 0.28/0.62 & ( P @ X4 ) )
% 0.28/0.62 | ? [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ B )
% 0.28/0.62 & ( P @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % bex_Un
% 0.28/0.62 thf(fact_273_ball__Un,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,P: secrecy_KS > $o] :
% 0.28/0.62 ( ( ! [X4: secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ X4 @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.28/0.62 => ( P @ X4 ) ) )
% 0.28/0.62 = ( ! [X4: secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ X4 @ A )
% 0.28/0.62 => ( P @ X4 ) )
% 0.28/0.62 & ! [X4: secrecy_KS] :
% 0.28/0.62 ( ( member_Secrecy_KS @ X4 @ B )
% 0.28/0.62 => ( P @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ball_Un
% 0.28/0.62 thf(fact_274_ball__Un,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,P: secrecy_chanID > $o] :
% 0.28/0.62 ( ( ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ ( sup_su370684444chanID @ A @ B ) )
% 0.28/0.62 => ( P @ X4 ) ) )
% 0.28/0.62 = ( ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ A )
% 0.28/0.62 => ( P @ X4 ) )
% 0.28/0.62 & ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ B )
% 0.28/0.62 => ( P @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % ball_Un
% 0.28/0.62 thf(fact_275_Un__assoc,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ ( sup_su1301156759ecy_KS @ A @ B ) @ C3 )
% 0.28/0.62 = ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_assoc
% 0.28/0.62 thf(fact_276_Un__assoc,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ ( sup_su370684444chanID @ A @ B ) @ C3 )
% 0.28/0.62 = ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_assoc
% 0.28/0.62 thf(fact_277_Un__absorb,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ A @ A )
% 0.28/0.62 = A ) ).
% 0.28/0.62
% 0.28/0.62 % Un_absorb
% 0.28/0.62 thf(fact_278_Un__absorb,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ A @ A )
% 0.28/0.62 = A ) ).
% 0.28/0.62
% 0.28/0.62 % Un_absorb
% 0.28/0.62 thf(fact_279_Un__commute,axiom,
% 0.28/0.62 ( sup_su1301156759ecy_KS
% 0.28/0.62 = ( ^ [A3: set_Secrecy_KS,B4: set_Secrecy_KS] : ( sup_su1301156759ecy_KS @ B4 @ A3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_commute
% 0.28/0.62 thf(fact_280_Un__commute,axiom,
% 0.28/0.62 ( sup_su370684444chanID
% 0.28/0.62 = ( ^ [A3: set_Secrecy_chanID,B4: set_Secrecy_chanID] : ( sup_su370684444chanID @ B4 @ A3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_commute
% 0.28/0.62 thf(fact_281_Un__left__absorb,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.28/0.62 = ( sup_su1301156759ecy_KS @ A @ B ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_left_absorb
% 0.28/0.62 thf(fact_282_Un__left__absorb,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ A @ B ) )
% 0.28/0.62 = ( sup_su370684444chanID @ A @ B ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_left_absorb
% 0.28/0.62 thf(fact_283_Un__left__commute,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,C3: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ A @ ( sup_su1301156759ecy_KS @ B @ C3 ) )
% 0.28/0.62 = ( sup_su1301156759ecy_KS @ B @ ( sup_su1301156759ecy_KS @ A @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_left_commute
% 0.28/0.62 thf(fact_284_Un__left__commute,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,C3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ A @ ( sup_su370684444chanID @ B @ C3 ) )
% 0.28/0.62 = ( sup_su370684444chanID @ B @ ( sup_su370684444chanID @ A @ C3 ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_left_commute
% 0.28/0.62 thf(fact_285_Un__empty__left,axiom,
% 0.28/0.62 ! [B: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ B )
% 0.28/0.62 = B ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty_left
% 0.28/0.62 thf(fact_286_Un__empty__left,axiom,
% 0.28/0.62 ! [B: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ B )
% 0.28/0.62 = B ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty_left
% 0.28/0.62 thf(fact_287_Un__empty__left,axiom,
% 0.28/0.62 ! [B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ B )
% 0.28/0.62 = B ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty_left
% 0.28/0.62 thf(fact_288_Un__empty__right,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ A @ bot_bo1943466239ecy_KS )
% 0.28/0.62 = A ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty_right
% 0.28/0.62 thf(fact_289_Un__empty__right,axiom,
% 0.28/0.62 ! [A: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ A @ bot_bo1785112429specID )
% 0.28/0.62 = A ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty_right
% 0.28/0.62 thf(fact_290_Un__empty__right,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ A @ bot_bo443197316chanID )
% 0.28/0.62 = A ) ).
% 0.28/0.62
% 0.28/0.62 % Un_empty_right
% 0.28/0.62 thf(fact_291_singleton__Un__iff,axiom,
% 0.28/0.62 ! [X3: secrecy_KS,A: set_Secrecy_KS,B: set_Secrecy_KS] :
% 0.28/0.62 ( ( ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS )
% 0.28/0.62 = ( sup_su1301156759ecy_KS @ A @ B ) )
% 0.28/0.62 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.62 & ( B = bot_bo1943466239ecy_KS ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % singleton_Un_iff
% 0.28/0.62 thf(fact_292_singleton__Un__iff,axiom,
% 0.28/0.62 ! [X3: secrecy_specID,A: set_Secrecy_specID,B: set_Secrecy_specID] :
% 0.28/0.62 ( ( ( insert1671894227specID @ X3 @ bot_bo1785112429specID )
% 0.28/0.62 = ( sup_su1712599557specID @ A @ B ) )
% 0.28/0.62 = ( ( ( A = bot_bo1785112429specID )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.62 & ( B = bot_bo1785112429specID ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % singleton_Un_iff
% 0.28/0.62 thf(fact_293_singleton__Un__iff,axiom,
% 0.28/0.62 ! [X3: secrecy_chanID,A: set_Secrecy_chanID,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( insert751661162chanID @ X3 @ bot_bo443197316chanID )
% 0.28/0.62 = ( sup_su370684444chanID @ A @ B ) )
% 0.28/0.62 = ( ( ( A = bot_bo443197316chanID )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.62 & ( B = bot_bo443197316chanID ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % singleton_Un_iff
% 0.28/0.62 thf(fact_294_Un__singleton__iff,axiom,
% 0.28/0.62 ! [A: set_Secrecy_KS,B: set_Secrecy_KS,X3: secrecy_KS] :
% 0.28/0.62 ( ( ( sup_su1301156759ecy_KS @ A @ B )
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.62 = ( ( ( A = bot_bo1943466239ecy_KS )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.62 & ( B = bot_bo1943466239ecy_KS ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert_Secrecy_KS @ X3 @ bot_bo1943466239ecy_KS ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_singleton_iff
% 0.28/0.62 thf(fact_295_Un__singleton__iff,axiom,
% 0.28/0.62 ! [A: set_Secrecy_specID,B: set_Secrecy_specID,X3: secrecy_specID] :
% 0.28/0.62 ( ( ( sup_su1712599557specID @ A @ B )
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.62 = ( ( ( A = bot_bo1785112429specID )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.62 & ( B = bot_bo1785112429specID ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert1671894227specID @ X3 @ bot_bo1785112429specID ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_singleton_iff
% 0.28/0.62 thf(fact_296_Un__singleton__iff,axiom,
% 0.28/0.62 ! [A: set_Secrecy_chanID,B: set_Secrecy_chanID,X3: secrecy_chanID] :
% 0.28/0.62 ( ( ( sup_su370684444chanID @ A @ B )
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.62 = ( ( ( A = bot_bo443197316chanID )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.62 & ( B = bot_bo443197316chanID ) )
% 0.28/0.62 | ( ( A
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) )
% 0.28/0.62 & ( B
% 0.28/0.62 = ( insert751661162chanID @ X3 @ bot_bo443197316chanID ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % Un_singleton_iff
% 0.28/0.62 thf(fact_297_insert__is__Un,axiom,
% 0.28/0.62 ( insert_Secrecy_KS
% 0.28/0.62 = ( ^ [A4: secrecy_KS] : ( sup_su1301156759ecy_KS @ ( insert_Secrecy_KS @ A4 @ bot_bo1943466239ecy_KS ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % insert_is_Un
% 0.28/0.62 thf(fact_298_insert__is__Un,axiom,
% 0.28/0.62 ( insert1671894227specID
% 0.28/0.62 = ( ^ [A4: secrecy_specID] : ( sup_su1712599557specID @ ( insert1671894227specID @ A4 @ bot_bo1785112429specID ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % insert_is_Un
% 0.28/0.62 thf(fact_299_insert__is__Un,axiom,
% 0.28/0.62 ( insert751661162chanID
% 0.28/0.62 = ( ^ [A4: secrecy_chanID] : ( sup_su370684444chanID @ ( insert751661162chanID @ A4 @ bot_bo443197316chanID ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % insert_is_Un
% 0.28/0.62 thf(fact_300_sup__bot_Oright__neutral,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ A2 @ bot_bo1943466239ecy_KS )
% 0.28/0.62 = A2 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.right_neutral
% 0.28/0.62 thf(fact_301_sup__bot_Oright__neutral,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ A2 @ bot_bo1785112429specID )
% 0.28/0.62 = A2 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.right_neutral
% 0.28/0.62 thf(fact_302_sup__bot_Oright__neutral,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ A2 @ bot_bo443197316chanID )
% 0.28/0.62 = A2 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.right_neutral
% 0.28/0.62 thf(fact_303_sup__bot_Oneutr__eq__iff,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.28/0.62 ( ( bot_bo1943466239ecy_KS
% 0.28/0.62 = ( sup_su1301156759ecy_KS @ A2 @ B2 ) )
% 0.28/0.62 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.28/0.62 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.neutr_eq_iff
% 0.28/0.62 thf(fact_304_sup__bot_Oneutr__eq__iff,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.28/0.62 ( ( bot_bo1785112429specID
% 0.28/0.62 = ( sup_su1712599557specID @ A2 @ B2 ) )
% 0.28/0.62 = ( ( A2 = bot_bo1785112429specID )
% 0.28/0.62 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.neutr_eq_iff
% 0.28/0.62 thf(fact_305_sup__bot_Oneutr__eq__iff,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.62 ( ( bot_bo443197316chanID
% 0.28/0.62 = ( sup_su370684444chanID @ A2 @ B2 ) )
% 0.28/0.62 = ( ( A2 = bot_bo443197316chanID )
% 0.28/0.62 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.neutr_eq_iff
% 0.28/0.62 thf(fact_306_sup__bot_Oleft__neutral,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ A2 )
% 0.28/0.62 = A2 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.left_neutral
% 0.28/0.62 thf(fact_307_sup__bot_Oleft__neutral,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ A2 )
% 0.28/0.62 = A2 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.left_neutral
% 0.28/0.62 thf(fact_308_sup__bot_Oleft__neutral,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ A2 )
% 0.28/0.62 = A2 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.left_neutral
% 0.28/0.62 thf(fact_309_sup__bot_Oeq__neutr__iff,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_KS,B2: set_Secrecy_KS] :
% 0.28/0.62 ( ( ( sup_su1301156759ecy_KS @ A2 @ B2 )
% 0.28/0.62 = bot_bo1943466239ecy_KS )
% 0.28/0.62 = ( ( A2 = bot_bo1943466239ecy_KS )
% 0.28/0.62 & ( B2 = bot_bo1943466239ecy_KS ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.eq_neutr_iff
% 0.28/0.62 thf(fact_310_sup__bot_Oeq__neutr__iff,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_specID,B2: set_Secrecy_specID] :
% 0.28/0.62 ( ( ( sup_su1712599557specID @ A2 @ B2 )
% 0.28/0.62 = bot_bo1785112429specID )
% 0.28/0.62 = ( ( A2 = bot_bo1785112429specID )
% 0.28/0.62 & ( B2 = bot_bo1785112429specID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.eq_neutr_iff
% 0.28/0.62 thf(fact_311_sup__bot_Oeq__neutr__iff,axiom,
% 0.28/0.62 ! [A2: set_Secrecy_chanID,B2: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( sup_su370684444chanID @ A2 @ B2 )
% 0.28/0.62 = bot_bo443197316chanID )
% 0.28/0.62 = ( ( A2 = bot_bo443197316chanID )
% 0.28/0.62 & ( B2 = bot_bo443197316chanID ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot.eq_neutr_iff
% 0.28/0.62 thf(fact_312_sup__bot__left,axiom,
% 0.28/0.62 ! [X3: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ bot_bo1943466239ecy_KS @ X3 )
% 0.28/0.62 = X3 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot_left
% 0.28/0.62 thf(fact_313_sup__bot__left,axiom,
% 0.28/0.62 ! [X3: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ bot_bo1785112429specID @ X3 )
% 0.28/0.62 = X3 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot_left
% 0.28/0.62 thf(fact_314_sup__bot__left,axiom,
% 0.28/0.62 ! [X3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ bot_bo443197316chanID @ X3 )
% 0.28/0.62 = X3 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot_left
% 0.28/0.62 thf(fact_315_sup__bot__right,axiom,
% 0.28/0.62 ! [X3: set_Secrecy_KS] :
% 0.28/0.62 ( ( sup_su1301156759ecy_KS @ X3 @ bot_bo1943466239ecy_KS )
% 0.28/0.62 = X3 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot_right
% 0.28/0.62 thf(fact_316_sup__bot__right,axiom,
% 0.28/0.62 ! [X3: set_Secrecy_specID] :
% 0.28/0.62 ( ( sup_su1712599557specID @ X3 @ bot_bo1785112429specID )
% 0.28/0.62 = X3 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot_right
% 0.28/0.62 thf(fact_317_sup__bot__right,axiom,
% 0.28/0.62 ! [X3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( sup_su370684444chanID @ X3 @ bot_bo443197316chanID )
% 0.28/0.62 = X3 ) ).
% 0.28/0.62
% 0.28/0.62 % sup_bot_right
% 0.28/0.62 thf(fact_318_ineM__Un1,axiom,
% 0.28/0.62 ! [P: secrecy_specID,A: set_Secrecy_chanID,E: secrecy_Expression,B: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ineM @ P @ A @ E )
% 0.28/0.62 => ( ineM @ P @ ( sup_su370684444chanID @ A @ B ) @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % ineM_Un1
% 0.28/0.62 thf(fact_319_TBtheorem5a__empty,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ( eout @ P @ E )
% 0.28/0.62 | ( eout @ Q @ E ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( ( loc @ PQ )
% 0.28/0.62 = bot_bo443197316chanID )
% 0.28/0.62 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5a_empty
% 0.28/0.62 thf(fact_320_correctCompositionKS__subcomp1,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Keys] :
% 0.28/0.62 ( ( correctCompositionKS @ C3 )
% 0.28/0.62 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.28/0.62 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) )
% 0.28/0.62 => ? [X: secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.28/0.62 & ( member_Secrecy_Keys @ Xa @ ( specKeys @ X ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_subcomp1
% 0.28/0.62 thf(fact_321_correctCompositionKS__subcomp2,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Secrets] :
% 0.28/0.62 ( ( correctCompositionKS @ C3 )
% 0.28/0.62 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.28/0.62 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) )
% 0.28/0.62 => ? [X: secrecy_specID] :
% 0.28/0.62 ( ( member740727610specID @ X @ ( subcomponents @ C3 ) )
% 0.28/0.62 & ( member2138796287ecrets @ Xa @ ( specSecrets @ X ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_subcomp2
% 0.28/0.62 thf(fact_322_TBtheorem2a,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( eout @ PQ @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( eout @ P @ E )
% 0.28/0.62 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem2a
% 0.28/0.62 thf(fact_323_correctCompositionKS__subcomp4,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Secrets] :
% 0.28/0.62 ( ( correctCompositionKS @ C3 )
% 0.28/0.62 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.28/0.62 => ( ( member2138796287ecrets @ Xa @ ( specSecrets @ X3 ) )
% 0.28/0.62 => ( member2138796287ecrets @ Xa @ ( specSecrets @ C3 ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_subcomp4
% 0.28/0.62 thf(fact_324_correctCompositionKS__subcomp3,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,X3: secrecy_specID,Xa: secrecy_Keys] :
% 0.28/0.62 ( ( correctCompositionKS @ C3 )
% 0.28/0.62 => ( ( member740727610specID @ X3 @ ( subcomponents @ C3 ) )
% 0.28/0.62 => ( ( member_Secrecy_Keys @ Xa @ ( specKeys @ X3 ) )
% 0.28/0.62 => ( member_Secrecy_Keys @ Xa @ ( specKeys @ C3 ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionKS_subcomp3
% 0.28/0.62 thf(fact_325_TBtheorem5a__notP1,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( eout @ P @ E )
% 0.28/0.62 => ( ~ ( eout @ Q @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5a_notP1
% 0.28/0.62 thf(fact_326_TBtheorem5a__notPQ,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.62 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetP )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5a_notPQ
% 0.28/0.62 thf(fact_327_TBtheorem5a__notP2,axiom,
% 0.28/0.62 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.62 ( ~ ( eout @ Q @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSet )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5a_notP2
% 0.28/0.62 thf(fact_328_out__exprChannelSingle__Set,axiom,
% 0.28/0.62 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.28/0.62 => ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % out_exprChannelSingle_Set
% 0.28/0.62 thf(fact_329_out__exprChannelSet__Single,axiom,
% 0.28/0.62 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( out_exprChannelSet @ P @ ( insert751661162chanID @ Ch @ bot_bo443197316chanID ) @ E )
% 0.28/0.62 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % out_exprChannelSet_Single
% 0.28/0.62 thf(fact_330_TBtheorem5b__notPQ,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set_Secrecy_chanID,E: secrecy_Expression,ChSetQ: set_Secrecy_chanID,M3: set_Secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.28/0.62 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.28/0.62 => ( ( M3
% 0.28/0.62 = ( sup_su370684444chanID @ ChSetP @ ChSetQ ) )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetP )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSetQ )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5b_notPQ
% 0.28/0.62 thf(fact_331_eout__know__s,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.62 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.28/0.62 = ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.28/0.62 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.28/0.62 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eout_know_s
% 0.28/0.62 thf(fact_332_not__know__s__not__eout,axiom,
% 0.28/0.62 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.28/0.62 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.28/0.62 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.62 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.62 => ~ ( eout @ A @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % not_know_s_not_eout
% 0.28/0.62 thf(fact_333_not__eout__eoutM,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,M3: set_Secrecy_chanID] :
% 0.28/0.62 ( ~ ( eout @ P @ E )
% 0.28/0.62 => ~ ( eoutM @ P @ M3 @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % not_eout_eoutM
% 0.28/0.62 thf(fact_334_eoutM__eout,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression] :
% 0.28/0.62 ( ( eoutM @ P @ M3 @ E )
% 0.28/0.62 => ( eout @ P @ E ) ) ).
% 0.28/0.62
% 0.28/0.62 % eoutM_eout
% 0.28/0.62 thf(fact_335_TBtheorem2b,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( eoutM @ PQ @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( eoutM @ P @ M3 @ E )
% 0.28/0.62 | ( eoutM @ Q @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem2b
% 0.28/0.62 thf(fact_336_TBtheorem5b__notP2,axiom,
% 0.28/0.62 ! [Q: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set_Secrecy_chanID] :
% 0.28/0.62 ( ~ ( eoutM @ Q @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.28/0.62 => ( ! [X: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X @ ChSet )
% 0.28/0.62 => ( member1967978193chanID @ X @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5b_notP2
% 0.28/0.62 thf(fact_337_TBtheorem5b__notP1,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( eoutM @ P @ M3 @ E )
% 0.28/0.62 => ( ~ ( eoutM @ Q @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ~ ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5b_notP1
% 0.28/0.62 thf(fact_338_eout__know__nonKS__k,axiom,
% 0.28/0.62 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.28/0.62 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.28/0.62 => ( ( eout @ A @ ( secrecy_kE @ M ) )
% 0.28/0.62 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.62 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eout_know_nonKS_k
% 0.28/0.62 thf(fact_339_eoutKnowCorrect__L1k,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.62 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.28/0.62 => ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.28/0.62 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.28/0.62 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eoutKnowCorrect_L1k
% 0.28/0.62 thf(fact_340_not__know__k__not__eout,axiom,
% 0.28/0.62 ! [M: secrecy_Keys,A: secrecy_specID] :
% 0.28/0.62 ( ~ ( member_Secrecy_Keys @ M @ ( specKeys @ A ) )
% 0.28/0.62 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.62 => ( ( knowle233900195orrect @ A @ ( secrecy_kKS @ M ) )
% 0.28/0.62 => ~ ( eout @ A @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % not_know_k_not_eout
% 0.28/0.62 thf(fact_341_eout__know__k,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,M: secrecy_Keys] :
% 0.28/0.62 ( ( knowle233900195orrect @ C3 @ ( secrecy_kKS @ M ) )
% 0.28/0.62 = ( ( eout @ C3 @ ( secrecy_kE @ M ) )
% 0.28/0.62 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C3 ) )
% 0.28/0.62 | ( knowle945212990e_know @ C3 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eout_know_k
% 0.28/0.62 thf(fact_342_eout__know__nonKS__s,axiom,
% 0.28/0.62 ! [M: secrecy_Secrets,A: secrecy_specID] :
% 0.28/0.62 ( ~ ( member2138796287ecrets @ M @ ( specSecrets @ A ) )
% 0.28/0.62 => ( ( eout @ A @ ( secrecy_sE @ M ) )
% 0.28/0.62 => ( ( knowle233900195orrect @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.62 => ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eout_know_nonKS_s
% 0.28/0.62 thf(fact_343_eoutKnowCorrect__L1s,axiom,
% 0.28/0.62 ! [C3: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.62 ( ( knowle233900195orrect @ C3 @ ( secrecy_sKS @ M ) )
% 0.28/0.62 => ( ( eout @ C3 @ ( secrecy_sE @ M ) )
% 0.28/0.62 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C3 ) )
% 0.28/0.62 | ( knowle945212990e_know @ C3 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eoutKnowCorrect_L1s
% 0.28/0.62 thf(fact_344_TBtheore54b__P,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( eoutM @ P @ M3 @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch2 @ ( out @ Q ) )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ M3 ) )
% 0.28/0.62 => ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheore54b_P
% 0.28/0.62 thf(fact_345_TBtheorem5b__PQ,axiom,
% 0.28/0.62 ! [P: secrecy_specID,M3: set_Secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ( eoutM @ P @ M3 @ E )
% 0.28/0.62 | ( eoutM @ Q @ M3 @ E ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.28/0.62 & ( member1967978193chanID @ Ch2 @ M3 )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( eoutM @ PQ @ M3 @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5b_PQ
% 0.28/0.62 thf(fact_346_TBtheorem45a__P,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.28/0.62 ( ( eout @ P @ E )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem45a_P
% 0.28/0.62 thf(fact_347_eout__def,axiom,
% 0.28/0.62 ( eout
% 0.28/0.62 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.28/0.62 ? [Ch3: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.28/0.62 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eout_def
% 0.28/0.62 thf(fact_348_eoutM__def,axiom,
% 0.28/0.62 ( eoutM
% 0.28/0.62 = ( ^ [SP: secrecy_specID,M4: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.62 ? [Ch3: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.28/0.62 & ( member1967978193chanID @ Ch3 @ M4 )
% 0.28/0.62 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % eoutM_def
% 0.28/0.62 thf(fact_349_out__exprChannelSet__def,axiom,
% 0.28/0.62 ( out_exprChannelSet
% 0.28/0.62 = ( ^ [SP: secrecy_specID,ChSet2: set_Secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.62 ( ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( member1967978193chanID @ X4 @ ChSet2 )
% 0.28/0.62 => ( ( member1967978193chanID @ X4 @ ( out @ SP ) )
% 0.28/0.62 & ( exprChannel @ X4 @ E2 ) ) )
% 0.28/0.62 & ! [X4: secrecy_chanID] :
% 0.28/0.62 ( ( ~ ( member1967978193chanID @ X4 @ ChSet2 )
% 0.28/0.62 & ( member1967978193chanID @ X4 @ ( out @ SP ) ) )
% 0.28/0.62 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % out_exprChannelSet_def
% 0.28/0.62 thf(fact_350_out__exprChannelSingle__def,axiom,
% 0.28/0.62 ( out_ex985543062Single
% 0.28/0.62 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.28/0.62 ( ( member1967978193chanID @ Ch3 @ ( out @ SP ) )
% 0.28/0.62 & ( exprChannel @ Ch3 @ E2 )
% 0.28/0.62 & ! [X4: secrecy_chanID,T: nat] :
% 0.28/0.62 ( ( ( member1967978193chanID @ X4 @ ( out @ SP ) )
% 0.28/0.62 & ( X4 != Ch3 ) )
% 0.28/0.62 => ~ ( exprChannel @ X4 @ E2 ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % out_exprChannelSingle_def
% 0.28/0.62 thf(fact_351_correctCompositionOut__prop1,axiom,
% 0.28/0.62 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X3: secrecy_chanID] :
% 0.28/0.62 ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ( member1967978193chanID @ X3 @ ( out @ PQ ) )
% 0.28/0.62 => ( ( member1967978193chanID @ X3 @ ( out @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ X3 @ ( out @ Q ) ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % correctCompositionOut_prop1
% 0.28/0.62 thf(fact_352_TBtheorem5a__PQ,axiom,
% 0.28/0.62 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.28/0.62 ( ( ( eout @ P @ E )
% 0.28/0.62 | ( eout @ Q @ E ) )
% 0.28/0.62 => ( ( ( subcomponents @ PQ )
% 0.28/0.62 = ( insert1671894227specID @ P @ ( insert1671894227specID @ Q @ bot_bo1785112429specID ) ) )
% 0.28/0.62 => ( ( correc990227761ionOut @ PQ )
% 0.28/0.62 => ( ? [Ch2: secrecy_chanID] :
% 0.28/0.62 ( ( ( member1967978193chanID @ Ch2 @ ( out @ P ) )
% 0.28/0.62 | ( member1967978193chanID @ Ch2 @ ( out @ Q ) ) )
% 0.28/0.62 & ( exprChannel @ Ch2 @ E )
% 0.28/0.62 & ~ ( member1967978193chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.28/0.62 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % TBtheorem5a_PQ
% 0.28/0.62 thf(fact_353_outStream__def,axiom,
% 0.28/0.62 ( outStream
% 0.28/0.62 = ( ^ [X4: secrecy_specID] :
% 0.28/0.62 ( ^ [Y4: set_Secrecy_chanID,Z: set_Secrecy_chanID] : ( Y4 = Z )
% 0.28/0.62 @ ( out @ X4 ) ) ) ) ).
