TSTP Solution File: ITP085^1 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP085^1 : TPTP v8.1.2. Released v7.5.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 03:18:06 EDT 2023
% Result : Theorem 0.56s 1.12s
% Output : Proof 0.56s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.18 % Problem : ITP085^1 : TPTP v8.1.2. Released v7.5.0.
% 0.18/0.19 % Command : do_cvc5 %s %d
% 0.20/0.41 % Computer : n015.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 13:38:09 EDT 2023
% 0.20/0.41 % CPUTime :
% 0.27/0.60 %----Proving TH0
% 0.27/0.61 %------------------------------------------------------------------------------
% 0.27/0.61 % File : ITP085^1 : TPTP v8.1.2. Released v7.5.0.
% 0.27/0.61 % Domain : Interactive Theorem Proving
% 0.27/0.61 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_155__3292644_1
% 0.27/0.61 % Version : Especial.
% 0.27/0.61 % English :
% 0.27/0.61
% 0.27/0.61 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.27/0.61 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.27/0.61 % Source : [Des21]
% 0.27/0.61 % Names : KnowledgeKeysSecrets/prob_155__3292644_1 [Des21]
% 0.27/0.61
% 0.27/0.61 % Status : Theorem
% 0.27/0.61 % Rating : 0.15 v8.1.0, 0.18 v7.5.0
% 0.27/0.61 % Syntax : Number of formulae : 489 ( 193 unt; 136 typ; 0 def)
% 0.27/0.61 % Number of atoms : 953 ( 694 equ; 0 cnn)
% 0.27/0.61 % Maximal formula atoms : 13 ( 2 avg)
% 0.27/0.61 % Number of connectives : 3297 ( 212 ~; 62 |; 128 &;2470 @)
% 0.27/0.61 % ( 0 <=>; 425 =>; 0 <=; 0 <~>)
% 0.27/0.61 % Maximal formula depth : 21 ( 6 avg)
% 0.27/0.61 % Number of types : 20 ( 19 usr)
% 0.27/0.61 % Number of type conns : 445 ( 445 >; 0 *; 0 +; 0 <<)
% 0.27/0.61 % Number of symbols : 118 ( 117 usr; 8 con; 0-3 aty)
% 0.27/0.61 % Number of variables : 1081 ( 27 ^; 973 !; 81 ?;1081 :)
% 0.27/0.61 % SPC : TH0_THM_EQU_NAR
% 0.27/0.61
% 0.27/0.61 % Comments : This file was generated by Sledgehammer 2021-02-23 15:33:57.162
% 0.27/0.61 %------------------------------------------------------------------------------
% 0.27/0.61 % Could-be-implicit typings (19)
% 0.27/0.61 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
% 0.27/0.61 list_l425507653ession: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OExpression_J_J,type,
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% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OSecrets_J_J,type,
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% 0.27/0.61
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% 0.27/0.61 set_li849033543y_Keys: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__List__Olist_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
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% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__List__Olist_It__Secrecy____types__OKS_J_J,type,
% 0.27/0.61 set_list_Secrecy_KS: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.27/0.61 list_S529945141ession: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OExpression_J,type,
% 0.27/0.61 set_Se1942955227ession: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__List__Olist_It__Secrecy____types__OSecrets_J,type,
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% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OSecrets_J,type,
% 0.27/0.61 set_Secrecy_Secrets: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 0.27/0.61 list_Secrecy_Keys: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKeys_J,type,
% 0.27/0.61 set_Secrecy_Keys: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.27/0.61 list_Secrecy_KS: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Set__Oset_It__Secrecy____types__OKS_J,type,
% 0.27/0.61 set_Secrecy_KS: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Secrecy____types__OExpression,type,
% 0.27/0.61 secrecy_Expression: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Secrecy____types__OSecrets,type,
% 0.27/0.61 secrecy_Secrets: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Secrecy____types__OspecID,type,
% 0.27/0.61 secrecy_specID: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Secrecy____types__OKeys,type,
% 0.27/0.61 secrecy_Keys: $tType ).
% 0.27/0.61
% 0.27/0.61 thf(ty_n_t__Secrecy____types__OKS,type,
% 0.27/0.61 secrecy_KS: $tType ).
% 0.27/0.61
% 0.27/0.61 % Explicit typings (117)
% 0.27/0.61 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 bNF_Gr275623750ession: set_li185139947ession > secrecy_Expression > set_li185139947ession ).
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% 0.27/0.61 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKS,type,
% 0.27/0.61 bNF_Gr660123862ecy_KS: set_list_Secrecy_KS > secrecy_KS > set_list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OKeys,type,
% 0.27/0.61 bNF_Gr414702370y_Keys: set_li849033543y_Keys > secrecy_Keys > set_li849033543y_Keys ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_BNF__Greatest__Fixpoint_OShift_001t__Secrecy____types__OSecrets,type,
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% 0.27/0.61 thf(sy_c_BNF__Greatest__Fixpoint_OSucc_001t__Secrecy____types__OExpression,type,
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% 0.27/0.61
% 0.27/0.61 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
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% 0.27/0.61
% 0.27/0.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowCorrect,type,
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% 0.27/0.61
% 0.27/0.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_OeoutKnowsECorrect,type,
% 0.27/0.61 knowle1268625169orrect: secrecy_specID > secrecy_Expression > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknow,type,
% 0.27/0.61 knowle945212990e_know: secrecy_specID > secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__vytwmzrumu_Oknows,type,
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% 0.27/0.61
% 0.27/0.61 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OExpression,type,
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% 0.27/0.61
% 0.27/0.61 thf(sy_c_ListExtras_Omem_001t__Secrecy____types__OKS,type,
% 0.27/0.61 mem_Secrecy_KS: secrecy_KS > list_Secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
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% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oappend_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.27/0.61 append1376766698ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS > list_list_Secrecy_KS ).
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% 0.27/0.61 thf(sy_c_List_Oappend_001t__Secrecy____types__OExpression,type,
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% 0.27/0.61 thf(sy_c_List_Oappend_001t__Secrecy____types__OKeys,type,
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% 0.27/0.61 thf(sy_c_List_Oconcat_001t__Secrecy____types__OKS,type,
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% 0.27/0.61 thf(sy_c_List_Odistinct__adj_001t__Secrecy____types__OExpression,type,
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% 0.27/0.61 thf(sy_c_List_Ofoldr_001t__List__Olist_It__Secrecy____types__OKS_J_001t__List__Olist_It__Secrecy____types__OKS_J,type,
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% 0.27/0.61 thf(sy_c_List_Oinsert_001t__Secrecy____types__OExpression,type,
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% 0.27/0.61 thf(sy_c_List_Olist_Otl_001t__Secrecy____types__OKS,type,
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% 0.27/0.61 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 listre1601064475ession: ( secrecy_KS > secrecy_Expression > $o ) > list_Secrecy_KS > list_S529945141ession > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Olistrelp_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.27/0.61 listre788412843ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 map_ta1624757057ession: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omap__tailrec__rev_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 map_ta623472337ession: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 maps_S599402637ession: ( secrecy_Expression > list_S529945141ession ) > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omaps_001t__Secrecy____types__OExpression_001t__Secrecy____types__OKS,type,
% 0.27/0.61 maps_S399472669ecy_KS: ( secrecy_Expression > list_Secrecy_KS ) > list_S529945141ession > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 maps_S1434541085ession: ( secrecy_KS > list_S529945141ession ) > list_Secrecy_KS > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omaps_001t__Secrecy____types__OKS_001t__Secrecy____types__OKS,type,
% 0.27/0.61 maps_S377605037ecy_KS: ( secrecy_KS > list_Secrecy_KS ) > list_Secrecy_KS > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omember_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 member2020590922ession: list_S529945141ession > secrecy_Expression > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Omember_001t__Secrecy____types__OKS,type,
% 0.27/0.61 member_Secrecy_KS: list_Secrecy_KS > secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 lexord1123423577ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > list_S529945141ession > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oord_Olexordp__eq_001t__Secrecy____types__OKS,type,
% 0.27/0.61 lexord948960489ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > list_Secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 produc1450295286ession: list_l425507653ession > list_l425507653ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oproduct__lists_001t__Secrecy____types__OKS,type,
% 0.27/0.61 produc713695622ecy_KS: list_list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oremdups__adj_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 remdup484344169ession: list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oremdups__adj_001t__Secrecy____types__OKS,type,
% 0.27/0.61 remdup351570169ecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Orev_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 rev_Se1073238207ession: list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Orev_001t__Secrecy____types__OKS,type,
% 0.27/0.61 rev_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Orotate1_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 rotate1237234450ession: list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Orotate1_001t__Secrecy____types__OKS,type,
% 0.27/0.61 rotate1_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 shuffl552897610ession: list_S529945141ession > list_S529945141ession > set_li185139947ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Oshuffles_001t__Secrecy____types__OKS,type,
% 0.27/0.61 shuffles_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > set_list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Osplice_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 splice1390717708ession: list_S529945141ession > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Osplice_001t__Secrecy____types__OKS,type,
% 0.27/0.61 splice_Secrecy_KS: list_Secrecy_KS > list_Secrecy_KS > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 subseq348280080ession: list_S529945141ession > list_l425507653ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Osubseqs_001t__Secrecy____types__OKS,type,
% 0.27/0.61 subseqs_Secrecy_KS: list_Secrecy_KS > list_list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 succes1388047762ession: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_List_Osuccessively_001t__Secrecy____types__OKS,type,
% 0.27/0.61 succes590251810ecy_KS: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_ODecr,type,
% 0.27/0.61 decr: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OEnc,type,
% 0.27/0.61 enc: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OEncrDecrKeys,type,
% 0.27/0.61 encrDecrKeys: secrecy_Keys > secrecy_Keys > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OExt,type,
% 0.27/0.61 ext: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OSign,type,
% 0.27/0.61 sign: secrecy_Keys > list_S529945141ession > list_S529945141ession ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_Oeout,type,
% 0.27/0.61 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_Oine,type,
% 0.27/0.61 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.27/0.61 notSpe1586871396tsExpr: secrecy_specID > list_S529945141ession > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OspecKeys,type,
% 0.27/0.61 specKeys: secrecy_specID > set_Secrecy_Keys ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.27/0.61 specKeysSecrets: secrecy_specID > set_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.27/0.61 specSecrets: secrecy_specID > set_Secrecy_Secrets ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy__types_OExpression2KSL,type,
% 0.27/0.61 secrec1371625429on2KSL: list_S529945141ession > list_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.27/0.61 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.27/0.61 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.27/0.61 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.27/0.61 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.27/0.61 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKS,type,
% 0.27/0.61 collect_Secrecy_KS: ( secrecy_KS > $o ) > set_Secrecy_KS ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OKeys,type,
% 0.27/0.61 collect_Secrecy_Keys: ( secrecy_Keys > $o ) > set_Secrecy_Keys ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_Set_OCollect_001t__Secrecy____types__OSecrets,type,
% 0.27/0.61 collec836099393ecrets: ( secrecy_Secrets > $o ) > set_Secrecy_Secrets ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OExpression_J,type,
% 0.27/0.61 member249235532ession: list_S529945141ession > set_li185139947ession > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKS_J,type,
% 0.27/0.61 member193705948ecy_KS: list_Secrecy_KS > set_list_Secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OKeys_J,type,
% 0.27/0.61 member341114536y_Keys: list_Secrecy_Keys > set_li849033543y_Keys > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__List__Olist_It__Secrecy____types__OSecrets_J,type,
% 0.27/0.61 member1138497285ecrets: list_Secrecy_Secrets > set_li2007071804ecrets > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__Secrecy____types__OExpression,type,
% 0.27/0.61 member279582780ession: secrecy_Expression > set_Se1942955227ession > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__Secrecy____types__OKS,type,
% 0.27/0.61 member_Secrecy_KS2: secrecy_KS > set_Secrecy_KS > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__Secrecy____types__OKeys,type,
% 0.27/0.61 member_Secrecy_Keys: secrecy_Keys > set_Secrecy_Keys > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_c_member_001t__Secrecy____types__OSecrets,type,
% 0.27/0.61 member2138796287ecrets: secrecy_Secrets > set_Secrecy_Secrets > $o ).
% 0.27/0.61
% 0.27/0.61 thf(sy_v_A,type,
% 0.27/0.61 a: secrecy_specID ).
% 0.27/0.61
% 0.27/0.61 thf(sy_v_m,type,
% 0.27/0.61 m: secrecy_Secrets ).
% 0.27/0.61
% 0.27/0.61 % Relevant facts (352)
% 0.27/0.61 thf(fact_0_assms,axiom,
% 0.27/0.61 knowle731562421_knows @ a @ ( cons_S112077679ession @ ( secrecy_sE @ m ) @ nil_Se901661471ession ) ).
% 0.27/0.61
% 0.27/0.61 % assms
% 0.27/0.61 thf(fact_1_KS_Oinject_I2_J,axiom,
% 0.27/0.61 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.27/0.61 ( ( ( secrecy_sKS @ X2 )
% 0.27/0.61 = ( secrecy_sKS @ Y2 ) )
% 0.27/0.61 = ( X2 = Y2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS.inject(2)
% 0.27/0.61 thf(fact_2_know2knows__s,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.61 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.61 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_sE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know2knows_s
% 0.27/0.61 thf(fact_3_know1s,axiom,
% 0.27/0.61 ! [C: secrecy_specID,M2: secrecy_Secrets] :
% 0.27/0.61 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_sKS @ M2 ) ) @ nil_Se901661471ession ) )
% 0.27/0.61 = ( knowle945212990e_know @ C @ ( secrecy_sKS @ M2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know1s
% 0.27/0.61 thf(fact_4_eoutKnowCorrect__L1s,axiom,
% 0.27/0.61 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.61 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 0.27/0.61 => ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.27/0.61 => ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 0.27/0.61 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % eoutKnowCorrect_L1s
% 0.27/0.61 thf(fact_5_eout__know__s,axiom,
% 0.27/0.61 ! [C: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.61 ( ( knowle233900195orrect @ C @ ( secrecy_sKS @ M ) )
% 0.27/0.61 = ( ( eout @ C @ ( secrecy_sE @ M ) )
% 0.27/0.61 = ( ( member2138796287ecrets @ M @ ( specSecrets @ C ) )
% 0.27/0.61 | ( knowle945212990e_know @ C @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % eout_know_s
% 0.27/0.61 thf(fact_6_know_Osimps_I2_J,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Secrets] :
% 0.27/0.61 ( ( knowle945212990e_know @ A @ ( secrecy_sKS @ M ) )
% 0.27/0.61 = ( ( ine @ A @ ( secrecy_sE @ M ) )
% 0.27/0.61 | ( member_Secrecy_KS2 @ ( secrecy_sKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know.simps(2)
% 0.27/0.61 thf(fact_7_KS2Expression_Osimps_I2_J,axiom,
% 0.27/0.61 ! [M: secrecy_Secrets] :
% 0.27/0.61 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.27/0.61 = ( secrecy_sE @ M ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS2Expression.simps(2)
% 0.27/0.61 thf(fact_8_knows4,axiom,
% 0.27/0.61 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.27/0.61 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.27/0.61 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K2 ) )
% 0.27/0.61 & ( knowle731562421_knows @ A @ ( enc @ K1 @ E ) ) )
% 0.27/0.61 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows4
% 0.27/0.61 thf(fact_9_knows5,axiom,
% 0.27/0.61 ! [IncrDecrKeys: secrecy_Keys > secrecy_Keys > $o,K1: secrecy_Keys,K2: secrecy_Keys,A: secrecy_specID,E: list_S529945141ession] :
% 0.27/0.61 ( ( ( IncrDecrKeys @ K1 @ K2 )
% 0.27/0.61 & ( knowle945212990e_know @ A @ ( secrecy_kKS @ K1 ) )
% 0.27/0.61 & ( knowle731562421_knows @ A @ ( sign @ K2 @ E ) ) )
% 0.27/0.61 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows5
% 0.27/0.61 thf(fact_10_knows6,axiom,
% 0.27/0.61 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.27/0.61 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.27/0.61 & ( knowle731562421_knows @ A @ E1 ) )
% 0.27/0.61 => ( knowle731562421_knows @ A @ ( enc @ K @ E1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows6
% 0.27/0.61 thf(fact_11_KS_Oinject_I1_J,axiom,
% 0.27/0.61 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.27/0.61 ( ( ( secrecy_kKS @ X1 )
% 0.27/0.61 = ( secrecy_kKS @ Y1 ) )
% 0.27/0.61 = ( X1 = Y1 ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS.inject(1)
% 0.27/0.61 thf(fact_12_Expression_Oinject_I2_J,axiom,
% 0.27/0.61 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.27/0.61 ( ( ( secrecy_sE @ X2 )
% 0.27/0.61 = ( secrecy_sE @ Y2 ) )
% 0.27/0.61 = ( X2 = Y2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % Expression.inject(2)
% 0.27/0.61 thf(fact_13_know1k,axiom,
% 0.27/0.61 ! [C: secrecy_specID,M1: secrecy_Keys] :
% 0.27/0.61 ( ( knowle731562421_knows @ C @ ( cons_S112077679ession @ ( secrec1016742679ession @ ( secrecy_kKS @ M1 ) ) @ nil_Se901661471ession ) )
% 0.27/0.61 = ( knowle945212990e_know @ C @ ( secrecy_kKS @ M1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know1k
% 0.27/0.61 thf(fact_14_knows__emptyexpression,axiom,
% 0.27/0.61 ! [C: secrecy_specID] : ( knowle731562421_knows @ C @ nil_Se901661471ession ) ).
% 0.27/0.61
% 0.27/0.61 % knows_emptyexpression
% 0.27/0.61 thf(fact_15_KS_Oexhaust,axiom,
% 0.27/0.61 ! [Y: secrecy_KS] :
% 0.27/0.61 ( ! [X12: secrecy_Keys] :
% 0.27/0.61 ( Y
% 0.27/0.61 != ( secrecy_kKS @ X12 ) )
% 0.27/0.61 => ~ ! [X22: secrecy_Secrets] :
% 0.27/0.61 ( Y
% 0.27/0.61 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS.exhaust
% 0.27/0.61 thf(fact_16_KS_Oinduct,axiom,
% 0.27/0.61 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.27/0.61 ( ! [X: secrecy_Keys] : ( P @ ( secrecy_kKS @ X ) )
% 0.27/0.61 => ( ! [X: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X ) )
% 0.27/0.61 => ( P @ KS ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS.induct
% 0.27/0.61 thf(fact_17_KS_Odistinct_I1_J,axiom,
% 0.27/0.61 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.27/0.61 ( ( secrecy_kKS @ X1 )
% 0.27/0.61 != ( secrecy_sKS @ X2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS.distinct(1)
% 0.27/0.61 thf(fact_18_knows7,axiom,
% 0.27/0.61 ! [A: secrecy_specID,K: secrecy_Keys,E1: list_S529945141ession] :
% 0.27/0.61 ( ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ K ) )
% 0.27/0.61 & ( knowle731562421_knows @ A @ E1 ) )
% 0.27/0.61 => ( knowle731562421_knows @ A @ ( sign @ K @ E1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows7
% 0.27/0.61 thf(fact_19_list_Oinject,axiom,
% 0.27/0.61 ! [X21: secrecy_Expression,X222: list_S529945141ession,Y21: secrecy_Expression,Y22: list_S529945141ession] :
% 0.27/0.61 ( ( ( cons_S112077679ession @ X21 @ X222 )
% 0.27/0.61 = ( cons_S112077679ession @ Y21 @ Y22 ) )
% 0.27/0.61 = ( ( X21 = Y21 )
% 0.27/0.61 & ( X222 = Y22 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.inject
% 0.27/0.61 thf(fact_20_list_Odistinct_I1_J,axiom,
% 0.27/0.61 ! [X21: secrecy_KS,X222: list_Secrecy_KS] :
% 0.27/0.61 ( nil_Secrecy_KS
% 0.27/0.61 != ( cons_Secrecy_KS @ X21 @ X222 ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.distinct(1)
% 0.27/0.61 thf(fact_21_list_Odistinct_I1_J,axiom,
% 0.27/0.61 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.27/0.61 ( nil_Se901661471ession
% 0.27/0.61 != ( cons_S112077679ession @ X21 @ X222 ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.distinct(1)
% 0.27/0.61 thf(fact_22_list_OdiscI,axiom,
% 0.27/0.61 ! [List: list_Secrecy_KS,X21: secrecy_KS,X222: list_Secrecy_KS] :
% 0.27/0.61 ( ( List
% 0.27/0.61 = ( cons_Secrecy_KS @ X21 @ X222 ) )
% 0.27/0.61 => ( List != nil_Secrecy_KS ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.discI
% 0.27/0.61 thf(fact_23_list_OdiscI,axiom,
% 0.27/0.61 ! [List: list_S529945141ession,X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.27/0.61 ( ( List
% 0.27/0.61 = ( cons_S112077679ession @ X21 @ X222 ) )
% 0.27/0.61 => ( List != nil_Se901661471ession ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.discI
% 0.27/0.61 thf(fact_24_list_Oexhaust,axiom,
% 0.27/0.61 ! [Y: list_Secrecy_KS] :
% 0.27/0.61 ( ( Y != nil_Secrecy_KS )
% 0.27/0.61 => ~ ! [X212: secrecy_KS,X223: list_Secrecy_KS] :
% 0.27/0.61 ( Y
% 0.27/0.61 != ( cons_Secrecy_KS @ X212 @ X223 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.exhaust
% 0.27/0.61 thf(fact_25_list_Oexhaust,axiom,
% 0.27/0.61 ! [Y: list_S529945141ession] :
% 0.27/0.61 ( ( Y != nil_Se901661471ession )
% 0.27/0.61 => ~ ! [X212: secrecy_Expression,X223: list_S529945141ession] :
% 0.27/0.61 ( Y
% 0.27/0.61 != ( cons_S112077679ession @ X212 @ X223 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.exhaust
% 0.27/0.61 thf(fact_26_list_Oinducts,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > $o,List: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X12: secrecy_KS,X22: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ X22 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X12 @ X22 ) ) )
% 0.27/0.61 => ( P @ List ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.inducts
% 0.27/0.61 thf(fact_27_list_Oinducts,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > $o,List: list_S529945141ession] :
% 0.27/0.61 ( ( P @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X12: secrecy_Expression,X22: list_S529945141ession] :
% 0.27/0.61 ( ( P @ X22 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X12 @ X22 ) ) )
% 0.27/0.61 => ( P @ List ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list.inducts
% 0.27/0.61 thf(fact_28_neq__Nil__conv,axiom,
% 0.27/0.61 ! [Xs: list_Secrecy_KS] :
% 0.27/0.61 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.61 = ( ? [Y3: secrecy_KS,Ys: list_Secrecy_KS] :
% 0.27/0.61 ( Xs
% 0.27/0.61 = ( cons_Secrecy_KS @ Y3 @ Ys ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % neq_Nil_conv
% 0.27/0.61 thf(fact_29_neq__Nil__conv,axiom,
% 0.27/0.61 ! [Xs: list_S529945141ession] :
% 0.27/0.61 ( ( Xs != nil_Se901661471ession )
% 0.27/0.61 = ( ? [Y3: secrecy_Expression,Ys: list_S529945141ession] :
% 0.27/0.61 ( Xs
% 0.27/0.61 = ( cons_S112077679ession @ Y3 @ Ys ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % neq_Nil_conv
% 0.27/0.61 thf(fact_30_list__induct2_H,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [Y4: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ Xs2 @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 0.27/0.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list_induct2'
% 0.27/0.61 thf(fact_31_list__induct2_H,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > list_S529945141ession > $o,Xs: list_Secrecy_KS,Ys2: list_S529945141ession] :
% 0.27/0.61 ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [Y4: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Secrecy_KS @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.27/0.61 ( ( P @ Xs2 @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 0.27/0.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list_induct2'
% 0.27/0.61 thf(fact_32_list__induct2_H,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > list_Secrecy_KS > $o,Xs: list_S529945141ession,Ys2: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [Y4: secrecy_KS,Ys3: list_Secrecy_KS] : ( P @ nil_Se901661471ession @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ Xs2 @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 0.27/0.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list_induct2'
% 0.27/0.61 thf(fact_33_list__induct2_H,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > list_S529945141ession > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.61 ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] : ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [Y4: secrecy_Expression,Ys3: list_S529945141ession] : ( P @ nil_Se901661471ession @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.27/0.61 ( ( P @ Xs2 @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 0.27/0.61 => ( P @ Xs @ Ys2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list_induct2'
% 0.27/0.61 thf(fact_34_splice_Oinduct,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 0.27/0.61 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ Ys3 @ Xs2 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % splice.induct
% 0.27/0.61 thf(fact_35_splice_Oinduct,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 0.27/0.61 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.27/0.61 ( ( P @ Ys3 @ Xs2 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % splice.induct
% 0.27/0.61 thf(fact_36_induct__list012,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.61 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Zs: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ Zs )
% 0.27/0.61 => ( ( P @ ( cons_Secrecy_KS @ Y4 @ Zs ) )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Zs ) ) ) ) )
% 0.27/0.61 => ( P @ Xs ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % induct_list012
% 0.27/0.61 thf(fact_37_induct__list012,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 0.27/0.61 ( ( P @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Zs: list_S529945141ession] :
% 0.27/0.61 ( ( P @ Zs )
% 0.27/0.61 => ( ( P @ ( cons_S112077679ession @ Y4 @ Zs ) )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Zs ) ) ) ) )
% 0.27/0.61 => ( P @ Xs ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % induct_list012
% 0.27/0.61 thf(fact_38_not__Cons__self2,axiom,
% 0.27/0.61 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.61 ( ( cons_S112077679ession @ X3 @ Xs )
% 0.27/0.61 != Xs ) ).
% 0.27/0.61
% 0.27/0.61 % not_Cons_self2
% 0.27/0.61 thf(fact_39_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.61 ! [P: ( secrecy_KS > secrecy_Expression ) > list_Secrecy_KS > list_S529945141ession > $o,A0: secrecy_KS > secrecy_Expression,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 0.27/0.61 ( ! [F: secrecy_KS > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Secrecy_KS @ X_1 )
% 0.27/0.61 => ( ! [F: secrecy_KS > secrecy_Expression,A3: secrecy_KS,As: list_Secrecy_KS,Bs: list_S529945141ession] :
% 0.27/0.61 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 0.27/0.61 => ( P @ F @ ( cons_Secrecy_KS @ A3 @ As ) @ Bs ) )
% 0.27/0.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % map_tailrec_rev.induct
% 0.27/0.61 thf(fact_40_map__tailrec__rev_Oinduct,axiom,
% 0.27/0.61 ! [P: ( secrecy_Expression > secrecy_Expression ) > list_S529945141ession > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.27/0.61 ( ! [F: secrecy_Expression > secrecy_Expression,X_1: list_S529945141ession] : ( P @ F @ nil_Se901661471ession @ X_1 )
% 0.27/0.61 => ( ! [F: secrecy_Expression > secrecy_Expression,A3: secrecy_Expression,As: list_S529945141ession,Bs: list_S529945141ession] :
% 0.27/0.61 ( ( P @ F @ As @ ( cons_S112077679ession @ ( F @ A3 ) @ Bs ) )
% 0.27/0.61 => ( P @ F @ ( cons_S112077679ession @ A3 @ As ) @ Bs ) )
% 0.27/0.61 => ( P @ A0 @ A1 @ A2 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % map_tailrec_rev.induct
% 0.27/0.61 thf(fact_41_list__nonempty__induct,axiom,
% 0.27/0.61 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 0.27/0.61 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.61 ( ( Xs2 != nil_Secrecy_KS )
% 0.27/0.61 => ( ( P @ Xs2 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 0.27/0.61 => ( P @ Xs ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list_nonempty_induct
% 0.27/0.61 thf(fact_42_list__nonempty__induct,axiom,
% 0.27/0.61 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 0.27/0.61 ( ( Xs != nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.61 ( ( Xs2 != nil_Se901661471ession )
% 0.27/0.61 => ( ( P @ Xs2 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 0.27/0.61 => ( P @ Xs ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % list_nonempty_induct
% 0.27/0.61 thf(fact_43_successively_Oinduct,axiom,
% 0.27/0.61 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 0.27/0.61 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS] : ( P @ P2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.61 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ P2 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) )
% 0.27/0.61 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % successively.induct
% 0.27/0.61 thf(fact_44_successively_Oinduct,axiom,
% 0.27/0.61 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 0.27/0.61 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression] : ( P @ P2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.61 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.61 ( ( P @ P2 @ ( cons_S112077679ession @ Y4 @ Xs2 ) )
% 0.27/0.61 => ( P @ P2 @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % successively.induct
% 0.27/0.61 thf(fact_45_remdups__adj_Oinduct,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > $o,A0: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.61 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.61 ( ( ( X = Y4 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) ) )
% 0.27/0.61 => ( ( ( X != Y4 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) )
% 0.27/0.61 => ( P @ A0 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % remdups_adj.induct
% 0.27/0.61 thf(fact_46_remdups__adj_Oinduct,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > $o,A0: list_S529945141ession] :
% 0.27/0.61 ( ( P @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.61 ( ( ( X = Y4 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) ) )
% 0.27/0.61 => ( ( ( X != Y4 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) )
% 0.27/0.61 => ( P @ A0 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % remdups_adj.induct
% 0.27/0.61 thf(fact_47_sorted__wrt_Oinduct,axiom,
% 0.27/0.61 ! [P: ( secrecy_KS > secrecy_KS > $o ) > list_Secrecy_KS > $o,A0: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS] :
% 0.27/0.61 ( ! [P2: secrecy_KS > secrecy_KS > $o] : ( P @ P2 @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [P2: secrecy_KS > secrecy_KS > $o,X: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ P2 @ Ys3 )
% 0.27/0.61 => ( P @ P2 @ ( cons_Secrecy_KS @ X @ Ys3 ) ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % sorted_wrt.induct
% 0.27/0.61 thf(fact_48_sorted__wrt_Oinduct,axiom,
% 0.27/0.61 ! [P: ( secrecy_Expression > secrecy_Expression > $o ) > list_S529945141ession > $o,A0: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession] :
% 0.27/0.61 ( ! [P2: secrecy_Expression > secrecy_Expression > $o] : ( P @ P2 @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [P2: secrecy_Expression > secrecy_Expression > $o,X: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.27/0.61 ( ( P @ P2 @ Ys3 )
% 0.27/0.61 => ( P @ P2 @ ( cons_S112077679ession @ X @ Ys3 ) ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % sorted_wrt.induct
% 0.27/0.61 thf(fact_49_remdups__adj_Ocases,axiom,
% 0.27/0.61 ! [X3: list_Secrecy_KS] :
% 0.27/0.61 ( ( X3 != nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.61 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % remdups_adj.cases
% 0.27/0.61 thf(fact_50_remdups__adj_Ocases,axiom,
% 0.27/0.61 ! [X3: list_S529945141ession] :
% 0.27/0.61 ( ( X3 != nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_Expression] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.61 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % remdups_adj.cases
% 0.27/0.61 thf(fact_51_mem__Collect__eq,axiom,
% 0.27/0.61 ! [A4: secrecy_Secrets,P: secrecy_Secrets > $o] :
% 0.27/0.61 ( ( member2138796287ecrets @ A4 @ ( collec836099393ecrets @ P ) )
% 0.27/0.61 = ( P @ A4 ) ) ).
% 0.27/0.61
% 0.27/0.61 % mem_Collect_eq
% 0.27/0.61 thf(fact_52_mem__Collect__eq,axiom,
% 0.27/0.61 ! [A4: secrecy_KS,P: secrecy_KS > $o] :
% 0.27/0.61 ( ( member_Secrecy_KS2 @ A4 @ ( collect_Secrecy_KS @ P ) )
% 0.27/0.61 = ( P @ A4 ) ) ).
% 0.27/0.61
% 0.27/0.61 % mem_Collect_eq
% 0.27/0.61 thf(fact_53_mem__Collect__eq,axiom,
% 0.27/0.61 ! [A4: secrecy_Keys,P: secrecy_Keys > $o] :
% 0.27/0.61 ( ( member_Secrecy_Keys @ A4 @ ( collect_Secrecy_Keys @ P ) )
% 0.27/0.61 = ( P @ A4 ) ) ).
% 0.27/0.61
% 0.27/0.61 % mem_Collect_eq
% 0.27/0.61 thf(fact_54_Collect__mem__eq,axiom,
% 0.27/0.61 ! [A: set_Secrecy_Secrets] :
% 0.27/0.61 ( ( collec836099393ecrets
% 0.27/0.61 @ ^ [X4: secrecy_Secrets] : ( member2138796287ecrets @ X4 @ A ) )
% 0.27/0.61 = A ) ).
% 0.27/0.61
% 0.27/0.61 % Collect_mem_eq
% 0.27/0.61 thf(fact_55_Collect__mem__eq,axiom,
% 0.27/0.61 ! [A: set_Secrecy_KS] :
% 0.27/0.61 ( ( collect_Secrecy_KS
% 0.27/0.61 @ ^ [X4: secrecy_KS] : ( member_Secrecy_KS2 @ X4 @ A ) )
% 0.27/0.61 = A ) ).
% 0.27/0.61
% 0.27/0.61 % Collect_mem_eq
% 0.27/0.61 thf(fact_56_Collect__mem__eq,axiom,
% 0.27/0.61 ! [A: set_Secrecy_Keys] :
% 0.27/0.61 ( ( collect_Secrecy_Keys
% 0.27/0.61 @ ^ [X4: secrecy_Keys] : ( member_Secrecy_Keys @ X4 @ A ) )
% 0.27/0.61 = A ) ).