% 0.28/0.62
% 0.28/0.62 % outStream_def
% 0.28/0.62 thf(fact_354_adv__not__know2,axiom,
% 0.28/0.62 ! [P: secrecy_specID,A: secrecy_specID,M: secrecy_Secrets] :
% 0.28/0.62 ( ( ord_le1802272080chanID @ ( out @ P ) @ ( ins @ A ) )
% 0.28/0.62 => ( ~ ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.28/0.62 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.53/0.71
% 0.53/0.71 % adv_not_know2
% 0.53/0.71
% 0.53/0.71 % Conjectures (1)
% 0.53/0.71 thf(conj_0,conjecture,
% 0.53/0.71 ~ ( member_Secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 0.53/0.71
% 0.53/0.71 %------------------------------------------------------------------------------
% 0.53/0.71 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.ecSk9lSevY/cvc5---1.0.5_22671.p...
% 0.53/0.71 (declare-sort $$unsorted 0)
% 0.53/0.71 (declare-sort tptp.list_S529945141ession 0)
% 0.53/0.71 (declare-sort tptp.set_Secrecy_Secrets 0)
% 0.53/0.71 (declare-sort tptp.set_Secrecy_specID 0)
% 0.53/0.71 (declare-sort tptp.set_Secrecy_chanID 0)
% 0.53/0.71 (declare-sort tptp.set_Secrecy_Keys 0)
% 0.53/0.71 (declare-sort tptp.set_Secrecy_KS 0)
% 0.53/0.71 (declare-sort tptp.secrecy_Expression 0)
% 0.53/0.71 (declare-sort tptp.secrecy_Secrets 0)
% 0.53/0.71 (declare-sort tptp.secrecy_specID 0)
% 0.53/0.71 (declare-sort tptp.secrecy_chanID 0)
% 0.53/0.71 (declare-sort tptp.secrecy_Keys 0)
% 0.53/0.71 (declare-sort tptp.secrecy_KS 0)
% 0.53/0.71 (declare-sort tptp.nat 0)
% 0.53/0.71 (declare-fun tptp.localSecrets (tptp.secrecy_specID) tptp.set_Secrecy_KS)
% 0.53/0.71 (declare-fun tptp.knowle233900195orrect (tptp.secrecy_specID tptp.secrecy_KS) Bool)
% 0.53/0.71 (declare-fun tptp.knowle945212990e_know (tptp.secrecy_specID tptp.secrecy_KS) Bool)
% 0.53/0.71 (declare-fun tptp.sup_su1301156759ecy_KS (tptp.set_Secrecy_KS tptp.set_Secrecy_KS) tptp.set_Secrecy_KS)
% 0.53/0.71 (declare-fun tptp.sup_su552545507y_Keys (tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys) tptp.set_Secrecy_Keys)
% 0.53/0.71 (declare-fun tptp.sup_su1029080330ecrets (tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets) tptp.set_Secrecy_Secrets)
% 0.53/0.71 (declare-fun tptp.sup_su370684444chanID (tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID) tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.sup_su1712599557specID (tptp.set_Secrecy_specID tptp.set_Secrecy_specID) tptp.set_Secrecy_specID)
% 0.53/0.71 (declare-fun tptp.mem_Se1967555118ession (tptp.secrecy_Expression tptp.list_S529945141ession) Bool)
% 0.53/0.71 (declare-fun tptp.bot_bot_Secrecy_KS_o (tptp.secrecy_KS) Bool)
% 0.53/0.71 (declare-fun tptp.bot_bo2072920570Keys_o (tptp.secrecy_Keys) Bool)
% 0.53/0.71 (declare-fun tptp.bot_bo1909946299rets_o (tptp.secrecy_Secrets) Bool)
% 0.53/0.71 (declare-fun tptp.bot_bo1012329985anID_o (tptp.secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.bot_bo1767780696ecID_o (tptp.secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.bot_bo1943466239ecy_KS () tptp.set_Secrecy_KS)
% 0.53/0.71 (declare-fun tptp.bot_bo701486667y_Keys () tptp.set_Secrecy_Keys)
% 0.53/0.71 (declare-fun tptp.bot_bo1124690338ecrets () tptp.set_Secrecy_Secrets)
% 0.53/0.71 (declare-fun tptp.bot_bo443197316chanID () tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.bot_bo1785112429specID () tptp.set_Secrecy_specID)
% 0.53/0.71 (declare-fun tptp.ord_le1802272080chanID (tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.correctCompositionKS (tptp.secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.eout (tptp.secrecy_specID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.eoutM (tptp.secrecy_specID tptp.set_Secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.exprChannel (tptp.secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.ine (tptp.secrecy_specID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.ineM (tptp.secrecy_specID tptp.set_Secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.ine_exprChannelSet (tptp.secrecy_specID tptp.set_Secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.ine_ex1303305700Single (tptp.secrecy_specID tptp.secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.notSpe1586871396tsExpr (tptp.secrecy_specID tptp.list_S529945141ession) Bool)
% 0.53/0.71 (declare-fun tptp.out_exprChannelSet (tptp.secrecy_specID tptp.set_Secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.out_ex985543062Single (tptp.secrecy_specID tptp.secrecy_chanID tptp.secrecy_Expression) Bool)
% 0.53/0.71 (declare-fun tptp.specKeys (tptp.secrecy_specID) tptp.set_Secrecy_Keys)
% 0.53/0.71 (declare-fun tptp.specKeysSecrets (tptp.secrecy_specID) tptp.set_Secrecy_KS)
% 0.53/0.71 (declare-fun tptp.specSecrets (tptp.secrecy_specID) tptp.set_Secrecy_Secrets)
% 0.53/0.71 (declare-fun tptp.secrecy_kE (tptp.secrecy_Keys) tptp.secrecy_Expression)
% 0.53/0.71 (declare-fun tptp.secrecy_sE (tptp.secrecy_Secrets) tptp.secrecy_Expression)
% 0.53/0.71 (declare-fun tptp.secrec1016742679ession (tptp.secrecy_KS) tptp.secrecy_Expression)
% 0.53/0.71 (declare-fun tptp.secrecy_kKS (tptp.secrecy_Keys) tptp.secrecy_KS)
% 0.53/0.71 (declare-fun tptp.secrecy_sKS (tptp.secrecy_Secrets) tptp.secrecy_KS)
% 0.53/0.71 (declare-fun tptp.collect_Secrecy_KS ((-> tptp.secrecy_KS Bool)) tptp.set_Secrecy_KS)
% 0.53/0.71 (declare-fun tptp.collect_Secrecy_Keys ((-> tptp.secrecy_Keys Bool)) tptp.set_Secrecy_Keys)
% 0.53/0.71 (declare-fun tptp.collec836099393ecrets ((-> tptp.secrecy_Secrets Bool)) tptp.set_Secrecy_Secrets)
% 0.53/0.71 (declare-fun tptp.collec625564175chanID ((-> tptp.secrecy_chanID Bool)) tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.collec1545797240specID ((-> tptp.secrecy_specID Bool)) tptp.set_Secrecy_specID)
% 0.53/0.71 (declare-fun tptp.insert_Secrecy_KS (tptp.secrecy_KS tptp.set_Secrecy_KS) tptp.set_Secrecy_KS)
% 0.53/0.71 (declare-fun tptp.insert_Secrecy_Keys (tptp.secrecy_Keys tptp.set_Secrecy_Keys) tptp.set_Secrecy_Keys)
% 0.53/0.71 (declare-fun tptp.insert565337510ecrets (tptp.secrecy_Secrets tptp.set_Secrecy_Secrets) tptp.set_Secrecy_Secrets)
% 0.53/0.71 (declare-fun tptp.insert751661162chanID (tptp.secrecy_chanID tptp.set_Secrecy_chanID) tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.insert1671894227specID (tptp.secrecy_specID tptp.set_Secrecy_specID) tptp.set_Secrecy_specID)
% 0.53/0.71 (declare-fun tptp.is_emp928984296chanID (tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.is_emp1849217361specID (tptp.set_Secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.is_sin1442426433ecy_KS (tptp.set_Secrecy_KS) Bool)
% 0.53/0.71 (declare-fun tptp.is_sin1096471309y_Keys (tptp.set_Secrecy_Keys) Bool)
% 0.53/0.71 (declare-fun tptp.is_sin1002224330ecrets (tptp.set_Secrecy_Secrets) Bool)
% 0.53/0.71 (declare-fun tptp.is_sin581274182chanID (tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.is_sin1501507247specID (tptp.set_Secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.the_el2054381829chanID (tptp.set_Secrecy_chanID) tptp.secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.the_el827131246specID (tptp.set_Secrecy_specID) tptp.secrecy_specID)
% 0.53/0.71 (declare-fun tptp.correctCompositionIn (tptp.secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.correc965049635ionLoc (tptp.secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.correc990227761ionOut (tptp.secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.inStream (tptp.secrecy_specID tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.ins (tptp.secrecy_specID) tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.loc (tptp.secrecy_specID) tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.locStream (tptp.secrecy_specID tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.out (tptp.secrecy_specID) tptp.set_Secrecy_chanID)
% 0.53/0.71 (declare-fun tptp.outStream (tptp.secrecy_specID tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.subcomponents (tptp.secrecy_specID) tptp.set_Secrecy_specID)
% 0.53/0.71 (declare-fun tptp.member_Secrecy_KS (tptp.secrecy_KS tptp.set_Secrecy_KS) Bool)
% 0.53/0.71 (declare-fun tptp.member_Secrecy_Keys (tptp.secrecy_Keys tptp.set_Secrecy_Keys) Bool)
% 0.53/0.71 (declare-fun tptp.member2138796287ecrets (tptp.secrecy_Secrets tptp.set_Secrecy_Secrets) Bool)
% 0.53/0.71 (declare-fun tptp.member1967978193chanID (tptp.secrecy_chanID tptp.set_Secrecy_chanID) Bool)
% 0.53/0.71 (declare-fun tptp.member740727610specID (tptp.secrecy_specID tptp.set_Secrecy_specID) Bool)
% 0.53/0.71 (declare-fun tptp.p () tptp.secrecy_specID)
% 0.53/0.71 (declare-fun tptp.pq () tptp.secrecy_specID)
% 0.53/0.71 (declare-fun tptp.q () tptp.secrecy_specID)
% 0.53/0.71 (declare-fun tptp.m () tptp.secrecy_KS)
% 0.53/0.71 (declare-fun tptp.secret () tptp.secrecy_Secrets)
% 0.53/0.71 (assert (not (@ (@ tptp.knowle945212990e_know tptp.q) tptp.m)))
% 0.53/0.71 (assert (= tptp.m (@ tptp.secrecy_sKS tptp.secret)))
% 0.53/0.71 (assert (@ (@ tptp.knowle945212990e_know tptp.pq) tptp.m))
% 0.53/0.71 (assert (@ (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS tptp.secret)) (@ tptp.localSecrets tptp.pq)))
% 0.53/0.71 (assert (forall ((X2 tptp.secrecy_Secrets) (Y2 tptp.secrecy_Secrets)) (= (= (@ tptp.secrecy_sKS X2) (@ tptp.secrecy_sKS Y2)) (= X2 Y2))))
% 0.53/0.71 (assert (not (@ (@ tptp.ine tptp.q) (@ tptp.secrecy_sE tptp.secret))))
% 0.53/0.71 (assert (@ tptp.correc965049635ionLoc tptp.pq))
% 0.53/0.71 (assert (not (@ (@ tptp.ine tptp.pq) (@ tptp.secrecy_sE tptp.secret))))
% 0.53/0.71 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (= (@ (@ tptp.knowle945212990e_know A) _let_1) (or (@ (@ tptp.ine A) (@ tptp.secrecy_sE M)) (@ (@ tptp.member_Secrecy_KS _let_1) (@ tptp.localSecrets A)))))))
% 0.53/0.71 (assert (= (@ tptp.subcomponents tptp.pq) (@ (@ tptp.insert1671894227specID tptp.p) (@ (@ tptp.insert1671894227specID tptp.q) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (@ tptp.correctCompositionIn tptp.pq))
% 0.53/0.71 (assert (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kKS X1) (@ tptp.secrecy_sKS X2)))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_KS Bool)) (KS tptp.secrecy_KS)) (=> (forall ((X tptp.secrecy_Keys)) (@ P (@ tptp.secrecy_kKS X))) (=> (forall ((X tptp.secrecy_Secrets)) (@ P (@ tptp.secrecy_sKS X))) (@ P KS)))))
% 0.53/0.71 (assert (forall ((X1 tptp.secrecy_Keys) (Y1 tptp.secrecy_Keys)) (= (= (@ tptp.secrecy_kKS X1) (@ tptp.secrecy_kKS Y1)) (= X1 Y1))))
% 0.53/0.71 (assert (forall ((X2 tptp.secrecy_Secrets) (Y2 tptp.secrecy_Secrets)) (= (= (@ tptp.secrecy_sE X2) (@ tptp.secrecy_sE Y2)) (= X2 Y2))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M tptp.secrecy_KS) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (not (@ (@ tptp.knowle945212990e_know P) M)) (=> (not (@ (@ tptp.knowle945212990e_know Q) M)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ tptp.knowle945212990e_know PQ) M)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sKS Secret))) (=> (not (@ (@ tptp.knowle945212990e_know P) _let_1)) (=> (not (@ (@ tptp.knowle945212990e_know Q) _let_1)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ tptp.ine PQ) (@ tptp.secrecy_sE Secret))))))))))
% 0.53/0.71 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_sKS M))) (not (@ (@ tptp.ine A) (@ tptp.secrecy_sE M))))))
% 0.53/0.71 (assert (forall ((Y tptp.secrecy_KS)) (=> (forall ((X12 tptp.secrecy_Keys)) (not (= Y (@ tptp.secrecy_kKS X12)))) (not (forall ((X22 tptp.secrecy_Secrets)) (not (= Y (@ tptp.secrecy_sKS X22))))))))
% 0.53/0.71 (assert (forall ((S tptp.secrecy_Secrets) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sE S))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS S)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine Q) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine P) _let_1)))))))))))
% 0.53/0.71 (assert (forall ((S tptp.secrecy_Secrets) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sE S))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS S)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine Q) _let_1)))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (S tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS S)))) (let ((_let_2 (@ tptp.secrecy_sE S))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (not (@ _let_1 (@ tptp.localSecrets Q))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.ine PQ) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (or (@ (@ tptp.ine P) E) (@ (@ tptp.ine Q) E)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (not (@ (@ tptp.ine P) E)) (=> (not (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ tptp.ine PQ) E))))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS A2) (@ (@ tptp.insert_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys A2) (@ (@ tptp.insert_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets A2) (@ (@ tptp.insert565337510ecrets A2) tptp.bot_bo1124690338ecrets))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID A2) (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID A2) (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((Ls tptp.secrecy_KS) (P tptp.secrecy_specID) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ls))) (=> (@ _let_1 (@ tptp.localSecrets P)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (@ _let_1 (@ tptp.localSecrets PQ)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (B2 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (B2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert751661162chanID B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (B2 tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert1671894227specID B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (B2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (B2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (B2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (= (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (= (@ _let_1 (@ (@ tptp.insert751661162chanID B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (= (@ _let_1 (@ (@ tptp.insert1671894227specID B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (B2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (= (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (B2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (= (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) A)) (or (= A2 B2) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID X3))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID X3))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_specID Bool))) (= (= tptp.bot_bo1785112429specID (@ tptp.collec1545797240specID P)) (forall ((X4 tptp.secrecy_specID)) (not (@ P X4))))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_chanID Bool))) (= (= tptp.bot_bo443197316chanID (@ tptp.collec625564175chanID P)) (forall ((X4 tptp.secrecy_chanID)) (not (@ P X4))))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_specID Bool))) (= (= (@ tptp.collec1545797240specID P) tptp.bot_bo1785112429specID) (forall ((X4 tptp.secrecy_specID)) (not (@ P X4))))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_chanID Bool))) (= (= (@ tptp.collec625564175chanID P) tptp.bot_bo443197316chanID) (forall ((X4 tptp.secrecy_chanID)) (not (@ P X4))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (= (forall ((X4 tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS X4) A))) (= A tptp.bot_bo1943466239ecy_KS))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Keys)) (= (forall ((X4 tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys X4) A))) (= A tptp.bot_bo701486667y_Keys))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Secrets)) (= (forall ((X4 tptp.secrecy_Secrets)) (not (@ (@ tptp.member2138796287ecrets X4) A))) (= A tptp.bot_bo1124690338ecrets))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (= (forall ((X4 tptp.secrecy_specID)) (not (@ (@ tptp.member740727610specID X4) A))) (= A tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (= (forall ((X4 tptp.secrecy_chanID)) (not (@ (@ tptp.member1967978193chanID X4) A))) (= A tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS C) tptp.bot_bo1943466239ecy_KS))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys C) tptp.bot_bo701486667y_Keys))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Secrets)) (not (@ (@ tptp.member2138796287ecrets C) tptp.bot_bo1124690338ecrets))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_specID)) (not (@ (@ tptp.member740727610specID C) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_chanID)) (not (@ (@ tptp.member1967978193chanID C) tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (= (exists ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS X4) A)) (not (= A tptp.bot_bo1943466239ecy_KS)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Keys)) (= (exists ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) A)) (not (= A tptp.bot_bo701486667y_Keys)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Secrets)) (= (exists ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) A)) (not (= A tptp.bot_bo1124690338ecrets)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (= (exists ((X4 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID X4) A)) (not (= A tptp.bot_bo1785112429specID)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (= (exists ((X4 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID X4) A)) (not (= A tptp.bot_bo443197316chanID)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (=> (forall ((Y3 tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS Y3) A))) (= A tptp.bot_bo1943466239ecy_KS))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Keys)) (=> (forall ((Y3 tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys Y3) A))) (= A tptp.bot_bo701486667y_Keys))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Secrets)) (=> (forall ((Y3 tptp.secrecy_Secrets)) (not (@ (@ tptp.member2138796287ecrets Y3) A))) (= A tptp.bot_bo1124690338ecrets))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (=> (forall ((Y3 tptp.secrecy_specID)) (not (@ (@ tptp.member740727610specID Y3) A))) (= A tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (=> (forall ((Y3 tptp.secrecy_chanID)) (not (@ (@ tptp.member1967978193chanID Y3) A))) (= A tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (A2 tptp.secrecy_KS)) (=> (= A tptp.bot_bo1943466239ecy_KS) (not (@ (@ tptp.member_Secrecy_KS A2) A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Keys) (A2 tptp.secrecy_Keys)) (=> (= A tptp.bot_bo701486667y_Keys) (not (@ (@ tptp.member_Secrecy_Keys A2) A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Secrets) (A2 tptp.secrecy_Secrets)) (=> (= A tptp.bot_bo1124690338ecrets) (not (@ (@ tptp.member2138796287ecrets A2) A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID) (A2 tptp.secrecy_specID)) (=> (= A tptp.bot_bo1785112429specID) (not (@ (@ tptp.member740727610specID A2) A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (A2 tptp.secrecy_chanID)) (=> (= A tptp.bot_bo443197316chanID) (not (@ (@ tptp.member1967978193chanID A2) A)))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets)) (not (@ (@ tptp.member2138796287ecrets A2) tptp.bot_bo1124690338ecrets))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID)) (not (@ (@ tptp.member740727610specID A2) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID)) (not (@ (@ tptp.member1967978193chanID A2) tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS A2) A) (exists ((B3 tptp.set_Secrecy_KS)) (and (= A (@ (@ tptp.insert_Secrecy_KS A2) B3)) (not (@ (@ tptp.member_Secrecy_KS A2) B3)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID A2) A) (exists ((B3 tptp.set_Secrecy_chanID)) (and (= A (@ (@ tptp.insert751661162chanID A2) B3)) (not (@ (@ tptp.member1967978193chanID A2) B3)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (=> (@ (@ tptp.member740727610specID A2) A) (exists ((B3 tptp.set_Secrecy_specID)) (and (= A (@ (@ tptp.insert1671894227specID A2) B3)) (not (@ (@ tptp.member740727610specID A2) B3)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys A2) A) (exists ((B3 tptp.set_Secrecy_Keys)) (and (= A (@ (@ tptp.insert_Secrecy_Keys A2) B3)) (not (@ (@ tptp.member_Secrecy_Keys A2) B3)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets A2) A) (exists ((B3 tptp.set_Secrecy_Secrets)) (and (= A (@ (@ tptp.insert565337510ecrets A2) B3)) (not (@ (@ tptp.member2138796287ecrets A2) B3)))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID) (Y tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID X3))) (let ((_let_2 (@ tptp.insert1671894227specID Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (Y tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID X3))) (let ((_let_2 (@ tptp.insert751661162chanID Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member_Secrecy_KS A2) A)) (=> (not (@ (@ tptp.member_Secrecy_KS B2) B)) (= (= (@ (@ tptp.insert_Secrecy_KS A2) A) (@ (@ tptp.insert_Secrecy_KS B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_KS)) (and (= A (@ (@ tptp.insert_Secrecy_KS B2) C2)) (not (@ (@ tptp.member_Secrecy_KS B2) C2)) (= B (@ (@ tptp.insert_Secrecy_KS A2) C2)) (not (@ (@ tptp.member_Secrecy_KS A2) C2))))))))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member1967978193chanID A2) A)) (=> (not (@ (@ tptp.member1967978193chanID B2) B)) (= (= (@ (@ tptp.insert751661162chanID A2) A) (@ (@ tptp.insert751661162chanID B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_chanID)) (and (= A (@ (@ tptp.insert751661162chanID B2) C2)) (not (@ (@ tptp.member1967978193chanID B2) C2)) (= B (@ (@ tptp.insert751661162chanID A2) C2)) (not (@ (@ tptp.member1967978193chanID A2) C2))))))))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member740727610specID A2) A)) (=> (not (@ (@ tptp.member740727610specID B2) B)) (= (= (@ (@ tptp.insert1671894227specID A2) A) (@ (@ tptp.insert1671894227specID B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_specID)) (and (= A (@ (@ tptp.insert1671894227specID B2) C2)) (not (@ (@ tptp.member740727610specID B2) C2)) (= B (@ (@ tptp.insert1671894227specID A2) C2)) (not (@ (@ tptp.member740727610specID A2) C2))))))))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member_Secrecy_Keys A2) A)) (=> (not (@ (@ tptp.member_Secrecy_Keys B2) B)) (= (= (@ (@ tptp.insert_Secrecy_Keys A2) A) (@ (@ tptp.insert_Secrecy_Keys B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_Keys)) (and (= A (@ (@ tptp.insert_Secrecy_Keys B2) C2)) (not (@ (@ tptp.member_Secrecy_Keys B2) C2)) (= B (@ (@ tptp.insert_Secrecy_Keys A2) C2)) (not (@ (@ tptp.member_Secrecy_Keys A2) C2))))))))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member2138796287ecrets A2) A)) (=> (not (@ (@ tptp.member2138796287ecrets B2) B)) (= (= (@ (@ tptp.insert565337510ecrets A2) A) (@ (@ tptp.insert565337510ecrets B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_Secrets)) (and (= A (@ (@ tptp.insert565337510ecrets B2) C2)) (not (@ (@ tptp.member2138796287ecrets B2) C2)) (= B (@ (@ tptp.insert565337510ecrets A2) C2)) (not (@ (@ tptp.member2138796287ecrets A2) C2))))))))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS A2) A) (= (@ (@ tptp.insert_Secrecy_KS A2) A) A))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID A2) A) (= (@ (@ tptp.insert751661162chanID A2) A) A))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (=> (@ (@ tptp.member740727610specID A2) A) (= (@ (@ tptp.insert1671894227specID A2) A) A))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys A2) A) (= (@ (@ tptp.insert_Secrecy_Keys A2) A) A))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets A2) A) (= (@ (@ tptp.insert565337510ecrets A2) A) A))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (@ (@ tptp.member_Secrecy_KS A2) (@ tptp.collect_Secrecy_KS P)) (@ P A2))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (P (-> tptp.secrecy_chanID Bool))) (= (@ (@ tptp.member1967978193chanID A2) (@ tptp.collec625564175chanID P)) (@ P A2))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (P (-> tptp.secrecy_specID Bool))) (= (@ (@ tptp.member740727610specID A2) (@ tptp.collec1545797240specID P)) (@ P A2))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (P (-> tptp.secrecy_Keys Bool))) (= (@ (@ tptp.member_Secrecy_Keys A2) (@ tptp.collect_Secrecy_Keys P)) (@ P A2))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (P (-> tptp.secrecy_Secrets Bool))) (= (@ (@ tptp.member2138796287ecrets A2) (@ tptp.collec836099393ecrets P)) (@ P A2))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (= (@ tptp.collect_Secrecy_KS (lambda ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS X4) A))) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (= (@ tptp.collec625564175chanID (lambda ((X4 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID X4) A))) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (= (@ tptp.collec1545797240specID (lambda ((X4 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID X4) A))) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Keys)) (= (@ tptp.collect_Secrecy_Keys (lambda ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) A))) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Secrets)) (= (@ tptp.collec836099393ecrets (lambda ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) A))) A)))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.insert_Secrecy_KS X3))) (let ((_let_2 (@ tptp.member_Secrecy_KS X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID X3))) (let ((_let_2 (@ tptp.member1967978193chanID X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID X3))) (let ((_let_2 (@ tptp.member740727610specID X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.insert_Secrecy_Keys X3))) (let ((_let_2 (@ tptp.member_Secrecy_Keys X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.insert565337510ecrets X3))) (let ((_let_2 (@ tptp.member2138796287ecrets X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X3) A) (not (forall ((B3 tptp.set_Secrecy_KS)) (=> (= A (@ (@ tptp.insert_Secrecy_KS X3) B3)) (@ (@ tptp.member_Secrecy_KS X3) B3)))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X3) A) (not (forall ((B3 tptp.set_Secrecy_chanID)) (=> (= A (@ (@ tptp.insert751661162chanID X3) B3)) (@ (@ tptp.member1967978193chanID X3) B3)))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (=> (@ (@ tptp.member740727610specID X3) A) (not (forall ((B3 tptp.set_Secrecy_specID)) (=> (= A (@ (@ tptp.insert1671894227specID X3) B3)) (@ (@ tptp.member740727610specID X3) B3)))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys X3) A) (not (forall ((B3 tptp.set_Secrecy_Keys)) (=> (= A (@ (@ tptp.insert_Secrecy_Keys X3) B3)) (@ (@ tptp.member_Secrecy_Keys X3) B3)))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets X3) A) (not (forall ((B3 tptp.set_Secrecy_Secrets)) (=> (= A (@ (@ tptp.insert565337510ecrets X3) B3)) (@ (@ tptp.member2138796287ecrets X3) B3)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (B2 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (B2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert751661162chanID B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (B2 tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert1671894227specID B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (B2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (B2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) B))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS)) (@ (@ tptp.member_Secrecy_KS A2) (@ (@ tptp.insert_Secrecy_KS A2) B))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID)) (@ (@ tptp.member1967978193chanID A2) (@ (@ tptp.insert751661162chanID A2) B))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID)) (@ (@ tptp.member740727610specID A2) (@ (@ tptp.insert1671894227specID A2) B))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys A2) (@ (@ tptp.insert_Secrecy_Keys A2) B))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets A2) (@ (@ tptp.insert565337510ecrets A2) B))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (B2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (=> (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (=> (@ _let_1 (@ (@ tptp.insert751661162chanID B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (=> (@ _let_1 (@ (@ tptp.insert1671894227specID B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Keys) (B2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (=> (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_Secrets) (B2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (=> (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID)) (=> (= (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID) (@ (@ tptp.insert1671894227specID B2) tptp.bot_bo1785112429specID)) (= A2 B2))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID)) (=> (= (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID) (@ (@ tptp.insert751661162chanID B2) tptp.bot_bo443197316chanID)) (= A2 B2))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (not (= (@ (@ tptp.insert1671894227specID A2) A) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (not (= (@ (@ tptp.insert751661162chanID A2) A) tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID) (C tptp.secrecy_specID) (D tptp.secrecy_specID)) (= (= (@ (@ tptp.insert1671894227specID A2) (@ (@ tptp.insert1671894227specID B2) tptp.bot_bo1785112429specID)) (@ (@ tptp.insert1671894227specID C) (@ (@ tptp.insert1671894227specID D) tptp.bot_bo1785112429specID))) (or (and (= A2 C) (= B2 D)) (and (= A2 D) (= B2 C))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID) (C tptp.secrecy_chanID) (D tptp.secrecy_chanID)) (= (= (@ (@ tptp.insert751661162chanID A2) (@ (@ tptp.insert751661162chanID B2) tptp.bot_bo443197316chanID)) (@ (@ tptp.insert751661162chanID C) (@ (@ tptp.insert751661162chanID D) tptp.bot_bo443197316chanID))) (or (and (= A2 C) (= B2 D)) (and (= A2 D) (= B2 C))))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_KS) (A2 tptp.secrecy_KS)) (= (@ (@ tptp.member_Secrecy_KS B2) (@ (@ tptp.insert_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_Keys) (A2 tptp.secrecy_Keys)) (= (@ (@ tptp.member_Secrecy_Keys B2) (@ (@ tptp.insert_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_Secrets) (A2 tptp.secrecy_Secrets)) (= (@ (@ tptp.member2138796287ecrets B2) (@ (@ tptp.insert565337510ecrets A2) tptp.bot_bo1124690338ecrets)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_specID) (A2 tptp.secrecy_specID)) (= (@ (@ tptp.member740727610specID B2) (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_chanID) (A2 tptp.secrecy_chanID)) (= (@ (@ tptp.member1967978193chanID B2) (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_KS) (A2 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS B2) (@ (@ tptp.insert_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_Keys) (A2 tptp.secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys B2) (@ (@ tptp.insert_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_Secrets) (A2 tptp.secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets B2) (@ (@ tptp.insert565337510ecrets A2) tptp.bot_bo1124690338ecrets)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_specID) (A2 tptp.secrecy_specID)) (=> (@ (@ tptp.member740727610specID B2) (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((B2 tptp.secrecy_chanID) (A2 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID B2) (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID)) (= B2 A2))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (forall ((M2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kE M2))) (=> (= Ks (@ tptp.secrecy_kKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (forall ((M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sE M2))) (=> (= Ks (@ tptp.secrecy_sKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (not (@ _let_1 (@ tptp.localSecrets Q))) (not (@ _let_1 (@ tptp.localSecrets PQ))))))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID)) (= (@ tptp.the_el827131246specID (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID)) X3)))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID)) (= (@ tptp.the_el2054381829chanID (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID)) X3)))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Keys tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Keys)))) (let ((_let_2 (@ tptp.secrecy_kE Keys))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (not (@ _let_1 (@ tptp.localSecrets Q))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))))
% 0.53/0.71 (assert (forall ((K tptp.secrecy_Keys) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kE K))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS K)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine Q) _let_1)))))))))))
% 0.53/0.71 (assert (forall ((K tptp.secrecy_Keys) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kE K))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS K)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine Q) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine P) _let_1)))))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS Key))) (=> (not (@ (@ tptp.knowle945212990e_know P) _let_1)) (=> (not (@ (@ tptp.knowle945212990e_know Q) _let_1)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ tptp.ine PQ) (@ tptp.secrecy_kE Key))))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID)) (@ tptp.is_sin1501507247specID (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID)) (@ tptp.is_sin581274182chanID (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_Secrets)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_sKS M)) (@ tptp.secrecy_sE M))))
% 0.53/0.71 (assert (forall ((X1 tptp.secrecy_Keys) (Y1 tptp.secrecy_Keys)) (= (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_kE Y1)) (= X1 Y1))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_Keys)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_kKS M)) (@ tptp.secrecy_kE M))))
% 0.53/0.71 (assert (= tptp.bot_bo1785112429specID (@ tptp.collec1545797240specID tptp.bot_bo1767780696ecID_o)))
% 0.53/0.71 (assert (= tptp.bot_bo443197316chanID (@ tptp.collec625564175chanID tptp.bot_bo1012329985anID_o)))
% 0.53/0.71 (assert (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_sE X2)))))
% 0.53/0.71 (assert (= tptp.is_sin1501507247specID (lambda ((A3 tptp.set_Secrecy_specID)) (= A3 (@ (@ tptp.insert1671894227specID (@ tptp.the_el827131246specID A3)) tptp.bot_bo1785112429specID)))))
% 0.53/0.71 (assert (= tptp.is_sin581274182chanID (lambda ((A3 tptp.set_Secrecy_chanID)) (= A3 (@ (@ tptp.insert751661162chanID (@ tptp.the_el2054381829chanID A3)) tptp.bot_bo443197316chanID)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (=> (not (= A tptp.bot_bo1943466239ecy_KS)) (=> (forall ((X tptp.secrecy_KS) (Y3 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X) A) (=> (@ (@ tptp.member_Secrecy_KS Y3) A) (= X Y3)))) (@ tptp.is_sin1442426433ecy_KS A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Keys)) (=> (not (= A tptp.bot_bo701486667y_Keys)) (=> (forall ((X tptp.secrecy_Keys) (Y3 tptp.secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys X) A) (=> (@ (@ tptp.member_Secrecy_Keys Y3) A) (= X Y3)))) (@ tptp.is_sin1096471309y_Keys A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_Secrets)) (=> (not (= A tptp.bot_bo1124690338ecrets)) (=> (forall ((X tptp.secrecy_Secrets) (Y3 tptp.secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets X) A) (=> (@ (@ tptp.member2138796287ecrets Y3) A) (= X Y3)))) (@ tptp.is_sin1002224330ecrets A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (=> (not (= A tptp.bot_bo1785112429specID)) (=> (forall ((X tptp.secrecy_specID) (Y3 tptp.secrecy_specID)) (=> (@ (@ tptp.member740727610specID X) A) (=> (@ (@ tptp.member740727610specID Y3) A) (= X Y3)))) (@ tptp.is_sin1501507247specID A)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (=> (not (= A tptp.bot_bo443197316chanID)) (=> (forall ((X tptp.secrecy_chanID) (Y3 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X) A) (=> (@ (@ tptp.member1967978193chanID Y3) A) (= X Y3)))) (@ tptp.is_sin581274182chanID A)))))
% 0.53/0.71 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M))) (not (@ (@ tptp.ine A) (@ tptp.secrecy_kE M))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (=> (@ tptp.is_sin1501507247specID A) (not (forall ((X tptp.secrecy_specID)) (not (= A (@ (@ tptp.insert1671894227specID X) tptp.bot_bo1785112429specID))))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (=> (@ tptp.is_sin581274182chanID A) (not (forall ((X tptp.secrecy_chanID)) (not (= A (@ (@ tptp.insert751661162chanID X) tptp.bot_bo443197316chanID))))))))
% 0.53/0.71 (assert (= tptp.is_sin1501507247specID (lambda ((A3 tptp.set_Secrecy_specID)) (exists ((X4 tptp.secrecy_specID)) (= A3 (@ (@ tptp.insert1671894227specID X4) tptp.bot_bo1785112429specID))))))
% 0.53/0.71 (assert (= tptp.is_sin581274182chanID (lambda ((A3 tptp.set_Secrecy_chanID)) (exists ((X4 tptp.secrecy_chanID)) (= A3 (@ (@ tptp.insert751661162chanID X4) tptp.bot_bo443197316chanID))))))
% 0.53/0.71 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (= (@ (@ tptp.knowle945212990e_know A) _let_1) (or (@ (@ tptp.ine A) (@ tptp.secrecy_kE M)) (@ (@ tptp.member_Secrecy_KS _let_1) (@ tptp.localSecrets A)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.ine P) E) (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (= (@ tptp.loc PQ) tptp.bot_bo443197316chanID) (@ (@ tptp.ine PQ) E)))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.ineM PQ) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (or (@ (@ (@ tptp.ineM P) M3) E) (@ (@ (@ tptp.ineM Q) M3) E)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (not (@ (@ (@ tptp.ineM P) M3) E)) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ (@ tptp.ineM PQ) M3) E))))))))
% 0.53/0.71 (assert (= tptp.is_emp1849217361specID (lambda ((A3 tptp.set_Secrecy_specID)) (= A3 tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (= tptp.is_emp928984296chanID (lambda ((A3 tptp.set_Secrecy_chanID)) (= A3 tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 (@ tptp.ins PQ)) (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (X3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 (@ tptp.ins PQ)) (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ tptp.ine P) E) (=> (not (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (and (@ (@ (@ tptp.ine_ex1303305700Single P) Ch2) E) (@ (@ tptp.member1967978193chanID Ch2) (@ tptp.loc PQ)))) (not (@ (@ tptp.ine PQ) E)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (M3 tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.ine P) E)) (not (@ (@ (@ tptp.ineM P) M3) E)))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ineM P) M3) E) (@ (@ tptp.ine P) E))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ (@ tptp.ineM P) M3) E) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ (@ (@ tptp.ine_ex1303305700Single P) Ch2) E) (@ _let_1 M3) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.ineM PQ) M3) E)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (not (@ _let_1 (@ tptp.loc PQ))) (=> (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins PQ)))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID)) (=> (@ tptp.correc965049635ionLoc X3) (=> (= (@ tptp.subcomponents X3) tptp.bot_bo1785112429specID) (= (@ tptp.loc X3) tptp.bot_bo443197316chanID)))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID) (M3 tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.ine_exprChannelSet Q) ChSetQ) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.ineM PQ) M3) E))))))))))
% 0.53/0.71 (assert (forall ((Q tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.ineM PQ) M3) E)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.ine_exprChannelSet Q) ChSetQ) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.ine PQ) E))))))))))
% 0.53/0.71 (assert (forall ((Q tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.ine PQ) E)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ (@ tptp.ineM P) M3) E) (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q))) (@ _let_1 M3) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ (@ tptp.ineM PQ) M3) E)))))))
% 0.53/0.71 (assert (= tptp.ine_exprChannelSet (lambda ((SP tptp.secrecy_specID) (ChSet2 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (@ _let_1 ChSet2) (and (@ _let_1 (@ tptp.ins SP)) (@ (@ tptp.exprChannel X4) E2))))) (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (and (not (@ _let_1 ChSet2)) (@ _let_1 (@ tptp.ins SP))) (not (@ (@ tptp.exprChannel X4) E2)))))))))
% 0.53/0.71 (assert (= tptp.ine (lambda ((SP tptp.secrecy_specID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.ins SP)) (@ (@ tptp.exprChannel Ch3) E2))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M tptp.secrecy_Expression) (X3 tptp.secrecy_chanID)) (=> (not (@ (@ tptp.ine P) M)) (=> (@ (@ tptp.exprChannel X3) M) (not (@ (@ tptp.member1967978193chanID X3) (@ tptp.ins P)))))))
% 0.53/0.71 (assert (= tptp.ineM (lambda ((SP tptp.secrecy_specID) (M4 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch3))) (and (@ _let_1 (@ tptp.ins SP)) (@ _let_1 M4) (@ (@ tptp.exprChannel Ch3) E2)))))))
% 0.53/0.71 (assert (forall ((Ch tptp.secrecy_chanID) (M3 tptp.set_Secrecy_chanID) (P tptp.secrecy_specID) (E tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (@ _let_1 M3) (=> (@ _let_1 (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) E) (@ (@ (@ tptp.ineM P) M3) E)))))))
% 0.53/0.71 (assert (= tptp.ine_ex1303305700Single (lambda ((SP tptp.secrecy_specID) (Ch3 tptp.secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.ins SP)) (@ (@ tptp.exprChannel Ch3) E2) (forall ((X4 tptp.secrecy_chanID) (T tptp.nat)) (=> (and (@ (@ tptp.member1967978193chanID X4) (@ tptp.ins SP)) (not (= X4 Ch3))) (not (@ (@ tptp.exprChannel X4) E2))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (Secrets tptp.secrecy_Secrets) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (let ((_let_2 (@ tptp.secrecy_sE Secrets))) (=> (@ (@ tptp.exprChannel X3) _let_2) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (and (not (@ _let_1 (@ tptp.ins P))) (not (@ _let_1 (@ tptp.ins Q)))))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (Keys tptp.secrecy_Keys) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (let ((_let_2 (@ tptp.secrecy_kE Keys))) (=> (@ (@ tptp.exprChannel X3) _let_2) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (and (not (@ _let_1 (@ tptp.ins P))) (not (@ _let_1 (@ tptp.ins Q)))))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (not (= ChSet tptp.bot_bo443197316chanID)) (@ (@ tptp.ine P) E)))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (= ChSet tptp.bot_bo443197316chanID) (not (@ (@ tptp.ine P) E))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_ex1303305700Single P) Ch) E) (@ (@ (@ tptp.ine_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E) (@ (@ (@ tptp.ine_ex1303305700Single P) Ch) E))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (M tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) M) (=> (forall ((X tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X) (@ tptp.ins PQ)) (not (@ (@ tptp.exprChannel X) M)))) (@ _let_1 (@ tptp.loc PQ))))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (not (@ (@ (@ tptp.ineM P) M3) E)) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 M3) (=> (@ _let_1 (@ tptp.ins PQ)) (not (@ (@ tptp.exprChannel Ch) E)))))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.ine P) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.ins P)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.ine PQ) E)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.ine P) E) (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q))) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.ine PQ) E)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.ineM P) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.ins Q)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ))) (@ _let_1 M3)))) (@ (@ (@ tptp.ineM PQ) M3) E)))))))
% 0.53/0.71 (assert (= tptp.locStream (lambda ((X4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ (lambda ((Y4 tptp.set_Secrecy_chanID) (Z tptp.set_Secrecy_chanID)) (= Y4 Z)) (@ tptp.loc X4)) __flatten_var_0))))
% 0.53/0.71 (assert (= tptp.inStream (lambda ((X4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ (lambda ((Y4 tptp.set_Secrecy_chanID) (Z tptp.set_Secrecy_chanID)) (= Y4 Z)) (@ tptp.ins X4)) __flatten_var_0))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_specID Bool))) (= (= (@ tptp.collec1545797240specID P) tptp.bot_bo1785112429specID) (= P tptp.bot_bo1767780696ecID_o))))
% 0.53/0.71 (assert (forall ((P (-> tptp.secrecy_chanID Bool))) (= (= (@ tptp.collec625564175chanID P) tptp.bot_bo443197316chanID) (= P tptp.bot_bo1012329985anID_o))))
% 0.53/0.71 (assert (= tptp.bot_bot_Secrecy_KS_o (lambda ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS X4) tptp.bot_bo1943466239ecy_KS))))
% 0.53/0.71 (assert (= tptp.bot_bo2072920570Keys_o (lambda ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) tptp.bot_bo701486667y_Keys))))
% 0.53/0.71 (assert (= tptp.bot_bo1909946299rets_o (lambda ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) tptp.bot_bo1124690338ecrets))))
% 0.53/0.71 (assert (= tptp.bot_bo1767780696ecID_o (lambda ((X4 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID X4) tptp.bot_bo1785112429specID))))
% 0.53/0.71 (assert (= tptp.bot_bo1012329985anID_o (lambda ((X4 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID X4) tptp.bot_bo443197316chanID))))
% 0.53/0.71 (assert (forall ((Secret tptp.secrecy_Secrets) (P tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (not (@ (@ tptp.member1967978193chanID Ch) (@ tptp.loc P)))))))))
% 0.53/0.71 (assert (forall ((Key tptp.secrecy_Keys) (P tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (not (@ (@ tptp.member1967978193chanID Ch) (@ tptp.loc P)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins Q)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_sE Secret))))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_sE Secret))))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins Q)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins P)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (@ _let_1 (@ tptp.specKeysSecrets PQ)) (or (@ _let_1 (@ tptp.specKeysSecrets P)) (@ _let_1 (@ tptp.specKeysSecrets Q)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (not (@ _let_1 (@ tptp.specKeysSecrets PQ))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (not (@ _let_1 (@ tptp.specKeysSecrets P)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (not (@ _let_1 (@ tptp.specKeysSecrets Q)))))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_KS) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS M))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (or (@ (@ tptp.knowle945212990e_know P) M) (@ (@ tptp.knowle945212990e_know Q) M)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ tptp.correctCompositionKS PQ) (@ (@ tptp.knowle945212990e_know PQ) M))))))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_KS) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS M))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (@ (@ tptp.knowle945212990e_know P) M) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ tptp.correctCompositionKS PQ) (@ (@ tptp.knowle945212990e_know PQ) M))))))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_KS) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS M))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (@ (@ tptp.knowle945212990e_know Q) M) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ tptp.correctCompositionKS PQ) (@ (@ tptp.knowle945212990e_know PQ) M))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins P)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins Q)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_kE Key))))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins Q)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_kE Key))))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (forall ((M2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kE M2))) (=> (= Ks (@ tptp.secrecy_kKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (forall ((M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sE M2))) (=> (= Ks (@ tptp.secrecy_sKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (not (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS (@ tptp.localSecrets P)) (@ tptp.localSecrets Q)))) (not (@ _let_1 (@ tptp.localSecrets PQ))))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS M)))) (let ((_let_2 (@ tptp.secrecy_sE M))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS (@ tptp.localSecrets P)) (@ tptp.localSecrets Q)))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS M)))) (let ((_let_2 (@ tptp.secrecy_kE M))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS (@ tptp.localSecrets P)) (@ tptp.localSecrets Q)))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))))))