% 0.27/0.61
% 0.27/0.61 % Collect_mem_eq
% 0.27/0.61 thf(fact_57_transpose_Ocases,axiom,
% 0.27/0.61 ! [X3: list_list_Secrecy_KS] :
% 0.27/0.61 ( ( X3 != nil_list_Secrecy_KS )
% 0.27/0.61 => ( ! [Xss: list_list_Secrecy_KS] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ Xss ) )
% 0.27/0.61 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Xss: list_list_Secrecy_KS] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_list_Secrecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % transpose.cases
% 0.27/0.61 thf(fact_58_transpose_Ocases,axiom,
% 0.27/0.61 ! [X3: list_l425507653ession] :
% 0.27/0.61 ( ( X3 != nil_li311616943ession )
% 0.27/0.61 => ( ! [Xss: list_l425507653ession] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_l533358079ession @ nil_Se901661471ession @ Xss ) )
% 0.27/0.61 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession,Xss: list_l425507653ession] :
% 0.27/0.61 ( X3
% 0.27/0.61 != ( cons_l533358079ession @ ( cons_S112077679ession @ X @ Xs2 ) @ Xss ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % transpose.cases
% 0.27/0.61 thf(fact_59_shuffles_Oinduct,axiom,
% 0.27/0.61 ! [P: list_Secrecy_KS > list_Secrecy_KS > $o,A0: list_Secrecy_KS,A1: list_Secrecy_KS] :
% 0.27/0.61 ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.27/0.61 => ( ! [Xs2: list_Secrecy_KS] : ( P @ Xs2 @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS,Y4: secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.61 ( ( P @ Xs2 @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.61 => ( ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % shuffles.induct
% 0.27/0.61 thf(fact_60_shuffles_Oinduct,axiom,
% 0.27/0.61 ! [P: list_S529945141ession > list_S529945141ession > $o,A0: list_S529945141ession,A1: list_S529945141ession] :
% 0.27/0.61 ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.27/0.61 => ( ! [Xs2: list_S529945141ession] : ( P @ Xs2 @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession,Y4: secrecy_Expression,Ys3: list_S529945141ession] :
% 0.27/0.61 ( ( P @ Xs2 @ ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.61 => ( ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) )
% 0.27/0.61 => ( P @ A0 @ A1 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % shuffles.induct
% 0.27/0.61 thf(fact_61_knows1k,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.61 = ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows1k
% 0.27/0.61 thf(fact_62_know2knows__k,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.61 => ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know2knows_k
% 0.27/0.61 thf(fact_63_knows2know__k,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.27/0.61 => ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows2know_k
% 0.27/0.61 thf(fact_64_know2knowsPQ__k,axiom,
% 0.27/0.61 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 0.27/0.61 ( ( ( knowle945212990e_know @ P @ ( secrecy_kKS @ M ) )
% 0.27/0.61 | ( knowle945212990e_know @ Q @ ( secrecy_kKS @ M ) ) )
% 0.27/0.61 => ( ( knowle731562421_knows @ P @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.27/0.61 | ( knowle731562421_knows @ Q @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know2knowsPQ_k
% 0.27/0.61 thf(fact_65_knows2knowPQ__k,axiom,
% 0.27/0.61 ! [P: secrecy_specID,M: secrecy_Keys,Q: secrecy_specID] :
% 0.27/0.61 ( ( ( knowle731562421_knows @ P @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.27/0.61 | ( knowle731562421_knows @ Q @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) )
% 0.27/0.61 => ( ( knowle945212990e_know @ P @ ( secrecy_kKS @ M ) )
% 0.27/0.61 | ( knowle945212990e_know @ Q @ ( secrecy_kKS @ M ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows2knowPQ_k
% 0.27/0.61 thf(fact_66_know2knows__neg__k,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.61 => ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know2knows_neg_k
% 0.27/0.61 thf(fact_67_knows2know__neg__k,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ~ ( knowle731562421_knows @ A @ ( cons_S112077679ession @ ( secrecy_kE @ M ) @ nil_Se901661471ession ) )
% 0.27/0.61 => ~ ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % knows2know_neg_k
% 0.27/0.61 thf(fact_68_know_Osimps_I1_J,axiom,
% 0.27/0.61 ! [A: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ( knowle945212990e_know @ A @ ( secrecy_kKS @ M ) )
% 0.27/0.61 = ( ( ine @ A @ ( secrecy_kE @ M ) )
% 0.27/0.61 | ( member_Secrecy_KS2 @ ( secrecy_kKS @ M ) @ ( localSecrets @ A ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % know.simps(1)
% 0.27/0.61 thf(fact_69_insert__Nil,axiom,
% 0.27/0.61 ! [X3: secrecy_KS] :
% 0.27/0.61 ( ( insert_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 0.27/0.61 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.27/0.61
% 0.27/0.61 % insert_Nil
% 0.27/0.61 thf(fact_70_insert__Nil,axiom,
% 0.27/0.61 ! [X3: secrecy_Expression] :
% 0.27/0.61 ( ( insert1173886601ession @ X3 @ nil_Se901661471ession )
% 0.27/0.61 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.27/0.61
% 0.27/0.61 % insert_Nil
% 0.27/0.61 thf(fact_71_Expression_Oinject_I1_J,axiom,
% 0.27/0.61 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.27/0.61 ( ( ( secrecy_kE @ X1 )
% 0.27/0.61 = ( secrecy_kE @ Y1 ) )
% 0.27/0.61 = ( X1 = Y1 ) ) ).
% 0.27/0.61
% 0.27/0.61 % Expression.inject(1)
% 0.27/0.61 thf(fact_72_Expression_Odistinct_I1_J,axiom,
% 0.27/0.61 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.27/0.61 ( ( secrecy_kE @ X1 )
% 0.27/0.61 != ( secrecy_sE @ X2 ) ) ).
% 0.27/0.61
% 0.27/0.61 % Expression.distinct(1)
% 0.27/0.61 thf(fact_73_KS2Expression_Osimps_I1_J,axiom,
% 0.27/0.61 ! [M: secrecy_Keys] :
% 0.27/0.61 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.27/0.61 = ( secrecy_kE @ M ) ) ).
% 0.27/0.61
% 0.27/0.61 % KS2Expression.simps(1)
% 0.27/0.61 thf(fact_74_eoutKnowCorrect__L1k,axiom,
% 0.27/0.61 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 0.27/0.61 => ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.27/0.61 => ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.27/0.61 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % eoutKnowCorrect_L1k
% 0.27/0.61 thf(fact_75_eout__know__k,axiom,
% 0.27/0.61 ! [C: secrecy_specID,M: secrecy_Keys] :
% 0.27/0.61 ( ( knowle233900195orrect @ C @ ( secrecy_kKS @ M ) )
% 0.27/0.61 = ( ( eout @ C @ ( secrecy_kE @ M ) )
% 0.27/0.61 = ( ( member_Secrecy_Keys @ M @ ( specKeys @ C ) )
% 0.27/0.61 | ( knowle945212990e_know @ C @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % eout_know_k
% 0.27/0.61 thf(fact_76_eoutKnowsECorrect__L1,axiom,
% 0.27/0.61 ! [C: secrecy_specID,E: secrecy_Expression] :
% 0.27/0.61 ( ( knowle1268625169orrect @ C @ E )
% 0.27/0.61 => ( ( eout @ C @ E )
% 0.27/0.61 => ( ? [K3: secrecy_Keys] :
% 0.27/0.61 ( ( E
% 0.27/0.61 = ( secrecy_kE @ K3 ) )
% 0.27/0.61 & ( member_Secrecy_Keys @ K3 @ ( specKeys @ C ) ) )
% 0.27/0.61 | ? [S: secrecy_Secrets] :
% 0.27/0.61 ( ( E
% 0.27/0.61 = ( secrecy_sE @ S ) )
% 0.27/0.61 & ( member2138796287ecrets @ S @ ( specSecrets @ C ) ) )
% 0.27/0.61 | ( knowle731562421_knows @ C @ ( cons_S112077679ession @ E @ nil_Se901661471ession ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % eoutKnowsECorrect_L1
% 0.27/0.61 thf(fact_77_eoutKnowsECorrect__def,axiom,
% 0.27/0.61 ( knowle1268625169orrect
% 0.27/0.61 = ( ^ [C2: secrecy_specID,E2: secrecy_Expression] :
% 0.27/0.61 ( ( eout @ C2 @ E2 )
% 0.27/0.61 = ( ? [K4: secrecy_Keys] :
% 0.27/0.61 ( ( E2
% 0.27/0.61 = ( secrecy_kE @ K4 ) )
% 0.27/0.61 & ( member_Secrecy_Keys @ K4 @ ( specKeys @ C2 ) ) )
% 0.27/0.61 | ? [S2: secrecy_Secrets] :
% 0.27/0.61 ( ( E2
% 0.27/0.61 = ( secrecy_sE @ S2 ) )
% 0.27/0.61 & ( member2138796287ecrets @ S2 @ ( specSecrets @ C2 ) ) )
% 0.27/0.61 | ( knowle731562421_knows @ C2 @ ( cons_S112077679ession @ E2 @ nil_Se901661471ession ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % eoutKnowsECorrect_def
% 0.27/0.61 thf(fact_78_product__lists_Osimps_I1_J,axiom,
% 0.27/0.61 ( ( produc1450295286ession @ nil_li311616943ession )
% 0.27/0.61 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 0.27/0.61
% 0.27/0.61 % product_lists.simps(1)
% 0.27/0.61 thf(fact_79_product__lists_Osimps_I1_J,axiom,
% 0.27/0.61 ( ( produc713695622ecy_KS @ nil_list_Secrecy_KS )
% 0.27/0.61 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 0.27/0.61
% 0.27/0.61 % product_lists.simps(1)
% 0.27/0.61 thf(fact_80_subseqs_Osimps_I1_J,axiom,
% 0.27/0.61 ( ( subseq348280080ession @ nil_Se901661471ession )
% 0.27/0.61 = ( cons_l533358079ession @ nil_Se901661471ession @ nil_li311616943ession ) ) ).
% 0.27/0.61
% 0.27/0.61 % subseqs.simps(1)
% 0.27/0.61 thf(fact_81_subseqs_Osimps_I1_J,axiom,
% 0.27/0.61 ( ( subseqs_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.61 = ( cons_list_Secrecy_KS @ nil_Secrecy_KS @ nil_list_Secrecy_KS ) ) ).
% 0.27/0.61
% 0.27/0.61 % subseqs.simps(1)
% 0.27/0.61 thf(fact_82_Expression2KSL_Osimps_I1_J,axiom,
% 0.27/0.61 ( ( secrec1371625429on2KSL @ nil_Se901661471ession )
% 0.27/0.61 = nil_Secrecy_KS ) ).
% 0.27/0.61
% 0.27/0.61 % Expression2KSL.simps(1)
% 0.27/0.61 thf(fact_83_list__ex1__simps_I1_J,axiom,
% 0.27/0.61 ! [P: secrecy_Expression > $o] :
% 0.27/0.61 ~ ( list_e1486860828ession @ P @ nil_Se901661471ession ) ).
% 0.27/0.61
% 0.27/0.61 % list_ex1_simps(1)
% 0.27/0.61 thf(fact_84_list__ex1__simps_I1_J,axiom,
% 0.27/0.61 ! [P: secrecy_KS > $o] :
% 0.27/0.61 ~ ( list_ex1_Secrecy_KS @ P @ nil_Secrecy_KS ) ).
% 0.27/0.61
% 0.27/0.61 % list_ex1_simps(1)
% 0.27/0.61 thf(fact_85_map__tailrec__rev_Oelims,axiom,
% 0.27/0.61 ! [X3: secrecy_KS > secrecy_Expression,Xa: list_Secrecy_KS,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 0.27/0.61 ( ( ( map_ta623472337ession @ X3 @ Xa @ Xb )
% 0.27/0.61 = Y )
% 0.27/0.61 => ( ( ( Xa = nil_Secrecy_KS )
% 0.27/0.61 => ( Y != Xb ) )
% 0.27/0.61 => ~ ! [A3: secrecy_KS,As: list_Secrecy_KS] :
% 0.27/0.61 ( ( Xa
% 0.27/0.61 = ( cons_Secrecy_KS @ A3 @ As ) )
% 0.27/0.61 => ( Y
% 0.27/0.61 != ( map_ta623472337ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % map_tailrec_rev.elims
% 0.27/0.61 thf(fact_86_map__tailrec__rev_Oelims,axiom,
% 0.27/0.61 ! [X3: secrecy_Expression > secrecy_Expression,Xa: list_S529945141ession,Xb: list_S529945141ession,Y: list_S529945141ession] :
% 0.27/0.61 ( ( ( map_ta1624757057ession @ X3 @ Xa @ Xb )
% 0.27/0.61 = Y )
% 0.27/0.61 => ( ( ( Xa = nil_Se901661471ession )
% 0.27/0.61 => ( Y != Xb ) )
% 0.27/0.61 => ~ ! [A3: secrecy_Expression,As: list_S529945141ession] :
% 0.27/0.61 ( ( Xa
% 0.27/0.61 = ( cons_S112077679ession @ A3 @ As ) )
% 0.27/0.61 => ( Y
% 0.27/0.61 != ( map_ta1624757057ession @ X3 @ As @ ( cons_S112077679ession @ ( X3 @ A3 ) @ Xb ) ) ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % map_tailrec_rev.elims
% 0.27/0.61 thf(fact_87_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.27/0.61 ! [Less: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.61 ~ ( lexord948960489ecy_KS @ Less @ ( cons_Secrecy_KS @ X3 @ Xs ) @ nil_Secrecy_KS ) ).
% 0.27/0.61
% 0.27/0.61 % ord.lexordp_eq_simps(3)
% 0.27/0.61 thf(fact_88_ord_Olexordp__eq__simps_I3_J,axiom,
% 0.27/0.61 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.61 ~ ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ nil_Se901661471ession ) ).
% 0.27/0.61
% 0.27/0.61 % ord.lexordp_eq_simps(3)
% 0.27/0.61 thf(fact_89_bind__simps_I1_J,axiom,
% 0.27/0.61 ! [F2: secrecy_Expression > list_S529945141ession] :
% 0.27/0.61 ( ( bind_S815874003ession @ nil_Se901661471ession @ F2 )
% 0.27/0.61 = nil_Se901661471ession ) ).
% 0.27/0.61
% 0.27/0.61 % bind_simps(1)
% 0.27/0.61 thf(fact_90_bind__simps_I1_J,axiom,
% 0.27/0.61 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 0.27/0.61 ( ( bind_S1823644515ecy_KS @ nil_Se901661471ession @ F2 )
% 0.27/0.61 = nil_Secrecy_KS ) ).
% 0.27/0.61
% 0.27/0.61 % bind_simps(1)
% 0.27/0.61 thf(fact_91_bind__simps_I1_J,axiom,
% 0.27/0.61 ! [F2: secrecy_KS > list_S529945141ession] :
% 0.27/0.61 ( ( bind_S711229283ession @ nil_Secrecy_KS @ F2 )
% 0.27/0.61 = nil_Se901661471ession ) ).
% 0.27/0.61
% 0.27/0.61 % bind_simps(1)
% 0.27/0.61 thf(fact_92_bind__simps_I1_J,axiom,
% 0.27/0.61 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 0.27/0.61 ( ( bind_S645462771ecy_KS @ nil_Secrecy_KS @ F2 )
% 0.27/0.61 = nil_Secrecy_KS ) ).
% 0.27/0.61
% 0.27/0.61 % bind_simps(1)
% 0.27/0.61 thf(fact_93_listrelp_Oinducts,axiom,
% 0.27/0.61 ! [R: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 0.27/0.61 ( ( listre788412843ecy_KS @ R @ X1 @ X2 )
% 0.27/0.61 => ( ( P @ nil_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.61 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.61 ( ( R @ X @ Y4 )
% 0.27/0.61 => ( ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 )
% 0.27/0.61 => ( ( P @ Xs2 @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) )
% 0.27/0.61 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % listrelp.inducts
% 0.27/0.61 thf(fact_94_listrelp_Oinducts,axiom,
% 0.27/0.61 ! [R: secrecy_KS > secrecy_Expression > $o,X1: list_Secrecy_KS,X2: list_S529945141ession,P: list_Secrecy_KS > list_S529945141ession > $o] :
% 0.27/0.61 ( ( listre1601064475ession @ R @ X1 @ X2 )
% 0.27/0.61 => ( ( P @ nil_Secrecy_KS @ nil_Se901661471ession )
% 0.27/0.61 => ( ! [X: secrecy_KS,Y4: secrecy_Expression,Xs2: list_Secrecy_KS,Ys3: list_S529945141ession] :
% 0.27/0.61 ( ( R @ X @ Y4 )
% 0.27/0.61 => ( ( listre1601064475ession @ R @ Xs2 @ Ys3 )
% 0.27/0.61 => ( ( P @ Xs2 @ Ys3 )
% 0.27/0.61 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) )
% 0.27/0.61 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.27/0.61
% 0.27/0.61 % listrelp.inducts
% 0.27/0.61 thf(fact_95_listrelp_Oinducts,axiom,
% 0.27/0.61 ! [R: secrecy_Expression > secrecy_KS > $o,X1: list_S529945141ession,X2: list_Secrecy_KS,P: list_S529945141ession > list_Secrecy_KS > $o] :
% 0.27/0.61 ( ( listre565996059ecy_KS @ R @ X1 @ X2 )
% 0.27/0.61 => ( ( P @ nil_Se901661471ession @ nil_Secrecy_KS )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Y4: secrecy_KS,Xs2: list_S529945141ession,Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( ( R @ X @ Y4 )
% 0.27/0.62 => ( ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 )
% 0.27/0.62 => ( ( P @ Xs2 @ Ys3 )
% 0.27/0.62 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) )
% 0.27/0.62 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.inducts
% 0.27/0.62 thf(fact_96_listrelp_Oinducts,axiom,
% 0.27/0.62 ! [R: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 0.27/0.62 ( ( listre84909707ession @ R @ X1 @ X2 )
% 0.27/0.62 => ( ( P @ nil_Se901661471ession @ nil_Se901661471ession )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.27/0.62 ( ( R @ X @ Y4 )
% 0.27/0.62 => ( ( listre84909707ession @ R @ Xs2 @ Ys3 )
% 0.27/0.62 => ( ( P @ Xs2 @ Ys3 )
% 0.27/0.62 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) )
% 0.27/0.62 => ( P @ X1 @ X2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.inducts
% 0.27/0.62 thf(fact_97_listrelp_Osimps,axiom,
% 0.27/0.62 ( listre788412843ecy_KS
% 0.27/0.62 = ( ^ [R2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( A12 = nil_Secrecy_KS )
% 0.27/0.62 & ( A22 = nil_Secrecy_KS ) )
% 0.27/0.62 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.27/0.62 & ( R2 @ X4 @ Y3 )
% 0.27/0.62 & ( listre788412843ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.simps
% 0.27/0.62 thf(fact_98_listrelp_Osimps,axiom,
% 0.27/0.62 ( listre1601064475ession
% 0.27/0.62 = ( ^ [R2: secrecy_KS > secrecy_Expression > $o,A12: list_Secrecy_KS,A22: list_S529945141ession] :
% 0.27/0.62 ( ( ( A12 = nil_Secrecy_KS )
% 0.27/0.62 & ( A22 = nil_Se901661471ession ) )
% 0.27/0.62 | ? [X4: secrecy_KS,Y3: secrecy_Expression,Xs3: list_Secrecy_KS,Ys: list_S529945141ession] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.27/0.62 & ( R2 @ X4 @ Y3 )
% 0.27/0.62 & ( listre1601064475ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.simps
% 0.27/0.62 thf(fact_99_listrelp_Osimps,axiom,
% 0.27/0.62 ( listre565996059ecy_KS
% 0.27/0.62 = ( ^ [R2: secrecy_Expression > secrecy_KS > $o,A12: list_S529945141ession,A22: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( A12 = nil_Se901661471ession )
% 0.27/0.62 & ( A22 = nil_Secrecy_KS ) )
% 0.27/0.62 | ? [X4: secrecy_Expression,Y3: secrecy_KS,Xs3: list_S529945141ession,Ys: list_Secrecy_KS] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.27/0.62 & ( R2 @ X4 @ Y3 )
% 0.27/0.62 & ( listre565996059ecy_KS @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.simps
% 0.27/0.62 thf(fact_100_listrelp_Osimps,axiom,
% 0.27/0.62 ( listre84909707ession
% 0.27/0.62 = ( ^ [R2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 0.27/0.62 ( ( ( A12 = nil_Se901661471ession )
% 0.27/0.62 & ( A22 = nil_Se901661471ession ) )
% 0.27/0.62 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.27/0.62 & ( R2 @ X4 @ Y3 )
% 0.27/0.62 & ( listre84909707ession @ R2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.simps
% 0.27/0.62 thf(fact_101_ord_Olexordp__eq__simps_I4_J,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) )
% 0.27/0.62 = ( ( Less @ X3 @ Y )
% 0.27/0.62 | ( ~ ( Less @ Y @ X3 )
% 0.27/0.62 & ( lexord1123423577ession @ Less @ Xs @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq_simps(4)
% 0.27/0.62 thf(fact_102_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( lexord1123423577ession @ Less @ Xs @ nil_Se901661471ession )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq_simps(2)
% 0.27/0.62 thf(fact_103_ord_Olexordp__eq__simps_I2_J,axiom,
% 0.27/0.62 ! [Less: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( lexord948960489ecy_KS @ Less @ Xs @ nil_Secrecy_KS )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq_simps(2)
% 0.27/0.62 thf(fact_104_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq_simps(1)
% 0.27/0.62 thf(fact_105_ord_Olexordp__eq__simps_I1_J,axiom,
% 0.27/0.62 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq_simps(1)
% 0.27/0.62 thf(fact_106_ord_Olexordp__eq_OCons,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( Less @ X3 @ Y )
% 0.27/0.62 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.Cons
% 0.27/0.62 thf(fact_107_ord_Olexordp__eq_OCons__eq,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ~ ( Less @ X3 @ Y )
% 0.27/0.62 => ( ~ ( Less @ Y @ X3 )
% 0.27/0.62 => ( ( lexord1123423577ession @ Less @ Xs @ Ys2 )
% 0.27/0.62 => ( lexord1123423577ession @ Less @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.Cons_eq
% 0.27/0.62 thf(fact_108_ord_Olexordp__eq_ONil,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,Ys2: list_S529945141ession] : ( lexord1123423577ession @ Less @ nil_Se901661471ession @ Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.Nil
% 0.27/0.62 thf(fact_109_ord_Olexordp__eq_ONil,axiom,
% 0.27/0.62 ! [Less: secrecy_KS > secrecy_KS > $o,Ys2: list_Secrecy_KS] : ( lexord948960489ecy_KS @ Less @ nil_Secrecy_KS @ Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.Nil
% 0.27/0.62 thf(fact_110_listrelp_OCons,axiom,
% 0.27/0.62 ! [R: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( R @ X3 @ Y )
% 0.27/0.62 => ( ( listre84909707ession @ R @ Xs @ Ys2 )
% 0.27/0.62 => ( listre84909707ession @ R @ ( cons_S112077679ession @ X3 @ Xs ) @ ( cons_S112077679ession @ Y @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.Cons
% 0.27/0.62 thf(fact_111_listrelp_ONil,axiom,
% 0.27/0.62 ! [R: secrecy_Expression > secrecy_Expression > $o] : ( listre84909707ession @ R @ nil_Se901661471ession @ nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.Nil
% 0.27/0.62 thf(fact_112_listrelp_ONil,axiom,
% 0.27/0.62 ! [R: secrecy_Expression > secrecy_KS > $o] : ( listre565996059ecy_KS @ R @ nil_Se901661471ession @ nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.Nil
% 0.27/0.62 thf(fact_113_listrelp_ONil,axiom,
% 0.27/0.62 ! [R: secrecy_KS > secrecy_Expression > $o] : ( listre1601064475ession @ R @ nil_Secrecy_KS @ nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.Nil
% 0.27/0.62 thf(fact_114_listrelp_ONil,axiom,
% 0.27/0.62 ! [R: secrecy_KS > secrecy_KS > $o] : ( listre788412843ecy_KS @ R @ nil_Secrecy_KS @ nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.Nil
% 0.27/0.62 thf(fact_115_map__tailrec__rev_Osimps_I2_J,axiom,
% 0.27/0.62 ! [F2: secrecy_Expression > secrecy_Expression,A4: secrecy_Expression,As2: list_S529945141ession,Bs2: list_S529945141ession] :
% 0.27/0.62 ( ( map_ta1624757057ession @ F2 @ ( cons_S112077679ession @ A4 @ As2 ) @ Bs2 )
% 0.27/0.62 = ( map_ta1624757057ession @ F2 @ As2 @ ( cons_S112077679ession @ ( F2 @ A4 ) @ Bs2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % map_tailrec_rev.simps(2)
% 0.27/0.62 thf(fact_116_ord_Olexordp__eq_Ocases,axiom,
% 0.27/0.62 ! [Less: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 0.27/0.62 ( ( lexord948960489ecy_KS @ Less @ A1 @ A2 )
% 0.27/0.62 => ( ( A1 != nil_Secrecy_KS )
% 0.27/0.62 => ( ! [X: secrecy_KS] :
% 0.27/0.62 ( ? [Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( A1
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.27/0.62 => ! [Y4: secrecy_KS] :
% 0.27/0.62 ( ? [Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( A2
% 0.27/0.62 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.62 => ~ ( Less @ X @ Y4 ) ) )
% 0.27/0.62 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( A1
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.27/0.62 => ! [Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( ( A2
% 0.27/0.62 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.62 => ( ~ ( Less @ X @ Y4 )
% 0.27/0.62 => ( ~ ( Less @ Y4 @ X )
% 0.27/0.62 => ~ ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.cases
% 0.27/0.62 thf(fact_117_ord_Olexordp__eq_Ocases,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.27/0.62 ( ( lexord1123423577ession @ Less @ A1 @ A2 )
% 0.27/0.62 => ( ( A1 != nil_Se901661471ession )
% 0.27/0.62 => ( ! [X: secrecy_Expression] :
% 0.27/0.62 ( ? [Xs2: list_S529945141ession] :
% 0.27/0.62 ( A1
% 0.27/0.62 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.27/0.62 => ! [Y4: secrecy_Expression] :
% 0.27/0.62 ( ? [Ys3: list_S529945141ession] :
% 0.27/0.62 ( A2
% 0.27/0.62 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.62 => ~ ( Less @ X @ Y4 ) ) )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( A1
% 0.27/0.62 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.27/0.62 => ! [Ys3: list_S529945141ession] :
% 0.27/0.62 ( ( A2
% 0.27/0.62 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.62 => ( ~ ( Less @ X @ Y4 )
% 0.27/0.62 => ( ~ ( Less @ Y4 @ X )
% 0.27/0.62 => ~ ( lexord1123423577ession @ Less @ Xs2 @ Ys3 ) ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.cases
% 0.27/0.62 thf(fact_118_ord_Olexordp__eq_Osimps,axiom,
% 0.27/0.62 ( lexord948960489ecy_KS
% 0.27/0.62 = ( ^ [Less2: secrecy_KS > secrecy_KS > $o,A12: list_Secrecy_KS,A22: list_Secrecy_KS] :
% 0.27/0.62 ( ? [Ys: list_Secrecy_KS] :
% 0.27/0.62 ( ( A12 = nil_Secrecy_KS )
% 0.27/0.62 & ( A22 = Ys ) )
% 0.27/0.62 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.27/0.62 & ( Less2 @ X4 @ Y3 ) )
% 0.27/0.62 | ? [X4: secrecy_KS,Y3: secrecy_KS,Xs3: list_Secrecy_KS,Ys: list_Secrecy_KS] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_Secrecy_KS @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_Secrecy_KS @ Y3 @ Ys ) )
% 0.27/0.62 & ~ ( Less2 @ X4 @ Y3 )
% 0.27/0.62 & ~ ( Less2 @ Y3 @ X4 )
% 0.27/0.62 & ( lexord948960489ecy_KS @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.simps
% 0.27/0.62 thf(fact_119_ord_Olexordp__eq_Osimps,axiom,
% 0.27/0.62 ( lexord1123423577ession
% 0.27/0.62 = ( ^ [Less2: secrecy_Expression > secrecy_Expression > $o,A12: list_S529945141ession,A22: list_S529945141ession] :
% 0.27/0.62 ( ? [Ys: list_S529945141ession] :
% 0.27/0.62 ( ( A12 = nil_Se901661471ession )
% 0.27/0.62 & ( A22 = Ys ) )
% 0.27/0.62 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.27/0.62 & ( Less2 @ X4 @ Y3 ) )
% 0.27/0.62 | ? [X4: secrecy_Expression,Y3: secrecy_Expression,Xs3: list_S529945141ession,Ys: list_S529945141ession] :
% 0.27/0.62 ( ( A12
% 0.27/0.62 = ( cons_S112077679ession @ X4 @ Xs3 ) )
% 0.27/0.62 & ( A22
% 0.27/0.62 = ( cons_S112077679ession @ Y3 @ Ys ) )
% 0.27/0.62 & ~ ( Less2 @ X4 @ Y3 )
% 0.27/0.62 & ~ ( Less2 @ Y3 @ X4 )
% 0.27/0.62 & ( lexord1123423577ession @ Less2 @ Xs3 @ Ys ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.simps
% 0.27/0.62 thf(fact_120_ord_Olexordp__eq_Oinducts,axiom,
% 0.27/0.62 ! [Less: secrecy_KS > secrecy_KS > $o,X1: list_Secrecy_KS,X2: list_Secrecy_KS,P: list_Secrecy_KS > list_Secrecy_KS > $o] :
% 0.27/0.62 ( ( lexord948960489ecy_KS @ Less @ X1 @ X2 )
% 0.27/0.62 => ( ! [X_1: list_Secrecy_KS] : ( P @ nil_Secrecy_KS @ X_1 )
% 0.27/0.62 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( ( Less @ X @ Y4 )
% 0.27/0.62 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) )
% 0.27/0.62 => ( ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS,Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( ~ ( Less @ X @ Y4 )
% 0.27/0.62 => ( ~ ( Less @ Y4 @ X )
% 0.27/0.62 => ( ( lexord948960489ecy_KS @ Less @ Xs2 @ Ys3 )
% 0.27/0.62 => ( ( P @ Xs2 @ Ys3 )
% 0.27/0.62 => ( P @ ( cons_Secrecy_KS @ X @ Xs2 ) @ ( cons_Secrecy_KS @ Y4 @ Ys3 ) ) ) ) ) )
% 0.27/0.62 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.inducts
% 0.27/0.62 thf(fact_121_ord_Olexordp__eq_Oinducts,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,X1: list_S529945141ession,X2: list_S529945141ession,P: list_S529945141ession > list_S529945141ession > $o] :
% 0.27/0.62 ( ( lexord1123423577ession @ Less @ X1 @ X2 )
% 0.27/0.62 => ( ! [X_1: list_S529945141ession] : ( P @ nil_Se901661471ession @ X_1 )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.27/0.62 ( ( Less @ X @ Y4 )
% 0.27/0.62 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession,Ys3: list_S529945141ession] :
% 0.27/0.62 ( ~ ( Less @ X @ Y4 )
% 0.27/0.62 => ( ~ ( Less @ Y4 @ X )
% 0.27/0.62 => ( ( lexord1123423577ession @ Less @ Xs2 @ Ys3 )
% 0.27/0.62 => ( ( P @ Xs2 @ Ys3 )
% 0.27/0.62 => ( P @ ( cons_S112077679ession @ X @ Xs2 ) @ ( cons_S112077679ession @ Y4 @ Ys3 ) ) ) ) ) )
% 0.27/0.62 => ( P @ X1 @ X2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq.inducts
% 0.27/0.62 thf(fact_122_listrelp_Ocases,axiom,
% 0.27/0.62 ! [R: secrecy_KS > secrecy_KS > $o,A1: list_Secrecy_KS,A2: list_Secrecy_KS] :
% 0.27/0.62 ( ( listre788412843ecy_KS @ R @ A1 @ A2 )
% 0.27/0.62 => ( ( ( A1 = nil_Secrecy_KS )
% 0.27/0.62 => ( A2 != nil_Secrecy_KS ) )
% 0.27/0.62 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( A1
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.27/0.62 => ! [Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( ( A2
% 0.27/0.62 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.62 => ( ( R @ X @ Y4 )
% 0.27/0.62 => ~ ( listre788412843ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.cases
% 0.27/0.62 thf(fact_123_listrelp_Ocases,axiom,
% 0.27/0.62 ! [R: secrecy_KS > secrecy_Expression > $o,A1: list_Secrecy_KS,A2: list_S529945141ession] :
% 0.27/0.62 ( ( listre1601064475ession @ R @ A1 @ A2 )
% 0.27/0.62 => ( ( ( A1 = nil_Secrecy_KS )
% 0.27/0.62 => ( A2 != nil_Se901661471ession ) )
% 0.27/0.62 => ~ ! [X: secrecy_KS,Y4: secrecy_Expression,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( A1
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.27/0.62 => ! [Ys3: list_S529945141ession] :
% 0.27/0.62 ( ( A2
% 0.27/0.62 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.62 => ( ( R @ X @ Y4 )
% 0.27/0.62 => ~ ( listre1601064475ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.cases
% 0.27/0.62 thf(fact_124_listrelp_Ocases,axiom,
% 0.27/0.62 ! [R: secrecy_Expression > secrecy_KS > $o,A1: list_S529945141ession,A2: list_Secrecy_KS] :
% 0.27/0.62 ( ( listre565996059ecy_KS @ R @ A1 @ A2 )
% 0.27/0.62 => ( ( ( A1 = nil_Se901661471ession )
% 0.27/0.62 => ( A2 != nil_Secrecy_KS ) )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Y4: secrecy_KS,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( A1
% 0.27/0.62 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.27/0.62 => ! [Ys3: list_Secrecy_KS] :
% 0.27/0.62 ( ( A2
% 0.27/0.62 = ( cons_Secrecy_KS @ Y4 @ Ys3 ) )
% 0.27/0.62 => ( ( R @ X @ Y4 )
% 0.27/0.62 => ~ ( listre565996059ecy_KS @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.cases
% 0.27/0.62 thf(fact_125_listrelp_Ocases,axiom,
% 0.27/0.62 ! [R: secrecy_Expression > secrecy_Expression > $o,A1: list_S529945141ession,A2: list_S529945141ession] :
% 0.27/0.62 ( ( listre84909707ession @ R @ A1 @ A2 )
% 0.27/0.62 => ( ( ( A1 = nil_Se901661471ession )
% 0.27/0.62 => ( A2 != nil_Se901661471ession ) )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( A1
% 0.27/0.62 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.27/0.62 => ! [Ys3: list_S529945141ession] :
% 0.27/0.62 ( ( A2
% 0.27/0.62 = ( cons_S112077679ession @ Y4 @ Ys3 ) )
% 0.27/0.62 => ( ( R @ X @ Y4 )
% 0.27/0.62 => ~ ( listre84909707ession @ R @ Xs2 @ Ys3 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % listrelp.cases
% 0.27/0.62 thf(fact_126_notSpecKeysSecretsExpr__L1,axiom,
% 0.27/0.62 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 0.27/0.62 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 0.27/0.62 => ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % notSpecKeysSecretsExpr_L1
% 0.27/0.62 thf(fact_127_member__rec_I2_J,axiom,
% 0.27/0.62 ! [Y: secrecy_Expression] :
% 0.27/0.62 ~ ( member2020590922ession @ nil_Se901661471ession @ Y ) ).
% 0.27/0.62
% 0.27/0.62 % member_rec(2)
% 0.27/0.62 thf(fact_128_member__rec_I2_J,axiom,
% 0.27/0.62 ! [Y: secrecy_KS] :
% 0.27/0.62 ~ ( member_Secrecy_KS @ nil_Secrecy_KS @ Y ) ).
% 0.27/0.62
% 0.27/0.62 % member_rec(2)
% 0.27/0.62 thf(fact_129_member__rec_I1_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Y: secrecy_Expression] :
% 0.27/0.62 ( ( member2020590922ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Y )
% 0.27/0.62 = ( ( X3 = Y )
% 0.27/0.62 | ( member2020590922ession @ Xs @ Y ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % member_rec(1)
% 0.27/0.62 thf(fact_130_splice_Oelims,axiom,
% 0.27/0.62 ! [X3: list_Secrecy_KS,Xa: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( splice_Secrecy_KS @ X3 @ Xa )
% 0.27/0.62 = Y )
% 0.27/0.62 => ( ( ( X3 = nil_Secrecy_KS )
% 0.27/0.62 => ( Y != Xa ) )
% 0.27/0.62 => ~ ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( X3
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ Xs2 ) )
% 0.27/0.62 => ( Y
% 0.27/0.62 != ( cons_Secrecy_KS @ X @ ( splice_Secrecy_KS @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % splice.elims
% 0.27/0.62 thf(fact_131_splice_Oelims,axiom,
% 0.27/0.62 ! [X3: list_S529945141ession,Xa: list_S529945141ession,Y: list_S529945141ession] :
% 0.27/0.62 ( ( ( splice1390717708ession @ X3 @ Xa )
% 0.27/0.62 = Y )
% 0.27/0.62 => ( ( ( X3 = nil_Se901661471ession )
% 0.27/0.62 => ( Y != Xa ) )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( X3
% 0.27/0.62 = ( cons_S112077679ession @ X @ Xs2 ) )
% 0.27/0.62 => ( Y
% 0.27/0.62 != ( cons_S112077679ession @ X @ ( splice1390717708ession @ Xa @ Xs2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % splice.elims
% 0.27/0.62 thf(fact_132_bind__simps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession,F2: secrecy_Expression > list_S529945141ession] :
% 0.27/0.62 ( ( bind_S815874003ession @ ( cons_S112077679ession @ X3 @ Xs ) @ F2 )
% 0.27/0.62 = ( append2089414218ession @ ( F2 @ X3 ) @ ( bind_S815874003ession @ Xs @ F2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % bind_simps(2)
% 0.27/0.62 thf(fact_133_append_Oassoc,axiom,
% 0.27/0.62 ! [A4: list_S529945141ession,B: list_S529945141ession,C3: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ ( append2089414218ession @ A4 @ B ) @ C3 )
% 0.27/0.62 = ( append2089414218ession @ A4 @ ( append2089414218ession @ B @ C3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append.assoc
% 0.27/0.62 thf(fact_134_append__assoc,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ ( append2089414218ession @ Xs @ Ys2 ) @ Zs2 )
% 0.27/0.62 = ( append2089414218ession @ Xs @ ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_assoc
% 0.27/0.62 thf(fact_135_append__same__eq,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Ys2 @ Xs )
% 0.27/0.62 = ( append2089414218ession @ Zs2 @ Xs ) )
% 0.27/0.62 = ( Ys2 = Zs2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_same_eq
% 0.27/0.62 thf(fact_136_same__append__eq,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.27/0.62 = ( append2089414218ession @ Xs @ Zs2 ) )
% 0.27/0.62 = ( Ys2 = Zs2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % same_append_eq
% 0.27/0.62 thf(fact_137_append_Oright__neutral,axiom,
% 0.27/0.62 ! [A4: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ A4 @ nil_Se901661471ession )
% 0.27/0.62 = A4 ) ).
% 0.27/0.62
% 0.27/0.62 % append.right_neutral
% 0.27/0.62 thf(fact_138_append_Oright__neutral,axiom,
% 0.27/0.62 ! [A4: list_Secrecy_KS] :
% 0.27/0.62 ( ( append_Secrecy_KS @ A4 @ nil_Secrecy_KS )
% 0.27/0.62 = A4 ) ).
% 0.27/0.62
% 0.27/0.62 % append.right_neutral
% 0.27/0.62 thf(fact_139_append__is__Nil__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.27/0.62 = nil_Se901661471ession )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_is_Nil_conv
% 0.27/0.62 thf(fact_140_append__is__Nil__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.27/0.62 = nil_Secrecy_KS )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_is_Nil_conv
% 0.27/0.62 thf(fact_141_Nil__is__append__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( nil_Se901661471ession
% 0.27/0.62 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_is_append_conv
% 0.27/0.62 thf(fact_142_Nil__is__append__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( nil_Secrecy_KS
% 0.27/0.62 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_is_append_conv
% 0.27/0.62 thf(fact_143_self__append__conv2,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Ys2
% 0.27/0.62 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % self_append_conv2
% 0.27/0.62 thf(fact_144_self__append__conv2,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Ys2
% 0.27/0.62 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % self_append_conv2
% 0.27/0.62 thf(fact_145_append__self__conv2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_self_conv2
% 0.27/0.62 thf(fact_146_append__self__conv2,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_self_conv2
% 0.27/0.62 thf(fact_147_self__append__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( Ys2 = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % self_append_conv
% 0.27/0.62 thf(fact_148_self__append__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % self_append_conv
% 0.27/0.62 thf(fact_149_append__self__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.27/0.62 = Xs )
% 0.27/0.62 = ( Ys2 = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_self_conv
% 0.27/0.62 thf(fact_150_append__self__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( append_Secrecy_KS @ Xs @ Ys2 )
% 0.27/0.62 = Xs )
% 0.27/0.62 = ( Ys2 = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_self_conv
% 0.27/0.62 thf(fact_151_append__Nil2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ Xs @ nil_Se901661471ession )
% 0.27/0.62 = Xs ) ).
% 0.27/0.62
% 0.27/0.62 % append_Nil2
% 0.27/0.62 thf(fact_152_append__Nil2,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( append_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 0.27/0.62 = Xs ) ).
% 0.27/0.62
% 0.27/0.62 % append_Nil2
% 0.27/0.62 thf(fact_153_split__Nil__iff,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( splice1390717708ession @ Xs @ Ys2 )
% 0.27/0.62 = nil_Se901661471ession )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % split_Nil_iff
% 0.27/0.62 thf(fact_154_split__Nil__iff,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( splice_Secrecy_KS @ Xs @ Ys2 )
% 0.27/0.62 = nil_Secrecy_KS )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % split_Nil_iff
% 0.27/0.62 thf(fact_155_splice__Nil2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( splice1390717708ession @ Xs @ nil_Se901661471ession )
% 0.27/0.62 = Xs ) ).
% 0.27/0.62
% 0.27/0.62 % splice_Nil2
% 0.27/0.62 thf(fact_156_splice__Nil2,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( splice_Secrecy_KS @ Xs @ nil_Secrecy_KS )
% 0.27/0.62 = Xs ) ).
% 0.27/0.62
% 0.27/0.62 % splice_Nil2
% 0.27/0.62 thf(fact_157_append1__eq__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS,Y: secrecy_KS] :
% 0.27/0.62 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.27/0.62 = ( append_Secrecy_KS @ Ys2 @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) )
% 0.27/0.62 = ( ( Xs = Ys2 )
% 0.27/0.62 & ( X3 = Y ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append1_eq_conv
% 0.27/0.62 thf(fact_158_append1__eq__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession,Y: secrecy_Expression] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.27/0.62 = ( append2089414218ession @ Ys2 @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) )
% 0.27/0.62 = ( ( Xs = Ys2 )
% 0.27/0.62 & ( X3 = Y ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append1_eq_conv
% 0.27/0.62 thf(fact_159_append__eq__appendI,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Xs1: list_S529945141ession,Zs2: list_S529945141ession,Ys2: list_S529945141ession,Us: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ Xs1 )
% 0.27/0.62 = Zs2 )
% 0.27/0.62 => ( ( Ys2
% 0.27/0.62 = ( append2089414218ession @ Xs1 @ Us ) )
% 0.27/0.62 => ( ( append2089414218ession @ Xs @ Ys2 )
% 0.27/0.62 = ( append2089414218ession @ Zs2 @ Us ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_eq_appendI
% 0.27/0.62 thf(fact_160_append__eq__append__conv2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession,Ts: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ Ys2 )
% 0.27/0.62 = ( append2089414218ession @ Zs2 @ Ts ) )
% 0.27/0.62 = ( ? [Us2: list_S529945141ession] :
% 0.27/0.62 ( ( ( Xs
% 0.27/0.62 = ( append2089414218ession @ Zs2 @ Us2 ) )
% 0.27/0.62 & ( ( append2089414218ession @ Us2 @ Ys2 )
% 0.27/0.62 = Ts ) )
% 0.27/0.62 | ( ( ( append2089414218ession @ Xs @ Us2 )
% 0.27/0.62 = Zs2 )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append2089414218ession @ Us2 @ Ts ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_eq_append_conv2
% 0.27/0.62 thf(fact_161_append__Cons,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ ( append2089414218ession @ Xs @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_Cons
% 0.27/0.62 thf(fact_162_Cons__eq__appendI,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs1: list_S529945141ession,Ys2: list_S529945141ession,Xs: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( ( cons_S112077679ession @ X3 @ Xs1 )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 => ( ( Xs
% 0.27/0.62 = ( append2089414218ession @ Xs1 @ Zs2 ) )
% 0.27/0.62 => ( ( cons_S112077679ession @ X3 @ Xs )
% 0.27/0.62 = ( append2089414218ession @ Ys2 @ Zs2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_eq_appendI
% 0.27/0.62 thf(fact_163_append_Oleft__neutral,axiom,
% 0.27/0.62 ! [A4: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ nil_Se901661471ession @ A4 )
% 0.27/0.62 = A4 ) ).
% 0.27/0.62
% 0.27/0.62 % append.left_neutral
% 0.27/0.62 thf(fact_164_append_Oleft__neutral,axiom,
% 0.27/0.62 ! [A4: list_Secrecy_KS] :
% 0.27/0.62 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ A4 )
% 0.27/0.62 = A4 ) ).
% 0.27/0.62
% 0.27/0.62 % append.left_neutral
% 0.27/0.62 thf(fact_165_append__Nil,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( append2089414218ession @ nil_Se901661471ession @ Ys2 )
% 0.27/0.62 = Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % append_Nil
% 0.27/0.62 thf(fact_166_append__Nil,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 0.27/0.62 = Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % append_Nil
% 0.27/0.62 thf(fact_167_eq__Nil__appendI,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( Xs = Ys2 )
% 0.27/0.62 => ( Xs
% 0.27/0.62 = ( append2089414218ession @ nil_Se901661471ession @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_Nil_appendI
% 0.27/0.62 thf(fact_168_eq__Nil__appendI,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs = Ys2 )
% 0.27/0.62 => ( Xs
% 0.27/0.62 = ( append_Secrecy_KS @ nil_Secrecy_KS @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % eq_Nil_appendI
% 0.27/0.62 thf(fact_169_knows2b,axiom,
% 0.27/0.62 ! [A: secrecy_specID,E: list_S529945141ession,E1: list_S529945141ession] :
% 0.27/0.62 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E @ E1 ) )
% 0.27/0.62 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.27/0.62
% 0.27/0.62 % knows2b
% 0.27/0.62 thf(fact_170_knows2a,axiom,
% 0.27/0.62 ! [A: secrecy_specID,E1: list_S529945141ession,E: list_S529945141ession] :
% 0.27/0.62 ( ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E ) )
% 0.27/0.62 => ( knowle731562421_knows @ A @ E ) ) ).
% 0.27/0.62
% 0.27/0.62 % knows2a
% 0.27/0.62 thf(fact_171_knows3,axiom,
% 0.27/0.62 ! [A: secrecy_specID,E1: list_S529945141ession,E22: list_S529945141ession] :
% 0.27/0.62 ( ( ( knowle731562421_knows @ A @ E1 )
% 0.27/0.62 & ( knowle731562421_knows @ A @ E22 ) )
% 0.27/0.62 => ( knowle731562421_knows @ A @ ( append2089414218ession @ E1 @ E22 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % knows3
% 0.27/0.62 thf(fact_172_ord_Olexordp__eq__pref,axiom,
% 0.27/0.62 ! [Less: secrecy_Expression > secrecy_Expression > $o,U: list_S529945141ession,V: list_S529945141ession] : ( lexord1123423577ession @ Less @ U @ ( append2089414218ession @ U @ V ) ) ).
% 0.27/0.62
% 0.27/0.62 % ord.lexordp_eq_pref
% 0.27/0.62 thf(fact_173_notSpecKeysSecretsExpr__L2,axiom,
% 0.27/0.62 ! [P: secrecy_specID,A4: secrecy_Expression,L: list_S529945141ession] :
% 0.27/0.62 ( ( notSpe1586871396tsExpr @ P @ ( cons_S112077679ession @ A4 @ L ) )
% 0.27/0.62 => ( notSpe1586871396tsExpr @ P @ L ) ) ).
% 0.27/0.62
% 0.27/0.62 % notSpecKeysSecretsExpr_L2
% 0.27/0.62 thf(fact_174_splice_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( splice1390717708ession @ ( cons_S112077679ession @ X3 @ Xs ) @ Ys2 )
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ ( splice1390717708ession @ Ys2 @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % splice.simps(2)
% 0.27/0.62 thf(fact_175_splice_Osimps_I1_J,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( splice1390717708ession @ nil_Se901661471ession @ Ys2 )
% 0.27/0.62 = Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % splice.simps(1)
% 0.27/0.62 thf(fact_176_splice_Osimps_I1_J,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( splice_Secrecy_KS @ nil_Secrecy_KS @ Ys2 )
% 0.27/0.62 = Ys2 ) ).
% 0.27/0.62
% 0.27/0.62 % splice.simps(1)
% 0.27/0.62 thf(fact_177_rev__nonempty__induct,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,P: list_Secrecy_KS > $o] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ! [X: secrecy_KS] : ( P @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.62 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs2 != nil_Secrecy_KS )
% 0.27/0.62 => ( ( P @ Xs2 )
% 0.27/0.62 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) ) )
% 0.27/0.62 => ( P @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_nonempty_induct
% 0.27/0.62 thf(fact_178_rev__nonempty__induct,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,P: list_S529945141ession > $o] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ! [X: secrecy_Expression] : ( P @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( Xs2 != nil_Se901661471ession )
% 0.27/0.62 => ( ( P @ Xs2 )
% 0.27/0.62 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) ) )
% 0.27/0.62 => ( P @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_nonempty_induct
% 0.27/0.62 thf(fact_179_append__eq__Cons__conv,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( append_Secrecy_KS @ Ys2 @ Zs2 )
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 & ( Zs2
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ Xs ) ) )
% 0.27/0.62 | ? [Ys4: list_Secrecy_KS] :
% 0.27/0.62 ( ( Ys2
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ Ys4 ) )
% 0.27/0.62 & ( ( append_Secrecy_KS @ Ys4 @ Zs2 )
% 0.27/0.62 = Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_eq_Cons_conv
% 0.27/0.62 thf(fact_180_append__eq__Cons__conv,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Zs2: list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Ys2 @ Zs2 )
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 & ( Zs2
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ Xs ) ) )
% 0.27/0.62 | ? [Ys4: list_S529945141ession] :
% 0.27/0.62 ( ( Ys2
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ Ys4 ) )
% 0.27/0.62 & ( ( append2089414218ession @ Ys4 @ Zs2 )
% 0.27/0.62 = Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_eq_Cons_conv
% 0.27/0.62 thf(fact_181_Cons__eq__append__conv,axiom,
% 0.27/0.62 ! [X3: secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( cons_Secrecy_KS @ X3 @ Xs )
% 0.27/0.62 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 0.27/0.62 = ( ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 & ( ( cons_Secrecy_KS @ X3 @ Xs )
% 0.27/0.62 = Zs2 ) )
% 0.27/0.62 | ? [Ys4: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( cons_Secrecy_KS @ X3 @ Ys4 )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 & ( Xs
% 0.27/0.62 = ( append_Secrecy_KS @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_eq_append_conv
% 0.27/0.62 thf(fact_182_Cons__eq__append__conv,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( ( cons_S112077679ession @ X3 @ Xs )
% 0.27/0.62 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.27/0.62 = ( ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 & ( ( cons_S112077679ession @ X3 @ Xs )
% 0.27/0.62 = Zs2 ) )
% 0.27/0.62 | ? [Ys4: list_S529945141ession] :
% 0.27/0.62 ( ( ( cons_S112077679ession @ X3 @ Ys4 )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 & ( Xs
% 0.27/0.62 = ( append2089414218ession @ Ys4 @ Zs2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_eq_append_conv
% 0.27/0.62 thf(fact_183_rev__exhaust,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ~ ! [Ys3: list_Secrecy_KS,Y4: secrecy_KS] :
% 0.27/0.62 ( Xs
% 0.27/0.62 != ( append_Secrecy_KS @ Ys3 @ ( cons_Secrecy_KS @ Y4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_exhaust
% 0.27/0.62 thf(fact_184_rev__exhaust,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ~ ! [Ys3: list_S529945141ession,Y4: secrecy_Expression] :
% 0.27/0.62 ( Xs
% 0.27/0.62 != ( append2089414218ession @ Ys3 @ ( cons_S112077679ession @ Y4 @ nil_Se901661471ession ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_exhaust
% 0.27/0.62 thf(fact_185_rev__induct,axiom,
% 0.27/0.62 ! [P: list_Secrecy_KS > $o,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( P @ nil_Secrecy_KS )
% 0.27/0.62 => ( ! [X: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( P @ Xs2 )
% 0.27/0.62 => ( P @ ( append_Secrecy_KS @ Xs2 @ ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) ) )
% 0.27/0.62 => ( P @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_induct
% 0.27/0.62 thf(fact_186_rev__induct,axiom,
% 0.27/0.62 ! [P: list_S529945141ession > $o,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( P @ nil_Se901661471ession )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( P @ Xs2 )
% 0.27/0.62 => ( P @ ( append2089414218ession @ Xs2 @ ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) ) )
% 0.27/0.62 => ( P @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_induct
% 0.27/0.62 thf(fact_187_maps__simps_I1_J,axiom,
% 0.27/0.62 ! [F2: secrecy_Expression > list_S529945141ession,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( maps_S599402637ession @ F2 @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( append2089414218ession @ ( F2 @ X3 ) @ ( maps_S599402637ession @ F2 @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % maps_simps(1)
% 0.27/0.62 thf(fact_188_ExtSign,axiom,
% 0.27/0.62 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 0.27/0.62 ( ( encrDecrKeys @ K12 @ K22 )
% 0.27/0.62 => ( ( ext @ K12 @ ( sign @ K22 @ E3 ) )
% 0.27/0.62 = E3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % ExtSign
% 0.27/0.62 thf(fact_189_DecrEnc,axiom,
% 0.27/0.62 ! [K12: secrecy_Keys,K22: secrecy_Keys,E3: list_S529945141ession] :
% 0.27/0.62 ( ( encrDecrKeys @ K12 @ K22 )
% 0.27/0.62 => ( ( decr @ K22 @ ( enc @ K12 @ E3 ) )
% 0.27/0.62 = E3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % DecrEnc
% 0.27/0.62 thf(fact_190_concat__eq__append__conv,axiom,
% 0.27/0.62 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( ( concat388015140ession @ Xss2 )
% 0.27/0.62 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.27/0.62 = ( ( ( Xss2 = nil_li311616943ession )
% 0.27/0.62 => ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 & ( Zs2 = nil_Se901661471ession ) ) )
% 0.27/0.62 & ( ( Xss2 != nil_li311616943ession )
% 0.27/0.62 => ? [Xss1: list_l425507653ession,Xs3: list_S529945141ession,Xs4: list_S529945141ession,Xss22: list_l425507653ession] :
% 0.27/0.62 ( ( Xss2
% 0.27/0.62 = ( append1105297242ession @ Xss1 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append2089414218ession @ ( concat388015140ession @ Xss1 ) @ Xs3 ) )
% 0.27/0.62 & ( Zs2
% 0.27/0.62 = ( append2089414218ession @ Xs4 @ ( concat388015140ession @ Xss22 ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat_eq_append_conv
% 0.27/0.62 thf(fact_191_concat__eq__append__conv,axiom,
% 0.27/0.62 ! [Xss2: list_list_Secrecy_KS,Ys2: list_Secrecy_KS,Zs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( concat_Secrecy_KS @ Xss2 )
% 0.27/0.62 = ( append_Secrecy_KS @ Ys2 @ Zs2 ) )
% 0.27/0.62 = ( ( ( Xss2 = nil_list_Secrecy_KS )
% 0.27/0.62 => ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 & ( Zs2 = nil_Secrecy_KS ) ) )
% 0.27/0.62 & ( ( Xss2 != nil_list_Secrecy_KS )
% 0.27/0.62 => ? [Xss1: list_list_Secrecy_KS,Xs3: list_Secrecy_KS,Xs4: list_Secrecy_KS,Xss22: list_list_Secrecy_KS] :
% 0.27/0.62 ( ( Xss2
% 0.27/0.62 = ( append1376766698ecy_KS @ Xss1 @ ( cons_list_Secrecy_KS @ ( append_Secrecy_KS @ Xs3 @ Xs4 ) @ Xss22 ) ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append_Secrecy_KS @ ( concat_Secrecy_KS @ Xss1 ) @ Xs3 ) )
% 0.27/0.62 & ( Zs2
% 0.27/0.62 = ( append_Secrecy_KS @ Xs4 @ ( concat_Secrecy_KS @ Xss22 ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat_eq_append_conv
% 0.27/0.62 thf(fact_192_rotate1_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( rotate1_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1.simps(2)
% 0.27/0.62 thf(fact_193_rotate1_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( rotate1237234450ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1.simps(2)
% 0.27/0.62 thf(fact_194_rotate1__is__Nil__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( rotate1237234450ession @ Xs )
% 0.27/0.62 = nil_Se901661471ession )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1_is_Nil_conv
% 0.27/0.62 thf(fact_195_rotate1__is__Nil__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( rotate1_Secrecy_KS @ Xs )
% 0.27/0.62 = nil_Secrecy_KS )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1_is_Nil_conv
% 0.27/0.62 thf(fact_196_concat__append,axiom,
% 0.27/0.62 ! [Xs: list_l425507653ession,Ys2: list_l425507653ession] :
% 0.27/0.62 ( ( concat388015140ession @ ( append1105297242ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append2089414218ession @ ( concat388015140ession @ Xs ) @ ( concat388015140ession @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat_append
% 0.27/0.62 thf(fact_197_rotate1_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( rotate1237234450ession @ nil_Se901661471ession )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1.simps(1)
% 0.27/0.62 thf(fact_198_rotate1_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( rotate1_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1.simps(1)
% 0.27/0.62 thf(fact_199_concat_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( concat388015140ession @ nil_li311616943ession )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % concat.simps(1)
% 0.27/0.62 thf(fact_200_concat_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( concat_Secrecy_KS @ nil_list_Secrecy_KS )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % concat.simps(1)
% 0.27/0.62 thf(fact_201_concat_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: list_S529945141ession,Xs: list_l425507653ession] :
% 0.27/0.62 ( ( concat388015140ession @ ( cons_l533358079ession @ X3 @ Xs ) )
% 0.27/0.62 = ( append2089414218ession @ X3 @ ( concat388015140ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat.simps(2)
% 0.27/0.62 thf(fact_202_maps__simps_I2_J,axiom,
% 0.27/0.62 ! [F2: secrecy_Expression > list_S529945141ession] :
% 0.27/0.62 ( ( maps_S599402637ession @ F2 @ nil_Se901661471ession )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % maps_simps(2)
% 0.27/0.62 thf(fact_203_maps__simps_I2_J,axiom,
% 0.27/0.62 ! [F2: secrecy_Expression > list_Secrecy_KS] :
% 0.27/0.62 ( ( maps_S399472669ecy_KS @ F2 @ nil_Se901661471ession )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % maps_simps(2)
% 0.27/0.62 thf(fact_204_maps__simps_I2_J,axiom,
% 0.27/0.62 ! [F2: secrecy_KS > list_S529945141ession] :
% 0.27/0.62 ( ( maps_S1434541085ession @ F2 @ nil_Secrecy_KS )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % maps_simps(2)
% 0.27/0.62 thf(fact_205_maps__simps_I2_J,axiom,
% 0.27/0.62 ! [F2: secrecy_KS > list_Secrecy_KS] :
% 0.27/0.62 ( ( maps_S377605037ecy_KS @ F2 @ nil_Secrecy_KS )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % maps_simps(2)
% 0.27/0.62 thf(fact_206_concat__eq__appendD,axiom,
% 0.27/0.62 ! [Xss2: list_l425507653ession,Ys2: list_S529945141ession,Zs2: list_S529945141ession] :
% 0.27/0.62 ( ( ( concat388015140ession @ Xss2 )
% 0.27/0.62 = ( append2089414218ession @ Ys2 @ Zs2 ) )
% 0.27/0.62 => ( ( Xss2 != nil_li311616943ession )
% 0.27/0.62 => ? [Xss12: list_l425507653ession,Xs2: list_S529945141ession,Xs5: list_S529945141ession,Xss23: list_l425507653ession] :
% 0.27/0.62 ( ( Xss2
% 0.27/0.62 = ( append1105297242ession @ Xss12 @ ( cons_l533358079ession @ ( append2089414218ession @ Xs2 @ Xs5 ) @ Xss23 ) ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append2089414218ession @ ( concat388015140ession @ Xss12 ) @ Xs2 ) )
% 0.27/0.62 & ( Zs2
% 0.27/0.62 = ( append2089414218ession @ Xs5 @ ( concat388015140ession @ Xss23 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat_eq_appendD
% 0.27/0.62 thf(fact_207_butlast__snoc,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 0.27/0.62 = Xs ) ).
% 0.27/0.62
% 0.27/0.62 % butlast_snoc
% 0.27/0.62 thf(fact_208_butlast__snoc,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 0.27/0.62 = Xs ) ).
% 0.27/0.62
% 0.27/0.62 % butlast_snoc
% 0.27/0.62 thf(fact_209_last__snoc,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) )
% 0.27/0.62 = X3 ) ).
% 0.27/0.62
% 0.27/0.62 % last_snoc
% 0.27/0.62 thf(fact_210_last__snoc,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) )
% 0.27/0.62 = X3 ) ).
% 0.27/0.62
% 0.27/0.62 % last_snoc
% 0.27/0.62 thf(fact_211_notSpecKeysSecretsExpr__def,axiom,
% 0.27/0.62 ( notSpe1586871396tsExpr
% 0.27/0.62 = ( ^ [P3: secrecy_specID,E2: list_S529945141ession] :
% 0.27/0.62 ( ! [X4: secrecy_Keys] :
% 0.27/0.62 ( ( mem_Se1967555118ession @ ( secrecy_kE @ X4 ) @ E2 )
% 0.27/0.62 => ~ ( member_Secrecy_KS2 @ ( secrecy_kKS @ X4 ) @ ( specKeysSecrets @ P3 ) ) )
% 0.27/0.62 & ! [Y3: secrecy_Secrets] :
% 0.27/0.62 ( ( mem_Se1967555118ession @ ( secrecy_sE @ Y3 ) @ E2 )
% 0.27/0.62 => ~ ( member_Secrecy_KS2 @ ( secrecy_sKS @ Y3 ) @ ( specKeysSecrets @ P3 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % notSpecKeysSecretsExpr_def
% 0.27/0.62 thf(fact_212_last__appendR,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Ys2 != nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_S1532390982ession @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_appendR
% 0.27/0.62 thf(fact_213_last__appendR,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Ys2 != nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_appendR
% 0.27/0.62 thf(fact_214_last__appendL,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_appendL
% 0.27/0.62 thf(fact_215_last__appendL,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_appendL
% 0.27/0.62 thf(fact_216_append__butlast__last__id,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( append_Secrecy_KS @ ( butlast_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( last_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) )
% 0.27/0.62 = Xs ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_butlast_last_id
% 0.27/0.62 thf(fact_217_append__butlast__last__id,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( append2089414218ession @ ( butlas171474643ession @ Xs ) @ ( cons_S112077679ession @ ( last_S1532390982ession @ Xs ) @ nil_Se901661471ession ) )
% 0.27/0.62 = Xs ) ) ).