% 0.53/0.71 (assert (= tptp.notSpe1586871396tsExpr (lambda ((P2 tptp.secrecy_specID) (E3 tptp.list_S529945141ession)) (and (forall ((X4 tptp.secrecy_Keys)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_kE X4)) E3) (not (@ (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS X4)) (@ tptp.specKeysSecrets P2))))) (forall ((Y5 tptp.secrecy_Secrets)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_sE Y5)) E3) (not (@ (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Y5)) (@ tptp.specKeysSecrets P2)))))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (= (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (= (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (= (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (= (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (= (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (= (= (@ (@ tptp.sup_su1301156759ecy_KS A) B) tptp.bot_bo1943466239ecy_KS) (and (= A tptp.bot_bo1943466239ecy_KS) (= B tptp.bot_bo1943466239ecy_KS)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (= (= (@ (@ tptp.sup_su1712599557specID A) B) tptp.bot_bo1785112429specID) (and (= A tptp.bot_bo1785112429specID) (= B tptp.bot_bo1785112429specID)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (= (= (@ (@ tptp.sup_su370684444chanID A) B) tptp.bot_bo443197316chanID) (and (= A tptp.bot_bo443197316chanID) (= B tptp.bot_bo443197316chanID)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID) (A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.sup_su1712599557specID A))) (let ((_let_2 (@ tptp.insert1671894227specID A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (let ((_let_2 (@ tptp.insert_Secrecy_KS A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (let ((_let_2 (@ tptp.insert751661162chanID A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (C3 tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID A2))) (= (@ (@ tptp.sup_su1712599557specID (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su1712599557specID B) C3))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (C3 tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.insert_Secrecy_KS A2))) (= (@ (@ tptp.sup_su1301156759ecy_KS (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS B) C3))))))
% 0.53/0.71 (assert (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (C3 tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID A2))) (= (@ (@ tptp.sup_su370684444chanID (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su370684444chanID B) C3))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B))))))
% 0.53/0.71 (assert (forall ((C tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (exists ((X4 tptp.secrecy_KS)) (and (@ (@ tptp.member_Secrecy_KS X4) (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (@ P X4))) (or (exists ((X4 tptp.secrecy_KS)) (and (@ (@ tptp.member_Secrecy_KS X4) A) (@ P X4))) (exists ((X4 tptp.secrecy_KS)) (and (@ (@ tptp.member_Secrecy_KS X4) B) (@ P X4)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (P (-> tptp.secrecy_chanID Bool))) (= (exists ((X4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID X4) (@ (@ tptp.sup_su370684444chanID A) B)) (@ P X4))) (or (exists ((X4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID X4) A) (@ P X4))) (exists ((X4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID X4) B) (@ P X4)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (forall ((X4 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X4) (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (@ P X4))) (and (forall ((X4 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X4) A) (@ P X4))) (forall ((X4 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X4) B) (@ P X4)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (P (-> tptp.secrecy_chanID Bool))) (= (forall ((X4 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X4) (@ (@ tptp.sup_su370684444chanID A) B)) (@ P X4))) (and (forall ((X4 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X4) A) (@ P X4))) (forall ((X4 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X4) B) (@ P X4)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (C3 tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (= (@ (@ tptp.sup_su1301156759ecy_KS (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS B) C3))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (C3 tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (= (@ (@ tptp.sup_su370684444chanID (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su370684444chanID B) C3))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS A) A) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID A) A) A)))
% 0.53/0.71 (assert (= tptp.sup_su1301156759ecy_KS (lambda ((A3 tptp.set_Secrecy_KS) (B4 tptp.set_Secrecy_KS)) (@ (@ tptp.sup_su1301156759ecy_KS B4) A3))))
% 0.53/0.71 (assert (= tptp.sup_su370684444chanID (lambda ((A3 tptp.set_Secrecy_chanID) (B4 tptp.set_Secrecy_chanID)) (@ (@ tptp.sup_su370684444chanID B4) A3))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (C3 tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (let ((_let_2 (@ tptp.sup_su1301156759ecy_KS B))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (C3 tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (let ((_let_2 (@ tptp.sup_su370684444chanID B))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))))
% 0.53/0.71 (assert (forall ((B tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS tptp.bot_bo1943466239ecy_KS) B) B)))
% 0.53/0.71 (assert (forall ((B tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID tptp.bot_bo1785112429specID) B) B)))
% 0.53/0.71 (assert (forall ((B tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID tptp.bot_bo443197316chanID) B) B)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS A) tptp.bot_bo1943466239ecy_KS) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID A) tptp.bot_bo1785112429specID) A)))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID A) tptp.bot_bo443197316chanID) A)))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.insert_Secrecy_KS X3) tptp.bot_bo1943466239ecy_KS))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (or (and (= A tptp.bot_bo1943466239ecy_KS) _let_2) (and _let_3 (= B tptp.bot_bo1943466239ecy_KS)) (and _let_3 _let_2))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su1712599557specID A) B)) (or (and (= A tptp.bot_bo1785112429specID) _let_2) (and _let_3 (= B tptp.bot_bo1785112429specID)) (and _let_3 _let_2))))))))
% 0.53/0.71 (assert (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) (or (and (= A tptp.bot_bo443197316chanID) _let_2) (and _let_3 (= B tptp.bot_bo443197316chanID)) (and _let_3 _let_2))))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.insert_Secrecy_KS X3) tptp.bot_bo1943466239ecy_KS))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su1301156759ecy_KS A) B) _let_1) (or (and (= A tptp.bot_bo1943466239ecy_KS) _let_2) (and _let_3 (= B tptp.bot_bo1943466239ecy_KS)) (and _let_3 _let_2))))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID) (X3 tptp.secrecy_specID)) (let ((_let_1 (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su1712599557specID A) B) _let_1) (or (and (= A tptp.bot_bo1785112429specID) _let_2) (and _let_3 (= B tptp.bot_bo1785112429specID)) (and _let_3 _let_2))))))))
% 0.53/0.71 (assert (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (X3 tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su370684444chanID A) B) _let_1) (or (and (= A tptp.bot_bo443197316chanID) _let_2) (and _let_3 (= B tptp.bot_bo443197316chanID)) (and _let_3 _let_2))))))))
% 0.53/0.71 (assert (= tptp.insert_Secrecy_KS (lambda ((A4 tptp.secrecy_KS) (__flatten_var_0 tptp.set_Secrecy_KS)) (@ (@ tptp.sup_su1301156759ecy_KS (@ (@ tptp.insert_Secrecy_KS A4) tptp.bot_bo1943466239ecy_KS)) __flatten_var_0))))
% 0.53/0.71 (assert (= tptp.insert1671894227specID (lambda ((A4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_specID)) (@ (@ tptp.sup_su1712599557specID (@ (@ tptp.insert1671894227specID A4) tptp.bot_bo1785112429specID)) __flatten_var_0))))
% 0.53/0.71 (assert (= tptp.insert751661162chanID (lambda ((A4 tptp.secrecy_chanID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ tptp.sup_su370684444chanID (@ (@ tptp.insert751661162chanID A4) tptp.bot_bo443197316chanID)) __flatten_var_0))))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS A2) tptp.bot_bo1943466239ecy_KS) A2)))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID A2) tptp.bot_bo1785112429specID) A2)))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID A2) tptp.bot_bo443197316chanID) A2)))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_KS) (B2 tptp.set_Secrecy_KS)) (= (= tptp.bot_bo1943466239ecy_KS (@ (@ tptp.sup_su1301156759ecy_KS A2) B2)) (and (= A2 tptp.bot_bo1943466239ecy_KS) (= B2 tptp.bot_bo1943466239ecy_KS)))))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_specID) (B2 tptp.set_Secrecy_specID)) (= (= tptp.bot_bo1785112429specID (@ (@ tptp.sup_su1712599557specID A2) B2)) (and (= A2 tptp.bot_bo1785112429specID) (= B2 tptp.bot_bo1785112429specID)))))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_chanID) (B2 tptp.set_Secrecy_chanID)) (= (= tptp.bot_bo443197316chanID (@ (@ tptp.sup_su370684444chanID A2) B2)) (and (= A2 tptp.bot_bo443197316chanID) (= B2 tptp.bot_bo443197316chanID)))))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS tptp.bot_bo1943466239ecy_KS) A2) A2)))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID tptp.bot_bo1785112429specID) A2) A2)))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID tptp.bot_bo443197316chanID) A2) A2)))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_KS) (B2 tptp.set_Secrecy_KS)) (= (= (@ (@ tptp.sup_su1301156759ecy_KS A2) B2) tptp.bot_bo1943466239ecy_KS) (and (= A2 tptp.bot_bo1943466239ecy_KS) (= B2 tptp.bot_bo1943466239ecy_KS)))))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_specID) (B2 tptp.set_Secrecy_specID)) (= (= (@ (@ tptp.sup_su1712599557specID A2) B2) tptp.bot_bo1785112429specID) (and (= A2 tptp.bot_bo1785112429specID) (= B2 tptp.bot_bo1785112429specID)))))
% 0.53/0.71 (assert (forall ((A2 tptp.set_Secrecy_chanID) (B2 tptp.set_Secrecy_chanID)) (= (= (@ (@ tptp.sup_su370684444chanID A2) B2) tptp.bot_bo443197316chanID) (and (= A2 tptp.bot_bo443197316chanID) (= B2 tptp.bot_bo443197316chanID)))))
% 0.53/0.71 (assert (forall ((X3 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS tptp.bot_bo1943466239ecy_KS) X3) X3)))
% 0.53/0.71 (assert (forall ((X3 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID tptp.bot_bo1785112429specID) X3) X3)))
% 0.53/0.71 (assert (forall ((X3 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID tptp.bot_bo443197316chanID) X3) X3)))
% 0.53/0.71 (assert (forall ((X3 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS X3) tptp.bot_bo1943466239ecy_KS) X3)))
% 0.53/0.71 (assert (forall ((X3 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID X3) tptp.bot_bo1785112429specID) X3)))
% 0.53/0.71 (assert (forall ((X3 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID X3) tptp.bot_bo443197316chanID) X3)))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (A tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.ineM P))) (=> (@ (@ _let_1 A) E) (@ (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) E)))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.eout P) E) (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (= (@ tptp.loc PQ) tptp.bot_bo443197316chanID) (@ (@ tptp.eout PQ) E)))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Keys)) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ (@ tptp.member_Secrecy_Keys Xa) (@ tptp.specKeys C3)) (exists ((X tptp.secrecy_specID)) (and (@ (@ tptp.member740727610specID X) (@ tptp.subcomponents C3)) (@ (@ tptp.member_Secrecy_Keys Xa) (@ tptp.specKeys X)))))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Secrets)) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ (@ tptp.member2138796287ecrets Xa) (@ tptp.specSecrets C3)) (exists ((X tptp.secrecy_specID)) (and (@ (@ tptp.member740727610specID X) (@ tptp.subcomponents C3)) (@ (@ tptp.member2138796287ecrets Xa) (@ tptp.specSecrets X)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.eout PQ) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (or (@ (@ tptp.eout P) E) (@ (@ tptp.eout Q) E)))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets Xa))) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ _let_1 (@ tptp.specSecrets X3)) (@ _let_1 (@ tptp.specSecrets C3))))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys Xa))) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ _let_1 (@ tptp.specKeys X3)) (@ _let_1 (@ tptp.specKeys C3))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ tptp.eout P) E) (=> (not (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (and (@ (@ (@ tptp.out_ex985543062Single P) Ch2) E) (@ (@ tptp.member1967978193chanID Ch2) (@ tptp.loc PQ)))) (not (@ (@ tptp.eout PQ) E)))))))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.out_exprChannelSet Q) ChSetQ) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.eout PQ) E))))))))))
% 0.53/0.71 (assert (forall ((Q tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.eout PQ) E)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.out_ex985543062Single P) Ch) E) (@ (@ (@ tptp.out_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.out_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E) (@ (@ (@ tptp.out_ex985543062Single P) Ch) E))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID) (M3 tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.out_exprChannelSet Q) ChSetQ) E) (=> (= M3 (@ (@ tptp.sup_su370684444chanID ChSetP) ChSetQ)) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.eoutM PQ) M3) E)))))))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (= (@ (@ tptp.knowle233900195orrect C3) _let_1) (= (@ (@ tptp.eout C3) (@ tptp.secrecy_sE M)) (or (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_Secrets) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (not (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets A))) (=> (not (@ (@ tptp.knowle945212990e_know A) _let_1)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (not (@ (@ tptp.eout A) (@ tptp.secrecy_sE M)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (M3 tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.eout P) E)) (not (@ (@ (@ tptp.eoutM P) M3) E)))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.eoutM P) M3) E) (@ (@ tptp.eout P) E))))
% 0.53/0.71 (assert (forall ((PQ tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.eoutM PQ) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (or (@ (@ (@ tptp.eoutM P) M3) E) (@ (@ (@ tptp.eoutM Q) M3) E)))))))
% 0.53/0.71 (assert (forall ((Q tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ (@ tptp.eoutM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.eoutM PQ) M3) E)))))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ (@ tptp.eoutM P) M3) E) (=> (not (@ (@ (@ tptp.eoutM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ (@ (@ tptp.out_ex985543062Single P) Ch2) E) (@ _let_1 M3) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.eoutM PQ) M3) E)))))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_Keys) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (not (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys A))) (=> (@ (@ tptp.eout A) (@ tptp.secrecy_kE M)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (@ (@ tptp.knowle945212990e_know A) _let_1)))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (@ (@ tptp.knowle233900195orrect C3) _let_1) (=> (@ (@ tptp.eout C3) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_Keys) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (not (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys A))) (=> (not (@ (@ tptp.knowle945212990e_know A) _let_1)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (not (@ (@ tptp.eout A) (@ tptp.secrecy_kE M)))))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (= (@ (@ tptp.knowle233900195orrect C3) _let_1) (= (@ (@ tptp.eout C3) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))))
% 0.53/0.71 (assert (forall ((M tptp.secrecy_Secrets) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (not (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets A))) (=> (@ (@ tptp.eout A) (@ tptp.secrecy_sE M)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (@ (@ tptp.knowle945212990e_know A) _let_1)))))))
% 0.53/0.71 (assert (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (@ (@ tptp.knowle233900195orrect C3) _let_1) (=> (@ (@ tptp.eout C3) (@ tptp.secrecy_sE M)) (or (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.eoutM P) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.out Q)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ))) (@ _let_1 M3)))) (@ (@ (@ tptp.eoutM PQ) M3) E)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ (@ tptp.eoutM P) M3) E) (@ (@ (@ tptp.eoutM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.out P)) (@ _let_1 (@ tptp.out Q))) (@ _let_1 M3) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ (@ tptp.eoutM PQ) M3) E)))))))
% 0.53/0.71 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.eout P) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.out P)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.eout PQ) E)))))))
% 0.53/0.71 (assert (= tptp.eout (lambda ((SP tptp.secrecy_specID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.out SP)) (@ (@ tptp.exprChannel Ch3) E2))))))
% 0.53/0.71 (assert (= tptp.eoutM (lambda ((SP tptp.secrecy_specID) (M4 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch3))) (and (@ _let_1 (@ tptp.out SP)) (@ _let_1 M4) (@ (@ tptp.exprChannel Ch3) E2)))))))
% 0.53/0.71 (assert (= tptp.out_exprChannelSet (lambda ((SP tptp.secrecy_specID) (ChSet2 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (@ _let_1 ChSet2) (and (@ _let_1 (@ tptp.out SP)) (@ (@ tptp.exprChannel X4) E2))))) (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (and (not (@ _let_1 ChSet2)) (@ _let_1 (@ tptp.out SP))) (not (@ (@ tptp.exprChannel X4) E2)))))))))
% 0.53/0.71 (assert (= tptp.out_ex985543062Single (lambda ((SP tptp.secrecy_specID) (Ch3 tptp.secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.out SP)) (@ (@ tptp.exprChannel Ch3) E2) (forall ((X4 tptp.secrecy_chanID) (T tptp.nat)) (=> (and (@ (@ tptp.member1967978193chanID X4) (@ tptp.out SP)) (not (= X4 Ch3))) (not (@ (@ tptp.exprChannel X4) E2))))))))
% 0.56/1.08 (assert (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (X3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ _let_1 (@ tptp.out PQ)) (or (@ _let_1 (@ tptp.out P)) (@ _let_1 (@ tptp.out Q)))))))))
% 0.56/1.08 (assert (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.eout P) E) (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.out P)) (@ _let_1 (@ tptp.out Q))) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.eout PQ) E)))))))
% 0.56/1.08 (assert (= tptp.outStream (lambda ((X4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ (lambda ((Y4 tptp.set_Secrecy_chanID) (Z tptp.set_Secrecy_chanID)) (= Y4 Z)) (@ tptp.out X4)) __flatten_var_0))))
% 0.56/1.08 (assert (forall ((P tptp.secrecy_specID) (A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (=> (@ (@ tptp.ord_le1802272080chanID (@ tptp.out P)) (@ tptp.ins A)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_sKS M))) (not (@ (@ tptp.eout P) (@ tptp.secrecy_sE M)))))))
% 0.56/1.08 (assert (not (not (@ (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS tptp.secret)) (@ tptp.localSecrets tptp.q)))))
% 0.56/1.08 (set-info :filename cvc5---1.0.5_22671)
% 0.56/1.08 (check-sat-assuming ( true ))
% 0.56/1.08 ------- get file name : TPTP file name is ITP091^1
% 0.56/1.08 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_22671.smt2...
% 0.56/1.08 --- Run --ho-elim --full-saturate-quant at 10...
% 0.56/1.08 % SZS status Theorem for ITP091^1
% 0.56/1.08 % SZS output start Proof for ITP091^1
% 0.56/1.08 (
% 0.56/1.08 (let ((_let_1 (@ tptp.secrecy_sKS tptp.secret))) (let ((_let_2 (@ tptp.member_Secrecy_KS _let_1))) (let ((_let_3 (@ _let_2 (@ tptp.localSecrets tptp.q)))) (let ((_let_4 (not (not _let_3)))) (let ((_let_5 (= tptp.outStream (lambda ((X4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ (lambda ((Y4 tptp.set_Secrecy_chanID) (Z tptp.set_Secrecy_chanID)) (= Y4 Z)) (@ tptp.out X4)) __flatten_var_0))))) (let ((_let_6 (= tptp.out_ex985543062Single (lambda ((SP tptp.secrecy_specID) (Ch3 tptp.secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.out SP)) (@ (@ tptp.exprChannel Ch3) E2) (forall ((X4 tptp.secrecy_chanID) (T tptp.nat)) (=> (and (@ (@ tptp.member1967978193chanID X4) (@ tptp.out SP)) (not (= X4 Ch3))) (not (@ (@ tptp.exprChannel X4) E2))))))))) (let ((_let_7 (= tptp.out_exprChannelSet (lambda ((SP tptp.secrecy_specID) (ChSet2 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (@ _let_1 ChSet2) (and (@ _let_1 (@ tptp.out SP)) (@ (@ tptp.exprChannel X4) E2))))) (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (and (not (@ _let_1 ChSet2)) (@ _let_1 (@ tptp.out SP))) (not (@ (@ tptp.exprChannel X4) E2)))))))))) (let ((_let_8 (= tptp.eoutM (lambda ((SP tptp.secrecy_specID) (M4 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch3))) (and (@ _let_1 (@ tptp.out SP)) (@ _let_1 M4) (@ (@ tptp.exprChannel Ch3) E2)))))))) (let ((_let_9 (= tptp.eout (lambda ((SP tptp.secrecy_specID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.out SP)) (@ (@ tptp.exprChannel Ch3) E2))))))) (let ((_let_10 (= tptp.notSpe1586871396tsExpr (lambda ((P2 tptp.secrecy_specID) (E3 tptp.list_S529945141ession)) (and (forall ((X4 tptp.secrecy_Keys)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_kE X4)) E3) (not (@ (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS X4)) (@ tptp.specKeysSecrets P2))))) (forall ((Y5 tptp.secrecy_Secrets)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_sE Y5)) E3) (not (@ (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Y5)) (@ tptp.specKeysSecrets P2)))))))))) (let ((_let_11 (= tptp.bot_bo1909946299rets_o (lambda ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) tptp.bot_bo1124690338ecrets))))) (let ((_let_12 (= tptp.bot_bo2072920570Keys_o (lambda ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) tptp.bot_bo701486667y_Keys))))) (let ((_let_13 (= tptp.bot_bot_Secrecy_KS_o (lambda ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS X4) tptp.bot_bo1943466239ecy_KS))))) (let ((_let_14 (= tptp.inStream (lambda ((X4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ (lambda ((Y4 tptp.set_Secrecy_chanID) (Z tptp.set_Secrecy_chanID)) (= Y4 Z)) (@ tptp.ins X4)) __flatten_var_0))))) (let ((_let_15 (= tptp.locStream (lambda ((X4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ (lambda ((Y4 tptp.set_Secrecy_chanID) (Z tptp.set_Secrecy_chanID)) (= Y4 Z)) (@ tptp.loc X4)) __flatten_var_0))))) (let ((_let_16 (= tptp.ine_ex1303305700Single (lambda ((SP tptp.secrecy_specID) (Ch3 tptp.secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.ins SP)) (@ (@ tptp.exprChannel Ch3) E2) (forall ((X4 tptp.secrecy_chanID) (T tptp.nat)) (=> (and (@ (@ tptp.member1967978193chanID X4) (@ tptp.ins SP)) (not (= X4 Ch3))) (not (@ (@ tptp.exprChannel X4) E2))))))))) (let ((_let_17 (= tptp.ineM (lambda ((SP tptp.secrecy_specID) (M4 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch3))) (and (@ _let_1 (@ tptp.ins SP)) (@ _let_1 M4) (@ (@ tptp.exprChannel Ch3) E2)))))))) (let ((_let_18 (= tptp.ine (lambda ((SP tptp.secrecy_specID) (E2 tptp.secrecy_Expression)) (exists ((Ch3 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.ins SP)) (@ (@ tptp.exprChannel Ch3) E2))))))) (let ((_let_19 (= tptp.ine_exprChannelSet (lambda ((SP tptp.secrecy_specID) (ChSet2 tptp.set_Secrecy_chanID) (E2 tptp.secrecy_Expression)) (and (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (@ _let_1 ChSet2) (and (@ _let_1 (@ tptp.ins SP)) (@ (@ tptp.exprChannel X4) E2))))) (forall ((X4 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X4))) (=> (and (not (@ _let_1 ChSet2)) (@ _let_1 (@ tptp.ins SP))) (not (@ (@ tptp.exprChannel X4) E2)))))))))) (let ((_let_20 (= tptp.is_emp928984296chanID (lambda ((A3 tptp.set_Secrecy_chanID)) (= A3 tptp.bot_bo443197316chanID))))) (let ((_let_21 (= tptp.is_emp1849217361specID (lambda ((A3 tptp.set_Secrecy_specID)) (= A3 tptp.bot_bo1785112429specID))))) (let ((_let_22 (= tptp.is_sin581274182chanID (lambda ((A3 tptp.set_Secrecy_chanID)) (= A3 (@ (@ tptp.insert751661162chanID (@ tptp.the_el2054381829chanID A3)) tptp.bot_bo443197316chanID)))))) (let ((_let_23 (= tptp.is_sin1501507247specID (lambda ((A3 tptp.set_Secrecy_specID)) (= A3 (@ (@ tptp.insert1671894227specID (@ tptp.the_el827131246specID A3)) tptp.bot_bo1785112429specID)))))) (let ((_let_24 (= tptp.bot_bo443197316chanID (@ tptp.collec625564175chanID tptp.bot_bo1012329985anID_o)))) (let ((_let_25 (= tptp.bot_bo1785112429specID (@ tptp.collec1545797240specID tptp.bot_bo1767780696ecID_o)))) (let ((_let_26 (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (= (@ (@ tptp.knowle945212990e_know A) _let_1) (or (@ (@ tptp.ine A) (@ tptp.secrecy_sE M)) (@ (@ tptp.member_Secrecy_KS _let_1) (@ tptp.localSecrets A)))))))) (let ((_let_27 (@ tptp.secrecy_sE tptp.secret))) (let ((_let_28 (= tptp.m _let_1))) (let ((_let_29 (@ tptp.knowle945212990e_know tptp.q))) (let ((_let_30 (not (@ _let_29 tptp.m)))) (let ((_let_31 (ho_85 k_84 tptp.secret))) (let ((_let_32 (ho_80 (ho_87 k_86 tptp.q) _let_31))) (let ((_let_33 (ho_83 (ho_82 k_81 _let_31) (ho_89 k_88 tptp.q)))) (let ((_let_34 (or (not (forall ((Ch3 tptp.secrecy_chanID)) (or (not (ho_49 (ho_48 k_47 Ch3) (ho_96 k_95 tptp.q))) (not (ho_94 (ho_93 k_92 Ch3) (ho_91 k_90 tptp.secret)))))) _let_33))) (let ((_let_35 (= _let_32 _let_34))) (let ((_let_36 (forall ((u |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID Bool)|) (e |u_(-> tptp.secrecy_specID Bool)|) (i tptp.set_Secrecy_specID)) (not (forall ((v |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID Bool)|)) (not (forall ((ii tptp.set_Secrecy_specID)) (= (ho_75 v ii) (ite (= i ii) e (ho_75 u ii)))))))))) (let ((_let_37 (forall ((x |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID Bool)|) (y |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID Bool)|)) (or (not (forall ((z tptp.set_Secrecy_specID)) (= (ho_75 x z) (ho_75 y z)))) (= x y))))) (let ((_let_38 (forall ((u |u_(-> tptp.secrecy_Expression Bool)|) (e Bool) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression Bool)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_39 (forall ((x |u_(-> tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_40 (forall ((u |u_(-> tptp.secrecy_Keys Bool)|) (e Bool) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys Bool)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_70 v ii) (ite (= i ii) e (ho_70 u ii)))))))))) (let ((_let_41 (forall ((x |u_(-> tptp.secrecy_Keys Bool)|) (y |u_(-> tptp.secrecy_Keys Bool)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_70 x z) (ho_70 y z)))) (= x y))))) (let ((_let_42 (forall ((u |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets Bool)|) (e |u_(-> tptp.set_Secrecy_Secrets Bool)|) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets Bool)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_43 (forall ((x |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets Bool)|) (y |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets Bool)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_44 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_KS)|) (e tptp.set_Secrecy_KS) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_KS)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_89 v ii) (ite (= i ii) e (ho_89 u ii)))))))))) (let ((_let_45 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_KS)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_89 x z) (ho_89 y z)))) (= x y))))) (let ((_let_46 (forall ((u |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|) (e tptp.secrecy_Expression) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_118 v ii) (ite (= i ii) e (ho_118 u ii)))))))))) (let ((_let_47 (forall ((x |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|) (y |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_118 x z) (ho_118 y z)))) (= x y))))) (let ((_let_48 (forall ((u |u_(-> tptp.secrecy_Secrets Bool)|) (e Bool) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets Bool)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_64 v ii) (ite (= i ii) e (ho_64 u ii)))))))))) (let ((_let_49 (forall ((x |u_(-> tptp.secrecy_Secrets Bool)|) (y |u_(-> tptp.secrecy_Secrets Bool)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_64 x z) (ho_64 y z)))) (= x y))))) (let ((_let_50 (forall ((u |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID)|) (e tptp.secrecy_specID) (i tptp.set_Secrecy_specID)) (not (forall ((v |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID)|)) (not (forall ((ii tptp.set_Secrecy_specID)) (= (ho_60 v ii) (ite (= i ii) e (ho_60 u ii)))))))))) (let ((_let_51 (forall ((x |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID)|) (y |u_(-> tptp.set_Secrecy_specID tptp.secrecy_specID)|)) (or (not (forall ((z tptp.set_Secrecy_specID)) (= (ho_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_52 (forall ((u |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID)|) (e tptp.secrecy_chanID) (i tptp.set_Secrecy_chanID)) (not (forall ((v |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID)|)) (not (forall ((ii tptp.set_Secrecy_chanID)) (= (ho_56 v ii) (ite (= i ii) e (ho_56 u ii)))))))))) (let ((_let_53 (forall ((x |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID)|) (y |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID)|)) (or (not (forall ((z tptp.set_Secrecy_chanID)) (= (ho_56 x z) (ho_56 y z)))) (= x y))))) (let ((_let_54 (forall ((u |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys Bool)|) (e |u_(-> tptp.set_Secrecy_Keys Bool)|) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys Bool)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_55 (forall ((x |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys Bool)|) (y |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys Bool)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_56 (forall ((u |u_(-> tptp.secrecy_Secrets tptp.secrecy_Expression)|) (e tptp.secrecy_Expression) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets tptp.secrecy_Expression)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_91 v ii) (ite (= i ii) e (ho_91 u ii)))))))))) (let ((_let_57 (forall ((x |u_(-> tptp.secrecy_Secrets tptp.secrecy_Expression)|) (y |u_(-> tptp.secrecy_Secrets tptp.secrecy_Expression)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_91 x z) (ho_91 y z)))) (= x y))))) (let ((_let_58 (forall ((u |u_(-> tptp.set_Secrecy_specID Bool)|) (e Bool) (i tptp.set_Secrecy_specID)) (not (forall ((v |u_(-> tptp.set_Secrecy_specID Bool)|)) (not (forall ((ii tptp.set_Secrecy_specID)) (= (ho_53 v ii) (ite (= i ii) e (ho_53 u ii)))))))))) (let ((_let_59 (forall ((x |u_(-> tptp.set_Secrecy_specID Bool)|) (y |u_(-> tptp.set_Secrecy_specID Bool)|)) (or (not (forall ((z tptp.set_Secrecy_specID)) (= (ho_53 x z) (ho_53 y z)))) (= x y))))) (let ((_let_60 (forall ((u |u_(-> tptp.set_Secrecy_Keys Bool)|) (e Bool) (i tptp.set_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.set_Secrecy_Keys Bool)|)) (not (forall ((ii tptp.set_Secrecy_Keys)) (= (ho_73 v ii) (ite (= i ii) e (ho_73 u ii)))))))))) (let ((_let_61 (forall ((x |u_(-> tptp.set_Secrecy_Keys Bool)|) (y |u_(-> tptp.set_Secrecy_Keys Bool)|)) (or (not (forall ((z tptp.set_Secrecy_Keys)) (= (ho_73 x z) (ho_73 y z)))) (= x y))))) (let ((_let_62 (forall ((u |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID Bool)|) (e |u_(-> tptp.set_Secrecy_chanID Bool)|) (i tptp.set_Secrecy_chanID)) (not (forall ((v |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID Bool)|)) (not (forall ((ii tptp.set_Secrecy_chanID)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_63 (forall ((x |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID Bool)|) (y |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID Bool)|)) (or (not (forall ((z tptp.set_Secrecy_chanID)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_64 (forall ((u |u_(-> tptp.set_Secrecy_Keys tptp.secrecy_Keys Bool)|) (e |u_(-> tptp.secrecy_Keys Bool)|) (i tptp.set_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.set_Secrecy_Keys tptp.secrecy_Keys Bool)|)) (not (forall ((ii tptp.set_Secrecy_Keys)) (= (ho_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_65 (forall ((x |u_(-> tptp.set_Secrecy_Keys tptp.secrecy_Keys Bool)|) (y |u_(-> tptp.set_Secrecy_Keys tptp.secrecy_Keys Bool)|)) (or (not (forall ((z tptp.set_Secrecy_Keys)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_66 (forall ((u |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID Bool)|) (e |u_(-> tptp.set_Secrecy_chanID Bool)|) (i tptp.secrecy_chanID)) (not (forall ((v |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID Bool)|)) (not (forall ((ii tptp.secrecy_chanID)) (= (ho_48 v ii) (ite (= i ii) e (ho_48 u ii)))))))))) (let ((_let_67 (forall ((x |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID Bool)|) (y |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID Bool)|)) (or (not (forall ((z tptp.secrecy_chanID)) (= (ho_48 x z) (ho_48 y z)))) (= x y))))) (let ((_let_68 (forall ((u |u_(-> tptp.secrecy_specID tptp.secrecy_KS Bool)|) (e |u_(-> tptp.secrecy_KS Bool)|) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.secrecy_KS Bool)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_87 v ii) (ite (= i ii) e (ho_87 u ii)))))))))) (let ((_let_69 (forall ((x |u_(-> tptp.secrecy_specID tptp.secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_specID tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_87 x z) (ho_87 y z)))) (= x y))))) (let ((_let_70 (forall ((u |u_(-> tptp.secrecy_Keys tptp.secrecy_KS)|) (e tptp.secrecy_KS) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.secrecy_KS)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_102 v ii) (ite (= i ii) e (ho_102 u ii)))))))))) (let ((_let_71 (forall ((x |u_(-> tptp.secrecy_Keys tptp.secrecy_KS)|) (y |u_(-> tptp.secrecy_Keys tptp.secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_102 x z) (ho_102 y z)))) (= x y))))) (let ((_let_72 (forall ((u |u_(-> tptp.set_Secrecy_chanID Bool)|) (e Bool) (i tptp.set_Secrecy_chanID)) (not (forall ((v |u_(-> tptp.set_Secrecy_chanID Bool)|)) (not (forall ((ii tptp.set_Secrecy_chanID)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_73 (forall ((x |u_(-> tptp.set_Secrecy_chanID Bool)|) (y |u_(-> tptp.set_Secrecy_chanID Bool)|)) (or (not (forall ((z tptp.set_Secrecy_chanID)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_74 (forall ((u |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (e |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_39 v ii) (ite (= i ii) e (ho_39 u ii)))))))))) (let ((_let_75 (forall ((x |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (y |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_39 x z) (ho_39 y z)))) (= x y))))) (let ((_let_76 (forall ((u |u_(-> tptp.secrecy_chanID Bool)|) (e Bool) (i tptp.secrecy_chanID)) (not (forall ((v |u_(-> tptp.secrecy_chanID Bool)|)) (not (forall ((ii tptp.secrecy_chanID)) (= (ho_22 v ii) (ite (= i ii) e (ho_22 u ii)))))))))) (let ((_let_77 (forall ((x |u_(-> tptp.secrecy_chanID Bool)|) (y |u_(-> tptp.secrecy_chanID Bool)|)) (or (not (forall ((z tptp.secrecy_chanID)) (= (ho_22 x z) (ho_22 y z)))) (= x y))))) (let ((_let_78 (forall ((u |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (e |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (i tptp.secrecy_chanID)) (not (forall ((v |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|)) (not (forall ((ii tptp.secrecy_chanID)) (= (ho_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_79 (forall ((x |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (y |u_(-> tptp.secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|)) (or (not (forall ((z tptp.secrecy_chanID)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_80 (forall ((u |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID Bool)|) (e |u_(-> tptp.secrecy_chanID Bool)|) (i tptp.set_Secrecy_chanID)) (not (forall ((v |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID Bool)|)) (not (forall ((ii tptp.set_Secrecy_chanID)) (= (ho_77 v ii) (ite (= i ii) e (ho_77 u ii)))))))))) (let ((_let_81 (forall ((x |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID Bool)|) (y |u_(-> tptp.set_Secrecy_chanID tptp.secrecy_chanID Bool)|)) (or (not (forall ((z tptp.set_Secrecy_chanID)) (= (ho_77 x z) (ho_77 y z)))) (= x y))))) (let ((_let_82 (forall ((u |u_(-> tptp.set_Secrecy_Secrets Bool)|) (e Bool) (i tptp.set_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.set_Secrecy_Secrets Bool)|)) (not (forall ((ii tptp.set_Secrecy_Secrets)) (= (ho_67 v ii) (ite (= i ii) e (ho_67 u ii)))))))))) (let ((_let_83 (forall ((x |u_(-> tptp.set_Secrecy_Secrets Bool)|) (y |u_(-> tptp.set_Secrecy_Secrets Bool)|)) (or (not (forall ((z tptp.set_Secrecy_Secrets)) (= (ho_67 x z) (ho_67 y z)))) (= x y))))) (let ((_let_84 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID Bool)|) (e |u_(-> tptp.set_Secrecy_specID Bool)|) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID Bool)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_85 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID Bool)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID Bool)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_86 (forall ((u |u_(-> tptp.secrecy_Secrets tptp.secrecy_KS)|) (e tptp.secrecy_KS) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets tptp.secrecy_KS)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_85 v ii) (ite (= i ii) e (ho_85 u ii)))))))))) (let ((_let_87 (forall ((x |u_(-> tptp.secrecy_Secrets tptp.secrecy_KS)|) (y |u_(-> tptp.secrecy_Secrets tptp.secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_85 x z) (ho_85 y z)))) (= x y))))) (let ((_let_88 (forall ((u |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (e tptp.set_Secrecy_specID) (i tptp.set_Secrecy_specID)) (not (forall ((v |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|)) (not (forall ((ii tptp.set_Secrecy_specID)) (= (ho_30 v ii) (ite (= i ii) e (ho_30 u ii)))))))))) (let ((_let_89 (forall ((x |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (y |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|)) (or (not (forall ((z tptp.set_Secrecy_specID)) (= (ho_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_90 (forall ((u |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (e tptp.set_Secrecy_KS) (i tptp.set_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|)) (not (forall ((ii tptp.set_Secrecy_KS)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_91 (forall ((x |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (y |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|)) (or (not (forall ((z tptp.set_Secrecy_KS)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_92 (forall ((u |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (e |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (i tptp.set_Secrecy_chanID)) (not (forall ((v |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|)) (not (forall ((ii tptp.set_Secrecy_chanID)) (= (ho_27 v ii) (ite (= i ii) e (ho_27 u ii)))))))))) (let ((_let_93 (forall ((x |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (y |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|)) (or (not (forall ((z tptp.set_Secrecy_chanID)) (= (ho_27 x z) (ho_27 y z)))) (= x y))))) (let ((_let_94 (forall ((u |u_(-> tptp.set_Secrecy_KS tptp.secrecy_KS Bool)|) (e |u_(-> tptp.secrecy_KS Bool)|) (i tptp.set_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_Secrecy_KS tptp.secrecy_KS Bool)|)) (not (forall ((ii tptp.set_Secrecy_KS)) (= (ho_79 v ii) (ite (= i ii) e (ho_79 u ii)))))))))) (let ((_let_95 (forall ((x |u_(-> tptp.set_Secrecy_KS tptp.secrecy_KS Bool)|) (y |u_(-> tptp.set_Secrecy_KS tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.set_Secrecy_KS)) (= (ho_79 x z) (ho_79 y z)))) (= x y))))) (let ((_let_96 (forall ((u |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (e |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (i tptp.set_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|)) (not (forall ((ii tptp.set_Secrecy_KS)) (= (ho_43 v ii) (ite (= i ii) e (ho_43 u ii)))))))))) (let ((_let_97 (forall ((x |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|) (y |u_(-> tptp.set_Secrecy_KS tptp.set_Secrecy_KS tptp.set_Secrecy_KS)|)) (or (not (forall ((z tptp.set_Secrecy_KS)) (= (ho_43 x z) (ho_43 y z)))) (= x y))))) (let ((_let_98 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (e |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_29 v ii) (ite (= i ii) e (ho_29 u ii)))))))))) (let ((_let_99 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_29 x z) (ho_29 y z)))) (= x y))))) (let ((_let_100 (forall ((u |u_(-> tptp.secrecy_specID Bool)|) (e Bool) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID Bool)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_101 (forall ((x |u_(-> tptp.secrecy_specID Bool)|) (y |u_(-> tptp.secrecy_specID Bool)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_102 (forall ((u |u_(-> tptp.set_Secrecy_Secrets tptp.secrecy_Secrets Bool)|) (e |u_(-> tptp.secrecy_Secrets Bool)|) (i tptp.set_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.set_Secrecy_Secrets tptp.secrecy_Secrets Bool)|)) (not (forall ((ii tptp.set_Secrecy_Secrets)) (= (ho_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_103 (forall ((x |u_(-> tptp.set_Secrecy_Secrets tptp.secrecy_Secrets Bool)|) (y |u_(-> tptp.set_Secrecy_Secrets tptp.secrecy_Secrets Bool)|)) (or (not (forall ((z tptp.set_Secrecy_Secrets)) (= (ho_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_104 (forall ((u |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS Bool)|) (e |u_(-> tptp.set_Secrecy_KS Bool)|) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS Bool)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_105 (forall ((x |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_KS tptp.set_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_106 (forall ((u |u_(-> tptp.secrecy_Keys tptp.secrecy_Expression)|) (e tptp.secrecy_Expression) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.secrecy_Expression)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_116 v ii) (ite (= i ii) e (ho_116 u ii)))))))))) (let ((_let_107 (forall ((x |u_(-> tptp.secrecy_Keys tptp.secrecy_Expression)|) (y |u_(-> tptp.secrecy_Keys tptp.secrecy_Expression)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_116 x z) (ho_116 y z)))) (= x y))))) (let ((_let_108 (forall ((u |u_(-> _u_(-> tptp.secrecy_specID Bool)_ tptp.set_Secrecy_specID)|) (e tptp.set_Secrecy_specID) (i |u_(-> tptp.secrecy_specID Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_specID Bool)_ tptp.set_Secrecy_specID)|)) (not (forall ((ii |u_(-> tptp.secrecy_specID Bool)|)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_109 (forall ((x |u_(-> _u_(-> tptp.secrecy_specID Bool)_ tptp.set_Secrecy_specID)|) (y |u_(-> _u_(-> tptp.secrecy_specID Bool)_ tptp.set_Secrecy_specID)|)) (or (not (forall ((z |u_(-> tptp.secrecy_specID Bool)|)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_110 (forall ((u |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (e tptp.set_Secrecy_chanID) (i tptp.set_Secrecy_chanID)) (not (forall ((v |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|)) (not (forall ((ii tptp.set_Secrecy_chanID)) (= (ho_20 v ii) (ite (= i ii) e (ho_20 u ii)))))))))) (let ((_let_111 (forall ((x |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|) (y |u_(-> tptp.set_Secrecy_chanID tptp.set_Secrecy_chanID)|)) (or (not (forall ((z tptp.set_Secrecy_chanID)) (= (ho_20 x z) (ho_20 y z)))) (= x y))))) (let ((_let_112 (forall ((u |u_(-> tptp.set_Secrecy_KS Bool)|) (e Bool) (i tptp.set_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_Secrecy_KS Bool)|)) (not (forall ((ii tptp.set_Secrecy_KS)) (= (ho_83 v ii) (ite (= i ii) e (ho_83 u ii)))))))))) (let ((_let_113 (forall ((x |u_(-> tptp.set_Secrecy_KS Bool)|) (y |u_(-> tptp.set_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.set_Secrecy_KS)) (= (ho_83 x z) (ho_83 y z)))) (= x y))))) (let ((_let_114 (forall ((u |u_(-> _u_(-> tptp.secrecy_chanID Bool)_ tptp.set_Secrecy_chanID)|) (e tptp.set_Secrecy_chanID) (i |u_(-> tptp.secrecy_chanID Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_chanID Bool)_ tptp.set_Secrecy_chanID)|)) (not (forall ((ii |u_(-> tptp.secrecy_chanID Bool)|)) (= (ho_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_115 (forall ((x |u_(-> _u_(-> tptp.secrecy_chanID Bool)_ tptp.set_Secrecy_chanID)|) (y |u_(-> _u_(-> tptp.secrecy_chanID Bool)_ tptp.set_Secrecy_chanID)|)) (or (not (forall ((z |u_(-> tptp.secrecy_chanID Bool)|)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_116 (forall ((u |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (e |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (i tptp.set_Secrecy_specID)) (not (forall ((v |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|)) (not (forall ((ii tptp.set_Secrecy_specID)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_117 (forall ((x |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|) (y |u_(-> tptp.set_Secrecy_specID tptp.set_Secrecy_specID tptp.set_Secrecy_specID)|)) (or (not (forall ((z tptp.set_Secrecy_specID)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_118 (forall ((u |u_(-> tptp.secrecy_KS Bool)|) (e Bool) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS Bool)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_119 (forall ((x |u_(-> tptp.secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_120 (forall ((u |u_(-> tptp.secrecy_chanID tptp.secrecy_Expression Bool)|) (e |u_(-> tptp.secrecy_Expression Bool)|) (i tptp.secrecy_chanID)) (not (forall ((v |u_(-> tptp.secrecy_chanID tptp.secrecy_Expression Bool)|)) (not (forall ((ii tptp.secrecy_chanID)) (= (ho_93 v ii) (ite (= i ii) e (ho_93 u ii)))))))))) (let ((_let_121 (forall ((x |u_(-> tptp.secrecy_chanID tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.secrecy_chanID tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.secrecy_chanID)) (= (ho_93 x z) (ho_93 y z)))) (= x y))))) (let ((_let_122 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_chanID)|) (e tptp.set_Secrecy_chanID) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_chanID)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_96 v ii) (ite (= i ii) e (ho_96 u ii)))))))))) (let ((_let_123 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_chanID)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_chanID)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_96 x z) (ho_96 y z)))) (= x y))))) (let ((_let_124 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID)|) (e tptp.set_Secrecy_specID) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_125 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_specID)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_126 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Secrets)|) (e tptp.set_Secrecy_Secrets) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Secrets)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_127 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Secrets)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_128 (forall ((u |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (e tptp.set_Secrecy_Keys) (i tptp.set_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (not (forall ((ii tptp.set_Secrecy_Keys)) (= (ho_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_129 (forall ((x |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (y |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (or (not (forall ((z tptp.set_Secrecy_Keys)) (= (ho_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_130 (forall ((u |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (e |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (i tptp.set_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (not (forall ((ii tptp.set_Secrecy_Keys)) (= (ho_126 v ii) (ite (= i ii) e (ho_126 u ii)))))))))) (let ((_let_131 (forall ((x |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (y |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (or (not (forall ((z tptp.set_Secrecy_Keys)) (= (ho_126 x z) (ho_126 y z)))) (= x y))))) (let ((_let_132 (forall ((u |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (e |u_(-> tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_104 v ii) (ite (= i ii) e (ho_104 u ii)))))))))) (let ((_let_133 (forall ((x |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|) (y |u_(-> tptp.secrecy_Keys tptp.set_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_104 x z) (ho_104 y z)))) (= x y))))) (let ((_let_134 (forall ((u |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (e tptp.set_Secrecy_Secrets) (i tptp.set_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (not (forall ((ii tptp.set_Secrecy_Secrets)) (= (ho_108 v ii) (ite (= i ii) e (ho_108 u ii)))))))))) (let ((_let_135 (forall ((x |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (y |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z tptp.set_Secrecy_Secrets)) (= (ho_108 x z) (ho_108 y z)))) (= x y))))) (let ((_let_136 (forall ((u |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (e |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_137 (forall ((x |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (y |u_(-> tptp.secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_138 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.set_Secrecy_KS)|) (e tptp.set_Secrecy_KS) (i |u_(-> tptp.secrecy_KS Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.set_Secrecy_KS)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS Bool)|)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_139 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.set_Secrecy_KS)|) (y |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.set_Secrecy_KS)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS Bool)|)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_140 (forall ((u |u_(-> _u_(-> tptp.secrecy_Keys Bool)_ tptp.set_Secrecy_Keys)|) (e tptp.set_Secrecy_Keys) (i |u_(-> tptp.secrecy_Keys Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Keys Bool)_ tptp.set_Secrecy_Keys)|)) (not (forall ((ii |u_(-> tptp.secrecy_Keys Bool)|)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_141 (forall ((x |u_(-> _u_(-> tptp.secrecy_Keys Bool)_ tptp.set_Secrecy_Keys)|) (y |u_(-> _u_(-> tptp.secrecy_Keys Bool)_ tptp.set_Secrecy_Keys)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Keys Bool)|)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_142 (forall ((u |u_(-> _u_(-> tptp.secrecy_Secrets Bool)_ tptp.set_Secrecy_Secrets)|) (e tptp.set_Secrecy_Secrets) (i |u_(-> tptp.secrecy_Secrets Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Secrets Bool)_ tptp.set_Secrecy_Secrets)|)) (not (forall ((ii |u_(-> tptp.secrecy_Secrets Bool)|)) (= (ho_114 v ii) (ite (= i ii) e (ho_114 u ii)))))))))) (let ((_let_143 (forall ((x |u_(-> _u_(-> tptp.secrecy_Secrets Bool)_ tptp.set_Secrecy_Secrets)|) (y |u_(-> _u_(-> tptp.secrecy_Secrets Bool)_ tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Secrets Bool)|)) (= (ho_114 x z) (ho_114 y z)))) (= x y))))) (let ((_let_144 (forall ((u |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (e |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (i tptp.set_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (not (forall ((ii tptp.set_Secrecy_Secrets)) (= (ho_128 v ii) (ite (= i ii) e (ho_128 u ii)))))))))) (let ((_let_145 (forall ((x |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (y |u_(-> tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z tptp.set_Secrecy_Secrets)) (= (ho_128 x z) (ho_128 y z)))) (= x y))))) (let ((_let_146 (forall ((u |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Keys)|) (e tptp.set_Secrecy_Keys) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Keys)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_147 (forall ((x |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Keys)|) (y |u_(-> tptp.secrecy_specID tptp.set_Secrecy_Keys)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_148 (forall ((BOUND_VARIABLE_15315 tptp.secrecy_chanID) (BOUND_VARIABLE_15316 tptp.set_Secrecy_chanID)) (= (ho_20 (ho_19 k_18 BOUND_VARIABLE_15315) BOUND_VARIABLE_15316) (ho_20 (ho_27 k_26 (ho_20 (ho_19 k_25 BOUND_VARIABLE_15315) (ho_24 k_23 k_21))) BOUND_VARIABLE_15316))))) (let ((_let_149 (forall ((BOUND_VARIABLE_15305 tptp.secrecy_specID) (BOUND_VARIABLE_15306 tptp.set_Secrecy_specID)) (= (ho_30 (ho_29 k_28 BOUND_VARIABLE_15305) BOUND_VARIABLE_15306) (ho_30 (ho_37 k_36 (ho_30 (ho_29 k_35 BOUND_VARIABLE_15305) (ho_34 k_33 k_31))) BOUND_VARIABLE_15306))))) (let ((_let_150 (forall ((BOUND_VARIABLE_15295 tptp.secrecy_KS) (BOUND_VARIABLE_15296 tptp.set_Secrecy_KS)) (= (ho_40 (ho_39 k_38 BOUND_VARIABLE_15295) BOUND_VARIABLE_15296) (ho_40 (ho_43 k_42 (ho_40 (ho_39 k_41 BOUND_VARIABLE_15295) tptp.bot_bo1943466239ecy_KS)) BOUND_VARIABLE_15296))))) (let ((_let_151 (forall ((BOUND_VARIABLE_15287 tptp.set_Secrecy_chanID) (BOUND_VARIABLE_15288 tptp.set_Secrecy_chanID)) (= (ho_20 (ho_27 k_44 BOUND_VARIABLE_15287) BOUND_VARIABLE_15288) (ho_20 (ho_27 k_26 BOUND_VARIABLE_15288) BOUND_VARIABLE_15287))))) (let ((_let_152 (forall ((BOUND_VARIABLE_15279 tptp.set_Secrecy_KS) (BOUND_VARIABLE_15280 tptp.set_Secrecy_KS)) (= (ho_40 (ho_43 k_45 BOUND_VARIABLE_15279) BOUND_VARIABLE_15280) (ho_40 (ho_43 k_42 BOUND_VARIABLE_15280) BOUND_VARIABLE_15279))))) (let ((_let_153 (forall ((BOUND_VARIABLE_15272 tptp.secrecy_chanID)) (= (ho_22 k_46 BOUND_VARIABLE_15272) (ho_49 (ho_48 k_47 BOUND_VARIABLE_15272) (ho_24 k_23 k_21)))))) (let ((_let_154 (forall ((BOUND_VARIABLE_15265 tptp.secrecy_specID)) (= (ho_32 k_50 BOUND_VARIABLE_15265) (ho_53 (ho_52 k_51 BOUND_VARIABLE_15265) (ho_34 k_33 k_31)))))) (let ((_let_155 (forall ((BOUND_VARIABLE_15256 tptp.set_Secrecy_chanID)) (= (ho_49 k_54 BOUND_VARIABLE_15256) (= BOUND_VARIABLE_15256 (ho_20 (ho_19 k_25 (ho_56 k_55 BOUND_VARIABLE_15256)) (ho_24 k_23 k_21))))))) (let ((_let_156 (forall ((BOUND_VARIABLE_15247 tptp.set_Secrecy_chanID)) (= (ho_49 k_57 BOUND_VARIABLE_15247) (not (forall ((X4 tptp.secrecy_chanID)) (not (= BOUND_VARIABLE_15247 (ho_20 (ho_19 k_25 X4) (ho_24 k_23 k_21)))))))))) (let ((_let_157 (forall ((BOUND_VARIABLE_15238 tptp.set_Secrecy_specID)) (= (ho_53 k_58 BOUND_VARIABLE_15238) (= BOUND_VARIABLE_15238 (ho_30 (ho_29 k_35 (ho_60 k_59 BOUND_VARIABLE_15238)) (ho_34 k_33 k_31))))))) (let ((_let_158 (forall ((BOUND_VARIABLE_15229 tptp.set_Secrecy_specID)) (= (ho_53 k_61 BOUND_VARIABLE_15229) (not (forall ((X4 tptp.secrecy_specID)) (not (= BOUND_VARIABLE_15229 (ho_30 (ho_29 k_35 X4) (ho_34 k_33 k_31)))))))))) (let ((_let_159 (forall ((BOUND_VARIABLE_15221 tptp.set_Secrecy_Secrets) (BOUND_VARIABLE_15222 tptp.secrecy_Secrets)) (= (ho_64 (ho_63 k_62 BOUND_VARIABLE_15221) BOUND_VARIABLE_15222) (ho_67 (ho_66 k_65 BOUND_VARIABLE_15222) BOUND_VARIABLE_15221))))) (let ((_let_160 (forall ((BOUND_VARIABLE_15213 tptp.set_Secrecy_Keys) (BOUND_VARIABLE_15214 tptp.secrecy_Keys)) (= (ho_70 (ho_69 k_68 BOUND_VARIABLE_15213) BOUND_VARIABLE_15214) (ho_73 (ho_72 k_71 BOUND_VARIABLE_15214) BOUND_VARIABLE_15213))))) (let ((_let_161 (forall ((BOUND_VARIABLE_15205 tptp.set_Secrecy_specID) (BOUND_VARIABLE_15206 tptp.secrecy_specID)) (= (ho_32 (ho_75 k_74 BOUND_VARIABLE_15205) BOUND_VARIABLE_15206) (ho_53 (ho_52 k_51 BOUND_VARIABLE_15206) BOUND_VARIABLE_15205))))) (let ((_let_162 (forall ((BOUND_VARIABLE_15197 tptp.set_Secrecy_chanID) (BOUND_VARIABLE_15198 tptp.secrecy_chanID)) (= (ho_22 (ho_77 k_76 BOUND_VARIABLE_15197) BOUND_VARIABLE_15198) (ho_49 (ho_48 k_47 BOUND_VARIABLE_15198) BOUND_VARIABLE_15197))))) (let ((_let_163 (forall ((BOUND_VARIABLE_15189 tptp.set_Secrecy_KS) (BOUND_VARIABLE_15190 tptp.secrecy_KS)) (= (ho_80 (ho_79 k_78 BOUND_VARIABLE_15189) BOUND_VARIABLE_15190) (ho_83 (ho_82 k_81 BOUND_VARIABLE_15190) BOUND_VARIABLE_15189))))) (let ((_let_164 (not _let_32))) (let ((_let_165 (forall ((BOUND_VARIABLE_15315 tptp.secrecy_chanID) (BOUND_VARIABLE_15316 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID (@ (@ tptp.insert751661162chanID BOUND_VARIABLE_15315) (@ tptp.collec625564175chanID tptp.bot_bo1012329985anID_o))) BOUND_VARIABLE_15316) (ll_17 BOUND_VARIABLE_15315 BOUND_VARIABLE_15316))))) (let ((_let_166 (forall ((BOUND_VARIABLE_15305 tptp.secrecy_specID) (BOUND_VARIABLE_15306 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID (@ (@ tptp.insert1671894227specID BOUND_VARIABLE_15305) (@ tptp.collec1545797240specID tptp.bot_bo1767780696ecID_o))) BOUND_VARIABLE_15306) (ll_16 BOUND_VARIABLE_15305 BOUND_VARIABLE_15306))))) (let ((_let_167 (forall ((BOUND_VARIABLE_15295 tptp.secrecy_KS) (BOUND_VARIABLE_15296 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS (@ (@ tptp.insert_Secrecy_KS BOUND_VARIABLE_15295) tptp.bot_bo1943466239ecy_KS)) BOUND_VARIABLE_15296) (ll_15 BOUND_VARIABLE_15295 BOUND_VARIABLE_15296))))) (let ((_let_168 (forall ((BOUND_VARIABLE_15287 tptp.set_Secrecy_chanID) (BOUND_VARIABLE_15288 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID BOUND_VARIABLE_15288) BOUND_VARIABLE_15287) (ll_14 BOUND_VARIABLE_15287 BOUND_VARIABLE_15288))))) (let ((_let_169 (forall ((BOUND_VARIABLE_15279 tptp.set_Secrecy_KS) (BOUND_VARIABLE_15280 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS BOUND_VARIABLE_15280) BOUND_VARIABLE_15279) (ll_13 BOUND_VARIABLE_15279 BOUND_VARIABLE_15280))))) (let ((_let_170 (forall ((BOUND_VARIABLE_15272 tptp.secrecy_chanID)) (= (@ (@ tptp.member1967978193chanID BOUND_VARIABLE_15272) (@ tptp.collec625564175chanID tptp.bot_bo1012329985anID_o)) (ll_12 BOUND_VARIABLE_15272))))) (let ((_let_171 (forall ((BOUND_VARIABLE_15265 tptp.secrecy_specID)) (= (@ (@ tptp.member740727610specID BOUND_VARIABLE_15265) (@ tptp.collec1545797240specID tptp.bot_bo1767780696ecID_o)) (ll_11 BOUND_VARIABLE_15265))))) (let ((_let_172 (forall ((BOUND_VARIABLE_15256 tptp.set_Secrecy_chanID)) (= (= BOUND_VARIABLE_15256 (@ (@ tptp.insert751661162chanID (@ tptp.the_el2054381829chanID BOUND_VARIABLE_15256)) (@ tptp.collec625564175chanID tptp.bot_bo1012329985anID_o))) (ll_10 BOUND_VARIABLE_15256))))) (let ((_let_173 (forall ((BOUND_VARIABLE_15247 tptp.set_Secrecy_chanID)) (= (ll_9 BOUND_VARIABLE_15247) (not (forall ((X4 tptp.secrecy_chanID)) (not (= (@ (@ tptp.insert751661162chanID X4) (@ tptp.collec625564175chanID tptp.bot_bo1012329985anID_o)) BOUND_VARIABLE_15247)))))))) (let ((_let_174 (forall ((BOUND_VARIABLE_15238 tptp.set_Secrecy_specID)) (= (= BOUND_VARIABLE_15238 (@ (@ tptp.insert1671894227specID (@ tptp.the_el827131246specID BOUND_VARIABLE_15238)) (@ tptp.collec1545797240specID tptp.bot_bo1767780696ecID_o))) (ll_8 BOUND_VARIABLE_15238))))) (let ((_let_175 (forall ((BOUND_VARIABLE_15229 tptp.set_Secrecy_specID)) (= (ll_7 BOUND_VARIABLE_15229) (not (forall ((X4 tptp.secrecy_specID)) (not (= (@ (@ tptp.insert1671894227specID X4) (@ tptp.collec1545797240specID tptp.bot_bo1767780696ecID_o)) BOUND_VARIABLE_15229)))))))) (let ((_let_176 (forall ((BOUND_VARIABLE_15221 tptp.set_Secrecy_Secrets) (BOUND_VARIABLE_15222 tptp.secrecy_Secrets)) (= (@ (@ tptp.member2138796287ecrets BOUND_VARIABLE_15222) BOUND_VARIABLE_15221) (ll_6 BOUND_VARIABLE_15221 BOUND_VARIABLE_15222))))) (let ((_let_177 (forall ((BOUND_VARIABLE_15213 tptp.set_Secrecy_Keys) (BOUND_VARIABLE_15214 tptp.secrecy_Keys)) (= (@ (@ tptp.member_Secrecy_Keys BOUND_VARIABLE_15214) BOUND_VARIABLE_15213) (ll_5 BOUND_VARIABLE_15213 BOUND_VARIABLE_15214))))) (let ((_let_178 (forall ((BOUND_VARIABLE_15205 tptp.set_Secrecy_specID) (BOUND_VARIABLE_15206 tptp.secrecy_specID)) (= (@ (@ tptp.member740727610specID BOUND_VARIABLE_15206) BOUND_VARIABLE_15205) (ll_4 BOUND_VARIABLE_15205 BOUND_VARIABLE_15206))))) (let ((_let_179 (forall ((BOUND_VARIABLE_15197 tptp.set_Secrecy_chanID) (BOUND_VARIABLE_15198 tptp.secrecy_chanID)) (= (@ (@ tptp.member1967978193chanID BOUND_VARIABLE_15198) BOUND_VARIABLE_15197) (ll_3 BOUND_VARIABLE_15197 BOUND_VARIABLE_15198))))) (let ((_let_180 (forall ((BOUND_VARIABLE_15189 tptp.set_Secrecy_KS) (BOUND_VARIABLE_15190 tptp.secrecy_KS)) (= (@ (@ tptp.member_Secrecy_KS BOUND_VARIABLE_15190) BOUND_VARIABLE_15189) (ll_2 BOUND_VARIABLE_15189 BOUND_VARIABLE_15190))))) (let ((_let_181 (and (not (@ _let_29 _let_1)) _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165))) (let ((_let_182 (ASSUME :args (_let_28)))) (let ((_let_183 (ASSUME :args (_let_25)))) (let ((_let_184 (ASSUME :args (_let_24)))) (let ((_let_185 (EQ_RESOLVE (ASSUME :args (_let_23)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_184 _let_183 _let_182) :args (_let_23 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_186 (EQ_RESOLVE (ASSUME :args (_let_22)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_185 _let_184 _let_183 _let_182) :args (_let_22 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_187 (EQ_RESOLVE (EQ_RESOLVE (ASSUME :args (_let_21)) (MACRO_SR_EQ_INTRO :args (_let_21 SB_DEFAULT SBA_FIXPOINT))) (MACRO_SR_EQ_INTRO (AND_INTRO _let_186 _let_185 _let_184 _let_183 _let_182) :args ((= tptp.is_emp1849217361specID (lambda ((A3 tptp.set_Secrecy_specID)) (= tptp.bot_bo1785112429specID A3))) SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_188 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_5)) (MACRO_SR_EQ_INTRO :args (_let_5 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_6)) (MACRO_SR_EQ_INTRO :args (_let_6 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_7)) (MACRO_SR_EQ_INTRO :args (_let_7 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_8)) (MACRO_SR_EQ_INTRO :args (_let_8 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))) (EQ_RESOLVE (ASSUME :args (_let_10)) (MACRO_SR_EQ_INTRO :args (_let_10 SB_DEFAULT SBA_FIXPOINT))) (ASSUME :args (_let_11)) (ASSUME 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_let_183 _let_182))) (let ((_let_189 (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (ho_85 k_84 M))) (= (or (not (forall ((Ch3 tptp.secrecy_chanID)) (or (not (ho_49 (ho_48 k_47 Ch3) (ho_96 k_95 A))) (not (ho_94 (ho_93 k_92 Ch3) (ho_91 k_90 M)))))) (ho_83 (ho_82 k_81 _let_1) (ho_89 k_88 A))) (ho_80 (ho_87 k_86 A) _let_1)))))) (let ((_let_190 (EQ_RESOLVE (ASSUME :args (_let_26)) (TRANS (MACRO_SR_EQ_INTRO _let_188 :args (_let_26 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (= (@ (@ tptp.knowle945212990e_know A) _let_1) (or (not (forall ((Ch3 tptp.secrecy_chanID)) (or (not (@ (@ tptp.member1967978193chanID Ch3) (@ tptp.ins A))) (not (@ (@ tptp.exprChannel Ch3) (@ tptp.secrecy_sE M)))))) (@ (@ tptp.member_Secrecy_KS _let_1) (@ tptp.localSecrets A)))))) _let_189))))))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_35)) :args ((or _let_32 (not _let_34) (not _let_35)))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_190 :args (tptp.q tptp.secret QUANTIFIERS_INST_E_MATCHING ((ho_83 (ho_82 k_81 (ho_85 k_84 M)) (ho_89 k_88 A))))) :args (_let_189)))) _let_190 :args (_let_35 false _let_189)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_NEG :args (_let_34 1)) :args ((or (not _let_33) _let_34))) (EQ_RESOLVE (ASSUME :args (_let_4)) (TRANS (MACRO_SR_EQ_INTRO :args (_let_4 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= _let_3 _let_33))))) :args (_let_34 false _let_33)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_30)) (MACRO_SR_EQ_INTRO _let_188 :args (_let_30 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args ((and _let_180 _let_179 _let_178 _let_177 _let_176 _let_175 _let_174 _let_173 _let_172 _let_171 _let_170 _let_169 _let_168 _let_167 _let_166 _let_165)))) :args (_let_181)) (PREPROCESS :args ((= _let_181 (and 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_let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36)))) :args ((and _let_164 _let_163 _let_162 _let_161 _let_160 _let_159 _let_158 _let_157 _let_156 _let_155 _let_154 _let_153 _let_152 _let_151 _let_150 _let_149 _let_148 _let_147 _let_146 _let_145 _let_144 _let_143 _let_142 _let_141 _let_140 _let_139 _let_138 _let_137 _let_136 _let_135 _let_134 _let_133 _let_132 _let_131 _let_130 _let_129 _let_128 _let_127 _let_126 _let_125 _let_124 _let_123 _let_122 _let_121 _let_120 _let_119 _let_118 _let_117 _let_116 _let_115 _let_114 _let_113 _let_112 _let_111 _let_110 _let_109 _let_108 _let_107 _let_106 _let_105 _let_104 _let_103 _let_102 _let_101 _let_100 _let_99 _let_98 _let_97 _let_96 _let_95 _let_94 _let_93 _let_92 _let_91 _let_90 _let_89 _let_88 _let_87 _let_86 _let_85 _let_84 _let_83 _let_82 _let_81 _let_80 _let_79 _let_78 _let_77 _let_76 _let_75 _let_74 _let_73 _let_72 _let_71 _let_70 _let_69 _let_68 _let_67 _let_66 _let_65 _let_64 _let_63 _let_62 _let_61 _let_60 _let_59 _let_58 _let_57 _let_56 _let_55 _let_54 _let_53 _let_52 _let_51 _let_50 _let_49 _let_48 _let_47 _let_46 _let_45 _let_44 _let_43 _let_42 _let_41 _let_40 _let_39 _let_38 _let_37 _let_36))) :args (0)) :args (false false _let_35 false _let_34 true _let_32)) :args (_let_30 _let_28 (@ (@ tptp.knowle945212990e_know tptp.pq) tptp.m) (@ _let_2 (@ tptp.localSecrets tptp.pq)) (forall ((X2 tptp.secrecy_Secrets) (Y2 tptp.secrecy_Secrets)) (= (= (@ tptp.secrecy_sKS X2) (@ tptp.secrecy_sKS Y2)) (= X2 Y2))) (not (@ (@ tptp.ine tptp.q) _let_27)) (@ tptp.correc965049635ionLoc tptp.pq) (not (@ (@ tptp.ine tptp.pq) _let_27)) _let_26 (= (@ tptp.subcomponents tptp.pq) (@ (@ tptp.insert1671894227specID tptp.p) (@ (@ tptp.insert1671894227specID tptp.q) tptp.bot_bo1785112429specID))) (@ tptp.correctCompositionIn tptp.pq) (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kKS X1) (@ tptp.secrecy_sKS X2)))) (forall ((P (-> 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(@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine Q) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine P) _let_1)))))))))) (forall ((S tptp.secrecy_Secrets) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sE S))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS S)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine Q) _let_1)))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (S tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS S)))) (let ((_let_2 (@ tptp.secrecy_sE S))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (not (@ _let_1 (@ tptp.localSecrets Q))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))) (forall ((PQ tptp.secrecy_specID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.ine PQ) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (or (@ (@ tptp.ine P) E) (@ (@ tptp.ine Q) E)))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q 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(forall ((Ls tptp.secrecy_KS) (P tptp.secrecy_specID) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ls))) (=> (@ _let_1 (@ tptp.localSecrets P)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (@ _let_1 (@ tptp.localSecrets PQ)))))) (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (B2 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) B))))) (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (B2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ tptp.insert751661162chanID B2) B))))) (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (B2 tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (=> (=> (not (@ _let_1 B)) (= A2 B2)) (@ _let_1 (@ (@ 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tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (= (@ _let_1 (@ (@ tptp.insert1671894227specID B2) A)) (or (= A2 B2) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_Keys) (B2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (= (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) A)) (or (= A2 B2) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_Secrets) (B2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (= (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) A)) (or (= A2 B2) (@ _let_1 A))))) (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID X3))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID X3))) (let ((_let_2 (@ _let_1 A))) (= (@ _let_1 _let_2) _let_2)))) (forall ((P (-> tptp.secrecy_specID Bool))) (= (= tptp.bot_bo1785112429specID (@ tptp.collec1545797240specID P)) (forall ((X4 tptp.secrecy_specID)) (not (@ P X4))))) (forall ((P (-> tptp.secrecy_chanID Bool))) (= (= tptp.bot_bo443197316chanID (@ tptp.collec625564175chanID P)) (forall ((X4 tptp.secrecy_chanID)) (not (@ P X4))))) (forall ((P (-> tptp.secrecy_specID Bool))) (= (= (@ tptp.collec1545797240specID P) tptp.bot_bo1785112429specID) (forall ((X4 tptp.secrecy_specID)) (not (@ P X4))))) (forall ((P (-> tptp.secrecy_chanID Bool))) (= (= (@ tptp.collec625564175chanID P) tptp.bot_bo443197316chanID) (forall ((X4 tptp.secrecy_chanID)) (not (@ P X4))))) (forall ((A tptp.set_Secrecy_KS)) (= (forall ((X4 tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS X4) A))) (= A tptp.bot_bo1943466239ecy_KS))) (forall ((A tptp.set_Secrecy_Keys)) (= (forall ((X4 tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys X4) A))) (= A tptp.bot_bo701486667y_Keys))) (forall ((A tptp.set_Secrecy_Secrets)) (= (forall ((X4 tptp.secrecy_Secrets)) (not (@ (@ 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tptp.member_Secrecy_KS X4) A)) (not (= A tptp.bot_bo1943466239ecy_KS)))) (forall ((A tptp.set_Secrecy_Keys)) (= (exists ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) A)) (not (= A tptp.bot_bo701486667y_Keys)))) (forall ((A tptp.set_Secrecy_Secrets)) (= (exists ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) A)) (not (= A tptp.bot_bo1124690338ecrets)))) (forall ((A tptp.set_Secrecy_specID)) (= (exists ((X4 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID X4) A)) (not (= A tptp.bot_bo1785112429specID)))) (forall ((A tptp.set_Secrecy_chanID)) (= (exists ((X4 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID X4) A)) (not (= A tptp.bot_bo443197316chanID)))) (forall ((A tptp.set_Secrecy_KS)) (=> (forall ((Y3 tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS Y3) A))) (= A tptp.bot_bo1943466239ecy_KS))) (forall ((A tptp.set_Secrecy_Keys)) (=> (forall ((Y3 tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys Y3) A))) (= A tptp.bot_bo701486667y_Keys))) (forall ((A tptp.set_Secrecy_Secrets)) (=> (forall ((Y3 tptp.secrecy_Secrets)) (not (@ (@ tptp.member2138796287ecrets Y3) A))) (= A tptp.bot_bo1124690338ecrets))) (forall ((A tptp.set_Secrecy_specID)) (=> (forall ((Y3 tptp.secrecy_specID)) (not (@ (@ tptp.member740727610specID Y3) A))) (= A tptp.bot_bo1785112429specID))) (forall ((A tptp.set_Secrecy_chanID)) (=> (forall ((Y3 tptp.secrecy_chanID)) (not (@ (@ tptp.member1967978193chanID Y3) A))) (= A tptp.bot_bo443197316chanID))) (forall ((A tptp.set_Secrecy_KS) (A2 tptp.secrecy_KS)) (=> (= A tptp.bot_bo1943466239ecy_KS) (not (@ (@ tptp.member_Secrecy_KS A2) A)))) (forall ((A tptp.set_Secrecy_Keys) (A2 tptp.secrecy_Keys)) (=> (= A tptp.bot_bo701486667y_Keys) (not (@ (@ tptp.member_Secrecy_Keys A2) A)))) (forall ((A tptp.set_Secrecy_Secrets) (A2 tptp.secrecy_Secrets)) (=> (= A tptp.bot_bo1124690338ecrets) (not (@ (@ tptp.member2138796287ecrets A2) A)))) (forall ((A tptp.set_Secrecy_specID) (A2 tptp.secrecy_specID)) (=> (= A tptp.bot_bo1785112429specID) (not (@ (@ tptp.member740727610specID A2) A)))) (forall ((A tptp.set_Secrecy_chanID) (A2 tptp.secrecy_chanID)) (=> (= A tptp.bot_bo443197316chanID) (not (@ (@ tptp.member1967978193chanID A2) A)))) (forall ((A2 tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS))) (forall ((A2 tptp.secrecy_Keys)) (not (@ (@ tptp.member_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys))) (forall ((A2 tptp.secrecy_Secrets)) (not (@ (@ tptp.member2138796287ecrets A2) tptp.bot_bo1124690338ecrets))) (forall ((A2 tptp.secrecy_specID)) (not (@ (@ tptp.member740727610specID A2) tptp.bot_bo1785112429specID))) (forall ((A2 tptp.secrecy_chanID)) (not (@ (@ tptp.member1967978193chanID A2) tptp.bot_bo443197316chanID))) (forall ((A2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS A2) A) (exists ((B3 tptp.set_Secrecy_KS)) (and (= A (@ (@ tptp.insert_Secrecy_KS A2) B3)) (not (@ (@ tptp.member_Secrecy_KS A2) B3)))))) (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID A2) A) (exists ((B3 tptp.set_Secrecy_chanID)) (and (= A (@ (@ tptp.insert751661162chanID A2) B3)) (not (@ (@ tptp.member1967978193chanID A2) B3)))))) (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (=> (@ (@ tptp.member740727610specID A2) A) (exists ((B3 tptp.set_Secrecy_specID)) (and (= A (@ (@ tptp.insert1671894227specID A2) B3)) (not (@ (@ tptp.member740727610specID A2) B3)))))) (forall ((A2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys A2) A) (exists ((B3 tptp.set_Secrecy_Keys)) (and (= A (@ (@ tptp.insert_Secrecy_Keys A2) B3)) (not (@ (@ tptp.member_Secrecy_Keys A2) B3)))))) (forall ((A2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets A2) A) (exists ((B3 tptp.set_Secrecy_Secrets)) (and (= A (@ (@ tptp.insert565337510ecrets A2) B3)) (not (@ (@ tptp.member2138796287ecrets A2) B3)))))) (forall ((X3 tptp.secrecy_specID) (Y tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID X3))) (let ((_let_2 (@ tptp.insert1671894227specID Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((X3 tptp.secrecy_chanID) (Y tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID X3))) (let ((_let_2 (@ tptp.insert751661162chanID Y))) (= (@ _let_1 (@ _let_2 A)) (@ _let_2 (@ _let_1 A)))))) (forall ((A2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member_Secrecy_KS A2) A)) (=> (not (@ (@ tptp.member_Secrecy_KS B2) B)) (= (= (@ (@ tptp.insert_Secrecy_KS A2) A) (@ (@ tptp.insert_Secrecy_KS B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_KS)) (and (= A (@ (@ tptp.insert_Secrecy_KS B2) C2)) (not (@ (@ tptp.member_Secrecy_KS B2) C2)) (= B (@ (@ tptp.insert_Secrecy_KS A2) C2)) (not (@ (@ tptp.member_Secrecy_KS A2) C2))))))))))) (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member1967978193chanID A2) A)) (=> (not (@ (@ tptp.member1967978193chanID B2) B)) (= (= (@ (@ tptp.insert751661162chanID A2) A) (@ (@ tptp.insert751661162chanID B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_chanID)) (and (= A (@ (@ tptp.insert751661162chanID B2) C2)) (not (@ (@ tptp.member1967978193chanID B2) C2)) (= B (@ (@ tptp.insert751661162chanID A2) C2)) (not (@ (@ tptp.member1967978193chanID A2) C2))))))))))) (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member740727610specID A2) A)) (=> (not (@ (@ tptp.member740727610specID B2) B)) (= (= (@ (@ tptp.insert1671894227specID A2) A) (@ (@ tptp.insert1671894227specID B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_specID)) (and (= A (@ (@ tptp.insert1671894227specID B2) C2)) (not (@ (@ tptp.member740727610specID B2) C2)) (= B (@ (@ tptp.insert1671894227specID A2) C2)) (not (@ (@ tptp.member740727610specID A2) C2))))))))))) (forall ((A2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member_Secrecy_Keys A2) A)) (=> (not (@ (@ tptp.member_Secrecy_Keys B2) B)) (= (= (@ (@ tptp.insert_Secrecy_Keys A2) A) (@ (@ tptp.insert_Secrecy_Keys B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_Keys)) (and (= A (@ (@ tptp.insert_Secrecy_Keys B2) C2)) (not (@ (@ tptp.member_Secrecy_Keys B2) C2)) (= B (@ (@ tptp.insert_Secrecy_Keys A2) C2)) (not (@ (@ tptp.member_Secrecy_Keys A2) C2))))))))))) (forall ((A2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (= A2 B2))) (=> (not (@ (@ tptp.member2138796287ecrets A2) A)) (=> (not (@ (@ tptp.member2138796287ecrets B2) B)) (= (= (@ (@ tptp.insert565337510ecrets A2) A) (@ (@ tptp.insert565337510ecrets B2) B)) (and (=> _let_1 (= A B)) (=> (not _let_1) (exists ((C2 tptp.set_Secrecy_Secrets)) (and (= A (@ (@ tptp.insert565337510ecrets B2) C2)) (not (@ (@ tptp.member2138796287ecrets B2) C2)) (= B (@ (@ tptp.insert565337510ecrets A2) C2)) (not (@ (@ tptp.member2138796287ecrets A2) C2))))))))))) (forall ((A2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS A2) A) (= (@ (@ tptp.insert_Secrecy_KS A2) A) A))) (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID A2) A) (= (@ (@ tptp.insert751661162chanID A2) A) A))) (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (=> (@ (@ tptp.member740727610specID A2) A) (= (@ (@ tptp.insert1671894227specID A2) A) A))) (forall ((A2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys A2) A) (= (@ (@ tptp.insert_Secrecy_Keys A2) A) A))) (forall ((A2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets A2) A) (= (@ (@ tptp.insert565337510ecrets A2) A) A))) (forall ((A2 tptp.secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (@ (@ tptp.member_Secrecy_KS A2) (@ tptp.collect_Secrecy_KS P)) (@ P A2))) (forall ((A2 tptp.secrecy_chanID) (P (-> tptp.secrecy_chanID Bool))) (= (@ (@ tptp.member1967978193chanID A2) (@ tptp.collec625564175chanID P)) (@ P A2))) (forall ((A2 tptp.secrecy_specID) (P (-> tptp.secrecy_specID Bool))) (= (@ (@ tptp.member740727610specID A2) (@ tptp.collec1545797240specID P)) (@ P A2))) (forall ((A2 tptp.secrecy_Keys) (P (-> tptp.secrecy_Keys Bool))) (= (@ (@ tptp.member_Secrecy_Keys A2) (@ tptp.collect_Secrecy_Keys P)) (@ P A2))) (forall ((A2 tptp.secrecy_Secrets) (P (-> tptp.secrecy_Secrets Bool))) (= (@ (@ tptp.member2138796287ecrets A2) (@ tptp.collec836099393ecrets P)) (@ P A2))) (forall ((A tptp.set_Secrecy_KS)) (= (@ tptp.collect_Secrecy_KS (lambda ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS X4) A))) A)) (forall ((A tptp.set_Secrecy_chanID)) (= (@ tptp.collec625564175chanID (lambda ((X4 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID X4) A))) A)) (forall ((A tptp.set_Secrecy_specID)) (= (@ tptp.collec1545797240specID (lambda ((X4 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID X4) A))) A)) (forall ((A tptp.set_Secrecy_Keys)) (= (@ tptp.collect_Secrecy_Keys (lambda ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) A))) A)) (forall ((A tptp.set_Secrecy_Secrets)) (= (@ tptp.collec836099393ecrets (lambda ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) A))) A)) (forall ((X3 tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.insert_Secrecy_KS X3))) (let ((_let_2 (@ tptp.member_Secrecy_KS X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID X3))) (let ((_let_2 (@ tptp.member1967978193chanID X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID X3))) (let ((_let_2 (@ tptp.member740727610specID X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((X3 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.insert_Secrecy_Keys X3))) (let ((_let_2 (@ tptp.member_Secrecy_Keys X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((X3 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.insert565337510ecrets X3))) (let ((_let_2 (@ tptp.member2138796287ecrets X3))) (=> (not (@ _let_2 A)) (=> (not (@ _let_2 B)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))) (forall ((X3 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X3) A) (not (forall ((B3 tptp.set_Secrecy_KS)) (=> (= A (@ (@ tptp.insert_Secrecy_KS X3) B3)) (@ (@ tptp.member_Secrecy_KS X3) B3)))))) (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X3) A) (not (forall ((B3 tptp.set_Secrecy_chanID)) (=> (= A (@ (@ tptp.insert751661162chanID X3) B3)) (@ (@ tptp.member1967978193chanID X3) B3)))))) (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (=> (@ (@ tptp.member740727610specID X3) A) (not (forall ((B3 tptp.set_Secrecy_specID)) (=> (= A (@ (@ tptp.insert1671894227specID X3) B3)) (@ (@ tptp.member740727610specID X3) B3)))))) (forall ((X3 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys X3) A) (not (forall ((B3 tptp.set_Secrecy_Keys)) (=> (= A (@ (@ tptp.insert_Secrecy_Keys X3) B3)) (@ (@ tptp.member_Secrecy_Keys X3) B3)))))) (forall ((X3 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets X3) A) (not (forall ((B3 tptp.set_Secrecy_Secrets)) (=> (= A (@ (@ tptp.insert565337510ecrets X3) B3)) (@ (@ tptp.member2138796287ecrets X3) B3)))))) (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (B2 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) B))))) (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (B2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert751661162chanID B2) B))))) (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (B2 tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert1671894227specID B2) B))))) (forall ((A2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (B2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) B))))) (forall ((A2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (B2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) B))))) (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS)) (@ (@ tptp.member_Secrecy_KS A2) (@ (@ tptp.insert_Secrecy_KS A2) B))) (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID)) (@ (@ tptp.member1967978193chanID A2) (@ (@ tptp.insert751661162chanID A2) B))) (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID)) (@ (@ tptp.member740727610specID A2) (@ (@ tptp.insert1671894227specID A2) B))) (forall ((A2 tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys A2) (@ (@ tptp.insert_Secrecy_Keys A2) B))) (forall ((A2 tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets A2) (@ (@ tptp.insert565337510ecrets A2) B))) (forall ((A2 tptp.secrecy_KS) (B2 tptp.secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS A2))) (=> (@ _let_1 (@ (@ tptp.insert_Secrecy_KS B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID A2))) (=> (@ _let_1 (@ (@ tptp.insert751661162chanID B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID A2))) (=> (@ _let_1 (@ (@ tptp.insert1671894227specID B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_Keys) (B2 tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys A2))) (=> (@ _let_1 (@ (@ tptp.insert_Secrecy_Keys B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_Secrets) (B2 tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets A2))) (=> (@ _let_1 (@ (@ tptp.insert565337510ecrets B2) A)) (=> (not (= A2 B2)) (@ _let_1 A))))) (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID)) (=> (= (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID) (@ (@ tptp.insert1671894227specID B2) tptp.bot_bo1785112429specID)) (= A2 B2))) (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID)) (=> (= (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID) (@ (@ tptp.insert751661162chanID B2) tptp.bot_bo443197316chanID)) (= A2 B2))) (forall ((A2 tptp.secrecy_specID) (A tptp.set_Secrecy_specID)) (not (= (@ (@ tptp.insert1671894227specID A2) A) tptp.bot_bo1785112429specID))) (forall ((A2 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID)) (not (= (@ (@ tptp.insert751661162chanID A2) A) tptp.bot_bo443197316chanID))) (forall ((A2 tptp.secrecy_specID) (B2 tptp.secrecy_specID) (C tptp.secrecy_specID) (D tptp.secrecy_specID)) (= (= (@ (@ tptp.insert1671894227specID A2) (@ (@ tptp.insert1671894227specID B2) tptp.bot_bo1785112429specID)) (@ (@ tptp.insert1671894227specID C) (@ (@ tptp.insert1671894227specID D) tptp.bot_bo1785112429specID))) (or (and (= A2 C) (= B2 D)) (and (= A2 D) (= B2 C))))) (forall ((A2 tptp.secrecy_chanID) (B2 tptp.secrecy_chanID) (C tptp.secrecy_chanID) (D tptp.secrecy_chanID)) (= (= (@ (@ tptp.insert751661162chanID A2) (@ (@ tptp.insert751661162chanID B2) tptp.bot_bo443197316chanID)) (@ (@ tptp.insert751661162chanID C) (@ (@ tptp.insert751661162chanID D) tptp.bot_bo443197316chanID))) (or (and (= A2 C) (= B2 D)) (and (= A2 D) (= B2 C))))) (forall ((B2 tptp.secrecy_KS) (A2 tptp.secrecy_KS)) (= (@ (@ tptp.member_Secrecy_KS B2) (@ (@ tptp.insert_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS)) (= B2 A2))) (forall ((B2 tptp.secrecy_Keys) (A2 tptp.secrecy_Keys)) (= (@ (@ tptp.member_Secrecy_Keys B2) (@ (@ tptp.insert_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys)) (= B2 A2))) (forall ((B2 tptp.secrecy_Secrets) (A2 tptp.secrecy_Secrets)) (= (@ (@ tptp.member2138796287ecrets B2) (@ (@ tptp.insert565337510ecrets A2) tptp.bot_bo1124690338ecrets)) (= B2 A2))) (forall ((B2 tptp.secrecy_specID) (A2 tptp.secrecy_specID)) (= (@ (@ tptp.member740727610specID B2) (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID)) (= B2 A2))) (forall ((B2 tptp.secrecy_chanID) (A2 tptp.secrecy_chanID)) (= (@ (@ tptp.member1967978193chanID B2) (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID)) (= B2 A2))) (forall ((B2 tptp.secrecy_KS) (A2 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS B2) (@ (@ tptp.insert_Secrecy_KS A2) tptp.bot_bo1943466239ecy_KS)) (= B2 A2))) (forall ((B2 tptp.secrecy_Keys) (A2 tptp.secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys B2) (@ (@ tptp.insert_Secrecy_Keys A2) tptp.bot_bo701486667y_Keys)) (= B2 A2))) (forall ((B2 tptp.secrecy_Secrets) (A2 tptp.secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets B2) (@ (@ tptp.insert565337510ecrets A2) tptp.bot_bo1124690338ecrets)) (= B2 A2))) (forall ((B2 tptp.secrecy_specID) (A2 tptp.secrecy_specID)) (=> (@ (@ tptp.member740727610specID B2) (@ (@ tptp.insert1671894227specID A2) tptp.bot_bo1785112429specID)) (= B2 A2))) (forall ((B2 tptp.secrecy_chanID) (A2 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID B2) (@ (@ tptp.insert751661162chanID A2) tptp.bot_bo443197316chanID)) (= B2 A2))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (forall ((M2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kE M2))) (=> (= Ks (@ tptp.secrecy_kKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (forall ((M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sE M2))) (=> (= Ks (@ tptp.secrecy_sKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (not (@ _let_1 (@ tptp.localSecrets Q))) (not (@ _let_1 (@ tptp.localSecrets PQ))))))))))) (forall ((X3 tptp.secrecy_specID)) (= (@ tptp.the_el827131246specID (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID)) X3)) (forall ((X3 tptp.secrecy_chanID)) (= (@ tptp.the_el2054381829chanID (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID)) X3)) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Keys tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Keys)))) (let ((_let_2 (@ tptp.secrecy_kE Keys))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (not (@ _let_1 (@ tptp.localSecrets Q))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))) (forall ((K tptp.secrecy_Keys) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kE K))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS K)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine P) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine Q) _let_1)))))))))) (forall ((K tptp.secrecy_Keys) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kE K))) (let ((_let_2 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS K)))) (=> (@ _let_2 (@ tptp.localSecrets PQ)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (not (@ (@ tptp.ine Q) _let_1)) (=> (not (@ _let_2 (@ tptp.localSecrets P))) (=> (not (@ _let_2 (@ tptp.localSecrets Q))) (@ (@ tptp.ine P) _let_1)))))))))) (forall ((P tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS Key))) (=> (not (@ (@ tptp.knowle945212990e_know P) _let_1)) (=> (not (@ (@ tptp.knowle945212990e_know Q) _let_1)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ tptp.ine PQ) (@ tptp.secrecy_kE Key))))))))) (forall ((X3 tptp.secrecy_specID)) (@ tptp.is_sin1501507247specID (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID))) (forall ((X3 tptp.secrecy_chanID)) (@ tptp.is_sin581274182chanID (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID))) (forall ((M tptp.secrecy_Secrets)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_sKS M)) (@ tptp.secrecy_sE M))) (forall ((X1 tptp.secrecy_Keys) (Y1 tptp.secrecy_Keys)) (= (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_kE Y1)) (= X1 Y1))) (forall ((M tptp.secrecy_Keys)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_kKS M)) (@ tptp.secrecy_kE M))) _let_25 _let_24 (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_sE X2)))) _let_23 _let_22 (forall ((A tptp.set_Secrecy_KS)) (=> (not (= A tptp.bot_bo1943466239ecy_KS)) (=> (forall ((X tptp.secrecy_KS) (Y3 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X) A) (=> (@ (@ tptp.member_Secrecy_KS Y3) A) (= X Y3)))) (@ tptp.is_sin1442426433ecy_KS A)))) (forall ((A tptp.set_Secrecy_Keys)) (=> (not (= A tptp.bot_bo701486667y_Keys)) (=> (forall ((X tptp.secrecy_Keys) (Y3 tptp.secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys X) A) (=> (@ (@ tptp.member_Secrecy_Keys Y3) A) (= X Y3)))) (@ tptp.is_sin1096471309y_Keys A)))) (forall ((A tptp.set_Secrecy_Secrets)) (=> (not (= A tptp.bot_bo1124690338ecrets)) (=> (forall ((X tptp.secrecy_Secrets) (Y3 tptp.secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets X) A) (=> (@ (@ tptp.member2138796287ecrets Y3) A) (= X Y3)))) (@ tptp.is_sin1002224330ecrets A)))) (forall ((A tptp.set_Secrecy_specID)) (=> (not (= A tptp.bot_bo1785112429specID)) (=> (forall ((X tptp.secrecy_specID) (Y3 tptp.secrecy_specID)) (=> (@ (@ tptp.member740727610specID X) A) (=> (@ (@ tptp.member740727610specID Y3) A) (= X Y3)))) (@ tptp.is_sin1501507247specID A)))) (forall ((A tptp.set_Secrecy_chanID)) (=> (not (= A tptp.bot_bo443197316chanID)) (=> (forall ((X tptp.secrecy_chanID) (Y3 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X) A) (=> (@ (@ tptp.member1967978193chanID Y3) A) (= X Y3)))) (@ tptp.is_sin581274182chanID A)))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M))) (not (@ (@ tptp.ine A) (@ tptp.secrecy_kE M))))) (forall ((A tptp.set_Secrecy_specID)) (=> (@ tptp.is_sin1501507247specID A) (not (forall ((X tptp.secrecy_specID)) (not (= A (@ (@ tptp.insert1671894227specID X) tptp.bot_bo1785112429specID))))))) (forall ((A tptp.set_Secrecy_chanID)) (=> (@ tptp.is_sin581274182chanID A) (not (forall ((X tptp.secrecy_chanID)) (not (= A (@ (@ tptp.insert751661162chanID X) tptp.bot_bo443197316chanID))))))) (= tptp.is_sin1501507247specID (lambda ((A3 tptp.set_Secrecy_specID)) (exists ((X4 tptp.secrecy_specID)) (= A3 (@ (@ tptp.insert1671894227specID X4) tptp.bot_bo1785112429specID))))) (= tptp.is_sin581274182chanID (lambda ((A3 tptp.set_Secrecy_chanID)) (exists ((X4 tptp.secrecy_chanID)) (= A3 (@ (@ tptp.insert751661162chanID X4) tptp.bot_bo443197316chanID))))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (= (@ (@ tptp.knowle945212990e_know A) _let_1) (or (@ (@ tptp.ine A) (@ tptp.secrecy_kE M)) (@ (@ tptp.member_Secrecy_KS _let_1) (@ tptp.localSecrets A)))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.ine P) E) (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (= (@ tptp.loc PQ) tptp.bot_bo443197316chanID) (@ (@ tptp.ine PQ) E)))))) (forall ((PQ tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.ineM PQ) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (or (@ (@ (@ tptp.ineM P) M3) E) (@ (@ (@ tptp.ineM Q) M3) E)))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (not (@ (@ (@ tptp.ineM P) M3) E)) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (not (@ (@ (@ tptp.ineM PQ) M3) E))))))) _let_21 _let_20 (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 (@ tptp.ins PQ)) (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (X3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 (@ tptp.ins PQ)) (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q)))))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ tptp.ine P) E) (=> (not (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (and (@ (@ (@ tptp.ine_ex1303305700Single P) Ch2) E) (@ (@ tptp.member1967978193chanID Ch2) (@ tptp.loc PQ)))) (not (@ (@ tptp.ine PQ) E)))))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (M3 tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.ine P) E)) (not (@ (@ (@ tptp.ineM P) M3) E)))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ineM P) M3) E) (@ (@ tptp.ine P) E))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ (@ tptp.ineM P) M3) E) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ (@ (@ tptp.ine_ex1303305700Single P) Ch2) E) (@ _let_1 M3) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.ineM PQ) M3) E)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (not (@ _let_1 (@ tptp.loc PQ))) (=> (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins PQ)))))))) (forall ((X3 tptp.secrecy_specID)) (=> (@ tptp.correc965049635ionLoc X3) (=> (= (@ tptp.subcomponents X3) tptp.bot_bo1785112429specID) (= (@ tptp.loc X3) tptp.bot_bo443197316chanID)))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID) (M3 tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.ine_exprChannelSet Q) ChSetQ) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.ineM PQ) M3) E))))))))) (forall ((Q tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.ineM PQ) M3) E)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.ine_exprChannelSet Q) ChSetQ) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.ine PQ) E))))))))) (forall ((Q tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.ine PQ) E)))))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ (@ tptp.ineM P) M3) E) (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q))) (@ _let_1 M3) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ (@ tptp.ineM PQ) M3) E)))))) _let_19 _let_18 (forall ((P tptp.secrecy_specID) (M tptp.secrecy_Expression) (X3 tptp.secrecy_chanID)) (=> (not (@ (@ tptp.ine P) M)) (=> (@ (@ tptp.exprChannel X3) M) (not (@ (@ tptp.member1967978193chanID X3) (@ tptp.ins P)))))) _let_17 (forall ((Ch tptp.secrecy_chanID) (M3 tptp.set_Secrecy_chanID) (P tptp.secrecy_specID) (E tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (@ _let_1 M3) (=> (@ _let_1 (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) E) (@ (@ (@ tptp.ineM P) M3) E)))))) _let_16 (forall ((X3 tptp.secrecy_chanID) (Secrets tptp.secrecy_Secrets) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (let ((_let_2 (@ tptp.secrecy_sE Secrets))) (=> (@ (@ tptp.exprChannel X3) _let_2) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (and (not (@ _let_1 (@ tptp.ins P))) (not (@ _let_1 (@ tptp.ins Q)))))))))) (forall ((X3 tptp.secrecy_chanID) (Keys tptp.secrecy_Keys) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (let ((_let_2 (@ tptp.secrecy_kE Keys))) (=> (@ (@ tptp.exprChannel X3) _let_2) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (and (not (@ _let_1 (@ tptp.ins P))) (not (@ _let_1 (@ tptp.ins Q)))))))))) (forall ((P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (not (= ChSet tptp.bot_bo443197316chanID)) (@ (@ tptp.ine P) E)))) (forall ((P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_exprChannelSet P) ChSet) E) (=> (= ChSet tptp.bot_bo443197316chanID) (not (@ (@ tptp.ine P) E))))) (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_ex1303305700Single P) Ch) E) (@ (@ (@ tptp.ine_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E))) (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.ine_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E) (@ (@ (@ tptp.ine_ex1303305700Single P) Ch) E))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (M tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) M) (=> (forall ((X tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X) (@ tptp.ins PQ)) (not (@ (@ tptp.exprChannel X) M)))) (@ _let_1 (@ tptp.loc PQ))))))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch))) (=> (not (@ (@ (@ tptp.ineM P) M3) E)) (=> (not (@ (@ (@ tptp.ineM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ _let_1 M3) (=> (@ _let_1 (@ tptp.ins PQ)) (not (@ (@ tptp.exprChannel Ch) E)))))))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.ine P) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.ins P)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.ine PQ) E)))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.ine P) E) (@ (@ tptp.ine Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.ins P)) (@ _let_1 (@ tptp.ins Q))) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.ine PQ) E)))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.ineM P) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.ins Q)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ))) (@ _let_1 M3)))) (@ (@ (@ tptp.ineM PQ) M3) E)))))) _let_15 _let_14 (forall ((P (-> tptp.secrecy_specID Bool))) (= (= (@ tptp.collec1545797240specID P) tptp.bot_bo1785112429specID) (= P tptp.bot_bo1767780696ecID_o))) (forall ((P (-> tptp.secrecy_chanID Bool))) (= (= (@ tptp.collec625564175chanID P) tptp.bot_bo443197316chanID) (= P tptp.bot_bo1012329985anID_o))) _let_13 _let_12 _let_11 (= tptp.bot_bo1767780696ecID_o (lambda ((X4 tptp.secrecy_specID)) (@ (@ tptp.member740727610specID X4) tptp.bot_bo1785112429specID))) (= tptp.bot_bo1012329985anID_o (lambda ((X4 tptp.secrecy_chanID)) (@ (@ tptp.member1967978193chanID X4) tptp.bot_bo443197316chanID))) (forall ((Secret tptp.secrecy_Secrets) (P tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (not (@ (@ tptp.member1967978193chanID Ch) (@ tptp.loc P)))))))) (forall ((Key tptp.secrecy_Keys) (P tptp.secrecy_specID) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (not (@ _let_1 (@ tptp.localSecrets P))) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (not (@ (@ tptp.member1967978193chanID Ch) (@ tptp.loc P)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins Q)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_sE Secret))))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_sE Secret))))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins Q)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Secret tptp.secrecy_Secrets) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_sE Secret)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS Secret)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins P)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (@ _let_1 (@ tptp.specKeysSecrets PQ)) (or (@ _let_1 (@ tptp.specKeysSecrets P)) (@ _let_1 (@ tptp.specKeysSecrets Q)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (not (@ _let_1 (@ tptp.specKeysSecrets PQ))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (not (@ _let_1 (@ tptp.specKeysSecrets P)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (not (@ _let_1 (@ tptp.specKeysSecrets Q)))))))) (forall ((M tptp.secrecy_KS) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS M))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (or (@ (@ tptp.knowle945212990e_know P) M) (@ (@ tptp.knowle945212990e_know Q) M)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ tptp.correctCompositionKS PQ) (@ (@ tptp.knowle945212990e_know PQ) M))))))))) (forall ((M tptp.secrecy_KS) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS M))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (@ (@ tptp.knowle945212990e_know P) M) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ tptp.correctCompositionKS PQ) (@ (@ tptp.knowle945212990e_know PQ) M))))))))) (forall ((M tptp.secrecy_KS) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (let ((_let_1 (@ tptp.member_Secrecy_KS M))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (@ (@ tptp.knowle945212990e_know