% 0.27/0.62
% 0.27/0.62 % append_butlast_last_id
% 0.27/0.62 thf(fact_218_butlast_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( butlas171474643ession @ nil_Se901661471ession )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % butlast.simps(1)
% 0.27/0.62 thf(fact_219_butlast_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( butlast_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % butlast.simps(1)
% 0.27/0.62 thf(fact_220_snoc__eq__iff__butlast,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( append_Secrecy_KS @ Xs @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 = ( ( Ys2 != nil_Secrecy_KS )
% 0.27/0.62 & ( ( butlast_Secrecy_KS @ Ys2 )
% 0.27/0.62 = Xs )
% 0.27/0.62 & ( ( last_Secrecy_KS @ Ys2 )
% 0.27/0.62 = X3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % snoc_eq_iff_butlast
% 0.27/0.62 thf(fact_221_snoc__eq__iff__butlast,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( append2089414218ession @ Xs @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.27/0.62 = Ys2 )
% 0.27/0.62 = ( ( Ys2 != nil_Se901661471ession )
% 0.27/0.62 & ( ( butlas171474643ession @ Ys2 )
% 0.27/0.62 = Xs )
% 0.27/0.62 & ( ( last_S1532390982ession @ Ys2 )
% 0.27/0.62 = X3 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % snoc_eq_iff_butlast
% 0.27/0.62 thf(fact_222_last__ConsR,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_ConsR
% 0.27/0.62 thf(fact_223_last__ConsR,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_ConsR
% 0.27/0.62 thf(fact_224_last__ConsL,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = X3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_ConsL
% 0.27/0.62 thf(fact_225_last__ConsL,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = X3 ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_ConsL
% 0.27/0.62 thf(fact_226_last_Osimps,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = X3 ) )
% 0.27/0.62 & ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last.simps
% 0.27/0.62 thf(fact_227_last_Osimps,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = X3 ) )
% 0.27/0.62 & ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( last_S1532390982ession @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last.simps
% 0.27/0.62 thf(fact_228_longest__common__suffix,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ? [Ss: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( append2089414218ession @ Xs5 @ Ss ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append2089414218ession @ Ys5 @ Ss ) )
% 0.27/0.62 & ( ( Xs5 = nil_Se901661471ession )
% 0.27/0.62 | ( Ys5 = nil_Se901661471ession )
% 0.27/0.62 | ( ( last_S1532390982ession @ Xs5 )
% 0.27/0.62 != ( last_S1532390982ession @ Ys5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % longest_common_suffix
% 0.27/0.62 thf(fact_229_longest__common__suffix,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ? [Ss: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( append_Secrecy_KS @ Xs5 @ Ss ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append_Secrecy_KS @ Ys5 @ Ss ) )
% 0.27/0.62 & ( ( Xs5 = nil_Secrecy_KS )
% 0.27/0.62 | ( Ys5 = nil_Secrecy_KS )
% 0.27/0.62 | ( ( last_Secrecy_KS @ Xs5 )
% 0.27/0.62 != ( last_Secrecy_KS @ Ys5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % longest_common_suffix
% 0.27/0.62 thf(fact_230_last__append,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_S1532390982ession @ Xs ) ) )
% 0.27/0.62 & ( ( Ys2 != nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_S1532390982ession @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_append
% 0.27/0.62 thf(fact_231_last__append,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Xs ) ) )
% 0.27/0.62 & ( ( Ys2 != nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_append
% 0.27/0.62 thf(fact_232_butlast_Osimps_I2_J,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = nil_Secrecy_KS ) )
% 0.27/0.62 & ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( butlast_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ ( butlast_Secrecy_KS @ Xs ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % butlast.simps(2)
% 0.27/0.62 thf(fact_233_butlast_Osimps_I2_J,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = nil_Se901661471ession ) )
% 0.27/0.62 & ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( butlas171474643ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ ( butlas171474643ession @ Xs ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % butlast.simps(2)
% 0.27/0.62 thf(fact_234_butlast__append,axiom,
% 0.27/0.62 ! [Ys2: list_S529945141ession,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( butlas171474643ession @ Xs ) ) )
% 0.27/0.62 & ( ( Ys2 != nil_Se901661471ession )
% 0.27/0.62 => ( ( butlas171474643ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append2089414218ession @ Xs @ ( butlas171474643ession @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % butlast_append
% 0.27/0.62 thf(fact_235_butlast__append,axiom,
% 0.27/0.62 ! [Ys2: list_Secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( butlast_Secrecy_KS @ Xs ) ) )
% 0.27/0.62 & ( ( Ys2 != nil_Secrecy_KS )
% 0.27/0.62 => ( ( butlast_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append_Secrecy_KS @ Xs @ ( butlast_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % butlast_append
% 0.27/0.62 thf(fact_236_mem_Osimps_I1_J,axiom,
% 0.27/0.62 ! [X3: secrecy_KS] :
% 0.27/0.62 ~ ( mem_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % mem.simps(1)
% 0.27/0.62 thf(fact_237_mem_Osimps_I1_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression] :
% 0.27/0.62 ~ ( mem_Se1967555118ession @ X3 @ nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % mem.simps(1)
% 0.27/0.62 thf(fact_238_mem_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Y: secrecy_Expression,L: list_S529945141ession] :
% 0.27/0.62 ( ( mem_Se1967555118ession @ X3 @ ( cons_S112077679ession @ Y @ L ) )
% 0.27/0.62 = ( ( X3 = Y )
% 0.27/0.62 | ( mem_Se1967555118ession @ X3 @ L ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % mem.simps(2)
% 0.27/0.62 thf(fact_239_concat__conv__foldr,axiom,
% 0.27/0.62 ( concat388015140ession
% 0.27/0.62 = ( ^ [Xss3: list_l425507653ession] : ( foldr_1531709715ession @ append2089414218ession @ Xss3 @ nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat_conv_foldr
% 0.27/0.62 thf(fact_240_concat__conv__foldr,axiom,
% 0.27/0.62 ( concat_Secrecy_KS
% 0.27/0.62 = ( ^ [Xss3: list_list_Secrecy_KS] : ( foldr_1711005747ecy_KS @ append_Secrecy_KS @ Xss3 @ nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % concat_conv_foldr
% 0.27/0.62 thf(fact_241_SuccI,axiom,
% 0.27/0.62 ! [Kl: list_Secrecy_Secrets,K: secrecy_Secrets,Kl2: set_li2007071804ecrets] :
% 0.27/0.62 ( ( member1138497285ecrets @ ( append186372209ecrets @ Kl @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl2 )
% 0.27/0.62 => ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ Kl ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccI
% 0.27/0.62 thf(fact_242_SuccI,axiom,
% 0.27/0.62 ! [Kl: list_Secrecy_Keys,K: secrecy_Keys,Kl2: set_li849033543y_Keys] :
% 0.27/0.62 ( ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl2 )
% 0.27/0.62 => ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ Kl ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccI
% 0.27/0.62 thf(fact_243_SuccI,axiom,
% 0.27/0.62 ! [Kl: list_Secrecy_KS,K: secrecy_KS,Kl2: set_list_Secrecy_KS] :
% 0.27/0.62 ( ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl2 )
% 0.27/0.62 => ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ Kl ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccI
% 0.27/0.62 thf(fact_244_SuccI,axiom,
% 0.27/0.62 ! [Kl: list_S529945141ession,K: secrecy_Expression,Kl2: set_li185139947ession] :
% 0.27/0.62 ( ( member249235532ession @ ( append2089414218ession @ Kl @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl2 )
% 0.27/0.62 => ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ Kl ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccI
% 0.27/0.62 thf(fact_245_SuccD,axiom,
% 0.27/0.62 ! [K: secrecy_Secrets,Kl2: set_li2007071804ecrets,Kl: list_Secrecy_Secrets] :
% 0.27/0.62 ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ Kl ) )
% 0.27/0.62 => ( member1138497285ecrets @ ( append186372209ecrets @ Kl @ ( cons_Secrecy_Secrets @ K @ nil_Secrecy_Secrets ) ) @ Kl2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccD
% 0.27/0.62 thf(fact_246_SuccD,axiom,
% 0.27/0.62 ! [K: secrecy_Keys,Kl2: set_li849033543y_Keys,Kl: list_Secrecy_Keys] :
% 0.27/0.62 ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ Kl ) )
% 0.27/0.62 => ( member341114536y_Keys @ ( append_Secrecy_Keys @ Kl @ ( cons_Secrecy_Keys @ K @ nil_Secrecy_Keys ) ) @ Kl2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccD
% 0.27/0.62 thf(fact_247_SuccD,axiom,
% 0.27/0.62 ! [K: secrecy_KS,Kl2: set_list_Secrecy_KS,Kl: list_Secrecy_KS] :
% 0.27/0.62 ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ Kl ) )
% 0.27/0.62 => ( member193705948ecy_KS @ ( append_Secrecy_KS @ Kl @ ( cons_Secrecy_KS @ K @ nil_Secrecy_KS ) ) @ Kl2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccD
% 0.27/0.62 thf(fact_248_SuccD,axiom,
% 0.27/0.62 ! [K: secrecy_Expression,Kl2: set_li185139947ession,Kl: list_S529945141ession] :
% 0.27/0.62 ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ Kl ) )
% 0.27/0.62 => ( member249235532ession @ ( append2089414218ession @ Kl @ ( cons_S112077679ession @ K @ nil_Se901661471ession ) ) @ Kl2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % SuccD
% 0.27/0.62 thf(fact_249_rev__eq__Cons__iff,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Y: secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( rev_Secrecy_KS @ Xs )
% 0.27/0.62 = ( cons_Secrecy_KS @ Y @ Ys2 ) )
% 0.27/0.62 = ( Xs
% 0.27/0.62 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Ys2 ) @ ( cons_Secrecy_KS @ Y @ nil_Secrecy_KS ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_eq_Cons_iff
% 0.27/0.62 thf(fact_250_rev__eq__Cons__iff,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Y: secrecy_Expression,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( rev_Se1073238207ession @ Xs )
% 0.27/0.62 = ( cons_S112077679ession @ Y @ Ys2 ) )
% 0.27/0.62 = ( Xs
% 0.27/0.62 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( cons_S112077679ession @ Y @ nil_Se901661471ession ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_eq_Cons_iff
% 0.27/0.62 thf(fact_251_Nil__is__rev__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( nil_Se901661471ession
% 0.27/0.62 = ( rev_Se1073238207ession @ Xs ) )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_is_rev_conv
% 0.27/0.62 thf(fact_252_Nil__is__rev__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( nil_Secrecy_KS
% 0.27/0.62 = ( rev_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_is_rev_conv
% 0.27/0.62 thf(fact_253_rev__is__Nil__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( rev_Se1073238207ession @ Xs )
% 0.27/0.62 = nil_Se901661471ession )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_is_Nil_conv
% 0.27/0.62 thf(fact_254_rev__is__Nil__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( rev_Secrecy_KS @ Xs )
% 0.27/0.62 = nil_Secrecy_KS )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_is_Nil_conv
% 0.27/0.62 thf(fact_255_rev__append,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( rev_Se1073238207ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append2089414218ession @ ( rev_Se1073238207ession @ Ys2 ) @ ( rev_Se1073238207ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_append
% 0.27/0.62 thf(fact_256_singleton__rev__conv,axiom,
% 0.27/0.62 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS )
% 0.27/0.62 = ( rev_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( Xs
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % singleton_rev_conv
% 0.27/0.62 thf(fact_257_singleton__rev__conv,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( cons_S112077679ession @ X3 @ nil_Se901661471ession )
% 0.27/0.62 = ( rev_Se1073238207ession @ Xs ) )
% 0.27/0.62 = ( Xs
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % singleton_rev_conv
% 0.27/0.62 thf(fact_258_rev__singleton__conv,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,X3: secrecy_KS] :
% 0.27/0.62 ( ( ( rev_Secrecy_KS @ Xs )
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.27/0.62 = ( Xs
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_singleton_conv
% 0.27/0.62 thf(fact_259_rev__singleton__conv,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,X3: secrecy_Expression] :
% 0.27/0.62 ( ( ( rev_Se1073238207ession @ Xs )
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.27/0.62 = ( Xs
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev_singleton_conv
% 0.27/0.62 thf(fact_260_rev_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( rev_Se1073238207ession @ nil_Se901661471ession )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % rev.simps(1)
% 0.27/0.62 thf(fact_261_rev_Osimps_I1_J,axiom,
% 0.27/0.62 ( ( rev_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % rev.simps(1)
% 0.27/0.62 thf(fact_262_rev_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( rev_Secrecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( append_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev.simps(2)
% 0.27/0.62 thf(fact_263_rev_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( rev_Se1073238207ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( append2089414218ession @ ( rev_Se1073238207ession @ Xs ) @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rev.simps(2)
% 0.27/0.62 thf(fact_264_empty__Shift,axiom,
% 0.27/0.62 ! [Kl2: set_li2007071804ecrets,K: secrecy_Secrets] :
% 0.27/0.62 ( ( member1138497285ecrets @ nil_Secrecy_Secrets @ Kl2 )
% 0.27/0.62 => ( ( member2138796287ecrets @ K @ ( bNF_Gr957048817ecrets @ Kl2 @ nil_Secrecy_Secrets ) )
% 0.27/0.62 => ( member1138497285ecrets @ nil_Secrecy_Secrets @ ( bNF_Gr28627573ecrets @ Kl2 @ K ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % empty_Shift
% 0.27/0.62 thf(fact_265_empty__Shift,axiom,
% 0.27/0.62 ! [Kl2: set_li849033543y_Keys,K: secrecy_Keys] :
% 0.27/0.62 ( ( member341114536y_Keys @ nil_Secrecy_Keys @ Kl2 )
% 0.27/0.62 => ( ( member_Secrecy_Keys @ K @ ( bNF_Gr344893606y_Keys @ Kl2 @ nil_Secrecy_Keys ) )
% 0.27/0.62 => ( member341114536y_Keys @ nil_Secrecy_Keys @ ( bNF_Gr414702370y_Keys @ Kl2 @ K ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % empty_Shift
% 0.27/0.62 thf(fact_266_empty__Shift,axiom,
% 0.27/0.62 ! [Kl2: set_li185139947ession,K: secrecy_Expression] :
% 0.27/0.62 ( ( member249235532ession @ nil_Se901661471ession @ Kl2 )
% 0.27/0.62 => ( ( member279582780ession @ K @ ( bNF_Gr979629770ession @ Kl2 @ nil_Se901661471ession ) )
% 0.27/0.62 => ( member249235532ession @ nil_Se901661471ession @ ( bNF_Gr275623750ession @ Kl2 @ K ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % empty_Shift
% 0.27/0.62 thf(fact_267_empty__Shift,axiom,
% 0.27/0.62 ! [Kl2: set_list_Secrecy_KS,K: secrecy_KS] :
% 0.27/0.62 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ Kl2 )
% 0.27/0.62 => ( ( member_Secrecy_KS2 @ K @ ( bNF_Gr577175642ecy_KS @ Kl2 @ nil_Secrecy_KS ) )
% 0.27/0.62 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( bNF_Gr660123862ecy_KS @ Kl2 @ K ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % empty_Shift
% 0.27/0.62 thf(fact_268_ShiftD,axiom,
% 0.27/0.62 ! [Kl: list_S529945141ession,Kl2: set_li185139947ession,K: secrecy_Expression] :
% 0.27/0.62 ( ( member249235532ession @ Kl @ ( bNF_Gr275623750ession @ Kl2 @ K ) )
% 0.27/0.62 => ( member249235532ession @ ( cons_S112077679ession @ K @ Kl ) @ Kl2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % ShiftD
% 0.27/0.62 thf(fact_269_Succ__Shift,axiom,
% 0.27/0.62 ! [Kl2: set_li185139947ession,K: secrecy_Expression,Kl: list_S529945141ession] :
% 0.27/0.62 ( ( bNF_Gr979629770ession @ ( bNF_Gr275623750ession @ Kl2 @ K ) @ Kl )
% 0.27/0.62 = ( bNF_Gr979629770ession @ Kl2 @ ( cons_S112077679ession @ K @ Kl ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Succ_Shift
% 0.27/0.62 thf(fact_270_last__rev,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( rev_Se1073238207ession @ Xs ) )
% 0.27/0.62 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_rev
% 0.27/0.62 thf(fact_271_last__rev,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_rev
% 0.27/0.62 thf(fact_272_hd__rev,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( hd_Sec357328890ession @ ( rev_Se1073238207ession @ Xs ) )
% 0.27/0.62 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_rev
% 0.27/0.62 thf(fact_273_hd__rev,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( hd_Secrecy_KS @ ( rev_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_rev
% 0.27/0.62 thf(fact_274_hd__append2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( hd_Sec357328890ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_append2
% 0.27/0.62 thf(fact_275_hd__append2,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( hd_Secrecy_KS @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_append2
% 0.27/0.62 thf(fact_276_hd__append,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( hd_Sec357328890ession @ Ys2 ) ) )
% 0.27/0.62 & ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( hd_Sec357328890ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( hd_Sec357328890ession @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_append
% 0.27/0.62 thf(fact_277_hd__append,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( hd_Secrecy_KS @ Ys2 ) ) )
% 0.27/0.62 & ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( hd_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( hd_Secrecy_KS @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_append
% 0.27/0.62 thf(fact_278_longest__common__prefix,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ? [Ps: list_S529945141ession,Xs5: list_S529945141ession,Ys5: list_S529945141ession] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( append2089414218ession @ Ps @ Xs5 ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append2089414218ession @ Ps @ Ys5 ) )
% 0.27/0.62 & ( ( Xs5 = nil_Se901661471ession )
% 0.27/0.62 | ( Ys5 = nil_Se901661471ession )
% 0.27/0.62 | ( ( hd_Sec357328890ession @ Xs5 )
% 0.27/0.62 != ( hd_Sec357328890ession @ Ys5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % longest_common_prefix
% 0.27/0.62 thf(fact_279_longest__common__prefix,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ? [Ps: list_Secrecy_KS,Xs5: list_Secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( append_Secrecy_KS @ Ps @ Xs5 ) )
% 0.27/0.62 & ( Ys2
% 0.27/0.62 = ( append_Secrecy_KS @ Ps @ Ys5 ) )
% 0.27/0.62 & ( ( Xs5 = nil_Secrecy_KS )
% 0.27/0.62 | ( Ys5 = nil_Secrecy_KS )
% 0.27/0.62 | ( ( hd_Secrecy_KS @ Xs5 )
% 0.27/0.62 != ( hd_Secrecy_KS @ Ys5 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % longest_common_prefix
% 0.27/0.62 thf(fact_280_hd__concat,axiom,
% 0.27/0.62 ! [Xs: list_l425507653ession] :
% 0.27/0.62 ( ( Xs != nil_li311616943ession )
% 0.27/0.62 => ( ( ( hd_lis1623417098ession @ Xs )
% 0.27/0.62 != nil_Se901661471ession )
% 0.27/0.62 => ( ( hd_Sec357328890ession @ ( concat388015140ession @ Xs ) )
% 0.27/0.62 = ( hd_Sec357328890ession @ ( hd_lis1623417098ession @ Xs ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_concat
% 0.27/0.62 thf(fact_281_hd__concat,axiom,
% 0.27/0.62 ! [Xs: list_list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_list_Secrecy_KS )
% 0.27/0.62 => ( ( ( hd_list_Secrecy_KS @ Xs )
% 0.27/0.62 != nil_Secrecy_KS )
% 0.27/0.62 => ( ( hd_Secrecy_KS @ ( concat_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( hd_Secrecy_KS @ ( hd_list_Secrecy_KS @ Xs ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_concat
% 0.27/0.62 thf(fact_282_list_Osel_I1_J,axiom,
% 0.27/0.62 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.27/0.62 ( ( hd_Sec357328890ession @ ( cons_S112077679ession @ X21 @ X222 ) )
% 0.27/0.62 = X21 ) ).
% 0.27/0.62
% 0.27/0.62 % list.sel(1)
% 0.27/0.62 thf(fact_283_rotate1__hd__tl,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( rotate1_Secrecy_KS @ Xs )
% 0.27/0.62 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ nil_Secrecy_KS ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1_hd_tl
% 0.27/0.62 thf(fact_284_rotate1__hd__tl,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( rotate1237234450ession @ Xs )
% 0.27/0.62 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ nil_Se901661471ession ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % rotate1_hd_tl
% 0.27/0.62 thf(fact_285_distinct__adj__append__iff,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( distin1076152135ession @ Xs )
% 0.27/0.62 & ( distin1076152135ession @ Ys2 )
% 0.27/0.62 & ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 | ( ( last_S1532390982ession @ Xs )
% 0.27/0.62 != ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_append_iff
% 0.27/0.62 thf(fact_286_distinct__adj__append__iff,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( distin1495927511ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( distin1495927511ecy_KS @ Xs )
% 0.27/0.62 & ( distin1495927511ecy_KS @ Ys2 )
% 0.27/0.62 & ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 | ( ( last_Secrecy_KS @ Xs )
% 0.27/0.62 != ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_append_iff
% 0.27/0.62 thf(fact_287_distinct__adj__Cons__Cons,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.27/0.62 = ( ( X3 != Y )
% 0.27/0.62 & ( distin1076152135ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_Cons_Cons
% 0.27/0.62 thf(fact_288_tl__append2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( tl_Sec1905266422ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append2089414218ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % tl_append2
% 0.27/0.62 thf(fact_289_tl__append2,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( tl_Secrecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % tl_append2
% 0.27/0.62 thf(fact_290_list_Ocollapse,axiom,
% 0.27/0.62 ! [List: list_Secrecy_KS] :
% 0.27/0.62 ( ( List != nil_Secrecy_KS )
% 0.27/0.62 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) )
% 0.27/0.62 = List ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.collapse
% 0.27/0.62 thf(fact_291_list_Ocollapse,axiom,
% 0.27/0.62 ! [List: list_S529945141ession] :
% 0.27/0.62 ( ( List != nil_Se901661471ession )
% 0.27/0.62 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) )
% 0.27/0.62 = List ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.collapse
% 0.27/0.62 thf(fact_292_hd__Cons__tl,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 => ( ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ Xs ) @ ( tl_Secrecy_KS @ Xs ) )
% 0.27/0.62 = Xs ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_Cons_tl
% 0.27/0.62 thf(fact_293_hd__Cons__tl,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 => ( ( cons_S112077679ession @ ( hd_Sec357328890ession @ Xs ) @ ( tl_Sec1905266422ession @ Xs ) )
% 0.27/0.62 = Xs ) ) ).
% 0.27/0.62
% 0.27/0.62 % hd_Cons_tl
% 0.27/0.62 thf(fact_294_list_Oexpand,axiom,
% 0.27/0.62 ! [List: list_S529945141ession,List2: list_S529945141ession] :
% 0.27/0.62 ( ( ( List = nil_Se901661471ession )
% 0.27/0.62 = ( List2 = nil_Se901661471ession ) )
% 0.27/0.62 => ( ( ( List != nil_Se901661471ession )
% 0.27/0.62 => ( ( List2 != nil_Se901661471ession )
% 0.27/0.62 => ( ( ( hd_Sec357328890ession @ List )
% 0.27/0.62 = ( hd_Sec357328890ession @ List2 ) )
% 0.27/0.62 & ( ( tl_Sec1905266422ession @ List )
% 0.27/0.62 = ( tl_Sec1905266422ession @ List2 ) ) ) ) )
% 0.27/0.62 => ( List = List2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.expand
% 0.27/0.62 thf(fact_295_list_Oexpand,axiom,
% 0.27/0.62 ! [List: list_Secrecy_KS,List2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( List = nil_Secrecy_KS )
% 0.27/0.62 = ( List2 = nil_Secrecy_KS ) )
% 0.27/0.62 => ( ( ( List != nil_Secrecy_KS )
% 0.27/0.62 => ( ( List2 != nil_Secrecy_KS )
% 0.27/0.62 => ( ( ( hd_Secrecy_KS @ List )
% 0.27/0.62 = ( hd_Secrecy_KS @ List2 ) )
% 0.27/0.62 & ( ( tl_Secrecy_KS @ List )
% 0.27/0.62 = ( tl_Secrecy_KS @ List2 ) ) ) ) )
% 0.27/0.62 => ( List = List2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.expand
% 0.27/0.62 thf(fact_296_distinct__adj__appendD1,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 => ( distin1076152135ession @ Xs ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_appendD1
% 0.27/0.62 thf(fact_297_distinct__adj__appendD2,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( distin1076152135ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 => ( distin1076152135ession @ Ys2 ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_appendD2
% 0.27/0.62 thf(fact_298_distinct__adj__Nil,axiom,
% 0.27/0.62 distin1076152135ession @ nil_Se901661471ession ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_Nil
% 0.27/0.62 thf(fact_299_distinct__adj__Nil,axiom,
% 0.27/0.62 distin1495927511ecy_KS @ nil_Secrecy_KS ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_Nil
% 0.27/0.62 thf(fact_300_distinct__adj__ConsD,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 => ( distin1076152135ession @ Xs ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_ConsD
% 0.27/0.62 thf(fact_301_list_Osel_I2_J,axiom,
% 0.27/0.62 ( ( tl_Sec1905266422ession @ nil_Se901661471ession )
% 0.27/0.62 = nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % list.sel(2)
% 0.27/0.62 thf(fact_302_list_Osel_I2_J,axiom,
% 0.27/0.62 ( ( tl_Secrecy_KS @ nil_Secrecy_KS )
% 0.27/0.62 = nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % list.sel(2)
% 0.27/0.62 thf(fact_303_list_Osel_I3_J,axiom,
% 0.27/0.62 ! [X21: secrecy_Expression,X222: list_S529945141ession] :
% 0.27/0.62 ( ( tl_Sec1905266422ession @ ( cons_S112077679ession @ X21 @ X222 ) )
% 0.27/0.62 = X222 ) ).
% 0.27/0.62
% 0.27/0.62 % list.sel(3)
% 0.27/0.62 thf(fact_304_tl__Nil,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( tl_Secrecy_KS @ Xs )
% 0.27/0.62 = nil_Secrecy_KS )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ? [X4: secrecy_KS] :
% 0.27/0.62 ( Xs
% 0.27/0.62 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % tl_Nil
% 0.27/0.62 thf(fact_305_tl__Nil,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( tl_Sec1905266422ession @ Xs )
% 0.27/0.62 = nil_Se901661471ession )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ? [X4: secrecy_Expression] :
% 0.27/0.62 ( Xs
% 0.27/0.62 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % tl_Nil
% 0.27/0.62 thf(fact_306_Nil__tl,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( nil_Secrecy_KS
% 0.27/0.62 = ( tl_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ? [X4: secrecy_KS] :
% 0.27/0.62 ( Xs
% 0.27/0.62 = ( cons_Secrecy_KS @ X4 @ nil_Secrecy_KS ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_tl
% 0.27/0.62 thf(fact_307_Nil__tl,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( nil_Se901661471ession
% 0.27/0.62 = ( tl_Sec1905266422ession @ Xs ) )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ? [X4: secrecy_Expression] :
% 0.27/0.62 ( Xs
% 0.27/0.62 = ( cons_S112077679ession @ X4 @ nil_Se901661471ession ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_tl
% 0.27/0.62 thf(fact_308_last__tl,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ( ( tl_Sec1905266422ession @ Xs )
% 0.27/0.62 != nil_Se901661471ession ) )
% 0.27/0.62 => ( ( last_S1532390982ession @ ( tl_Sec1905266422ession @ Xs ) )
% 0.27/0.62 = ( last_S1532390982ession @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_tl
% 0.27/0.62 thf(fact_309_last__tl,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ( ( tl_Secrecy_KS @ Xs )
% 0.27/0.62 != nil_Secrecy_KS ) )
% 0.27/0.62 => ( ( last_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) )
% 0.27/0.62 = ( last_Secrecy_KS @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % last_tl
% 0.27/0.62 thf(fact_310_distinct__adj__singleton,axiom,
% 0.27/0.62 ! [X3: secrecy_KS] : ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_singleton
% 0.27/0.62 thf(fact_311_distinct__adj__singleton,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression] : ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_singleton
% 0.27/0.62 thf(fact_312_list_Oexhaust__sel,axiom,
% 0.27/0.62 ! [List: list_Secrecy_KS] :
% 0.27/0.62 ( ( List != nil_Secrecy_KS )
% 0.27/0.62 => ( List
% 0.27/0.62 = ( cons_Secrecy_KS @ ( hd_Secrecy_KS @ List ) @ ( tl_Secrecy_KS @ List ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.exhaust_sel
% 0.27/0.62 thf(fact_313_list_Oexhaust__sel,axiom,
% 0.27/0.62 ! [List: list_S529945141ession] :
% 0.27/0.62 ( ( List != nil_Se901661471ession )
% 0.27/0.62 => ( List
% 0.27/0.62 = ( cons_S112077679ession @ ( hd_Sec357328890ession @ List ) @ ( tl_Sec1905266422ession @ List ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % list.exhaust_sel
% 0.27/0.62 thf(fact_314_distinct__adj__Cons,axiom,
% 0.27/0.62 ! [X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( distin1495927511ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ( ( X3
% 0.27/0.62 != ( hd_Secrecy_KS @ Xs ) )
% 0.27/0.62 & ( distin1495927511ecy_KS @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_Cons
% 0.27/0.62 thf(fact_315_distinct__adj__Cons,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( distin1076152135ession @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ( ( X3
% 0.27/0.62 != ( hd_Sec357328890ession @ Xs ) )
% 0.27/0.62 & ( distin1076152135ession @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % distinct_adj_Cons
% 0.27/0.62 thf(fact_316_successively__append__iff,axiom,
% 0.27/0.62 ! [P: secrecy_Expression > secrecy_Expression > $o,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( succes1388047762ession @ P @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( succes1388047762ession @ P @ Xs )
% 0.27/0.62 & ( succes1388047762ession @ P @ Ys2 )
% 0.27/0.62 & ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 | ( P @ ( last_S1532390982ession @ Xs ) @ ( hd_Sec357328890ession @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively_append_iff
% 0.27/0.62 thf(fact_317_successively__append__iff,axiom,
% 0.27/0.62 ! [P: secrecy_KS > secrecy_KS > $o,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( succes590251810ecy_KS @ P @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( succes590251810ecy_KS @ P @ Xs )
% 0.27/0.62 & ( succes590251810ecy_KS @ P @ Ys2 )
% 0.27/0.62 & ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 | ( P @ ( last_Secrecy_KS @ Xs ) @ ( hd_Secrecy_KS @ Ys2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively_append_iff
% 0.27/0.62 thf(fact_318_Cons__in__shuffles__iff,axiom,
% 0.27/0.62 ! [Z: secrecy_KS,Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( member193705948ecy_KS @ ( cons_Secrecy_KS @ Z @ Zs2 ) @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( ( Xs != nil_Secrecy_KS )
% 0.27/0.62 & ( ( hd_Secrecy_KS @ Xs )
% 0.27/0.62 = Z )
% 0.27/0.62 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ ( tl_Secrecy_KS @ Xs ) @ Ys2 ) ) )
% 0.27/0.62 | ( ( Ys2 != nil_Secrecy_KS )
% 0.27/0.62 & ( ( hd_Secrecy_KS @ Ys2 )
% 0.27/0.62 = Z )
% 0.27/0.62 & ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ ( tl_Secrecy_KS @ Ys2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_in_shuffles_iff
% 0.27/0.62 thf(fact_319_Cons__in__shuffles__iff,axiom,
% 0.27/0.62 ! [Z: secrecy_Expression,Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( ( Xs != nil_Se901661471ession )
% 0.27/0.62 & ( ( hd_Sec357328890ession @ Xs )
% 0.27/0.62 = Z )
% 0.27/0.62 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ ( tl_Sec1905266422ession @ Xs ) @ Ys2 ) ) )
% 0.27/0.62 | ( ( Ys2 != nil_Se901661471ession )
% 0.27/0.62 & ( ( hd_Sec357328890ession @ Ys2 )
% 0.27/0.62 = Z )
% 0.27/0.62 & ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ ( tl_Sec1905266422ession @ Ys2 ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_in_shuffles_iff
% 0.27/0.62 thf(fact_320_Nil__in__shuffles,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 & ( Ys2 = nil_Se901661471ession ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_in_shuffles
% 0.27/0.62 thf(fact_321_Nil__in__shuffles,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 & ( Ys2 = nil_Secrecy_KS ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_in_shuffles
% 0.27/0.62 thf(fact_322_shufflesE,axiom,
% 0.27/0.62 ! [Zs2: list_Secrecy_KS,Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( member193705948ecy_KS @ Zs2 @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 => ( ( ( Zs2 = Xs )
% 0.27/0.62 => ( Ys2 != nil_Secrecy_KS ) )
% 0.27/0.62 => ( ( ( Zs2 = Ys2 )
% 0.27/0.62 => ( Xs != nil_Secrecy_KS ) )
% 0.27/0.62 => ( ! [X: secrecy_KS,Xs5: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ Xs5 ) )
% 0.27/0.62 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 0.27/0.62 ( ( Zs2
% 0.27/0.62 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 0.27/0.62 => ( ( X = Z2 )
% 0.27/0.62 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs5 @ Ys2 ) ) ) ) )
% 0.27/0.62 => ~ ! [Y4: secrecy_KS,Ys5: list_Secrecy_KS] :
% 0.27/0.62 ( ( Ys2
% 0.27/0.62 = ( cons_Secrecy_KS @ Y4 @ Ys5 ) )
% 0.27/0.62 => ! [Z2: secrecy_KS,Zs3: list_Secrecy_KS] :
% 0.27/0.62 ( ( Zs2
% 0.27/0.62 = ( cons_Secrecy_KS @ Z2 @ Zs3 ) )
% 0.27/0.62 => ( ( Y4 = Z2 )
% 0.27/0.62 => ~ ( member193705948ecy_KS @ Zs3 @ ( shuffles_Secrecy_KS @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % shufflesE
% 0.27/0.62 thf(fact_323_shufflesE,axiom,
% 0.27/0.62 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.27/0.62 => ( ( ( Zs2 = Xs )
% 0.27/0.62 => ( Ys2 != nil_Se901661471ession ) )
% 0.27/0.62 => ( ( ( Zs2 = Ys2 )
% 0.27/0.62 => ( Xs != nil_Se901661471ession ) )
% 0.27/0.62 => ( ! [X: secrecy_Expression,Xs5: list_S529945141ession] :
% 0.27/0.62 ( ( Xs
% 0.27/0.62 = ( cons_S112077679ession @ X @ Xs5 ) )
% 0.27/0.62 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 0.27/0.62 ( ( Zs2
% 0.27/0.62 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 0.27/0.62 => ( ( X = Z2 )
% 0.27/0.62 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs5 @ Ys2 ) ) ) ) )
% 0.27/0.62 => ~ ! [Y4: secrecy_Expression,Ys5: list_S529945141ession] :
% 0.27/0.62 ( ( Ys2
% 0.27/0.62 = ( cons_S112077679ession @ Y4 @ Ys5 ) )
% 0.27/0.62 => ! [Z2: secrecy_Expression,Zs3: list_S529945141ession] :
% 0.27/0.62 ( ( Zs2
% 0.27/0.62 = ( cons_S112077679ession @ Z2 @ Zs3 ) )
% 0.27/0.62 => ( ( Y4 = Z2 )
% 0.27/0.62 => ~ ( member249235532ession @ Zs3 @ ( shuffl552897610ession @ Xs @ Ys5 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % shufflesE
% 0.27/0.62 thf(fact_324_successively_Osimps_I2_J,axiom,
% 0.27/0.62 ! [P: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS] : ( succes590251810ecy_KS @ P @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.simps(2)
% 0.27/0.62 thf(fact_325_successively_Osimps_I2_J,axiom,
% 0.27/0.62 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression] : ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.simps(2)
% 0.27/0.62 thf(fact_326_successively_Oelims_I1_J,axiom,
% 0.27/0.62 ! [X3: secrecy_KS > secrecy_KS > $o,Xa: list_Secrecy_KS,Y: $o] :
% 0.27/0.62 ( ( ( succes590251810ecy_KS @ X3 @ Xa )
% 0.27/0.62 = Y )
% 0.27/0.62 => ( ( ( Xa = nil_Secrecy_KS )
% 0.27/0.62 => ~ Y )
% 0.27/0.62 => ( ( ? [X: secrecy_KS] :
% 0.27/0.62 ( Xa
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.62 => ~ Y )
% 0.27/0.62 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.27/0.62 => ( Y
% 0.27/0.62 = ( ~ ( ( X3 @ X @ Y4 )
% 0.27/0.62 & ( succes590251810ecy_KS @ X3 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.elims(1)
% 0.27/0.62 thf(fact_327_successively_Oelims_I1_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession,Y: $o] :
% 0.27/0.62 ( ( ( succes1388047762ession @ X3 @ Xa )
% 0.27/0.62 = Y )
% 0.27/0.62 => ( ( ( Xa = nil_Se901661471ession )
% 0.27/0.62 => ~ Y )
% 0.27/0.62 => ( ( ? [X: secrecy_Expression] :
% 0.27/0.62 ( Xa
% 0.27/0.62 = ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.62 => ~ Y )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.27/0.62 => ( Y
% 0.27/0.62 = ( ~ ( ( X3 @ X @ Y4 )
% 0.27/0.62 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.elims(1)
% 0.27/0.62 thf(fact_328_successively_Oelims_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_KS > secrecy_KS > $o,Xa: list_Secrecy_KS] :
% 0.27/0.62 ( ( succes590251810ecy_KS @ X3 @ Xa )
% 0.27/0.62 => ( ( Xa != nil_Secrecy_KS )
% 0.27/0.62 => ( ! [X: secrecy_KS] :
% 0.27/0.62 ( Xa
% 0.27/0.62 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.62 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.27/0.62 => ~ ( ( X3 @ X @ Y4 )
% 0.27/0.62 & ( succes590251810ecy_KS @ X3 @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.elims(2)
% 0.27/0.62 thf(fact_329_successively_Oelims_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession] :
% 0.27/0.62 ( ( succes1388047762ession @ X3 @ Xa )
% 0.27/0.62 => ( ( Xa != nil_Se901661471ession )
% 0.27/0.62 => ( ! [X: secrecy_Expression] :
% 0.27/0.62 ( Xa
% 0.27/0.62 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.27/0.62 => ~ ( ( X3 @ X @ Y4 )
% 0.27/0.62 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.elims(2)
% 0.27/0.62 thf(fact_330_successively_Osimps_I1_J,axiom,
% 0.27/0.62 ! [P: secrecy_Expression > secrecy_Expression > $o] : ( succes1388047762ession @ P @ nil_Se901661471ession ) ).
% 0.27/0.62
% 0.27/0.62 % successively.simps(1)
% 0.27/0.62 thf(fact_331_successively_Osimps_I1_J,axiom,
% 0.27/0.62 ! [P: secrecy_KS > secrecy_KS > $o] : ( succes590251810ecy_KS @ P @ nil_Secrecy_KS ) ).
% 0.27/0.62
% 0.27/0.62 % successively.simps(1)
% 0.27/0.62 thf(fact_332_successively_Osimps_I3_J,axiom,
% 0.27/0.62 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.27/0.62 = ( ( P @ X3 @ Y )
% 0.27/0.62 & ( succes1388047762ession @ P @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.simps(3)
% 0.27/0.62 thf(fact_333_successively_Oelims_I3_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression > secrecy_Expression > $o,Xa: list_S529945141ession] :
% 0.27/0.62 ( ~ ( succes1388047762ession @ X3 @ Xa )
% 0.27/0.62 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.62 ( ( Xa
% 0.27/0.62 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.27/0.62 => ( ( X3 @ X @ Y4 )
% 0.27/0.62 & ( succes1388047762ession @ X3 @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively.elims(3)
% 0.27/0.62 thf(fact_334_Nil__in__shufflesI,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 => ( ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 => ( member249235532ession @ nil_Se901661471ession @ ( shuffl552897610ession @ Xs @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_in_shufflesI
% 0.27/0.62 thf(fact_335_Nil__in__shufflesI,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 => ( ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 => ( member193705948ecy_KS @ nil_Secrecy_KS @ ( shuffles_Secrecy_KS @ Xs @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Nil_in_shufflesI
% 0.27/0.62 thf(fact_336_Cons__in__shuffles__rightI,axiom,
% 0.27/0.62 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession,Z: secrecy_Expression] :
% 0.27/0.62 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.27/0.62 => ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ Xs @ ( cons_S112077679ession @ Z @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_in_shuffles_rightI
% 0.27/0.62 thf(fact_337_Cons__in__shuffles__leftI,axiom,
% 0.27/0.62 ! [Zs2: list_S529945141ession,Xs: list_S529945141ession,Ys2: list_S529945141ession,Z: secrecy_Expression] :
% 0.27/0.62 ( ( member249235532ession @ Zs2 @ ( shuffl552897610ession @ Xs @ Ys2 ) )
% 0.27/0.62 => ( member249235532ession @ ( cons_S112077679ession @ Z @ Zs2 ) @ ( shuffl552897610ession @ ( cons_S112077679ession @ Z @ Xs ) @ Ys2 ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % Cons_in_shuffles_leftI
% 0.27/0.62 thf(fact_338_successively__Cons,axiom,
% 0.27/0.62 ! [P: secrecy_KS > secrecy_KS > $o,X3: secrecy_KS,Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( succes590251810ecy_KS @ P @ ( cons_Secrecy_KS @ X3 @ Xs ) )
% 0.27/0.62 = ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ( ( P @ X3 @ ( hd_Secrecy_KS @ Xs ) )
% 0.27/0.62 & ( succes590251810ecy_KS @ P @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively_Cons
% 0.27/0.62 thf(fact_339_successively__Cons,axiom,
% 0.27/0.62 ! [P: secrecy_Expression > secrecy_Expression > $o,X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( succes1388047762ession @ P @ ( cons_S112077679ession @ X3 @ Xs ) )
% 0.27/0.62 = ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ( ( P @ X3 @ ( hd_Sec357328890ession @ Xs ) )
% 0.27/0.62 & ( succes1388047762ession @ P @ Xs ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % successively_Cons
% 0.27/0.62 thf(fact_340_remdups__adj__append_H,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession,Ys2: list_S529945141ession] :
% 0.27/0.62 ( ( ( Xs = nil_Se901661471ession )
% 0.27/0.62 | ( Ys2 = nil_Se901661471ession )
% 0.27/0.62 | ( ( last_S1532390982ession @ Xs )
% 0.27/0.62 != ( hd_Sec357328890ession @ Ys2 ) ) )
% 0.27/0.62 => ( ( remdup484344169ession @ ( append2089414218ession @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append2089414218ession @ ( remdup484344169ession @ Xs ) @ ( remdup484344169ession @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_append'
% 0.27/0.62 thf(fact_341_remdups__adj__append_H,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS,Ys2: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( Xs = nil_Secrecy_KS )
% 0.27/0.62 | ( Ys2 = nil_Secrecy_KS )
% 0.27/0.62 | ( ( last_Secrecy_KS @ Xs )
% 0.27/0.62 != ( hd_Secrecy_KS @ Ys2 ) ) )
% 0.27/0.62 => ( ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs @ Ys2 ) )
% 0.27/0.62 = ( append_Secrecy_KS @ ( remdup351570169ecy_KS @ Xs ) @ ( remdup351570169ecy_KS @ Ys2 ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_append'
% 0.27/0.62 thf(fact_342_remdups__adj__append,axiom,
% 0.27/0.62 ! [Xs_1: list_Secrecy_KS,X3: secrecy_KS,Xs_2: list_Secrecy_KS] :
% 0.27/0.62 ( ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs_1 @ ( cons_Secrecy_KS @ X3 @ Xs_2 ) ) )
% 0.27/0.62 = ( append_Secrecy_KS @ ( remdup351570169ecy_KS @ ( append_Secrecy_KS @ Xs_1 @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ) @ ( tl_Secrecy_KS @ ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X3 @ Xs_2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_append
% 0.27/0.62 thf(fact_343_remdups__adj__append,axiom,
% 0.27/0.62 ! [Xs_1: list_S529945141ession,X3: secrecy_Expression,Xs_2: list_S529945141ession] :
% 0.27/0.62 ( ( remdup484344169ession @ ( append2089414218ession @ Xs_1 @ ( cons_S112077679ession @ X3 @ Xs_2 ) ) )
% 0.27/0.62 = ( append2089414218ession @ ( remdup484344169ession @ ( append2089414218ession @ Xs_1 @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ) @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs_2 ) ) ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_append
% 0.27/0.62 thf(fact_344_remdups__adj__Nil__iff,axiom,
% 0.27/0.62 ! [Xs: list_S529945141ession] :
% 0.27/0.62 ( ( ( remdup484344169ession @ Xs )
% 0.27/0.62 = nil_Se901661471ession )
% 0.27/0.62 = ( Xs = nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_Nil_iff
% 0.27/0.62 thf(fact_345_remdups__adj__Nil__iff,axiom,
% 0.27/0.62 ! [Xs: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( remdup351570169ecy_KS @ Xs )
% 0.27/0.62 = nil_Secrecy_KS )
% 0.27/0.62 = ( Xs = nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_Nil_iff
% 0.27/0.62 thf(fact_346_remdups__adj__Cons__alt,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.62 ( ( cons_S112077679ession @ X3 @ ( tl_Sec1905266422ession @ ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) )
% 0.27/0.62 = ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj_Cons_alt
% 0.27/0.62 thf(fact_347_remdups__adj_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_KS] :
% 0.27/0.62 ( ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) )
% 0.27/0.62 = ( cons_Secrecy_KS @ X3 @ nil_Secrecy_KS ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj.simps(2)
% 0.27/0.62 thf(fact_348_remdups__adj_Osimps_I2_J,axiom,
% 0.27/0.62 ! [X3: secrecy_Expression] :
% 0.27/0.62 ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) )
% 0.27/0.62 = ( cons_S112077679ession @ X3 @ nil_Se901661471ession ) ) ).
% 0.27/0.62
% 0.27/0.62 % remdups_adj.simps(2)
% 0.27/0.62 thf(fact_349_remdups__adj_Oelims,axiom,
% 0.27/0.62 ! [X3: list_Secrecy_KS,Y: list_Secrecy_KS] :
% 0.27/0.62 ( ( ( remdup351570169ecy_KS @ X3 )
% 0.27/0.62 = Y )
% 0.27/0.62 => ( ( ( X3 = nil_Secrecy_KS )
% 0.27/0.62 => ( Y != nil_Secrecy_KS ) )
% 0.27/0.62 => ( ! [X: secrecy_KS] :
% 0.27/0.62 ( ( X3
% 0.27/0.62 = ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) )
% 0.27/0.62 => ( Y
% 0.27/0.62 != ( cons_Secrecy_KS @ X @ nil_Secrecy_KS ) ) )
% 0.27/0.72 => ~ ! [X: secrecy_KS,Y4: secrecy_KS,Xs2: list_Secrecy_KS] :
% 0.27/0.72 ( ( X3
% 0.27/0.72 = ( cons_Secrecy_KS @ X @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) )
% 0.27/0.72 => ~ ( ( ( X = Y4 )
% 0.27/0.72 => ( Y
% 0.27/0.72 = ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ X @ Xs2 ) ) ) )
% 0.27/0.72 & ( ( X != Y4 )
% 0.27/0.72 => ( Y
% 0.27/0.72 = ( cons_Secrecy_KS @ X @ ( remdup351570169ecy_KS @ ( cons_Secrecy_KS @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.72
% 0.27/0.72 % remdups_adj.elims
% 0.27/0.72 thf(fact_350_remdups__adj_Oelims,axiom,
% 0.27/0.72 ! [X3: list_S529945141ession,Y: list_S529945141ession] :
% 0.27/0.72 ( ( ( remdup484344169ession @ X3 )
% 0.27/0.72 = Y )
% 0.27/0.72 => ( ( ( X3 = nil_Se901661471ession )
% 0.27/0.72 => ( Y != nil_Se901661471ession ) )
% 0.27/0.72 => ( ! [X: secrecy_Expression] :
% 0.27/0.72 ( ( X3
% 0.27/0.72 = ( cons_S112077679ession @ X @ nil_Se901661471ession ) )
% 0.27/0.72 => ( Y
% 0.27/0.72 != ( cons_S112077679ession @ X @ nil_Se901661471ession ) ) )
% 0.27/0.72 => ~ ! [X: secrecy_Expression,Y4: secrecy_Expression,Xs2: list_S529945141ession] :
% 0.27/0.72 ( ( X3
% 0.27/0.72 = ( cons_S112077679ession @ X @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) )
% 0.27/0.72 => ~ ( ( ( X = Y4 )
% 0.27/0.72 => ( Y
% 0.27/0.72 = ( remdup484344169ession @ ( cons_S112077679ession @ X @ Xs2 ) ) ) )
% 0.27/0.72 & ( ( X != Y4 )
% 0.27/0.72 => ( Y
% 0.27/0.72 = ( cons_S112077679ession @ X @ ( remdup484344169ession @ ( cons_S112077679ession @ Y4 @ Xs2 ) ) ) ) ) ) ) ) ) ) ).
% 0.27/0.72
% 0.27/0.72 % remdups_adj.elims
% 0.27/0.72 thf(fact_351_remdups__adj_Osimps_I3_J,axiom,
% 0.27/0.72 ! [X3: secrecy_Expression,Y: secrecy_Expression,Xs: list_S529945141ession] :
% 0.27/0.72 ( ( ( X3 = Y )
% 0.27/0.72 => ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.27/0.72 = ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ Xs ) ) ) )
% 0.27/0.72 & ( ( X3 != Y )
% 0.27/0.72 => ( ( remdup484344169ession @ ( cons_S112077679ession @ X3 @ ( cons_S112077679ession @ Y @ Xs ) ) )
% 0.27/0.72 = ( cons_S112077679ession @ X3 @ ( remdup484344169ession @ ( cons_S112077679ession @ Y @ Xs ) ) ) ) ) ) ).
% 0.27/0.72
% 0.27/0.72 % remdups_adj.simps(3)
% 0.27/0.72
% 0.27/0.72 % Conjectures (1)
% 0.27/0.72 thf(conj_0,conjecture,
% 0.27/0.72 knowle945212990e_know @ a @ ( secrecy_sKS @ m ) ).
% 0.27/0.72
% 0.27/0.72 %------------------------------------------------------------------------------
% 0.27/0.72 ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.2L9YsPT6U6/cvc5---1.0.5_7361.p...
% 0.27/0.72 (declare-sort $$unsorted 0)
% 0.27/0.72 (declare-sort tptp.list_l425507653ession 0)
% 0.27/0.72 (declare-sort tptp.set_li185139947ession 0)
% 0.27/0.72 (declare-sort tptp.set_li2007071804ecrets 0)
% 0.27/0.72 (declare-sort tptp.set_li849033543y_Keys 0)
% 0.27/0.72 (declare-sort tptp.list_list_Secrecy_KS 0)
% 0.27/0.72 (declare-sort tptp.set_list_Secrecy_KS 0)
% 0.27/0.72 (declare-sort tptp.list_S529945141ession 0)
% 0.27/0.72 (declare-sort tptp.set_Se1942955227ession 0)
% 0.27/0.72 (declare-sort tptp.list_Secrecy_Secrets 0)
% 0.27/0.72 (declare-sort tptp.set_Secrecy_Secrets 0)
% 0.27/0.72 (declare-sort tptp.list_Secrecy_Keys 0)
% 0.27/0.72 (declare-sort tptp.set_Secrecy_Keys 0)
% 0.27/0.72 (declare-sort tptp.list_Secrecy_KS 0)
% 0.27/0.72 (declare-sort tptp.set_Secrecy_KS 0)
% 0.27/0.72 (declare-sort tptp.secrecy_Expression 0)
% 0.27/0.72 (declare-sort tptp.secrecy_Secrets 0)
% 0.27/0.72 (declare-sort tptp.secrecy_specID 0)
% 0.27/0.72 (declare-sort tptp.secrecy_Keys 0)
% 0.27/0.72 (declare-sort tptp.secrecy_KS 0)
% 0.27/0.72 (declare-fun tptp.bNF_Gr275623750ession (tptp.set_li185139947ession tptp.secrecy_Expression) tptp.set_li185139947ession)
% 0.27/0.72 (declare-fun tptp.bNF_Gr660123862ecy_KS (tptp.set_list_Secrecy_KS tptp.secrecy_KS) tptp.set_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.bNF_Gr414702370y_Keys (tptp.set_li849033543y_Keys tptp.secrecy_Keys) tptp.set_li849033543y_Keys)
% 0.27/0.72 (declare-fun tptp.bNF_Gr28627573ecrets (tptp.set_li2007071804ecrets tptp.secrecy_Secrets) tptp.set_li2007071804ecrets)
% 0.27/0.72 (declare-fun tptp.bNF_Gr979629770ession (tptp.set_li185139947ession tptp.list_S529945141ession) tptp.set_Se1942955227ession)
% 0.27/0.72 (declare-fun tptp.bNF_Gr577175642ecy_KS (tptp.set_list_Secrecy_KS tptp.list_Secrecy_KS) tptp.set_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.bNF_Gr344893606y_Keys (tptp.set_li849033543y_Keys tptp.list_Secrecy_Keys) tptp.set_Secrecy_Keys)
% 0.27/0.72 (declare-fun tptp.bNF_Gr957048817ecrets (tptp.set_li2007071804ecrets tptp.list_Secrecy_Secrets) tptp.set_Secrecy_Secrets)
% 0.27/0.72 (declare-fun tptp.localSecrets (tptp.secrecy_specID) tptp.set_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.knowle233900195orrect (tptp.secrecy_specID tptp.secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.knowle1268625169orrect (tptp.secrecy_specID tptp.secrecy_Expression) Bool)
% 0.27/0.72 (declare-fun tptp.knowle945212990e_know (tptp.secrecy_specID tptp.secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.knowle731562421_knows (tptp.secrecy_specID tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.mem_Se1967555118ession (tptp.secrecy_Expression tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.mem_Secrecy_KS (tptp.secrecy_KS tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.append1105297242ession (tptp.list_l425507653ession tptp.list_l425507653ession) tptp.list_l425507653ession)
% 0.27/0.72 (declare-fun tptp.append1376766698ecy_KS (tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS) tptp.list_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.append2089414218ession (tptp.list_S529945141ession tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.append_Secrecy_KS (tptp.list_Secrecy_KS tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.append_Secrecy_Keys (tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys) tptp.list_Secrecy_Keys)
% 0.27/0.72 (declare-fun tptp.append186372209ecrets (tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets) tptp.list_Secrecy_Secrets)
% 0.27/0.72 (declare-fun tptp.bind_S815874003ession (tptp.list_S529945141ession (-> tptp.secrecy_Expression tptp.list_S529945141ession)) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.bind_S1823644515ecy_KS (tptp.list_S529945141ession (-> tptp.secrecy_Expression tptp.list_Secrecy_KS)) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.bind_S711229283ession (tptp.list_Secrecy_KS (-> tptp.secrecy_KS tptp.list_S529945141ession)) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.bind_S645462771ecy_KS (tptp.list_Secrecy_KS (-> tptp.secrecy_KS tptp.list_Secrecy_KS)) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.butlas171474643ession (tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.butlast_Secrecy_KS (tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.concat388015140ession (tptp.list_l425507653ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.concat_Secrecy_KS (tptp.list_list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.distin1076152135ession (tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.distin1495927511ecy_KS (tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.foldr_1531709715ession ((-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession) tptp.list_l425507653ession tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.foldr_1711005747ecy_KS ((-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS) tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.insert1173886601ession (tptp.secrecy_Expression tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.insert_Secrecy_KS (tptp.secrecy_KS tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.last_S1532390982ession (tptp.list_S529945141ession) tptp.secrecy_Expression)
% 0.27/0.72 (declare-fun tptp.last_Secrecy_KS (tptp.list_Secrecy_KS) tptp.secrecy_KS)
% 0.27/0.72 (declare-fun tptp.cons_l533358079ession (tptp.list_S529945141ession tptp.list_l425507653ession) tptp.list_l425507653ession)
% 0.27/0.72 (declare-fun tptp.cons_list_Secrecy_KS (tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS) tptp.list_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.cons_S112077679ession (tptp.secrecy_Expression tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.cons_Secrecy_KS (tptp.secrecy_KS tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.cons_Secrecy_Keys (tptp.secrecy_Keys tptp.list_Secrecy_Keys) tptp.list_Secrecy_Keys)
% 0.27/0.72 (declare-fun tptp.cons_Secrecy_Secrets (tptp.secrecy_Secrets tptp.list_Secrecy_Secrets) tptp.list_Secrecy_Secrets)
% 0.27/0.72 (declare-fun tptp.nil_li311616943ession () tptp.list_l425507653ession)
% 0.27/0.72 (declare-fun tptp.nil_list_Secrecy_KS () tptp.list_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.nil_Se901661471ession () tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.nil_Secrecy_KS () tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.nil_Secrecy_Keys () tptp.list_Secrecy_Keys)
% 0.27/0.72 (declare-fun tptp.nil_Secrecy_Secrets () tptp.list_Secrecy_Secrets)
% 0.27/0.72 (declare-fun tptp.hd_lis1623417098ession (tptp.list_l425507653ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.hd_list_Secrecy_KS (tptp.list_list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.hd_Sec357328890ession (tptp.list_S529945141ession) tptp.secrecy_Expression)
% 0.27/0.72 (declare-fun tptp.hd_Secrecy_KS (tptp.list_Secrecy_KS) tptp.secrecy_KS)
% 0.27/0.72 (declare-fun tptp.tl_Sec1905266422ession (tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.tl_Secrecy_KS (tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.list_e1486860828ession ((-> tptp.secrecy_Expression Bool) tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.list_ex1_Secrecy_KS ((-> tptp.secrecy_KS Bool) tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.listre84909707ession ((-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.listre565996059ecy_KS ((-> tptp.secrecy_Expression tptp.secrecy_KS Bool) tptp.list_S529945141ession tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.listre1601064475ession ((-> tptp.secrecy_KS tptp.secrecy_Expression Bool) tptp.list_Secrecy_KS tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.listre788412843ecy_KS ((-> tptp.secrecy_KS tptp.secrecy_KS Bool) tptp.list_Secrecy_KS tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.map_ta1624757057ession ((-> tptp.secrecy_Expression tptp.secrecy_Expression) tptp.list_S529945141ession tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.map_ta623472337ession ((-> tptp.secrecy_KS tptp.secrecy_Expression) tptp.list_Secrecy_KS tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.maps_S599402637ession ((-> tptp.secrecy_Expression tptp.list_S529945141ession) tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.maps_S399472669ecy_KS ((-> tptp.secrecy_Expression tptp.list_Secrecy_KS) tptp.list_S529945141ession) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.maps_S1434541085ession ((-> tptp.secrecy_KS tptp.list_S529945141ession) tptp.list_Secrecy_KS) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.maps_S377605037ecy_KS ((-> tptp.secrecy_KS tptp.list_Secrecy_KS) tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.member2020590922ession (tptp.list_S529945141ession tptp.secrecy_Expression) Bool)
% 0.27/0.72 (declare-fun tptp.member_Secrecy_KS (tptp.list_Secrecy_KS tptp.secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.lexord1123423577ession ((-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.lexord948960489ecy_KS ((-> tptp.secrecy_KS tptp.secrecy_KS Bool) tptp.list_Secrecy_KS tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.produc1450295286ession (tptp.list_l425507653ession) tptp.list_l425507653ession)
% 0.27/0.72 (declare-fun tptp.produc713695622ecy_KS (tptp.list_list_Secrecy_KS) tptp.list_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.remdup484344169ession (tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.remdup351570169ecy_KS (tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.rev_Se1073238207ession (tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.rev_Secrecy_KS (tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.rotate1237234450ession (tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.rotate1_Secrecy_KS (tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.shuffl552897610ession (tptp.list_S529945141ession tptp.list_S529945141ession) tptp.set_li185139947ession)
% 0.27/0.72 (declare-fun tptp.shuffles_Secrecy_KS (tptp.list_Secrecy_KS tptp.list_Secrecy_KS) tptp.set_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.splice1390717708ession (tptp.list_S529945141ession tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.splice_Secrecy_KS (tptp.list_Secrecy_KS tptp.list_Secrecy_KS) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.subseq348280080ession (tptp.list_S529945141ession) tptp.list_l425507653ession)
% 0.27/0.72 (declare-fun tptp.subseqs_Secrecy_KS (tptp.list_Secrecy_KS) tptp.list_list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.succes1388047762ession ((-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.succes590251810ecy_KS ((-> tptp.secrecy_KS tptp.secrecy_KS Bool) tptp.list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.decr (tptp.secrecy_Keys tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.enc (tptp.secrecy_Keys tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.encrDecrKeys (tptp.secrecy_Keys tptp.secrecy_Keys) Bool)
% 0.27/0.72 (declare-fun tptp.ext (tptp.secrecy_Keys tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.sign (tptp.secrecy_Keys tptp.list_S529945141ession) tptp.list_S529945141ession)
% 0.27/0.72 (declare-fun tptp.eout (tptp.secrecy_specID tptp.secrecy_Expression) Bool)
% 0.27/0.72 (declare-fun tptp.ine (tptp.secrecy_specID tptp.secrecy_Expression) Bool)
% 0.27/0.72 (declare-fun tptp.notSpe1586871396tsExpr (tptp.secrecy_specID tptp.list_S529945141ession) Bool)
% 0.27/0.72 (declare-fun tptp.specKeys (tptp.secrecy_specID) tptp.set_Secrecy_Keys)
% 0.27/0.72 (declare-fun tptp.specKeysSecrets (tptp.secrecy_specID) tptp.set_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.specSecrets (tptp.secrecy_specID) tptp.set_Secrecy_Secrets)
% 0.27/0.72 (declare-fun tptp.secrec1371625429on2KSL (tptp.list_S529945141ession) tptp.list_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.secrecy_kE (tptp.secrecy_Keys) tptp.secrecy_Expression)
% 0.27/0.72 (declare-fun tptp.secrecy_sE (tptp.secrecy_Secrets) tptp.secrecy_Expression)
% 0.27/0.72 (declare-fun tptp.secrec1016742679ession (tptp.secrecy_KS) tptp.secrecy_Expression)
% 0.27/0.72 (declare-fun tptp.secrecy_kKS (tptp.secrecy_Keys) tptp.secrecy_KS)
% 0.27/0.72 (declare-fun tptp.secrecy_sKS (tptp.secrecy_Secrets) tptp.secrecy_KS)
% 0.27/0.72 (declare-fun tptp.collect_Secrecy_KS ((-> tptp.secrecy_KS Bool)) tptp.set_Secrecy_KS)
% 0.27/0.72 (declare-fun tptp.collect_Secrecy_Keys ((-> tptp.secrecy_Keys Bool)) tptp.set_Secrecy_Keys)
% 0.27/0.72 (declare-fun tptp.collec836099393ecrets ((-> tptp.secrecy_Secrets Bool)) tptp.set_Secrecy_Secrets)
% 0.27/0.72 (declare-fun tptp.member249235532ession (tptp.list_S529945141ession tptp.set_li185139947ession) Bool)
% 0.27/0.72 (declare-fun tptp.member193705948ecy_KS (tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.member341114536y_Keys (tptp.list_Secrecy_Keys tptp.set_li849033543y_Keys) Bool)
% 0.27/0.72 (declare-fun tptp.member1138497285ecrets (tptp.list_Secrecy_Secrets tptp.set_li2007071804ecrets) Bool)
% 0.27/0.72 (declare-fun tptp.member279582780ession (tptp.secrecy_Expression tptp.set_Se1942955227ession) Bool)
% 0.27/0.72 (declare-fun tptp.member_Secrecy_KS2 (tptp.secrecy_KS tptp.set_Secrecy_KS) Bool)
% 0.27/0.72 (declare-fun tptp.member_Secrecy_Keys (tptp.secrecy_Keys tptp.set_Secrecy_Keys) Bool)
% 0.27/0.72 (declare-fun tptp.member2138796287ecrets (tptp.secrecy_Secrets tptp.set_Secrecy_Secrets) Bool)
% 0.27/0.72 (declare-fun tptp.a () tptp.secrecy_specID)
% 0.27/0.72 (declare-fun tptp.m () tptp.secrecy_Secrets)
% 0.27/0.72 (assert (@ (@ tptp.knowle731562421_knows tptp.a) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_sE tptp.m)) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((X2 tptp.secrecy_Secrets) (Y2 tptp.secrecy_Secrets)) (= (= (@ tptp.secrecy_sKS X2) (@ tptp.secrecy_sKS Y2)) (= X2 Y2))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (=> (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_sKS M)) (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_sE M)) tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M2))) (= (@ (@ tptp.knowle731562421_knows C) (@ (@ tptp.cons_S112077679ession (@ tptp.secrec1016742679ession _let_1)) tptp.nil_Se901661471ession)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (=> (@ (@ tptp.knowle233900195orrect C) _let_1) (=> (@ (@ tptp.eout C) (@ tptp.secrecy_sE M)) (or (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets C)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (M tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M))) (= (@ (@ tptp.knowle233900195orrect C) _let_1) (= (@ (@ tptp.eout C) (@ tptp.secrecy_sE M)) (or (@ (@ tptp.member2138796287ecrets M) (@ tptp.specSecrets C)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))))
% 0.27/0.72 (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_KS2 _let_1) (@ tptp.localSecrets A)))))))
% 0.27/0.72 (assert (forall ((M tptp.secrecy_Secrets)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_sKS M)) (@ tptp.secrecy_sE M))))
% 0.27/0.72 (assert (forall ((IncrDecrKeys (-> tptp.secrecy_Keys tptp.secrecy_Keys Bool)) (K1 tptp.secrecy_Keys) (K2 tptp.secrecy_Keys) (A tptp.secrecy_specID) (E tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (and (@ (@ IncrDecrKeys K1) K2) (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS K2)) (@ _let_1 (@ (@ tptp.enc K1) E))) (@ _let_1 E)))))
% 0.27/0.72 (assert (forall ((IncrDecrKeys (-> tptp.secrecy_Keys tptp.secrecy_Keys Bool)) (K1 tptp.secrecy_Keys) (K2 tptp.secrecy_Keys) (A tptp.secrecy_specID) (E tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (and (@ (@ IncrDecrKeys K1) K2) (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS K1)) (@ _let_1 (@ (@ tptp.sign K2) E))) (@ _let_1 E)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (K tptp.secrecy_Keys) (E1 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (and (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS K)) (@ _let_1 E1)) (@ _let_1 (@ (@ tptp.enc K) E1))))))
% 0.27/0.72 (assert (forall ((X1 tptp.secrecy_Keys) (Y1 tptp.secrecy_Keys)) (= (= (@ tptp.secrecy_kKS X1) (@ tptp.secrecy_kKS Y1)) (= X1 Y1))))
% 0.27/0.72 (assert (forall ((X2 tptp.secrecy_Secrets) (Y2 tptp.secrecy_Secrets)) (= (= (@ tptp.secrecy_sE X2) (@ tptp.secrecy_sE Y2)) (= X2 Y2))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (M1 tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M1))) (= (@ (@ tptp.knowle731562421_knows C) (@ (@ tptp.cons_S112077679ession (@ tptp.secrec1016742679ession _let_1)) tptp.nil_Se901661471ession)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID)) (@ (@ tptp.knowle731562421_knows C) tptp.nil_Se901661471ession)))
% 0.27/0.72 (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))))))))
% 0.27/0.72 (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)))))
% 0.27/0.72 (assert (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kKS X1) (@ tptp.secrecy_sKS X2)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (K tptp.secrecy_Keys) (E1 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (and (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS K)) (@ _let_1 E1)) (@ _let_1 (@ (@ tptp.sign K) E1))))))
% 0.27/0.72 (assert (forall ((X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession) (Y21 tptp.secrecy_Expression) (Y22 tptp.list_S529945141ession)) (= (= (@ (@ tptp.cons_S112077679ession X21) X222) (@ (@ tptp.cons_S112077679ession Y21) Y22)) (and (= X21 Y21) (= X222 Y22)))))
% 0.27/0.72 (assert (forall ((X21 tptp.secrecy_KS) (X222 tptp.list_Secrecy_KS)) (not (= tptp.nil_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X21) X222)))))
% 0.27/0.72 (assert (forall ((X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession)) (not (= tptp.nil_Se901661471ession (@ (@ tptp.cons_S112077679ession X21) X222)))))
% 0.27/0.72 (assert (forall ((List tptp.list_Secrecy_KS) (X21 tptp.secrecy_KS) (X222 tptp.list_Secrecy_KS)) (=> (= List (@ (@ tptp.cons_Secrecy_KS X21) X222)) (not (= List tptp.nil_Secrecy_KS)))))
% 0.27/0.72 (assert (forall ((List tptp.list_S529945141ession) (X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession)) (=> (= List (@ (@ tptp.cons_S112077679ession X21) X222)) (not (= List tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((Y tptp.list_Secrecy_KS)) (=> (not (= Y tptp.nil_Secrecy_KS)) (not (forall ((X212 tptp.secrecy_KS) (X223 tptp.list_Secrecy_KS)) (not (= Y (@ (@ tptp.cons_Secrecy_KS X212) X223))))))))
% 0.27/0.72 (assert (forall ((Y tptp.list_S529945141ession)) (=> (not (= Y tptp.nil_Se901661471ession)) (not (forall ((X212 tptp.secrecy_Expression) (X223 tptp.list_S529945141ession)) (not (= Y (@ (@ tptp.cons_S112077679ession X212) X223))))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS Bool)) (List tptp.list_Secrecy_KS)) (=> (@ P tptp.nil_Secrecy_KS) (=> (forall ((X12 tptp.secrecy_KS) (X22 tptp.list_Secrecy_KS)) (=> (@ P X22) (@ P (@ (@ tptp.cons_Secrecy_KS X12) X22)))) (@ P List)))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession Bool)) (List tptp.list_S529945141ession)) (=> (@ P tptp.nil_Se901661471ession) (=> (forall ((X12 tptp.secrecy_Expression) (X22 tptp.list_S529945141ession)) (=> (@ P X22) (@ P (@ (@ tptp.cons_S112077679ession X12) X22)))) (@ P List)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (not (= Xs tptp.nil_Secrecy_KS)) (exists ((Y3 tptp.secrecy_KS) (Ys tptp.list_Secrecy_KS)) (= Xs (@ (@ tptp.cons_Secrecy_KS Y3) Ys))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (not (= Xs tptp.nil_Se901661471ession)) (exists ((Y3 tptp.secrecy_Expression) (Ys tptp.list_S529945141ession)) (= Xs (@ (@ tptp.cons_S112077679ession Y3) Ys))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (@ (@ P tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) tptp.nil_Secrecy_KS)) (=> (forall ((Y4 tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Secrecy_KS) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Y4 tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_S529945141ession)) (=> (@ (@ P tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) tptp.nil_Se901661471ession)) (=> (forall ((Y4 tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Secrecy_KS) (@ (@ tptp.cons_S112077679ession Y4) Ys3))) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Y4 tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_Secrecy_KS)) (=> (@ (@ P tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) tptp.nil_Secrecy_KS)) (=> (forall ((Y4 tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Se901661471ession) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Y4 tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ (@ P tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) tptp.nil_Se901661471ession)) (=> (forall ((Y4 tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Se901661471ession) (@ (@ tptp.cons_S112077679ession Y4) Ys3))) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Y4 tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))) (@ (@ P Xs) Ys2)))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)) (A0 tptp.list_Secrecy_KS) (A1 tptp.list_Secrecy_KS)) (=> (forall ((X_1 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Secrecy_KS) X_1)) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ P Ys3) Xs2) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) Ys3))) (@ (@ P A0) A1)))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)) (A0 tptp.list_S529945141ession) (A1 tptp.list_S529945141ession)) (=> (forall ((X_1 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Se901661471ession) X_1)) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ P Ys3) Xs2) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) Ys3))) (@ (@ P A0) A1)))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS)) (=> (@ P tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS)) (@ P (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Zs tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_Secrecy_KS X) _let_1)))))) (@ P Xs))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession Bool)) (Xs tptp.list_S529945141ession)) (=> (@ P tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression)) (@ P (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Zs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Zs))) (=> (@ P Zs) (=> (@ P _let_1) (@ P (@ (@ tptp.cons_S112077679ession X) _let_1)))))) (@ P Xs))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (not (= (@ (@ tptp.cons_S112077679ession X3) Xs) Xs))))
% 0.27/0.72 (assert (forall ((P (-> (-> tptp.secrecy_KS tptp.secrecy_Expression) tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)) (A0 (-> tptp.secrecy_KS tptp.secrecy_Expression)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_S529945141ession)) (=> (forall ((F (-> tptp.secrecy_KS tptp.secrecy_Expression)) (X_1 tptp.list_S529945141ession)) (@ (@ (@ P F) tptp.nil_Secrecy_KS) X_1)) (=> (forall ((F (-> tptp.secrecy_KS tptp.secrecy_Expression)) (A3 tptp.secrecy_KS) (As tptp.list_Secrecy_KS) (Bs tptp.list_S529945141ession)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_S112077679ession (@ F A3)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_Secrecy_KS A3) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.27/0.72 (assert (forall ((P (-> (-> tptp.secrecy_Expression tptp.secrecy_Expression) tptp.list_S529945141ession tptp.list_S529945141ession Bool)) (A0 (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (A1 tptp.list_S529945141ession) (A2 tptp.list_S529945141ession)) (=> (forall ((F (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (X_1 tptp.list_S529945141ession)) (@ (@ (@ P F) tptp.nil_Se901661471ession) X_1)) (=> (forall ((F (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (A3 tptp.secrecy_Expression) (As tptp.list_S529945141ession) (Bs tptp.list_S529945141ession)) (let ((_let_1 (@ P F))) (=> (@ (@ _let_1 As) (@ (@ tptp.cons_S112077679ession (@ F A3)) Bs)) (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession A3) As)) Bs)))) (@ (@ (@ P A0) A1) A2)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS Bool))) (=> (not (= Xs tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (@ P (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (not (= Xs2 tptp.nil_Secrecy_KS)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2))))) (@ P Xs))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession Bool))) (=> (not (= Xs tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (@ P (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (not (= Xs2 tptp.nil_Se901661471ession)) (=> (@ P Xs2) (@ P (@ (@ tptp.cons_S112077679ession X) Xs2))))) (@ P Xs))))))
% 0.27/0.72 (assert (forall ((P (-> (-> tptp.secrecy_KS tptp.secrecy_KS Bool) tptp.list_Secrecy_KS Bool)) (A0 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS)) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ P P2) tptp.nil_Secrecy_KS)) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X tptp.secrecy_KS)) (@ (@ P P2) (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_Secrecy_KS X) _let_1)))))) (@ (@ P A0) A1))))))
% 0.27/0.72 (assert (forall ((P (-> (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession Bool)) (A0 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ P P2) tptp.nil_Se901661471ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X tptp.secrecy_Expression)) (@ (@ P P2) (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_S112077679ession X) _let_1)))))) (@ (@ P A0) A1))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS Bool)) (A0 tptp.list_Secrecy_KS)) (=> (@ P tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS)) (@ P (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (let ((_let_2 (@ tptp.cons_Secrecy_KS X))) (let ((_let_3 (= X Y4))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession Bool)) (A0 tptp.list_S529945141ession)) (=> (@ P tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression)) (@ P (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (let ((_let_2 (@ tptp.cons_S112077679ession X))) (let ((_let_3 (= X Y4))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))))