Q) M) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionIn PQ) (=> (@ tptp.correctCompositionKS PQ) (@ (@ tptp.knowle945212990e_know PQ) M))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins P)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)))) (let ((_let_2 (@ tptp.member1967978193chanID Ch))) (let ((_let_3 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_3 (@ tptp.localSecrets PQ))) (=> (@ _let_2 (@ tptp.ins Q)) (=> _let_1 (=> (not (@ _let_3 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (and (@ _let_2 (@ tptp.ins PQ)) _let_1)))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins P)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_kE Key))))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Key tptp.secrecy_Keys) (Ch tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS Key)))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.localSecrets PQ))) (=> (@ (@ tptp.member1967978193chanID Ch) (@ tptp.ins Q)) (=> (@ (@ tptp.exprChannel Ch) (@ tptp.secrecy_kE Key)) (=> (not (@ _let_1 (@ tptp.specKeysSecrets PQ))) (=> (@ tptp.correctCompositionIn PQ) (exists ((Ch4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID Ch4) (@ tptp.ins PQ)) (@ (@ tptp.exprChannel Ch4) (@ tptp.secrecy_kE Key))))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (Ks tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS Ks))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (forall ((M2 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kE M2))) (=> (= Ks (@ tptp.secrecy_kKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (forall ((M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sE M2))) (=> (= Ks (@ tptp.secrecy_sKS M2)) (and (not (@ (@ tptp.ine P) _let_1)) (not (@ (@ tptp.ine Q) _let_1)))))) (=> (not (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS (@ tptp.localSecrets P)) (@ tptp.localSecrets Q)))) (not (@ _let_1 (@ tptp.localSecrets PQ))))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_sKS M)))) (let ((_let_2 (@ tptp.secrecy_sE M))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS (@ tptp.localSecrets P)) (@ tptp.localSecrets Q)))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_KS (@ tptp.secrecy_kKS M)))) (let ((_let_2 (@ tptp.secrecy_kE M))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc965049635ionLoc PQ) (=> (@ tptp.correctCompositionKS PQ) (=> (not (@ _let_1 (@ tptp.specKeysSecrets P))) (=> (not (@ _let_1 (@ tptp.specKeysSecrets Q))) (=> (not (@ (@ tptp.ine P) _let_2)) (=> (not (@ (@ tptp.ine Q) _let_2)) (=> (not (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS (@ tptp.localSecrets P)) (@ tptp.localSecrets Q)))) (not (@ _let_1 (@ tptp.localSecrets PQ)))))))))))))) _let_10 (forall ((C tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B))))) (forall ((C tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B))))) (forall ((C tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B))))) (forall ((C tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B))))) (forall ((C tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (=> (not (@ _let_1 B)) (@ _let_1 A)) (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B))))) (forall ((C tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (= (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (= (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (= (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (= (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((C tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (= (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) (or (@ _let_1 A) (@ _let_1 B))))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (= (= (@ (@ tptp.sup_su1301156759ecy_KS A) B) tptp.bot_bo1943466239ecy_KS) (and (= A tptp.bot_bo1943466239ecy_KS) (= B tptp.bot_bo1943466239ecy_KS)))) (forall ((A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (= (= (@ (@ tptp.sup_su1712599557specID A) B) tptp.bot_bo1785112429specID) (and (= A tptp.bot_bo1785112429specID) (= B tptp.bot_bo1785112429specID)))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (= (= (@ (@ tptp.sup_su370684444chanID A) B) tptp.bot_bo443197316chanID) (and (= A tptp.bot_bo443197316chanID) (= B tptp.bot_bo443197316chanID)))) (forall ((A tptp.set_Secrecy_specID) (A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.sup_su1712599557specID A))) (let ((_let_2 (@ tptp.insert1671894227specID A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A tptp.set_Secrecy_KS) (A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (let ((_let_2 (@ tptp.insert_Secrecy_KS A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A tptp.set_Secrecy_chanID) (A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (let ((_let_2 (@ tptp.insert751661162chanID A2))) (= (@ _let_1 (@ _let_2 B)) (@ _let_2 (@ _let_1 B)))))) (forall ((A2 tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (C3 tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.insert1671894227specID A2))) (= (@ (@ tptp.sup_su1712599557specID (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su1712599557specID B) C3))))) (forall ((A2 tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (C3 tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.insert_Secrecy_KS A2))) (= (@ (@ tptp.sup_su1301156759ecy_KS (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS B) C3))))) (forall ((A2 tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (C3 tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.insert751661162chanID A2))) (= (@ (@ tptp.sup_su370684444chanID (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su370684444chanID B) C3))))) (forall ((C tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) (=> (not (@ _let_1 A)) (@ _let_1 B))))) (forall ((C tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B))))) (forall ((C tptp.secrecy_Keys) (A tptp.set_Secrecy_Keys) (B tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B))))) (forall ((C tptp.secrecy_Secrets) (A tptp.set_Secrecy_Secrets) (B tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B))))) (forall ((C tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B))))) (forall ((C tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B))))) (forall ((C tptp.secrecy_specID) (B tptp.set_Secrecy_specID) (A tptp.set_Secrecy_specID)) (let ((_let_1 (@ tptp.member740727610specID C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1712599557specID A) B))))) (forall ((C tptp.secrecy_Keys) (B tptp.set_Secrecy_Keys) (A tptp.set_Secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su552545507y_Keys A) B))))) (forall ((C tptp.secrecy_Secrets) (B tptp.set_Secrecy_Secrets) (A tptp.set_Secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1029080330ecrets A) B))))) (forall ((C tptp.secrecy_KS) (B tptp.set_Secrecy_KS) (A tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.member_Secrecy_KS C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B))))) (forall ((C tptp.secrecy_chanID) (B tptp.set_Secrecy_chanID) (A tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B))))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (exists ((X4 tptp.secrecy_KS)) (and (@ (@ tptp.member_Secrecy_KS X4) (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (@ P X4))) (or (exists ((X4 tptp.secrecy_KS)) (and (@ (@ tptp.member_Secrecy_KS X4) A) (@ P X4))) (exists ((X4 tptp.secrecy_KS)) (and (@ (@ tptp.member_Secrecy_KS X4) B) (@ P X4)))))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (P (-> tptp.secrecy_chanID Bool))) (= (exists ((X4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID X4) (@ (@ tptp.sup_su370684444chanID A) B)) (@ P X4))) (or (exists ((X4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID X4) A) (@ P X4))) (exists ((X4 tptp.secrecy_chanID)) (and (@ (@ tptp.member1967978193chanID X4) B) (@ P X4)))))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (forall ((X4 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X4) (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (@ P X4))) (and (forall ((X4 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X4) A) (@ P X4))) (forall ((X4 tptp.secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS X4) B) (@ P X4)))))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (P (-> tptp.secrecy_chanID Bool))) (= (forall ((X4 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X4) (@ (@ tptp.sup_su370684444chanID A) B)) (@ P X4))) (and (forall ((X4 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X4) A) (@ P X4))) (forall ((X4 tptp.secrecy_chanID)) (=> (@ (@ tptp.member1967978193chanID X4) B) (@ P X4)))))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (C3 tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (= (@ (@ tptp.sup_su1301156759ecy_KS (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su1301156759ecy_KS B) C3))))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (C3 tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (= (@ (@ tptp.sup_su370684444chanID (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.sup_su370684444chanID B) C3))))) (forall ((A tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS A) A) A)) (forall ((A tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID A) A) A)) (= tptp.sup_su1301156759ecy_KS (lambda ((A3 tptp.set_Secrecy_KS) (B4 tptp.set_Secrecy_KS)) (@ (@ tptp.sup_su1301156759ecy_KS B4) A3))) (= tptp.sup_su370684444chanID (lambda ((A3 tptp.set_Secrecy_chanID) (B4 tptp.set_Secrecy_chanID)) (@ (@ tptp.sup_su370684444chanID B4) A3))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (C3 tptp.set_Secrecy_KS)) (let ((_let_1 (@ tptp.sup_su1301156759ecy_KS A))) (let ((_let_2 (@ tptp.sup_su1301156759ecy_KS B))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (C3 tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.sup_su370684444chanID A))) (let ((_let_2 (@ tptp.sup_su370684444chanID B))) (= (@ _let_1 (@ _let_2 C3)) (@ _let_2 (@ _let_1 C3)))))) (forall ((B tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS tptp.bot_bo1943466239ecy_KS) B) B)) (forall ((B tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID tptp.bot_bo1785112429specID) B) B)) (forall ((B tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID tptp.bot_bo443197316chanID) B) B)) (forall ((A tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS A) tptp.bot_bo1943466239ecy_KS) A)) (forall ((A tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID A) tptp.bot_bo1785112429specID) A)) (forall ((A tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID A) tptp.bot_bo443197316chanID) A)) (forall ((X3 tptp.secrecy_KS) (A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.insert_Secrecy_KS X3) tptp.bot_bo1943466239ecy_KS))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su1301156759ecy_KS A) B)) (or (and (= A tptp.bot_bo1943466239ecy_KS) _let_2) (and _let_3 (= B tptp.bot_bo1943466239ecy_KS)) (and _let_3 _let_2))))))) (forall ((X3 tptp.secrecy_specID) (A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID)) (let ((_let_1 (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su1712599557specID A) B)) (or (and (= A tptp.bot_bo1785112429specID) _let_2) (and _let_3 (= B tptp.bot_bo1785112429specID)) (and _let_3 _let_2))))))) (forall ((X3 tptp.secrecy_chanID) (A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) (or (and (= A tptp.bot_bo443197316chanID) _let_2) (and _let_3 (= B tptp.bot_bo443197316chanID)) (and _let_3 _let_2))))))) (forall ((A tptp.set_Secrecy_KS) (B tptp.set_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.insert_Secrecy_KS X3) tptp.bot_bo1943466239ecy_KS))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su1301156759ecy_KS A) B) _let_1) (or (and (= A tptp.bot_bo1943466239ecy_KS) _let_2) (and _let_3 (= B tptp.bot_bo1943466239ecy_KS)) (and _let_3 _let_2))))))) (forall ((A tptp.set_Secrecy_specID) (B tptp.set_Secrecy_specID) (X3 tptp.secrecy_specID)) (let ((_let_1 (@ (@ tptp.insert1671894227specID X3) tptp.bot_bo1785112429specID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su1712599557specID A) B) _let_1) (or (and (= A tptp.bot_bo1785112429specID) _let_2) (and _let_3 (= B tptp.bot_bo1785112429specID)) (and _let_3 _let_2))))))) (forall ((A tptp.set_Secrecy_chanID) (B tptp.set_Secrecy_chanID) (X3 tptp.secrecy_chanID)) (let ((_let_1 (@ (@ tptp.insert751661162chanID X3) tptp.bot_bo443197316chanID))) (let ((_let_2 (= B _let_1))) (let ((_let_3 (= A _let_1))) (= (= (@ (@ tptp.sup_su370684444chanID A) B) _let_1) (or (and (= A tptp.bot_bo443197316chanID) _let_2) (and _let_3 (= B tptp.bot_bo443197316chanID)) (and _let_3 _let_2))))))) (= tptp.insert_Secrecy_KS (lambda ((A4 tptp.secrecy_KS) (__flatten_var_0 tptp.set_Secrecy_KS)) (@ (@ tptp.sup_su1301156759ecy_KS (@ (@ tptp.insert_Secrecy_KS A4) tptp.bot_bo1943466239ecy_KS)) __flatten_var_0))) (= tptp.insert1671894227specID (lambda ((A4 tptp.secrecy_specID) (__flatten_var_0 tptp.set_Secrecy_specID)) (@ (@ tptp.sup_su1712599557specID (@ (@ tptp.insert1671894227specID A4) tptp.bot_bo1785112429specID)) __flatten_var_0))) (= tptp.insert751661162chanID (lambda ((A4 tptp.secrecy_chanID) (__flatten_var_0 tptp.set_Secrecy_chanID)) (@ (@ tptp.sup_su370684444chanID (@ (@ tptp.insert751661162chanID A4) tptp.bot_bo443197316chanID)) __flatten_var_0))) (forall ((A2 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS A2) tptp.bot_bo1943466239ecy_KS) A2)) (forall ((A2 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID A2) tptp.bot_bo1785112429specID) A2)) (forall ((A2 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID A2) tptp.bot_bo443197316chanID) A2)) (forall ((A2 tptp.set_Secrecy_KS) (B2 tptp.set_Secrecy_KS)) (= (= tptp.bot_bo1943466239ecy_KS (@ (@ tptp.sup_su1301156759ecy_KS A2) B2)) (and (= A2 tptp.bot_bo1943466239ecy_KS) (= B2 tptp.bot_bo1943466239ecy_KS)))) (forall ((A2 tptp.set_Secrecy_specID) (B2 tptp.set_Secrecy_specID)) (= (= tptp.bot_bo1785112429specID (@ (@ tptp.sup_su1712599557specID A2) B2)) (and (= A2 tptp.bot_bo1785112429specID) (= B2 tptp.bot_bo1785112429specID)))) (forall ((A2 tptp.set_Secrecy_chanID) (B2 tptp.set_Secrecy_chanID)) (= (= tptp.bot_bo443197316chanID (@ (@ tptp.sup_su370684444chanID A2) B2)) (and (= A2 tptp.bot_bo443197316chanID) (= B2 tptp.bot_bo443197316chanID)))) (forall ((A2 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS tptp.bot_bo1943466239ecy_KS) A2) A2)) (forall ((A2 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID tptp.bot_bo1785112429specID) A2) A2)) (forall ((A2 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID tptp.bot_bo443197316chanID) A2) A2)) (forall ((A2 tptp.set_Secrecy_KS) (B2 tptp.set_Secrecy_KS)) (= (= (@ (@ tptp.sup_su1301156759ecy_KS A2) B2) tptp.bot_bo1943466239ecy_KS) (and (= A2 tptp.bot_bo1943466239ecy_KS) (= B2 tptp.bot_bo1943466239ecy_KS)))) (forall ((A2 tptp.set_Secrecy_specID) (B2 tptp.set_Secrecy_specID)) (= (= (@ (@ tptp.sup_su1712599557specID A2) B2) tptp.bot_bo1785112429specID) (and (= A2 tptp.bot_bo1785112429specID) (= B2 tptp.bot_bo1785112429specID)))) (forall ((A2 tptp.set_Secrecy_chanID) (B2 tptp.set_Secrecy_chanID)) (= (= (@ (@ tptp.sup_su370684444chanID A2) B2) tptp.bot_bo443197316chanID) (and (= A2 tptp.bot_bo443197316chanID) (= B2 tptp.bot_bo443197316chanID)))) (forall ((X3 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS tptp.bot_bo1943466239ecy_KS) X3) X3)) (forall ((X3 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID tptp.bot_bo1785112429specID) X3) X3)) (forall ((X3 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID tptp.bot_bo443197316chanID) X3) X3)) (forall ((X3 tptp.set_Secrecy_KS)) (= (@ (@ tptp.sup_su1301156759ecy_KS X3) tptp.bot_bo1943466239ecy_KS) X3)) (forall ((X3 tptp.set_Secrecy_specID)) (= (@ (@ tptp.sup_su1712599557specID X3) tptp.bot_bo1785112429specID) X3)) (forall ((X3 tptp.set_Secrecy_chanID)) (= (@ (@ tptp.sup_su370684444chanID X3) tptp.bot_bo443197316chanID) X3)) (forall ((P tptp.secrecy_specID) (A tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (B tptp.set_Secrecy_chanID)) (let ((_let_1 (@ tptp.ineM P))) (=> (@ (@ _let_1 A) E) (@ (@ _let_1 (@ (@ tptp.sup_su370684444chanID A) B)) E)))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.eout P) E) (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (= (@ tptp.loc PQ) tptp.bot_bo443197316chanID) (@ (@ tptp.eout PQ) E)))))) (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Keys)) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ (@ tptp.member_Secrecy_Keys Xa) (@ tptp.specKeys C3)) (exists ((X tptp.secrecy_specID)) (and (@ (@ tptp.member740727610specID X) (@ tptp.subcomponents C3)) (@ (@ tptp.member_Secrecy_Keys Xa) (@ tptp.specKeys X)))))))) (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Secrets)) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ (@ tptp.member2138796287ecrets Xa) (@ tptp.specSecrets C3)) (exists ((X tptp.secrecy_specID)) (and (@ (@ tptp.member740727610specID X) (@ tptp.subcomponents C3)) (@ (@ tptp.member2138796287ecrets Xa) (@ tptp.specSecrets X)))))))) (forall ((PQ tptp.secrecy_specID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.eout PQ) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (or (@ (@ tptp.eout P) E) (@ (@ tptp.eout Q) E)))))) (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member2138796287ecrets Xa))) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ _let_1 (@ tptp.specSecrets X3)) (@ _let_1 (@ tptp.specSecrets C3))))))) (forall ((C3 tptp.secrecy_specID) (X3 tptp.secrecy_specID) (Xa tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member_Secrecy_Keys Xa))) (=> (@ tptp.correctCompositionKS C3) (=> (@ (@ tptp.member740727610specID X3) (@ tptp.subcomponents C3)) (=> (@ _let_1 (@ tptp.specKeys X3)) (@ _let_1 (@ tptp.specKeys C3))))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ tptp.eout P) E) (=> (not (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (and (@ (@ (@ tptp.out_ex985543062Single P) Ch2) E) (@ (@ tptp.member1967978193chanID Ch2) (@ tptp.loc PQ)))) (not (@ (@ tptp.eout PQ) E)))))))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.out_exprChannelSet Q) ChSetQ) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.eout PQ) E))))))))) (forall ((Q tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ tptp.eout PQ) E)))))))) (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.out_ex985543062Single P) Ch) E) (@ (@ (@ tptp.out_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E))) (forall ((P tptp.secrecy_specID) (Ch tptp.secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.out_exprChannelSet P) (@ (@ tptp.insert751661162chanID Ch) tptp.bot_bo443197316chanID)) E) (@ (@ (@ tptp.out_ex985543062Single P) Ch) E))) (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (ChSetP tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (ChSetQ tptp.set_Secrecy_chanID) (M3 tptp.set_Secrecy_chanID)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSetP) E) (=> (@ (@ (@ tptp.out_exprChannelSet Q) ChSetQ) E) (=> (= M3 (@ (@ tptp.sup_su370684444chanID ChSetP) ChSetQ)) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetP) (@ _let_1 (@ tptp.loc PQ))))) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSetQ) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.eoutM PQ) M3) E)))))))))) (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (= (@ (@ tptp.knowle233900195orrect C3) _let_1) (= (@ (@ tptp.eout C3) (@ tptp.secrecy_sE M)) (or (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))) (forall ((M tptp.secrecy_Secrets) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (not (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets A))) (=> (not (@ (@ tptp.knowle945212990e_know A) _let_1)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (not (@ (@ tptp.eout A) (@ tptp.secrecy_sE M)))))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (M3 tptp.set_Secrecy_chanID)) (=> (not (@ (@ tptp.eout P) E)) (not (@ (@ (@ tptp.eoutM P) M3) E)))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression)) (=> (@ (@ (@ tptp.eoutM P) M3) E) (@ (@ tptp.eout P) E))) (forall ((PQ tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (P tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.eoutM PQ) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (or (@ (@ (@ tptp.eoutM P) M3) E) (@ (@ (@ tptp.eoutM Q) M3) E)))))) (forall ((Q tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (ChSet tptp.set_Secrecy_chanID)) (=> (not (@ (@ (@ tptp.eoutM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ (@ (@ tptp.out_exprChannelSet P) ChSet) E) (=> (forall ((X tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X))) (=> (@ _let_1 ChSet) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.eoutM PQ) M3) E)))))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (@ (@ (@ tptp.eoutM P) M3) E) (=> (not (@ (@ (@ tptp.eoutM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ (@ (@ tptp.out_ex985543062Single P) Ch2) E) (@ _let_1 M3) (@ _let_1 (@ tptp.loc PQ))))) (not (@ (@ (@ tptp.eoutM PQ) M3) E)))))))) (forall ((M tptp.secrecy_Keys) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (not (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys A))) (=> (@ (@ tptp.eout A) (@ tptp.secrecy_kE M)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (@ (@ tptp.knowle945212990e_know A) _let_1)))))) (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (@ (@ tptp.knowle233900195orrect C3) _let_1) (=> (@ (@ tptp.eout C3) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))) (forall ((M tptp.secrecy_Keys) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (not (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys A))) (=> (not (@ (@ tptp.knowle945212990e_know A) _let_1)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (not (@ (@ tptp.eout A) (@ tptp.secrecy_kE M)))))))) (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (= (@ (@ tptp.knowle233900195orrect C3) _let_1) (= (@ (@ tptp.eout C3) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))) (forall ((M tptp.secrecy_Secrets) (A tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (not (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets A))) (=> (@ (@ tptp.eout A) (@ tptp.secrecy_sE M)) (=> (@ (@ tptp.knowle233900195orrect A) _let_1) (@ (@ tptp.knowle945212990e_know A) _let_1)))))) (forall ((C3 tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (@ (@ tptp.knowle233900195orrect C3) _let_1) (=> (@ (@ tptp.eout C3) (@ tptp.secrecy_sE M)) (or (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets C3)) (@ (@ tptp.knowle945212990e_know C3) _let_1)))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ (@ tptp.eoutM P) M3) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.out Q)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ))) (@ _let_1 M3)))) (@ (@ (@ tptp.eoutM PQ) M3) E)))))) (forall ((P tptp.secrecy_specID) (M3 tptp.set_Secrecy_chanID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ (@ tptp.eoutM P) M3) E) (@ (@ (@ tptp.eoutM Q) M3) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.out P)) (@ _let_1 (@ tptp.out Q))) (@ _let_1 M3) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ (@ tptp.eoutM PQ) M3) E)))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (PQ tptp.secrecy_specID) (Q tptp.secrecy_specID)) (=> (@ (@ tptp.eout P) E) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (@ _let_1 (@ tptp.out P)) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.eout PQ) E)))))) _let_9 _let_8 _let_7 _let_6 (forall ((PQ tptp.secrecy_specID) (P tptp.secrecy_specID) (Q tptp.secrecy_specID) (X3 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID X3))) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (@ _let_1 (@ tptp.out PQ)) (or (@ _let_1 (@ tptp.out P)) (@ _let_1 (@ tptp.out Q)))))))) (forall ((P tptp.secrecy_specID) (E tptp.secrecy_Expression) (Q tptp.secrecy_specID) (PQ tptp.secrecy_specID)) (=> (or (@ (@ tptp.eout P) E) (@ (@ tptp.eout Q) E)) (=> (= (@ tptp.subcomponents PQ) (@ (@ tptp.insert1671894227specID P) (@ (@ tptp.insert1671894227specID Q) tptp.bot_bo1785112429specID))) (=> (@ tptp.correc990227761ionOut PQ) (=> (exists ((Ch2 tptp.secrecy_chanID)) (let ((_let_1 (@ tptp.member1967978193chanID Ch2))) (and (or (@ _let_1 (@ tptp.out P)) (@ _let_1 (@ tptp.out Q))) (@ (@ tptp.exprChannel Ch2) E) (not (@ _let_1 (@ tptp.loc PQ)))))) (@ (@ tptp.eout PQ) E)))))) _let_5 (forall ((P tptp.secrecy_specID) (A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (=> (@ (@ tptp.ord_le1802272080chanID (@ tptp.out P)) (@ tptp.ins A)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_sKS M))) (not (@ (@ tptp.eout P) (@ tptp.secrecy_sE M)))))) _let_4 true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.56/1.09 )
% 0.56/1.09 % SZS output end Proof for ITP091^1
% 0.56/1.09 % cvc5---1.0.5 exiting
% 0.56/1.09 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------