% 0.27/0.72 (assert (forall ((P (-> (-> tptp.secrecy_KS tptp.secrecy_KS Bool) tptp.list_Secrecy_KS Bool)) (A0 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS)) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ P P2) tptp.nil_Secrecy_KS)) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_Secrecy_KS X) Ys3))))) (@ (@ P A0) A1)))))
% 0.27/0.72 (assert (forall ((P (-> (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession Bool)) (A0 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ P P2) tptp.nil_Se901661471ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_S112077679ession X) Ys3))))) (@ (@ P A0) A1)))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_Secrecy_KS)) (=> (not (= X3 tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (not (= X3 (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS)))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (not (= X3 (@ (@ tptp.cons_Secrecy_KS X) (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_S529945141ession)) (=> (not (= X3 tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (not (= X3 (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession)))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (not (= X3 (@ (@ tptp.cons_S112077679ession X) (@ (@ tptp.cons_S112077679ession Y4) Xs2))))))))))
% 0.27/0.72 (assert (forall ((A4 tptp.secrecy_Secrets) (P (-> tptp.secrecy_Secrets Bool))) (= (@ (@ tptp.member2138796287ecrets A4) (@ tptp.collec836099393ecrets P)) (@ P A4))))
% 0.27/0.72 (assert (forall ((A4 tptp.secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (@ (@ tptp.member_Secrecy_KS2 A4) (@ tptp.collect_Secrecy_KS P)) (@ P A4))))
% 0.27/0.72 (assert (forall ((A4 tptp.secrecy_Keys) (P (-> tptp.secrecy_Keys Bool))) (= (@ (@ tptp.member_Secrecy_Keys A4) (@ tptp.collect_Secrecy_Keys P)) (@ P A4))))
% 0.27/0.72 (assert (forall ((A tptp.set_Secrecy_Secrets)) (= (@ tptp.collec836099393ecrets (lambda ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) A))) A)))
% 0.27/0.72 (assert (forall ((A tptp.set_Secrecy_KS)) (= (@ tptp.collect_Secrecy_KS (lambda ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS2 X4) A))) A)))
% 0.27/0.72 (assert (forall ((A tptp.set_Secrecy_Keys)) (= (@ tptp.collect_Secrecy_Keys (lambda ((X4 tptp.secrecy_Keys)) (@ (@ tptp.member_Secrecy_Keys X4) A))) A)))
% 0.27/0.72 (assert (forall ((X3 tptp.list_list_Secrecy_KS)) (=> (not (= X3 tptp.nil_list_Secrecy_KS)) (=> (forall ((Xss tptp.list_list_Secrecy_KS)) (not (= X3 (@ (@ tptp.cons_list_Secrecy_KS tptp.nil_Secrecy_KS) Xss)))) (not (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Xss tptp.list_list_Secrecy_KS)) (not (= X3 (@ (@ tptp.cons_list_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X) Xs2)) Xss)))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_l425507653ession)) (=> (not (= X3 tptp.nil_li311616943ession)) (=> (forall ((Xss tptp.list_l425507653ession)) (not (= X3 (@ (@ tptp.cons_l533358079ession tptp.nil_Se901661471ession) Xss)))) (not (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Xss tptp.list_l425507653ession)) (not (= X3 (@ (@ tptp.cons_l533358079ession (@ (@ tptp.cons_S112077679ession X) Xs2)) Xss)))))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)) (A0 tptp.list_Secrecy_KS) (A1 tptp.list_Secrecy_KS)) (=> (forall ((X_1 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Secrecy_KS) X_1)) (=> (forall ((Xs2 tptp.list_Secrecy_KS)) (@ (@ P Xs2) tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Y4 tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)) (A0 tptp.list_S529945141ession) (A1 tptp.list_S529945141ession)) (=> (forall ((X_1 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Se901661471ession) X_1)) (=> (forall ((Xs2 tptp.list_S529945141ession)) (@ (@ P Xs2) tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Y4 tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (= (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M)) (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M)) (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession)) (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M)))))
% 0.27/0.72 (assert (forall ((P tptp.secrecy_specID) (M tptp.secrecy_Keys) (Q tptp.secrecy_specID)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))) (let ((_let_2 (@ tptp.secrecy_kKS M))) (=> (or (@ (@ tptp.knowle945212990e_know P) _let_2) (@ (@ tptp.knowle945212990e_know Q) _let_2)) (or (@ (@ tptp.knowle731562421_knows P) _let_1) (@ (@ tptp.knowle731562421_knows Q) _let_1)))))))
% 0.27/0.72 (assert (forall ((P tptp.secrecy_specID) (M tptp.secrecy_Keys) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (let ((_let_2 (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))) (=> (or (@ (@ tptp.knowle731562421_knows P) _let_2) (@ (@ tptp.knowle731562421_knows Q) _let_2)) (or (@ (@ tptp.knowle945212990e_know P) _let_1) (@ (@ tptp.knowle945212990e_know Q) _let_1)))))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M))) (not (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (not (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))) (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M))))))
% 0.27/0.72 (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_KS2 _let_1) (@ tptp.localSecrets A)))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS)) (= (@ (@ tptp.insert_Secrecy_KS X3) tptp.nil_Secrecy_KS) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression)) (= (@ (@ tptp.insert1173886601ession X3) tptp.nil_Se901661471ession) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((X1 tptp.secrecy_Keys) (Y1 tptp.secrecy_Keys)) (= (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_kE Y1)) (= X1 Y1))))
% 0.27/0.72 (assert (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_sE X2)))))
% 0.27/0.72 (assert (forall ((M tptp.secrecy_Keys)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_kKS M)) (@ tptp.secrecy_kE M))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (@ (@ tptp.knowle233900195orrect C) _let_1) (=> (@ (@ tptp.eout C) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (= (@ (@ tptp.knowle233900195orrect C) _let_1) (= (@ (@ tptp.eout C) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))))
% 0.27/0.72 (assert (forall ((C tptp.secrecy_specID) (E tptp.secrecy_Expression)) (=> (@ (@ tptp.knowle1268625169orrect C) E) (=> (@ (@ tptp.eout C) E) (or (exists ((K3 tptp.secrecy_Keys)) (and (= E (@ tptp.secrecy_kE K3)) (@ (@ tptp.member_Secrecy_Keys K3) (@ tptp.specKeys C)))) (exists ((S tptp.secrecy_Secrets)) (and (= E (@ tptp.secrecy_sE S)) (@ (@ tptp.member2138796287ecrets S) (@ tptp.specSecrets C)))) (@ (@ tptp.knowle731562421_knows C) (@ (@ tptp.cons_S112077679ession E) tptp.nil_Se901661471ession)))))))
% 0.27/0.72 (assert (= tptp.knowle1268625169orrect (lambda ((C2 tptp.secrecy_specID) (E2 tptp.secrecy_Expression)) (= (@ (@ tptp.eout C2) E2) (or (exists ((K4 tptp.secrecy_Keys)) (and (= E2 (@ tptp.secrecy_kE K4)) (@ (@ tptp.member_Secrecy_Keys K4) (@ tptp.specKeys C2)))) (exists ((S2 tptp.secrecy_Secrets)) (and (= E2 (@ tptp.secrecy_sE S2)) (@ (@ tptp.member2138796287ecrets S2) (@ tptp.specSecrets C2)))) (@ (@ tptp.knowle731562421_knows C2) (@ (@ tptp.cons_S112077679ession E2) tptp.nil_Se901661471ession)))))))
% 0.27/0.72 (assert (= (@ tptp.produc1450295286ession tptp.nil_li311616943ession) (@ (@ tptp.cons_l533358079ession tptp.nil_Se901661471ession) tptp.nil_li311616943ession)))
% 0.27/0.72 (assert (= (@ tptp.produc713695622ecy_KS tptp.nil_list_Secrecy_KS) (@ (@ tptp.cons_list_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_list_Secrecy_KS)))
% 0.27/0.72 (assert (= (@ tptp.subseq348280080ession tptp.nil_Se901661471ession) (@ (@ tptp.cons_l533358079ession tptp.nil_Se901661471ession) tptp.nil_li311616943ession)))
% 0.27/0.72 (assert (= (@ tptp.subseqs_Secrecy_KS tptp.nil_Secrecy_KS) (@ (@ tptp.cons_list_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_list_Secrecy_KS)))
% 0.27/0.72 (assert (= (@ tptp.secrec1371625429on2KSL tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_Expression Bool))) (not (@ (@ tptp.list_e1486860828ession P) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_KS Bool))) (not (@ (@ tptp.list_ex1_Secrecy_KS P) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_KS tptp.secrecy_Expression)) (Xa tptp.list_Secrecy_KS) (Xb tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ (@ (@ tptp.map_ta623472337ession X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_Secrecy_KS) (not (= Y Xb))) (not (forall ((A3 tptp.secrecy_KS) (As tptp.list_Secrecy_KS)) (=> (= Xa (@ (@ tptp.cons_Secrecy_KS A3) As)) (not (= Y (@ (@ (@ tptp.map_ta623472337ession X3) As) (@ (@ tptp.cons_S112077679ession (@ X3 A3)) Xb)))))))))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (Xa tptp.list_S529945141ession) (Xb tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ (@ (@ tptp.map_ta1624757057ession X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_Se901661471ession) (not (= Y Xb))) (not (forall ((A3 tptp.secrecy_Expression) (As tptp.list_S529945141ession)) (=> (= Xa (@ (@ tptp.cons_S112077679ession A3) As)) (not (= Y (@ (@ (@ tptp.map_ta1624757057ession X3) As) (@ (@ tptp.cons_S112077679ession (@ X3 A3)) Xb)))))))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (not (@ (@ (@ tptp.lexord948960489ecy_KS Less) (@ (@ tptp.cons_Secrecy_KS X3) Xs)) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (not (@ (@ (@ tptp.lexord1123423577ession Less) (@ (@ tptp.cons_S112077679ession X3) Xs)) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession))) (= (@ (@ tptp.bind_S815874003ession tptp.nil_Se901661471ession) F2) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_Expression tptp.list_Secrecy_KS))) (= (@ (@ tptp.bind_S1823644515ecy_KS tptp.nil_Se901661471ession) F2) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_KS tptp.list_S529945141ession))) (= (@ (@ tptp.bind_S711229283ession tptp.nil_Secrecy_KS) F2) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_KS tptp.list_Secrecy_KS))) (= (@ (@ tptp.bind_S645462771ecy_KS tptp.nil_Secrecy_KS) F2) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X1 tptp.list_Secrecy_KS) (X2 tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool))) (=> (@ (@ (@ tptp.listre788412843ecy_KS R) X1) X2) (=> (@ (@ P tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre788412843ecy_KS R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))))) (@ (@ P X1) X2))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (X1 tptp.list_Secrecy_KS) (X2 tptp.list_S529945141ession) (P (-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool))) (=> (@ (@ (@ tptp.listre1601064475ession R) X1) X2) (=> (@ (@ P tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre1601064475ession R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))))) (@ (@ P X1) X2))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (X1 tptp.list_S529945141ession) (X2 tptp.list_Secrecy_KS) (P (-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool))) (=> (@ (@ (@ tptp.listre565996059ecy_KS R) X1) X2) (=> (@ (@ P tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre565996059ecy_KS R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))))) (@ (@ P X1) X2))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X1 tptp.list_S529945141ession) (X2 tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool))) (=> (@ (@ (@ tptp.listre84909707ession R) X1) X2) (=> (@ (@ P tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre84909707ession R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))))) (@ (@ P X1) X2))))))
% 0.27/0.72 (assert (= tptp.listre788412843ecy_KS (lambda ((R2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A12 tptp.list_Secrecy_KS) (A22 tptp.list_Secrecy_KS)) (or (and (= A12 tptp.nil_Secrecy_KS) (= A22 tptp.nil_Secrecy_KS)) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre788412843ecy_KS R2) Xs3) Ys)))))))
% 0.27/0.72 (assert (= tptp.listre1601064475ession (lambda ((R2 (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (A12 tptp.list_Secrecy_KS) (A22 tptp.list_S529945141ession)) (or (and (= A12 tptp.nil_Secrecy_KS) (= A22 tptp.nil_Se901661471ession)) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre1601064475ession R2) Xs3) Ys)))))))
% 0.27/0.72 (assert (= tptp.listre565996059ecy_KS (lambda ((R2 (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (A12 tptp.list_S529945141ession) (A22 tptp.list_Secrecy_KS)) (or (and (= A12 tptp.nil_Se901661471ession) (= A22 tptp.nil_Secrecy_KS)) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre565996059ecy_KS R2) Xs3) Ys)))))))
% 0.27/0.72 (assert (= tptp.listre84909707ession (lambda ((R2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A12 tptp.list_S529945141ession) (A22 tptp.list_S529945141ession)) (or (and (= A12 tptp.nil_Se901661471ession) (= A22 tptp.nil_Se901661471ession)) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre84909707ession R2) Xs3) Ys)))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Y tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.lexord1123423577ession Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2)) (or (@ (@ Less X3) Y) (and (not (@ (@ Less Y) X3)) (@ (@ _let_1 Xs) Ys2)))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xs tptp.list_S529945141ession)) (= (@ (@ (@ tptp.lexord1123423577ession Less) Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS)) (= (@ (@ (@ tptp.lexord948960489ecy_KS Less) Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Ys2 tptp.list_S529945141ession)) (@ (@ (@ tptp.lexord1123423577ession Less) tptp.nil_Se901661471ession) Ys2)))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Ys2 tptp.list_Secrecy_KS)) (@ (@ (@ tptp.lexord948960489ecy_KS Less) tptp.nil_Secrecy_KS) Ys2)))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ (@ Less X3) Y) (@ (@ (@ tptp.lexord1123423577ession Less) (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2)))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.lexord1123423577ession Less))) (=> (not (@ (@ Less X3) Y)) (=> (not (@ (@ Less Y) X3)) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2))))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Ys2 tptp.list_S529945141ession)) (@ (@ (@ tptp.lexord1123423577ession Less) tptp.nil_Se901661471ession) Ys2)))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Ys2 tptp.list_Secrecy_KS)) (@ (@ (@ tptp.lexord948960489ecy_KS Less) tptp.nil_Secrecy_KS) Ys2)))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.listre84909707ession R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2)))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ (@ tptp.listre84909707ession R) tptp.nil_Se901661471ession) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_KS Bool))) (@ (@ (@ tptp.listre565996059ecy_KS R) tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_KS tptp.secrecy_Expression Bool))) (@ (@ (@ tptp.listre1601064475ession R) tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ (@ tptp.listre788412843ecy_KS R) tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (A4 tptp.secrecy_Expression) (As2 tptp.list_S529945141ession) (Bs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.map_ta1624757057ession F2))) (= (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession A4) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_S112077679ession (@ F2 A4)) Bs2))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_Secrecy_KS)) (=> (@ (@ (@ tptp.lexord948960489ecy_KS Less) A1) A2) (=> (not (= A1 tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (=> (exists ((Xs2 tptp.list_Secrecy_KS)) (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2))) (forall ((Y4 tptp.secrecy_KS)) (=> (exists ((Ys3 tptp.list_Secrecy_KS)) (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))) (not (@ (@ Less X) Y4)))))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (forall ((Ys3 tptp.list_Secrecy_KS)) (=> (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (not (@ (@ (@ tptp.lexord948960489ecy_KS Less) Xs2) Ys3))))))))))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession) (A2 tptp.list_S529945141ession)) (=> (@ (@ (@ tptp.lexord1123423577ession Less) A1) A2) (=> (not (= A1 tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (=> (exists ((Xs2 tptp.list_S529945141ession)) (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2))) (forall ((Y4 tptp.secrecy_Expression)) (=> (exists ((Ys3 tptp.list_S529945141ession)) (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3))) (not (@ (@ Less X) Y4)))))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2)) (forall ((Ys3 tptp.list_S529945141ession)) (=> (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (not (@ (@ (@ tptp.lexord1123423577ession Less) Xs2) Ys3))))))))))))))
% 0.27/0.72 (assert (= tptp.lexord948960489ecy_KS (lambda ((Less2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A12 tptp.list_Secrecy_KS) (A22 tptp.list_Secrecy_KS)) (or (exists ((Ys tptp.list_Secrecy_KS)) (and (= A12 tptp.nil_Secrecy_KS) (= A22 Ys))) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (@ (@ Less2 X4) Y3))) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (not (@ (@ Less2 X4) Y3)) (not (@ (@ Less2 Y3) X4)) (@ (@ (@ tptp.lexord948960489ecy_KS Less2) Xs3) Ys)))))))
% 0.27/0.72 (assert (= tptp.lexord1123423577ession (lambda ((Less2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A12 tptp.list_S529945141ession) (A22 tptp.list_S529945141ession)) (or (exists ((Ys tptp.list_S529945141ession)) (and (= A12 tptp.nil_Se901661471ession) (= A22 Ys))) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (@ (@ Less2 X4) Y3))) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (not (@ (@ Less2 X4) Y3)) (not (@ (@ Less2 Y3) X4)) (@ (@ (@ tptp.lexord1123423577ession Less2) Xs3) Ys)))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X1 tptp.list_Secrecy_KS) (X2 tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool))) (=> (@ (@ (@ tptp.lexord948960489ecy_KS Less) X1) X2) (=> (forall ((X_1 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Secrecy_KS) X_1)) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ Less X) Y4) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (=> (@ (@ (@ tptp.lexord948960489ecy_KS Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))))))) (@ (@ P X1) X2)))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X1 tptp.list_S529945141ession) (X2 tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool))) (=> (@ (@ (@ tptp.lexord1123423577ession Less) X1) X2) (=> (forall ((X_1 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Se901661471ession) X_1)) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ Less X) Y4) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (=> (@ (@ (@ tptp.lexord1123423577ession Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3))))))) (@ (@ P X1) X2)))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_Secrecy_KS)) (=> (@ (@ (@ tptp.listre788412843ecy_KS R) A1) A2) (=> (=> (= A1 tptp.nil_Secrecy_KS) (not (= A2 tptp.nil_Secrecy_KS))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (forall ((Ys3 tptp.list_Secrecy_KS)) (=> (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre788412843ecy_KS R) Xs2) Ys3))))))))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_S529945141ession)) (=> (@ (@ (@ tptp.listre1601064475ession R) A1) A2) (=> (=> (= A1 tptp.nil_Secrecy_KS) (not (= A2 tptp.nil_Se901661471ession))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_Secrecy_KS)) (=> (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (forall ((Ys3 tptp.list_S529945141ession)) (=> (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre1601064475ession R) Xs2) Ys3))))))))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (A1 tptp.list_S529945141ession) (A2 tptp.list_Secrecy_KS)) (=> (@ (@ (@ tptp.listre565996059ecy_KS R) A1) A2) (=> (=> (= A1 tptp.nil_Se901661471ession) (not (= A2 tptp.nil_Secrecy_KS))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_S529945141ession)) (=> (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2)) (forall ((Ys3 tptp.list_Secrecy_KS)) (=> (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre565996059ecy_KS R) Xs2) Ys3))))))))))))
% 0.27/0.72 (assert (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession) (A2 tptp.list_S529945141ession)) (=> (@ (@ (@ tptp.listre84909707ession R) A1) A2) (=> (=> (= A1 tptp.nil_Se901661471ession) (not (= A2 tptp.nil_Se901661471ession))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2)) (forall ((Ys3 tptp.list_S529945141ession)) (=> (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre84909707ession R) Xs2) Ys3))))))))))))
% 0.27/0.72 (assert (forall ((P tptp.secrecy_specID) (A4 tptp.secrecy_Expression) (L tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession A4))) (let ((_let_2 (@ tptp.notSpe1586871396tsExpr P))) (=> (@ _let_2 (@ _let_1 L)) (@ _let_2 (@ _let_1 tptp.nil_Se901661471ession)))))))
% 0.27/0.72 (assert (forall ((Y tptp.secrecy_Expression)) (not (@ (@ tptp.member2020590922ession tptp.nil_Se901661471ession) Y))))
% 0.27/0.72 (assert (forall ((Y tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS tptp.nil_Secrecy_KS) Y))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Y tptp.secrecy_Expression)) (= (@ (@ tptp.member2020590922ession (@ (@ tptp.cons_S112077679ession X3) Xs)) Y) (or (= X3 Y) (@ (@ tptp.member2020590922ession Xs) Y)))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_Secrecy_KS) (Xa tptp.list_Secrecy_KS) (Y tptp.list_Secrecy_KS)) (=> (= (@ (@ tptp.splice_Secrecy_KS X3) Xa) Y) (=> (=> (= X3 tptp.nil_Secrecy_KS) (not (= Y Xa))) (not (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_Secrecy_KS Xa) Xs2))))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_S529945141ession) (Xa tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ (@ tptp.splice1390717708ession X3) Xa) Y) (=> (=> (= X3 tptp.nil_Se901661471ession) (not (= Y Xa))) (not (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice1390717708ession Xa) Xs2))))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession))) (= (@ (@ tptp.bind_S815874003ession (@ (@ tptp.cons_S112077679ession X3) Xs)) F2) (@ (@ tptp.append2089414218ession (@ F2 X3)) (@ (@ tptp.bind_S815874003ession Xs) F2)))))
% 0.27/0.72 (assert (forall ((A4 tptp.list_S529945141ession) (B tptp.list_S529945141ession) (C3 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession A4))) (= (@ (@ tptp.append2089414218ession (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.append2089414218ession B) C3))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (= (@ (@ tptp.append2089414218ession (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append2089414218ession Ys2) Zs2))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Ys2) Xs) (@ (@ tptp.append2089414218ession Zs2) Xs)) (= Ys2 Zs2))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))))
% 0.27/0.72 (assert (forall ((A4 tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession A4) tptp.nil_Se901661471ession) A4)))
% 0.27/0.72 (assert (forall ((A4 tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS A4) tptp.nil_Secrecy_KS) A4)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) tptp.nil_Se901661471ession) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) Ys2) tptp.nil_Secrecy_KS) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= tptp.nil_Se901661471ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= tptp.nil_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (= (= Ys2 (@ (@ tptp.append2089414218ession Xs) Ys2)) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (= (= Ys2 (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) Ys2) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) Ys2) Ys2) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= Xs (@ (@ tptp.append2089414218ession Xs) Ys2)) (= Ys2 tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= Xs (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (= Ys2 tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) Xs) (= Ys2 tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) Ys2) Xs) (= Ys2 tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession Xs) tptp.nil_Se901661471ession) Xs)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS Xs) tptp.nil_Secrecy_KS) Xs)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.splice1390717708ession Xs) Ys2) tptp.nil_Se901661471ession) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.splice_Secrecy_KS Xs) Ys2) tptp.nil_Secrecy_KS) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (@ (@ tptp.splice1390717708ession Xs) tptp.nil_Se901661471ession) Xs)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (@ (@ tptp.splice_Secrecy_KS Xs) tptp.nil_Secrecy_KS) Xs)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Ys2 tptp.list_Secrecy_KS) (Y tptp.secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS)) (@ (@ tptp.append_Secrecy_KS Ys2) (@ (@ tptp.cons_Secrecy_KS Y) tptp.nil_Secrecy_KS))) (and (= Xs Ys2) (= X3 Y)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession) (Y tptp.secrecy_Expression)) (= (= (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession)) (@ (@ tptp.append2089414218ession Ys2) (@ (@ tptp.cons_S112077679ession Y) tptp.nil_Se901661471ession))) (and (= Xs Ys2) (= X3 Y)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Xs1 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Us tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append2089414218ession Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append2089414218ession Zs2) Us)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession) (Ts tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) (@ (@ tptp.append2089414218ession Zs2) Ts)) (exists ((Us2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Us2))) (or (and (= Xs (@ (@ tptp.append2089414218ession Zs2) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append2089414218ession Xs) Us2) Zs2) (= Ys2 (@ _let_1 Ts)))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ (@ tptp.append2089414218ession (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append2089414218ession Xs) Ys2))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs1 tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append2089414218ession Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append2089414218ession Ys2) Zs2)))))))
% 0.27/0.72 (assert (forall ((A4 tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession tptp.nil_Se901661471ession) A4) A4)))
% 0.27/0.72 (assert (forall ((A4 tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS tptp.nil_Secrecy_KS) A4) A4)))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession tptp.nil_Se901661471ession) Ys2) Ys2)))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS tptp.nil_Secrecy_KS) Ys2) Ys2)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append2089414218ession tptp.nil_Se901661471ession) Ys2)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_Secrecy_KS tptp.nil_Secrecy_KS) Ys2)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (E tptp.list_S529945141ession) (E1 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (@ _let_1 (@ (@ tptp.append2089414218ession E) E1)) (@ _let_1 E)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (E1 tptp.list_S529945141ession) (E tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (@ _let_1 (@ (@ tptp.append2089414218ession E1) E)) (@ _let_1 E)))))
% 0.27/0.72 (assert (forall ((A tptp.secrecy_specID) (E1 tptp.list_S529945141ession) (E22 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (and (@ _let_1 E1) (@ _let_1 E22)) (@ _let_1 (@ (@ tptp.append2089414218ession E1) E22))))))
% 0.27/0.72 (assert (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (U tptp.list_S529945141ession) (V tptp.list_S529945141ession)) (@ (@ (@ tptp.lexord1123423577ession Less) U) (@ (@ tptp.append2089414218ession U) V))))
% 0.27/0.72 (assert (forall ((P tptp.secrecy_specID) (A4 tptp.secrecy_Expression) (L tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.notSpe1586871396tsExpr P))) (=> (@ _let_1 (@ (@ tptp.cons_S112077679ession A4) L)) (@ _let_1 L)))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ (@ tptp.splice1390717708ession (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.splice1390717708ession Ys2) Xs))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession)) (= (@ (@ tptp.splice1390717708ession tptp.nil_Se901661471ession) Ys2) Ys2)))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS)) (= (@ (@ tptp.splice_Secrecy_KS tptp.nil_Secrecy_KS) Ys2) Ys2)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS Bool))) (=> (not (= Xs tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (@ P (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (not (= Xs2 tptp.nil_Secrecy_KS)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_Secrecy_KS Xs2) (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS)))))) (@ P Xs))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession Bool))) (=> (not (= Xs tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (@ P (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (not (= Xs2 tptp.nil_Se901661471ession)) (=> (@ P Xs2) (@ P (@ (@ tptp.append2089414218ession Xs2) (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession)))))) (@ P Xs))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS) (Zs2 tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) Xs))) (= (= (@ (@ tptp.append_Secrecy_KS Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_Secrecy_KS) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_Secrecy_KS)) (and (= Ys2 (@ (@ tptp.cons_Secrecy_KS X3) Ys4)) (= (@ (@ tptp.append_Secrecy_KS Ys4) Zs2) Xs))))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) Xs))) (= (= (@ (@ tptp.append2089414218ession Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_Se901661471ession) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_S529945141ession)) (and (= Ys2 (@ (@ tptp.cons_S112077679ession X3) Ys4)) (= (@ (@ tptp.append2089414218ession Ys4) Zs2) Xs))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS) (Zs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) Xs))) (= (= _let_1 (@ (@ tptp.append_Secrecy_KS Ys2) Zs2)) (or (and (= Ys2 tptp.nil_Secrecy_KS) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_Secrecy_KS)) (and (= (@ (@ tptp.cons_Secrecy_KS X3) Ys4) Ys2) (= Xs (@ (@ tptp.append_Secrecy_KS Ys4) Zs2)))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) Xs))) (= (= _let_1 (@ (@ tptp.append2089414218ession Ys2) Zs2)) (or (and (= Ys2 tptp.nil_Se901661471ession) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_S529945141ession)) (and (= (@ (@ tptp.cons_S112077679ession X3) Ys4) Ys2) (= Xs (@ (@ tptp.append2089414218ession Ys4) Zs2)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (not (forall ((Ys3 tptp.list_Secrecy_KS) (Y4 tptp.secrecy_KS)) (not (= Xs (@ (@ tptp.append_Secrecy_KS Ys3) (@ (@ tptp.cons_Secrecy_KS Y4) tptp.nil_Secrecy_KS)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (not (forall ((Ys3 tptp.list_S529945141ession) (Y4 tptp.secrecy_Expression)) (not (= Xs (@ (@ tptp.append2089414218ession Ys3) (@ (@ tptp.cons_S112077679ession Y4) tptp.nil_Se901661471ession)))))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_Secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS)) (=> (@ P tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_Secrecy_KS Xs2) (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))))) (@ P Xs)))))
% 0.27/0.72 (assert (forall ((P (-> tptp.list_S529945141ession Bool)) (Xs tptp.list_S529945141ession)) (=> (@ P tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (@ P Xs2) (@ P (@ (@ tptp.append2089414218ession Xs2) (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))))) (@ P Xs)))))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.maps_S599402637ession F2))) (= (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.append2089414218ession (@ F2 X3)) (@ _let_1 Xs))))))
% 0.27/0.72 (assert (forall ((K12 tptp.secrecy_Keys) (K22 tptp.secrecy_Keys) (E3 tptp.list_S529945141ession)) (=> (@ (@ tptp.encrDecrKeys K12) K22) (= (@ (@ tptp.ext K12) (@ (@ tptp.sign K22) E3)) E3))))
% 0.27/0.72 (assert (forall ((K12 tptp.secrecy_Keys) (K22 tptp.secrecy_Keys) (E3 tptp.list_S529945141ession)) (=> (@ (@ tptp.encrDecrKeys K12) K22) (= (@ (@ tptp.decr K22) (@ (@ tptp.enc K12) E3)) E3))))
% 0.27/0.72 (assert (forall ((Xss2 tptp.list_l425507653ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (= Xss2 tptp.nil_li311616943ession))) (= (= (@ tptp.concat388015140ession Xss2) (@ (@ tptp.append2089414218ession Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_Se901661471ession) (= Zs2 tptp.nil_Se901661471ession))) (=> (not _let_1) (exists ((Xss1 tptp.list_l425507653ession) (Xs3 tptp.list_S529945141ession) (Xs4 tptp.list_S529945141ession) (Xss22 tptp.list_l425507653ession)) (and (= Xss2 (@ (@ tptp.append1105297242ession Xss1) (@ (@ tptp.cons_l533358079ession (@ (@ tptp.append2089414218ession Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append2089414218ession (@ tptp.concat388015140ession Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append2089414218ession Xs4) (@ tptp.concat388015140ession Xss22)))))))))))
% 0.27/0.72 (assert (forall ((Xss2 tptp.list_list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS) (Zs2 tptp.list_Secrecy_KS)) (let ((_let_1 (= Xss2 tptp.nil_list_Secrecy_KS))) (= (= (@ tptp.concat_Secrecy_KS Xss2) (@ (@ tptp.append_Secrecy_KS Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_Secrecy_KS) (= Zs2 tptp.nil_Secrecy_KS))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_Secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Xs4 tptp.list_Secrecy_KS) (Xss22 tptp.list_list_Secrecy_KS)) (and (= Xss2 (@ (@ tptp.append1376766698ecy_KS Xss1) (@ (@ tptp.cons_list_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_Secrecy_KS (@ tptp.concat_Secrecy_KS Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_Secrecy_KS Xs4) (@ tptp.concat_Secrecy_KS Xss22)))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (= (@ tptp.rotate1_Secrecy_KS (@ _let_1 Xs)) (@ (@ tptp.append_Secrecy_KS Xs) (@ _let_1 tptp.nil_Secrecy_KS))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ tptp.rotate1237234450ession (@ _let_1 Xs)) (@ (@ tptp.append2089414218ession Xs) (@ _let_1 tptp.nil_Se901661471ession))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.rotate1237234450ession Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.rotate1_Secrecy_KS Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_l425507653ession) (Ys2 tptp.list_l425507653ession)) (= (@ tptp.concat388015140ession (@ (@ tptp.append1105297242ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.concat388015140ession Xs)) (@ tptp.concat388015140ession Ys2)))))
% 0.27/0.72 (assert (= (@ tptp.rotate1237234450ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession))
% 0.27/0.72 (assert (= (@ tptp.rotate1_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (= (@ tptp.concat388015140ession tptp.nil_li311616943ession) tptp.nil_Se901661471ession))
% 0.27/0.72 (assert (= (@ tptp.concat_Secrecy_KS tptp.nil_list_Secrecy_KS) tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (forall ((X3 tptp.list_S529945141ession) (Xs tptp.list_l425507653ession)) (= (@ tptp.concat388015140ession (@ (@ tptp.cons_l533358079ession X3) Xs)) (@ (@ tptp.append2089414218ession X3) (@ tptp.concat388015140ession Xs)))))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession))) (= (@ (@ tptp.maps_S599402637ession F2) tptp.nil_Se901661471ession) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_Expression tptp.list_Secrecy_KS))) (= (@ (@ tptp.maps_S399472669ecy_KS F2) tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_KS tptp.list_S529945141ession))) (= (@ (@ tptp.maps_S1434541085ession F2) tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((F2 (-> tptp.secrecy_KS tptp.list_Secrecy_KS))) (= (@ (@ tptp.maps_S377605037ecy_KS F2) tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((Xss2 tptp.list_l425507653ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (=> (= (@ tptp.concat388015140ession Xss2) (@ (@ tptp.append2089414218ession Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_li311616943ession)) (exists ((Xss12 tptp.list_l425507653ession) (Xs2 tptp.list_S529945141ession) (Xs5 tptp.list_S529945141ession) (Xss23 tptp.list_l425507653ession)) (and (= Xss2 (@ (@ tptp.append1105297242ession Xss12) (@ (@ tptp.cons_l533358079ession (@ (@ tptp.append2089414218ession Xs2) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append2089414218ession (@ tptp.concat388015140ession Xss12)) Xs2)) (= Zs2 (@ (@ tptp.append2089414218ession Xs5) (@ tptp.concat388015140ession Xss23)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (= (@ tptp.butlast_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) Xs)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (= (@ tptp.butlas171474643ession (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) Xs)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) X3)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (= (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) X3)))
% 0.27/0.72 (assert (= tptp.notSpe1586871396tsExpr (lambda ((P3 tptp.secrecy_specID) (E2 tptp.list_S529945141ession)) (and (forall ((X4 tptp.secrecy_Keys)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_kE X4)) E2) (not (@ (@ tptp.member_Secrecy_KS2 (@ tptp.secrecy_kKS X4)) (@ tptp.specKeysSecrets P3))))) (forall ((Y3 tptp.secrecy_Secrets)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_sE Y3)) E2) (not (@ (@ tptp.member_Secrecy_KS2 (@ tptp.secrecy_sKS Y3)) (@ tptp.specKeysSecrets P3)))))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (=> (not (= Ys2 tptp.nil_Se901661471ession)) (= (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.last_S1532390982ession Ys2)))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (=> (not (= Ys2 tptp.nil_Secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ tptp.last_Secrecy_KS Ys2)))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (=> (= Ys2 tptp.nil_Se901661471ession) (= (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.last_S1532390982ession Xs)))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (=> (= Ys2 tptp.nil_Secrecy_KS) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ tptp.last_Secrecy_KS Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS (@ tptp.butlast_Secrecy_KS Xs)) (@ (@ tptp.cons_Secrecy_KS (@ tptp.last_Secrecy_KS Xs)) tptp.nil_Secrecy_KS)) Xs))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ (@ tptp.append2089414218ession (@ tptp.butlas171474643ession Xs)) (@ (@ tptp.cons_S112077679ession (@ tptp.last_S1532390982ession Xs)) tptp.nil_Se901661471ession)) Xs))))
% 0.27/0.72 (assert (= (@ tptp.butlas171474643ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession))
% 0.27/0.72 (assert (= (@ tptp.butlast_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS)) Ys2) (and (not (= Ys2 tptp.nil_Secrecy_KS)) (= (@ tptp.butlast_Secrecy_KS Ys2) Xs) (= (@ tptp.last_Secrecy_KS Ys2) X3)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession)) Ys2) (and (not (= Ys2 tptp.nil_Se901661471ession)) (= (@ tptp.butlas171474643ession Ys2) Xs) (= (@ tptp.last_S1532390982ession Ys2) X3)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)) (@ tptp.last_Secrecy_KS Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.last_S1532390982ession (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ tptp.last_S1532390982ession Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (=> (= Xs tptp.nil_Secrecy_KS) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)) X3))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (=> (= Xs tptp.nil_Se901661471ession) (= (@ tptp.last_S1532390982ession (@ (@ tptp.cons_S112077679ession X3) Xs)) X3))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.last_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_Secrecy_KS))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_Secrecy_KS Xs))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.last_S1532390982ession (@ (@ tptp.cons_S112077679ession X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_Se901661471ession))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_S1532390982ession Xs))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (exists ((Ss tptp.list_S529945141ession) (Xs5 tptp.list_S529945141ession) (Ys5 tptp.list_S529945141ession)) (and (= Xs (@ (@ tptp.append2089414218ession Xs5) Ss)) (= Ys2 (@ (@ tptp.append2089414218ession Ys5) Ss)) (or (= Xs5 tptp.nil_Se901661471ession) (= Ys5 tptp.nil_Se901661471ession) (not (= (@ tptp.last_S1532390982ession Xs5) (@ tptp.last_S1532390982ession Ys5))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (exists ((Ss tptp.list_Secrecy_KS) (Xs5 tptp.list_Secrecy_KS) (Ys5 tptp.list_Secrecy_KS)) (and (= Xs (@ (@ tptp.append_Secrecy_KS Xs5) Ss)) (= Ys2 (@ (@ tptp.append_Secrecy_KS Ys5) Ss)) (or (= Xs5 tptp.nil_Secrecy_KS) (= Ys5 tptp.nil_Secrecy_KS) (not (= (@ tptp.last_Secrecy_KS Xs5) (@ tptp.last_Secrecy_KS Ys5))))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_Se901661471ession))) (and (=> _let_2 (= _let_1 (@ tptp.last_S1532390982ession Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_S1532390982ession Ys2))))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_Secrecy_KS))) (and (=> _let_2 (= _let_1 (@ tptp.last_Secrecy_KS Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_Secrecy_KS Ys2))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (let ((_let_2 (@ tptp.butlast_Secrecy_KS (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_Secrecy_KS))) (and (=> _let_3 (= _let_2 tptp.nil_Secrecy_KS)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_Secrecy_KS Xs))))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (let ((_let_2 (@ tptp.butlas171474643ession (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_Se901661471ession))) (and (=> _let_3 (= _let_2 tptp.nil_Se901661471ession)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas171474643ession Xs))))))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (let ((_let_2 (@ tptp.butlas171474643ession (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_Se901661471ession))) (and (=> _let_3 (= _let_2 (@ tptp.butlas171474643ession Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas171474643ession Ys2))))))))))
% 0.27/0.72 (assert (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.append_Secrecy_KS Xs))) (let ((_let_2 (@ tptp.butlast_Secrecy_KS (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_Secrecy_KS))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_Secrecy_KS Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_Secrecy_KS Ys2))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS)) (not (@ (@ tptp.mem_Secrecy_KS X3) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression)) (not (@ (@ tptp.mem_Se1967555118ession X3) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (L tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.mem_Se1967555118ession X3))) (= (@ _let_1 (@ (@ tptp.cons_S112077679ession Y) L)) (or (= X3 Y) (@ _let_1 L))))))
% 0.27/0.72 (assert (= tptp.concat388015140ession (lambda ((Xss3 tptp.list_l425507653ession)) (@ (@ (@ tptp.foldr_1531709715ession tptp.append2089414218ession) Xss3) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (= tptp.concat_Secrecy_KS (lambda ((Xss3 tptp.list_list_Secrecy_KS)) (@ (@ (@ tptp.foldr_1711005747ecy_KS tptp.append_Secrecy_KS) Xss3) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Kl tptp.list_Secrecy_Secrets) (K tptp.secrecy_Secrets) (Kl2 tptp.set_li2007071804ecrets)) (=> (@ (@ tptp.member1138497285ecrets (@ (@ tptp.append186372209ecrets Kl) (@ (@ tptp.cons_Secrecy_Secrets K) tptp.nil_Secrecy_Secrets))) Kl2) (@ (@ tptp.member2138796287ecrets K) (@ (@ tptp.bNF_Gr957048817ecrets Kl2) Kl)))))
% 0.27/0.72 (assert (forall ((Kl tptp.list_Secrecy_Keys) (K tptp.secrecy_Keys) (Kl2 tptp.set_li849033543y_Keys)) (=> (@ (@ tptp.member341114536y_Keys (@ (@ tptp.append_Secrecy_Keys Kl) (@ (@ tptp.cons_Secrecy_Keys K) tptp.nil_Secrecy_Keys))) Kl2) (@ (@ tptp.member_Secrecy_Keys K) (@ (@ tptp.bNF_Gr344893606y_Keys Kl2) Kl)))))
% 0.27/0.72 (assert (forall ((Kl tptp.list_Secrecy_KS) (K tptp.secrecy_KS) (Kl2 tptp.set_list_Secrecy_KS)) (=> (@ (@ tptp.member193705948ecy_KS (@ (@ tptp.append_Secrecy_KS Kl) (@ (@ tptp.cons_Secrecy_KS K) tptp.nil_Secrecy_KS))) Kl2) (@ (@ tptp.member_Secrecy_KS2 K) (@ (@ tptp.bNF_Gr577175642ecy_KS Kl2) Kl)))))
% 0.27/0.72 (assert (forall ((Kl tptp.list_S529945141ession) (K tptp.secrecy_Expression) (Kl2 tptp.set_li185139947ession)) (=> (@ (@ tptp.member249235532ession (@ (@ tptp.append2089414218ession Kl) (@ (@ tptp.cons_S112077679ession K) tptp.nil_Se901661471ession))) Kl2) (@ (@ tptp.member279582780ession K) (@ (@ tptp.bNF_Gr979629770ession Kl2) Kl)))))
% 0.27/0.72 (assert (forall ((K tptp.secrecy_Secrets) (Kl2 tptp.set_li2007071804ecrets) (Kl tptp.list_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets K) (@ (@ tptp.bNF_Gr957048817ecrets Kl2) Kl)) (@ (@ tptp.member1138497285ecrets (@ (@ tptp.append186372209ecrets Kl) (@ (@ tptp.cons_Secrecy_Secrets K) tptp.nil_Secrecy_Secrets))) Kl2))))
% 0.27/0.72 (assert (forall ((K tptp.secrecy_Keys) (Kl2 tptp.set_li849033543y_Keys) (Kl tptp.list_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys K) (@ (@ tptp.bNF_Gr344893606y_Keys Kl2) Kl)) (@ (@ tptp.member341114536y_Keys (@ (@ tptp.append_Secrecy_Keys Kl) (@ (@ tptp.cons_Secrecy_Keys K) tptp.nil_Secrecy_Keys))) Kl2))))
% 0.27/0.72 (assert (forall ((K tptp.secrecy_KS) (Kl2 tptp.set_list_Secrecy_KS) (Kl tptp.list_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS2 K) (@ (@ tptp.bNF_Gr577175642ecy_KS Kl2) Kl)) (@ (@ tptp.member193705948ecy_KS (@ (@ tptp.append_Secrecy_KS Kl) (@ (@ tptp.cons_Secrecy_KS K) tptp.nil_Secrecy_KS))) Kl2))))
% 0.27/0.72 (assert (forall ((K tptp.secrecy_Expression) (Kl2 tptp.set_li185139947ession) (Kl tptp.list_S529945141ession)) (=> (@ (@ tptp.member279582780ession K) (@ (@ tptp.bNF_Gr979629770ession Kl2) Kl)) (@ (@ tptp.member249235532ession (@ (@ tptp.append2089414218ession Kl) (@ (@ tptp.cons_S112077679ession K) tptp.nil_Se901661471ession))) Kl2))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Y tptp.secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS Y))) (= (= (@ tptp.rev_Secrecy_KS Xs) (@ _let_1 Ys2)) (= Xs (@ (@ tptp.append_Secrecy_KS (@ tptp.rev_Secrecy_KS Ys2)) (@ _let_1 tptp.nil_Secrecy_KS)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Y tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession Y))) (= (= (@ tptp.rev_Se1073238207ession Xs) (@ _let_1 Ys2)) (= Xs (@ (@ tptp.append2089414218ession (@ tptp.rev_Se1073238207ession Ys2)) (@ _let_1 tptp.nil_Se901661471ession)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (= tptp.nil_Se901661471ession (@ tptp.rev_Se1073238207ession Xs)) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (= tptp.nil_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.rev_Se1073238207ession Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.rev_Secrecy_KS Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (@ tptp.rev_Se1073238207ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.rev_Se1073238207ession Ys2)) (@ tptp.rev_Se1073238207ession Xs)))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (= (= _let_1 (@ tptp.rev_Secrecy_KS Xs)) (= Xs _let_1)))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (= (= _let_1 (@ tptp.rev_Se1073238207ession Xs)) (= Xs _let_1)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (= (= (@ tptp.rev_Secrecy_KS Xs) _let_1) (= Xs _let_1)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (= (= (@ tptp.rev_Se1073238207ession Xs) _let_1) (= Xs _let_1)))))
% 0.27/0.72 (assert (= (@ tptp.rev_Se1073238207ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession))
% 0.27/0.72 (assert (= (@ tptp.rev_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (= (@ tptp.rev_Secrecy_KS (@ _let_1 Xs)) (@ (@ tptp.append_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (@ _let_1 tptp.nil_Secrecy_KS))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ tptp.rev_Se1073238207ession (@ _let_1 Xs)) (@ (@ tptp.append2089414218ession (@ tptp.rev_Se1073238207ession Xs)) (@ _let_1 tptp.nil_Se901661471ession))))))
% 0.27/0.72 (assert (forall ((Kl2 tptp.set_li2007071804ecrets) (K tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member1138497285ecrets tptp.nil_Secrecy_Secrets))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member2138796287ecrets K) (@ (@ tptp.bNF_Gr957048817ecrets Kl2) tptp.nil_Secrecy_Secrets)) (@ _let_1 (@ (@ tptp.bNF_Gr28627573ecrets Kl2) K)))))))
% 0.27/0.72 (assert (forall ((Kl2 tptp.set_li849033543y_Keys) (K tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member341114536y_Keys tptp.nil_Secrecy_Keys))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_Secrecy_Keys K) (@ (@ tptp.bNF_Gr344893606y_Keys Kl2) tptp.nil_Secrecy_Keys)) (@ _let_1 (@ (@ tptp.bNF_Gr414702370y_Keys Kl2) K)))))))
% 0.27/0.72 (assert (forall ((Kl2 tptp.set_li185139947ession) (K tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.member249235532ession tptp.nil_Se901661471ession))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member279582780ession K) (@ (@ tptp.bNF_Gr979629770ession Kl2) tptp.nil_Se901661471ession)) (@ _let_1 (@ (@ tptp.bNF_Gr275623750ession Kl2) K)))))))
% 0.27/0.72 (assert (forall ((Kl2 tptp.set_list_Secrecy_KS) (K tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member193705948ecy_KS tptp.nil_Secrecy_KS))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_Secrecy_KS2 K) (@ (@ tptp.bNF_Gr577175642ecy_KS Kl2) tptp.nil_Secrecy_KS)) (@ _let_1 (@ (@ tptp.bNF_Gr660123862ecy_KS Kl2) K)))))))
% 0.27/0.72 (assert (forall ((Kl tptp.list_S529945141ession) (Kl2 tptp.set_li185139947ession) (K tptp.secrecy_Expression)) (=> (@ (@ tptp.member249235532ession Kl) (@ (@ tptp.bNF_Gr275623750ession Kl2) K)) (@ (@ tptp.member249235532ession (@ (@ tptp.cons_S112077679ession K) Kl)) Kl2))))
% 0.27/0.72 (assert (forall ((Kl2 tptp.set_li185139947ession) (K tptp.secrecy_Expression) (Kl tptp.list_S529945141ession)) (= (@ (@ tptp.bNF_Gr979629770ession (@ (@ tptp.bNF_Gr275623750ession Kl2) K)) Kl) (@ (@ tptp.bNF_Gr979629770ession Kl2) (@ (@ tptp.cons_S112077679ession K) Kl)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.last_S1532390982ession (@ tptp.rev_Se1073238207ession Xs)) (@ tptp.hd_Sec357328890ession Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (@ tptp.hd_Secrecy_KS Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession (@ tptp.rev_Se1073238207ession Xs)) (@ tptp.last_S1532390982ession Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (@ tptp.last_Secrecy_KS Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.hd_Sec357328890ession Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ tptp.hd_Secrecy_KS Xs)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.hd_Sec357328890ession (@ (@ tptp.append2089414218ession Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_Se901661471ession))) (and (=> _let_2 (= _let_1 (@ tptp.hd_Sec357328890ession Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_Sec357328890ession Xs))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.hd_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_Secrecy_KS))) (and (=> _let_2 (= _let_1 (@ tptp.hd_Secrecy_KS Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_Secrecy_KS Xs))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (exists ((Ps tptp.list_S529945141ession) (Xs5 tptp.list_S529945141ession) (Ys5 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_Se901661471ession) (= Ys5 tptp.nil_Se901661471ession) (not (= (@ tptp.hd_Sec357328890ession Xs5) (@ tptp.hd_Sec357328890ession Ys5)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (exists ((Ps tptp.list_Secrecy_KS) (Xs5 tptp.list_Secrecy_KS) (Ys5 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.append_Secrecy_KS Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_Secrecy_KS) (= Ys5 tptp.nil_Secrecy_KS) (not (= (@ tptp.hd_Secrecy_KS Xs5) (@ tptp.hd_Secrecy_KS Ys5)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_l425507653ession)) (let ((_let_1 (@ tptp.hd_lis1623417098ession Xs))) (=> (not (= Xs tptp.nil_li311616943ession)) (=> (not (= _let_1 tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession (@ tptp.concat388015140ession Xs)) (@ tptp.hd_Sec357328890ession _let_1)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_list_Secrecy_KS)) (let ((_let_1 (@ tptp.hd_list_Secrecy_KS Xs))) (=> (not (= Xs tptp.nil_list_Secrecy_KS)) (=> (not (= _let_1 tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS (@ tptp.concat_Secrecy_KS Xs)) (@ tptp.hd_Secrecy_KS _let_1)))))))
% 0.27/0.72 (assert (forall ((X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession)) (= (@ tptp.hd_Sec357328890ession (@ (@ tptp.cons_S112077679ession X21) X222)) X21)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.rotate1_Secrecy_KS Xs) (@ (@ tptp.append_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS Xs)) tptp.nil_Secrecy_KS))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.rotate1237234450ession Xs) (@ (@ tptp.append2089414218ession (@ tptp.tl_Sec1905266422ession Xs)) (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession Xs)) tptp.nil_Se901661471ession))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (@ tptp.distin1076152135ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (and (@ tptp.distin1076152135ession Xs) (@ tptp.distin1076152135ession Ys2) (or (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession) (not (= (@ tptp.last_S1532390982ession Xs) (@ tptp.hd_Sec357328890ession Ys2))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (@ tptp.distin1495927511ecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (and (@ tptp.distin1495927511ecy_KS Xs) (@ tptp.distin1495927511ecy_KS Ys2) (or (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS) (not (= (@ tptp.last_Secrecy_KS Xs) (@ tptp.hd_Secrecy_KS Ys2))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y) Xs))) (= (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) _let_1)) (and (not (= X3 Y)) (@ tptp.distin1076152135ession _let_1))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.tl_Sec1905266422ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.tl_Sec1905266422ession Xs)) Ys2)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.tl_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ (@ tptp.append_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) Ys2)))))
% 0.27/0.72 (assert (forall ((List tptp.list_Secrecy_KS)) (=> (not (= List tptp.nil_Secrecy_KS)) (= (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS List)) (@ tptp.tl_Secrecy_KS List)) List))))
% 0.27/0.72 (assert (forall ((List tptp.list_S529945141ession)) (=> (not (= List tptp.nil_Se901661471ession)) (= (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession List)) (@ tptp.tl_Sec1905266422ession List)) List))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS Xs)) (@ tptp.tl_Secrecy_KS Xs)) Xs))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession Xs)) (@ tptp.tl_Sec1905266422ession Xs)) Xs))))
% 0.27/0.72 (assert (forall ((List tptp.list_S529945141ession) (List2 tptp.list_S529945141ession)) (let ((_let_1 (= List2 tptp.nil_Se901661471ession))) (let ((_let_2 (= List tptp.nil_Se901661471ession))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_Sec357328890ession List) (@ tptp.hd_Sec357328890ession List2)) (= (@ tptp.tl_Sec1905266422ession List) (@ tptp.tl_Sec1905266422ession List2))))) (= List List2)))))))
% 0.27/0.72 (assert (forall ((List tptp.list_Secrecy_KS) (List2 tptp.list_Secrecy_KS)) (let ((_let_1 (= List2 tptp.nil_Secrecy_KS))) (let ((_let_2 (= List tptp.nil_Secrecy_KS))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_Secrecy_KS List) (@ tptp.hd_Secrecy_KS List2)) (= (@ tptp.tl_Secrecy_KS List) (@ tptp.tl_Secrecy_KS List2))))) (= List List2)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ tptp.distin1076152135ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.distin1076152135ession Xs))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ tptp.distin1076152135ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.distin1076152135ession Ys2))))
% 0.27/0.72 (assert (@ tptp.distin1076152135ession tptp.nil_Se901661471ession))
% 0.27/0.72 (assert (@ tptp.distin1495927511ecy_KS tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (=> (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ tptp.distin1076152135ession Xs))))
% 0.27/0.72 (assert (= (@ tptp.tl_Sec1905266422ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession))
% 0.27/0.72 (assert (= (@ tptp.tl_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS))
% 0.27/0.72 (assert (forall ((X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession)) (= (@ tptp.tl_Sec1905266422ession (@ (@ tptp.cons_S112077679ession X21) X222)) X222)))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.tl_Secrecy_KS Xs) tptp.nil_Secrecy_KS) (or (= Xs tptp.nil_Secrecy_KS) (exists ((X4 tptp.secrecy_KS)) (= Xs (@ (@ tptp.cons_Secrecy_KS X4) tptp.nil_Secrecy_KS)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.tl_Sec1905266422ession Xs) tptp.nil_Se901661471ession) (or (= Xs tptp.nil_Se901661471ession) (exists ((X4 tptp.secrecy_Expression)) (= Xs (@ (@ tptp.cons_S112077679ession X4) tptp.nil_Se901661471ession)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (= tptp.nil_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) (or (= Xs tptp.nil_Secrecy_KS) (exists ((X4 tptp.secrecy_KS)) (= Xs (@ (@ tptp.cons_Secrecy_KS X4) tptp.nil_Secrecy_KS)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (= tptp.nil_Se901661471ession (@ tptp.tl_Sec1905266422ession Xs)) (or (= Xs tptp.nil_Se901661471ession) (exists ((X4 tptp.secrecy_Expression)) (= Xs (@ (@ tptp.cons_S112077679ession X4) tptp.nil_Se901661471ession)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.tl_Sec1905266422ession Xs))) (=> (or (= Xs tptp.nil_Se901661471ession) (not (= _let_1 tptp.nil_Se901661471ession))) (= (@ tptp.last_S1532390982ession _let_1) (@ tptp.last_S1532390982ession Xs))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.tl_Secrecy_KS Xs))) (=> (or (= Xs tptp.nil_Secrecy_KS) (not (= _let_1 tptp.nil_Secrecy_KS))) (= (@ tptp.last_Secrecy_KS _let_1) (@ tptp.last_Secrecy_KS Xs))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS)) (@ tptp.distin1495927511ecy_KS (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression)) (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((List tptp.list_Secrecy_KS)) (=> (not (= List tptp.nil_Secrecy_KS)) (= List (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS List)) (@ tptp.tl_Secrecy_KS List))))))
% 0.27/0.72 (assert (forall ((List tptp.list_S529945141ession)) (=> (not (= List tptp.nil_Se901661471ession)) (= List (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession List)) (@ tptp.tl_Sec1905266422ession List))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (= (@ tptp.distin1495927511ecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)) (or (= Xs tptp.nil_Secrecy_KS) (and (not (= X3 (@ tptp.hd_Secrecy_KS Xs))) (@ tptp.distin1495927511ecy_KS Xs))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (= (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) Xs)) (or (= Xs tptp.nil_Se901661471ession) (and (not (= X3 (@ tptp.hd_Sec357328890ession Xs))) (@ tptp.distin1076152135ession Xs))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.succes1388047762ession P))) (= (@ _let_1 (@ (@ tptp.append2089414218ession Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession) (@ (@ P (@ tptp.last_S1532390982ession Xs)) (@ tptp.hd_Sec357328890ession Ys2))))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.succes590251810ecy_KS P))) (= (@ _let_1 (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS) (@ (@ P (@ tptp.last_Secrecy_KS Xs)) (@ tptp.hd_Secrecy_KS Ys2))))))))
% 0.27/0.72 (assert (forall ((Z tptp.secrecy_KS) (Zs2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.shuffles_Secrecy_KS Xs))) (let ((_let_2 (@ tptp.member193705948ecy_KS Zs2))) (= (@ (@ tptp.member193705948ecy_KS (@ (@ tptp.cons_Secrecy_KS Z) Zs2)) (@ _let_1 Ys2)) (or (and (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS Xs) Z) (@ _let_2 (@ (@ tptp.shuffles_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) Ys2))) (and (not (= Ys2 tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS Ys2) Z) (@ _let_2 (@ _let_1 (@ tptp.tl_Secrecy_KS Ys2))))))))))
% 0.27/0.72 (assert (forall ((Z tptp.secrecy_Expression) (Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.shuffl552897610ession Xs))) (let ((_let_2 (@ tptp.member249235532ession Zs2))) (= (@ (@ tptp.member249235532ession (@ (@ tptp.cons_S112077679ession Z) Zs2)) (@ _let_1 Ys2)) (or (and (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession Xs) Z) (@ _let_2 (@ (@ tptp.shuffl552897610ession (@ tptp.tl_Sec1905266422ession Xs)) Ys2))) (and (not (= Ys2 tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession Ys2) Z) (@ _let_2 (@ _let_1 (@ tptp.tl_Sec1905266422ession Ys2))))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (@ (@ tptp.member249235532ession tptp.nil_Se901661471ession) (@ (@ tptp.shuffl552897610ession Xs) Ys2)) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (@ (@ tptp.member193705948ecy_KS tptp.nil_Secrecy_KS) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys2)) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))))
% 0.27/0.72 (assert (forall ((Zs2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (@ (@ tptp.member193705948ecy_KS Zs2) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys2)) (=> (=> (= Zs2 Xs) (not (= Ys2 tptp.nil_Secrecy_KS))) (=> (=> (= Zs2 Ys2) (not (= Xs tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Xs5 tptp.list_Secrecy_KS)) (=> (= Xs (@ (@ tptp.cons_Secrecy_KS X) Xs5)) (forall ((Z2 tptp.secrecy_KS) (Zs3 tptp.list_Secrecy_KS)) (=> (= Zs2 (@ (@ tptp.cons_Secrecy_KS Z2) Zs3)) (=> (= X Z2) (not (@ (@ tptp.member193705948ecy_KS Zs3) (@ (@ tptp.shuffles_Secrecy_KS Xs5) Ys2)))))))) (not (forall ((Y4 tptp.secrecy_KS) (Ys5 tptp.list_Secrecy_KS)) (=> (= Ys2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys5)) (forall ((Z2 tptp.secrecy_KS) (Zs3 tptp.list_Secrecy_KS)) (=> (= Zs2 (@ (@ tptp.cons_Secrecy_KS Z2) Zs3)) (=> (= Y4 Z2) (not (@ (@ tptp.member193705948ecy_KS Zs3) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys5)))))))))))))))
% 0.27/0.72 (assert (forall ((Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ (@ tptp.member249235532ession Zs2) (@ (@ tptp.shuffl552897610ession Xs) Ys2)) (=> (=> (= Zs2 Xs) (not (= Ys2 tptp.nil_Se901661471ession))) (=> (=> (= Zs2 Ys2) (not (= Xs tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Xs5 tptp.list_S529945141ession)) (=> (= Xs (@ (@ tptp.cons_S112077679ession X) Xs5)) (forall ((Z2 tptp.secrecy_Expression) (Zs3 tptp.list_S529945141ession)) (=> (= Zs2 (@ (@ tptp.cons_S112077679ession Z2) Zs3)) (=> (= X Z2) (not (@ (@ tptp.member249235532ession Zs3) (@ (@ tptp.shuffl552897610ession Xs5) Ys2)))))))) (not (forall ((Y4 tptp.secrecy_Expression) (Ys5 tptp.list_S529945141ession)) (=> (= Ys2 (@ (@ tptp.cons_S112077679ession Y4) Ys5)) (forall ((Z2 tptp.secrecy_Expression) (Zs3 tptp.list_S529945141ession)) (=> (= Zs2 (@ (@ tptp.cons_S112077679ession Z2) Zs3)) (=> (= Y4 Z2) (not (@ (@ tptp.member249235532ession Zs3) (@ (@ tptp.shuffl552897610ession Xs) Ys5)))))))))))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X3 tptp.secrecy_KS)) (@ (@ tptp.succes590251810ecy_KS P) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression)) (@ (@ tptp.succes1388047762ession P) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xa tptp.list_Secrecy_KS) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.succes590251810ecy_KS X3) Xa) Y) (=> (=> (= Xa tptp.nil_Secrecy_KS) _let_1) (=> (=> (exists ((X tptp.secrecy_KS)) (= Xa (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) _let_1) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_Secrecy_KS X) _let_1)) (= Y (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes590251810ecy_KS X3) _let_1))))))))))))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xa tptp.list_S529945141ession) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.succes1388047762ession X3) Xa) Y) (=> (=> (= Xa tptp.nil_Se901661471ession) _let_1) (=> (=> (exists ((X tptp.secrecy_Expression)) (= Xa (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) _let_1) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_S112077679ession X) _let_1)) (= Y (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes1388047762ession X3) _let_1))))))))))))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xa tptp.list_Secrecy_KS)) (=> (@ (@ tptp.succes590251810ecy_KS X3) Xa) (=> (not (= Xa tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (not (= Xa (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS)))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_Secrecy_KS X) _let_1)) (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes590251810ecy_KS X3) _let_1))))))))))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xa tptp.list_S529945141ession)) (=> (@ (@ tptp.succes1388047762ession X3) Xa) (=> (not (= Xa tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (not (= Xa (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession)))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_S112077679ession X) _let_1)) (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes1388047762ession X3) _let_1))))))))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ tptp.succes1388047762ession P) tptp.nil_Se901661471ession)))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ tptp.succes590251810ecy_KS P) tptp.nil_Secrecy_KS)))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y) Xs))) (let ((_let_2 (@ tptp.succes1388047762ession P))) (= (@ _let_2 (@ (@ tptp.cons_S112077679ession X3) _let_1)) (and (@ (@ P X3) Y) (@ _let_2 _let_1)))))))
% 0.27/0.72 (assert (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xa tptp.list_S529945141ession)) (=> (not (@ (@ tptp.succes1388047762ession X3) Xa)) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_S112077679ession X) _let_1)) (and (@ (@ X3 X) Y4) (@ (@ tptp.succes1388047762ession X3) _let_1)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (= Xs tptp.nil_Se901661471ession) (=> (= Ys2 tptp.nil_Se901661471ession) (@ (@ tptp.member249235532ession tptp.nil_Se901661471ession) (@ (@ tptp.shuffl552897610ession Xs) Ys2))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (= Xs tptp.nil_Secrecy_KS) (=> (= Ys2 tptp.nil_Secrecy_KS) (@ (@ tptp.member193705948ecy_KS tptp.nil_Secrecy_KS) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys2))))))
% 0.27/0.72 (assert (forall ((Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Z tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.cons_S112077679ession Z))) (let ((_let_2 (@ tptp.shuffl552897610ession Xs))) (=> (@ (@ tptp.member249235532ession Zs2) (@ _let_2 Ys2)) (@ (@ tptp.member249235532ession (@ _let_1 Zs2)) (@ _let_2 (@ _let_1 Ys2))))))))
% 0.27/0.72 (assert (forall ((Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Z tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.cons_S112077679ession Z))) (=> (@ (@ tptp.member249235532ession Zs2) (@ (@ tptp.shuffl552897610ession Xs) Ys2)) (@ (@ tptp.member249235532ession (@ _let_1 Zs2)) (@ (@ tptp.shuffl552897610ession (@ _let_1 Xs)) Ys2))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.succes590251810ecy_KS P))) (= (@ _let_1 (@ (@ tptp.cons_Secrecy_KS X3) Xs)) (or (= Xs tptp.nil_Secrecy_KS) (and (@ (@ P X3) (@ tptp.hd_Secrecy_KS Xs)) (@ _let_1 Xs)))))))
% 0.27/0.72 (assert (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.succes1388047762ession P))) (= (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (or (= Xs tptp.nil_Se901661471ession) (and (@ (@ P X3) (@ tptp.hd_Sec357328890ession Xs)) (@ _let_1 Xs)))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (or (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession) (not (= (@ tptp.last_S1532390982ession Xs) (@ tptp.hd_Sec357328890ession Ys2)))) (= (@ tptp.remdup484344169ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.remdup484344169ession Xs)) (@ tptp.remdup484344169ession Ys2))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (or (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS) (not (= (@ tptp.last_Secrecy_KS Xs) (@ tptp.hd_Secrecy_KS Ys2)))) (= (@ tptp.remdup351570169ecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ (@ tptp.append_Secrecy_KS (@ tptp.remdup351570169ecy_KS Xs)) (@ tptp.remdup351570169ecy_KS Ys2))))))
% 0.27/0.72 (assert (forall ((Xs_1 tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Xs_2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (let ((_let_2 (@ _let_1 Xs_2))) (let ((_let_3 (@ tptp.append_Secrecy_KS Xs_1))) (= (@ tptp.remdup351570169ecy_KS (@ _let_3 _let_2)) (@ (@ tptp.append_Secrecy_KS (@ tptp.remdup351570169ecy_KS (@ _let_3 (@ _let_1 tptp.nil_Secrecy_KS)))) (@ tptp.tl_Secrecy_KS (@ tptp.remdup351570169ecy_KS _let_2)))))))))
% 0.27/0.72 (assert (forall ((Xs_1 tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Xs_2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (let ((_let_2 (@ _let_1 Xs_2))) (let ((_let_3 (@ tptp.append2089414218ession Xs_1))) (= (@ tptp.remdup484344169ession (@ _let_3 _let_2)) (@ (@ tptp.append2089414218ession (@ tptp.remdup484344169ession (@ _let_3 (@ _let_1 tptp.nil_Se901661471ession)))) (@ tptp.tl_Sec1905266422ession (@ tptp.remdup484344169ession _let_2)))))))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.remdup484344169ession Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))))
% 0.27/0.72 (assert (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.remdup351570169ecy_KS Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (let ((_let_2 (@ tptp.remdup484344169ession (@ _let_1 Xs)))) (= (@ _let_1 (@ tptp.tl_Sec1905266422ession _let_2)) _let_2)))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (= (@ tptp.remdup351570169ecy_KS _let_1) _let_1))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (= (@ tptp.remdup484344169ession _let_1) _let_1))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_Secrecy_KS) (Y tptp.list_Secrecy_KS)) (=> (= (@ tptp.remdup351570169ecy_KS X3) Y) (=> (=> (= X3 tptp.nil_Secrecy_KS) (not (= Y tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (= X3 _let_1) (not (= Y _let_1))))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (let ((_let_2 (@ tptp.cons_Secrecy_KS X))) (let ((_let_3 (= X Y4))) (=> (= X3 (@ _let_2 _let_1)) (not (and (=> _let_3 (= Y (@ tptp.remdup351570169ecy_KS (@ _let_2 Xs2)))) (=> (not _let_3) (= Y (@ _let_2 (@ tptp.remdup351570169ecy_KS _let_1)))))))))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ tptp.remdup484344169ession X3) Y) (=> (=> (= X3 tptp.nil_Se901661471ession) (not (= Y tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (= X3 _let_1) (not (= Y _let_1))))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (let ((_let_2 (@ tptp.cons_S112077679ession X))) (let ((_let_3 (= X Y4))) (=> (= X3 (@ _let_2 _let_1)) (not (and (=> _let_3 (= Y (@ tptp.remdup484344169ession (@ _let_2 Xs2)))) (=> (not _let_3) (= Y (@ _let_2 (@ tptp.remdup484344169ession _let_1)))))))))))))))))
% 0.27/0.72 (assert (forall ((X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y) Xs))) (let ((_let_2 (@ tptp.cons_S112077679ession X3))) (let ((_let_3 (@ tptp.remdup484344169ession (@ _let_2 _let_1)))) (let ((_let_4 (= X3 Y))) (and (=> _let_4 (= _let_3 (@ tptp.remdup484344169ession (@ _let_2 Xs)))) (=> (not _let_4) (= _let_3 (@ _let_2 (@ tptp.remdup484344169ession _let_1)))))))))))
% 0.27/0.72 (assert (not (@ (@ tptp.knowle945212990e_know tptp.a) (@ tptp.secrecy_sKS tptp.m))))
% 0.27/0.72 (set-info :filename cvc5---1.0.5_7361)
% 0.27/0.72 (check-sat-assuming ( true ))
% 0.27/0.72 ------- get file name : TPTP file name is ITP085^1
% 0.56/1.12 ------- cvc5-thf : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_7361.smt2...
% 0.56/1.12 --- Run --ho-elim --full-saturate-quant at 10...
% 0.56/1.12 % SZS status Theorem for ITP085^1
% 0.56/1.12 % SZS output start Proof for ITP085^1
% 0.56/1.12 (
% 0.56/1.12 (let ((_let_1 (not (@ (@ tptp.knowle945212990e_know tptp.a) (@ tptp.secrecy_sKS tptp.m))))) (let ((_let_2 (= tptp.concat_Secrecy_KS (lambda ((Xss3 tptp.list_list_Secrecy_KS)) (@ (@ (@ tptp.foldr_1711005747ecy_KS tptp.append_Secrecy_KS) Xss3) tptp.nil_Secrecy_KS))))) (let ((_let_3 (= tptp.notSpe1586871396tsExpr (lambda ((P3 tptp.secrecy_specID) (E2 tptp.list_S529945141ession)) (and (forall ((X4 tptp.secrecy_Keys)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_kE X4)) E2) (not (@ (@ tptp.member_Secrecy_KS2 (@ tptp.secrecy_kKS X4)) (@ tptp.specKeysSecrets P3))))) (forall ((Y3 tptp.secrecy_Secrets)) (=> (@ (@ tptp.mem_Se1967555118ession (@ tptp.secrecy_sE Y3)) E2) (not (@ (@ tptp.member_Secrecy_KS2 (@ tptp.secrecy_sKS Y3)) (@ tptp.specKeysSecrets P3)))))))))) (let ((_let_4 (@ tptp.concat388015140ession tptp.nil_li311616943ession))) (let ((_let_5 (= _let_4 tptp.nil_Se901661471ession))) (let ((_let_6 (= (@ tptp.secrec1371625429on2KSL tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS))) (let ((_let_7 (@ (@ tptp.cons_list_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_list_Secrecy_KS))) (let ((_let_8 (@ (@ tptp.cons_l533358079ession tptp.nil_Se901661471ession) tptp.nil_li311616943ession))) (let ((_let_9 (= tptp.knowle1268625169orrect (lambda ((C2 tptp.secrecy_specID) (E2 tptp.secrecy_Expression)) (= (@ (@ tptp.eout C2) E2) (or (exists ((K4 tptp.secrecy_Keys)) (and (= E2 (@ tptp.secrecy_kE K4)) (@ (@ tptp.member_Secrecy_Keys K4) (@ tptp.specKeys C2)))) (exists ((S2 tptp.secrecy_Secrets)) (and (= E2 (@ tptp.secrecy_sE S2)) (@ (@ tptp.member2138796287ecrets S2) (@ tptp.specSecrets C2)))) (@ (@ tptp.knowle731562421_knows C2) (@ (@ tptp.cons_S112077679ession E2) tptp.nil_Se901661471ession)))))))) (let ((_let_10 (forall ((M tptp.secrecy_Secrets)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_sKS M)) (@ tptp.secrecy_sE M))))) (let ((_let_11 (forall ((C tptp.secrecy_specID) (M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M2))) (= (@ (@ tptp.knowle731562421_knows C) (@ (@ tptp.cons_S112077679ession (@ tptp.secrec1016742679ession _let_1)) tptp.nil_Se901661471ession)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))) (let ((_let_12 (@ tptp.cons_S112077679ession (@ tptp.secrecy_sE tptp.m)))) (let ((_let_13 (@ tptp.knowle731562421_knows tptp.a))) (let ((_let_14 (@ _let_13 (@ _let_12 tptp.nil_Se901661471ession)))) (let ((_let_15 (ho_13 k_14 tptp.nil_li311616943ession))) (let ((_let_16 (ho_74 k_73 tptp.m))) (let ((_let_17 (ho_76 k_75 tptp.a))) (let ((_let_18 (ho_25 _let_17 (ho_20 (ho_28 k_27 _let_16) _let_15)))) (let ((_let_19 (ho_78 k_77 tptp.m))) (let ((_let_20 (ho_82 k_81 _let_19))) (let ((_let_21 (= _let_16 _let_20))) (let ((_let_22 (ho_25 _let_17 (ho_20 (ho_28 k_27 _let_20) _let_15)))) (let ((_let_23 (forall ((u |u_(-> tptp.secrecy_KS tptp.set_list_Secrecy_KS)|) (e tptp.set_list_Secrecy_KS) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.set_list_Secrecy_KS)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_241 v ii) (ite (= i ii) e (ho_241 u ii)))))))))) (let ((_let_24 (forall ((x |u_(-> tptp.secrecy_KS tptp.set_list_Secrecy_KS)|) (y |u_(-> tptp.secrecy_KS tptp.set_list_Secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_241 x z) (ho_241 y z)))) (= x y))))) (let ((_let_25 (forall ((u |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession Bool)|) (e |u_(-> tptp.set_li185139947ession Bool)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession Bool)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_226 v ii) (ite (= i ii) e (ho_226 u ii)))))))))) (let ((_let_26 (forall ((x |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession Bool)|) (y |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession Bool)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_226 x z) (ho_226 y z)))) (= x y))))) (let ((_let_27 (forall ((u |u_(-> tptp.secrecy_Expression tptp.set_li185139947ession)|) (e tptp.set_li185139947ession) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.set_li185139947ession)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_238 v ii) (ite (= i ii) e (ho_238 u ii)))))))))) (let ((_let_28 (forall ((x |u_(-> tptp.secrecy_Expression tptp.set_li185139947ession)|) (y |u_(-> tptp.secrecy_Expression tptp.set_li185139947ession)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_238 x z) (ho_238 y z)))) (= x y))))) (let ((_let_29 (forall ((u |u_(-> tptp.secrecy_Expression tptp.set_Se1942955227ession Bool)|) (e |u_(-> tptp.set_Se1942955227ession Bool)|) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.set_Se1942955227ession Bool)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_223 v ii) (ite (= i ii) e (ho_223 u ii)))))))))) (let ((_let_30 (forall ((x |u_(-> tptp.secrecy_Expression tptp.set_Se1942955227ession Bool)|) (y |u_(-> tptp.secrecy_Expression tptp.set_Se1942955227ession Bool)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_223 x z) (ho_223 y z)))) (= x y))))) (let ((_let_31 (forall ((u |u_(-> tptp.set_li185139947ession Bool)|) (e Bool) (i tptp.set_li185139947ession)) (not (forall ((v |u_(-> tptp.set_li185139947ession Bool)|)) (not (forall ((ii tptp.set_li185139947ession)) (= (ho_227 v ii) (ite (= i ii) e (ho_227 u ii)))))))))) (let ((_let_32 (forall ((x |u_(-> tptp.set_li185139947ession Bool)|) (y |u_(-> tptp.set_li185139947ession Bool)|)) (or (not (forall ((z tptp.set_li185139947ession)) (= (ho_227 x z) (ho_227 y z)))) (= x y))))) (let ((_let_33 (forall ((u |u_(-> tptp.set_li185139947ession tptp.list_S529945141ession tptp.set_Se1942955227ession)|) (e |u_(-> tptp.list_S529945141ession tptp.set_Se1942955227ession)|) (i tptp.set_li185139947ession)) (not (forall ((v |u_(-> tptp.set_li185139947ession tptp.list_S529945141ession tptp.set_Se1942955227ession)|)) (not (forall ((ii tptp.set_li185139947ession)) (= (ho_220 v ii) (ite (= i ii) e (ho_220 u ii)))))))))) (let ((_let_34 (forall ((x |u_(-> tptp.set_li185139947ession tptp.list_S529945141ession tptp.set_Se1942955227ession)|) (y |u_(-> tptp.set_li185139947ession tptp.list_S529945141ession tptp.set_Se1942955227ession)|)) (or (not (forall ((z tptp.set_li185139947ession)) (= (ho_220 x z) (ho_220 y z)))) (= x y))))) (let ((_let_35 (forall ((u |u_(-> tptp.list_S529945141ession tptp.set_Se1942955227ession)|) (e tptp.set_Se1942955227ession) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.set_Se1942955227ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_221 v ii) (ite (= i ii) e (ho_221 u ii)))))))))) (let ((_let_36 (forall ((x |u_(-> tptp.list_S529945141ession tptp.set_Se1942955227ession)|) (y |u_(-> tptp.list_S529945141ession tptp.set_Se1942955227ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_221 x z) (ho_221 y z)))) (= x y))))) (let ((_let_37 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|) (e tptp.set_Secrecy_KS) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_215 v ii) (ite (= i ii) e (ho_215 u ii)))))))))) (let ((_let_38 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_215 x z) (ho_215 y z)))) (= x y))))) (let ((_let_39 (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_69 v ii) (ite (= i ii) e (ho_69 u ii)))))))))) (let ((_let_40 (forall ((x |u_(-> tptp.secrecy_Secrets Bool)|) (y |u_(-> tptp.secrecy_Secrets Bool)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_69 x z) (ho_69 y z)))) (= x y))))) (let ((_let_41 (forall ((u |u_(-> tptp.list_Secrecy_Keys tptp.set_li849033543y_Keys Bool)|) (e |u_(-> tptp.set_li849033543y_Keys Bool)|) (i tptp.list_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.list_Secrecy_Keys tptp.set_li849033543y_Keys Bool)|)) (not (forall ((ii tptp.list_Secrecy_Keys)) (= (ho_211 v ii) (ite (= i ii) e (ho_211 u ii)))))))))) (let ((_let_42 (forall ((x |u_(-> tptp.list_Secrecy_Keys tptp.set_li849033543y_Keys Bool)|) (y |u_(-> tptp.list_Secrecy_Keys tptp.set_li849033543y_Keys Bool)|)) (or (not (forall ((z tptp.list_Secrecy_Keys)) (= (ho_211 x z) (ho_211 y z)))) (= x y))))) (let ((_let_43 (forall ((u |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (e tptp.list_Secrecy_Keys) (i tptp.list_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|)) (not (forall ((ii tptp.list_Secrecy_Keys)) (= (ho_207 v ii) (ite (= i ii) e (ho_207 u ii)))))))))) (let ((_let_44 (forall ((x |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (y |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|)) (or (not (forall ((z tptp.list_Secrecy_Keys)) (= (ho_207 x z) (ho_207 y z)))) (= x y))))) (let ((_let_45 (forall ((u |u_(-> tptp.set_li849033543y_Keys Bool)|) (e Bool) (i tptp.set_li849033543y_Keys)) (not (forall ((v |u_(-> tptp.set_li849033543y_Keys Bool)|)) (not (forall ((ii tptp.set_li849033543y_Keys)) (= (ho_212 v ii) (ite (= i ii) e (ho_212 u ii)))))))))) (let ((_let_46 (forall ((x |u_(-> tptp.set_li849033543y_Keys Bool)|) (y |u_(-> tptp.set_li849033543y_Keys Bool)|)) (or (not (forall ((z tptp.set_li849033543y_Keys)) (= (ho_212 x z) (ho_212 y z)))) (= x y))))) (let ((_let_47 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_180 v ii) (ite (= i ii) e (ho_180 u ii)))))))))) (let ((_let_48 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_180 x z) (ho_180 y z)))) (= x y))))) (let ((_let_49 (forall ((u |u_(-> tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|) (e tptp.set_li2007071804ecrets) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_232 v ii) (ite (= i ii) e (ho_232 u ii)))))))))) (let ((_let_50 (forall ((x |u_(-> tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|) (y |u_(-> tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_232 x z) (ho_232 y z)))) (= x y))))) (let ((_let_51 (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_119 v ii) (ite (= i ii) e (ho_119 u ii)))))))))) (let ((_let_52 (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_119 x z) (ho_119 y z)))) (= x y))))) (let ((_let_53 (forall ((u |u_(-> tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|) (e tptp.set_Secrecy_Keys) (i tptp.list_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (not (forall ((ii tptp.list_Secrecy_Keys)) (= (ho_204 v ii) (ite (= i ii) e (ho_204 u ii)))))))))) (let ((_let_54 (forall ((x |u_(-> tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|) (y |u_(-> tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (or (not (forall ((z tptp.list_Secrecy_Keys)) (= (ho_204 x z) (ho_204 y z)))) (= x y))))) (let ((_let_55 (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_84 v ii) (ite (= i ii) e (ho_84 u ii)))))))))) (let ((_let_56 (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_84 x z) (ho_84 y z)))) (= x y))))) (let ((_let_57 (forall ((u |u_(-> tptp.list_Secrecy_Secrets tptp.set_li2007071804ecrets Bool)|) (e |u_(-> tptp.set_li2007071804ecrets Bool)|) (i tptp.list_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.list_Secrecy_Secrets tptp.set_li2007071804ecrets Bool)|)) (not (forall ((ii tptp.list_Secrecy_Secrets)) (= (ho_200 v ii) (ite (= i ii) e (ho_200 u ii)))))))))) (let ((_let_58 (forall ((x |u_(-> tptp.list_Secrecy_Secrets tptp.set_li2007071804ecrets Bool)|) (y |u_(-> tptp.list_Secrecy_Secrets tptp.set_li2007071804ecrets Bool)|)) (or (not (forall ((z tptp.list_Secrecy_Secrets)) (= (ho_200 x z) (ho_200 y z)))) (= x y))))) (let ((_let_59 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession Bool)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_24 v ii) (ite (= i ii) e (ho_24 u ii)))))))))) (let ((_let_60 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (y |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_24 x z) (ho_24 y z)))) (= x y))))) (let ((_let_61 (forall ((u |u_(-> tptp.secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (e |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (i tptp.secrecy_Secrets)) (not (forall ((v |u_(-> tptp.secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|)) (not (forall ((ii tptp.secrecy_Secrets)) (= (ho_195 v ii) (ite (= i ii) e (ho_195 u ii)))))))))) (let ((_let_62 (forall ((x |u_(-> tptp.secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (y |u_(-> tptp.secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|)) (or (not (forall ((z tptp.secrecy_Secrets)) (= (ho_195 x z) (ho_195 y z)))) (= x y))))) (let ((_let_63 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS Bool)|) (e |u_(-> tptp.set_list_Secrecy_KS Bool)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS Bool)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_217 v ii) (ite (= i ii) e (ho_217 u ii)))))))))) (let ((_let_64 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS Bool)|) (y |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_217 x z) (ho_217 y z)))) (= x y))))) (let ((_let_65 (forall ((u |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (e tptp.list_Secrecy_Secrets) (i tptp.list_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|)) (not (forall ((ii tptp.list_Secrecy_Secrets)) (= (ho_196 v ii) (ite (= i ii) e (ho_196 u ii)))))))))) (let ((_let_66 (forall ((x |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (y |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|)) (or (not (forall ((z tptp.list_Secrecy_Secrets)) (= (ho_196 x z) (ho_196 y z)))) (= x y))))) (let ((_let_67 (forall ((u |u_(-> tptp.set_li2007071804ecrets tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (e |u_(-> tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (i tptp.set_li2007071804ecrets)) (not (forall ((v |u_(-> tptp.set_li2007071804ecrets tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (not (forall ((ii tptp.set_li2007071804ecrets)) (= (ho_192 v ii) (ite (= i ii) e (ho_192 u ii)))))))))) (let ((_let_68 (forall ((x |u_(-> tptp.set_li2007071804ecrets tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (y |u_(-> tptp.set_li2007071804ecrets tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z tptp.set_li2007071804ecrets)) (= (ho_192 x z) (ho_192 y z)))) (= x y))))) (let ((_let_69 (forall ((u |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression)|) (e tptp.secrecy_Expression) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_188 v ii) (ite (= i ii) e (ho_188 u ii)))))))))) (let ((_let_70 (forall ((x |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression)|) (y |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_188 x z) (ho_188 y z)))) (= x y))))) (let ((_let_71 (forall ((u |u_(-> tptp.set_li2007071804ecrets Bool)|) (e Bool) (i tptp.set_li2007071804ecrets)) (not (forall ((v |u_(-> tptp.set_li2007071804ecrets Bool)|)) (not (forall ((ii tptp.set_li2007071804ecrets)) (= (ho_201 v ii) (ite (= i ii) e (ho_201 u ii)))))))))) (let ((_let_72 (forall ((x |u_(-> tptp.set_li2007071804ecrets Bool)|) (y |u_(-> tptp.set_li2007071804ecrets Bool)|)) (or (not (forall ((z tptp.set_li2007071804ecrets)) (= (ho_201 x z) (ho_201 y z)))) (= x y))))) (let ((_let_73 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS)|) (e tptp.secrecy_KS) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_186 v ii) (ite (= i ii) e (ho_186 u ii)))))))))) (let ((_let_74 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_186 x z) (ho_186 y z)))) (= x y))))) (let ((_let_75 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (i |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (= (ho_182 v ii) (ite (= i ii) e (ho_182 u ii)))))))))) (let ((_let_76 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (= (ho_182 x z) (ho_182 y z)))) (= x y))))) (let ((_let_77 (forall ((u |u_(-> tptp.set_li185139947ession tptp.secrecy_Expression tptp.set_li185139947ession)|) (e |u_(-> tptp.secrecy_Expression tptp.set_li185139947ession)|) (i tptp.set_li185139947ession)) (not (forall ((v |u_(-> tptp.set_li185139947ession tptp.secrecy_Expression tptp.set_li185139947ession)|)) (not (forall ((ii tptp.set_li185139947ession)) (= (ho_237 v ii) (ite (= i ii) e (ho_237 u ii)))))))))) (let ((_let_78 (forall ((x |u_(-> tptp.set_li185139947ession tptp.secrecy_Expression tptp.set_li185139947ession)|) (y |u_(-> tptp.set_li185139947ession tptp.secrecy_Expression tptp.set_li185139947ession)|)) (or (not (forall ((z tptp.set_li185139947ession)) (= (ho_237 x z) (ho_237 y z)))) (= x y))))) (let ((_let_79 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_Secrecy_KS tptp.list_S529945141ession)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession)|) (i |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_Secrecy_KS tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (= (ho_179 v ii) (ite (= i ii) e (ho_179 u ii)))))))))) (let ((_let_80 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_Secrecy_KS tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_Secrecy_KS tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (= (ho_179 x z) (ho_179 y z)))) (= x y))))) (let ((_let_81 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_S529945141ession tptp.list_Secrecy_KS)|) (e |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS)|) (i |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_S529945141ession tptp.list_Secrecy_KS)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (= (ho_177 v ii) (ite (= i ii) e (ho_177 u ii)))))))))) (let ((_let_82 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_S529945141ession tptp.list_Secrecy_KS)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_S529945141ession tptp.list_Secrecy_KS)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (= (ho_177 x z) (ho_177 y z)))) (= x y))))) (let ((_let_83 (forall ((u |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (e |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (i tptp.list_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (not (forall ((ii tptp.list_list_Secrecy_KS)) (= (ho_173 v ii) (ite (= i ii) e (ho_173 u ii)))))))))) (let ((_let_84 (forall ((x |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (y |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_list_Secrecy_KS)) (= (ho_173 x z) (ho_173 y z)))) (= x y))))) (let ((_let_85 (forall ((u |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession tptp.list_l425507653ession)|) (e |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession)|) (i tptp.list_l425507653ession)) (not (forall ((v |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession tptp.list_l425507653ession)|)) (not (forall ((ii tptp.list_l425507653ession)) (= (ho_168 v ii) (ite (= i ii) e (ho_168 u ii)))))))))) (let ((_let_86 (forall ((x |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession tptp.list_l425507653ession)|) (y |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession tptp.list_l425507653ession)|)) (or (not (forall ((z tptp.list_l425507653ession)) (= (ho_168 x z) (ho_168 y z)))) (= x y))))) (let ((_let_87 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (i |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (= (ho_163 v ii) (ite (= i ii) e (ho_163 u ii)))))))))) (let ((_let_88 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (= (ho_163 x z) (ho_163 y z)))) (= x y))))) (let ((_let_89 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_159 v ii) (ite (= i ii) e (ho_159 u ii)))))))))) (let ((_let_90 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_159 x z) (ho_159 y z)))) (= x y))))) (let ((_let_91 (forall ((u |u_(-> tptp.set_li2007071804ecrets tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|) (e |u_(-> tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|) (i tptp.set_li2007071804ecrets)) (not (forall ((v |u_(-> tptp.set_li2007071804ecrets tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|)) (not (forall ((ii tptp.set_li2007071804ecrets)) (= (ho_231 v ii) (ite (= i ii) e (ho_231 u ii)))))))))) (let ((_let_92 (forall ((x |u_(-> tptp.set_li2007071804ecrets tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|) (y |u_(-> tptp.set_li2007071804ecrets tptp.secrecy_Secrets tptp.set_li2007071804ecrets)|)) (or (not (forall ((z tptp.set_li2007071804ecrets)) (= (ho_231 x z) (ho_231 y z)))) (= x y))))) (let ((_let_93 (forall ((u |u_(-> tptp.set_Se1942955227ession Bool)|) (e Bool) (i tptp.set_Se1942955227ession)) (not (forall ((v |u_(-> tptp.set_Se1942955227ession Bool)|)) (not (forall ((ii tptp.set_Se1942955227ession)) (= (ho_224 v ii) (ite (= i ii) e (ho_224 u ii)))))))))) (let ((_let_94 (forall ((x |u_(-> tptp.set_Se1942955227ession Bool)|) (y |u_(-> tptp.set_Se1942955227ession Bool)|)) (or (not (forall ((z tptp.set_Se1942955227ession)) (= (ho_224 x z) (ho_224 y z)))) (= x y))))) (let ((_let_95 (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_71 v ii) (ite (= i ii) e (ho_71 u ii)))))))))) (let ((_let_96 (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_71 x z) (ho_71 y z)))) (= x y))))) (let ((_let_97 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS Bool)|) (e |u_(-> tptp.secrecy_KS Bool)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS Bool)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_157 v ii) (ite (= i ii) e (ho_157 u ii)))))))))) (let ((_let_98 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS Bool)|) (y |u_(-> tptp.list_Secrecy_KS tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_157 x z) (ho_157 y z)))) (= x y))))) (let ((_let_99 (forall ((u |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession Bool)|) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession Bool)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_153 v ii) (ite (= i ii) e (ho_153 u ii)))))))))) (let ((_let_100 (forall ((x |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession Bool)|) (y |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession Bool)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_153 x z) (ho_153 y z)))) (= x y))))) (let ((_let_101 (forall ((u |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (e |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_145 v ii) (ite (= i ii) e (ho_145 u ii)))))))))) (let ((_let_102 (forall ((x |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (y |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_145 x z) (ho_145 y z)))) (= x y))))) (let ((_let_103 (forall ((u |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_147 v ii) (ite (= i ii) e (ho_147 u ii)))))))))) (let ((_let_104 (forall ((x |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_147 x z) (ho_147 y z)))) (= x y))))) (let ((_let_105 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (= (ho_146 v ii) (ite (= i ii) e (ho_146 u ii)))))))))) (let ((_let_106 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (= (ho_146 x z) (ho_146 y z)))) (= x y))))) (let ((_let_107 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (= (ho_142 v ii) (ite (= i ii) e (ho_142 u ii)))))))))) (let ((_let_108 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (= (ho_142 x z) (ho_142 y z)))) (= x y))))) (let ((_let_109 (forall ((u |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (e |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_137 v ii) (ite (= i ii) e (ho_137 u ii)))))))))) (let ((_let_110 (forall ((x |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (y |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_137 x z) (ho_137 y z)))) (= x y))))) (let ((_let_111 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (= (ho_138 v ii) (ite (= i ii) e (ho_138 u ii)))))))))) (let ((_let_112 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)_ tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (= (ho_138 x z) (ho_138 y z)))) (= x y))))) (let ((_let_113 (forall ((u |u_(-> tptp.set_li849033543y_Keys tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|) (e |u_(-> tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|) (i tptp.set_li849033543y_Keys)) (not (forall ((v |u_(-> tptp.set_li849033543y_Keys tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (not (forall ((ii tptp.set_li849033543y_Keys)) (= (ho_203 v ii) (ite (= i ii) e (ho_203 u ii)))))))))) (let ((_let_114 (forall ((x |u_(-> tptp.set_li849033543y_Keys tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|) (y |u_(-> tptp.set_li849033543y_Keys tptp.list_Secrecy_Keys tptp.set_Secrecy_Keys)|)) (or (not (forall ((z tptp.set_li849033543y_Keys)) (= (ho_203 x z) (ho_203 y z)))) (= x y))))) (let ((_let_115 (forall ((u |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_135 v ii) (ite (= i ii) e (ho_135 u ii)))))))))) (let ((_let_116 (forall ((x |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|) (y |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_135 x z) (ho_135 y z)))) (= x y))))) (let ((_let_117 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|) (i |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (= (ho_131 v ii) (ite (= i ii) e (ho_131 u ii)))))))))) (let ((_let_118 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (= (ho_131 x z) (ho_131 y z)))) (= x y))))) (let ((_let_119 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_Secrecy_KS Bool)|) (i |u_(-> tptp.secrecy_KS Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS Bool)|)) (= (ho_129 v ii) (ite (= i ii) e (ho_129 u ii)))))))))) (let ((_let_120 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|) (y |u_(-> _u_(-> tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS Bool)|)) (= (ho_129 x z) (ho_129 y z)))) (= x y))))) (let ((_let_121 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession Bool)|) (i |u_(-> tptp.secrecy_Expression Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression Bool)|)) (= (ho_127 v ii) (ite (= i ii) e (ho_127 u ii)))))))))) (let ((_let_122 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|) (y |u_(-> _u_(-> tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression Bool)|)) (= (ho_127 x z) (ho_127 y z)))) (= x y))))) (let ((_let_123 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (e tptp.list_list_Secrecy_KS) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_125 v ii) (ite (= i ii) e (ho_125 u ii)))))))))) (let ((_let_124 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_125 x z) (ho_125 y z)))) (= x y))))) (let ((_let_125 (forall ((u |u_(-> tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (e tptp.set_Secrecy_Secrets) (i tptp.list_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (not (forall ((ii tptp.list_Secrecy_Secrets)) (= (ho_193 v ii) (ite (= i ii) e (ho_193 u ii)))))))))) (let ((_let_126 (forall ((x |u_(-> tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|) (y |u_(-> tptp.list_Secrecy_Secrets tptp.set_Secrecy_Secrets)|)) (or (not (forall ((z tptp.list_Secrecy_Secrets)) (= (ho_193 x z) (ho_193 y z)))) (= x y))))) (let ((_let_127 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession)|) (e tptp.list_l425507653ession) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_123 v ii) (ite (= i ii) e (ho_123 u ii)))))))))) (let ((_let_128 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession)|) (y |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_123 x z) (ho_123 y z)))) (= x y))))) (let ((_let_129 (forall ((u |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_139 v ii) (ite (= i ii) e (ho_139 u ii)))))))))) (let ((_let_130 (forall ((x |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|) (y |u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_139 x z) (ho_139 y z)))) (= x y))))) (let ((_let_131 (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_57 v ii) (ite (= i ii) e (ho_57 u ii)))))))))) (let ((_let_132 (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_57 x z) (ho_57 y z)))) (= x y))))) (let ((_let_133 (forall ((u |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (e |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_149 v ii) (ite (= i ii) e (ho_149 u ii)))))))))) (let ((_let_134 (forall ((x |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_149 x z) (ho_149 y z)))) (= x y))))) (let ((_let_135 (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_115 v ii) (ite (= i ii) e (ho_115 u ii)))))))))) (let ((_let_136 (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_115 x z) (ho_115 y z)))) (= x y))))) (let ((_let_137 (forall ((u |u_(-> tptp.set_li849033543y_Keys tptp.secrecy_Keys tptp.set_li849033543y_Keys)|) (e |u_(-> tptp.secrecy_Keys tptp.set_li849033543y_Keys)|) (i tptp.set_li849033543y_Keys)) (not (forall ((v |u_(-> tptp.set_li849033543y_Keys tptp.secrecy_Keys tptp.set_li849033543y_Keys)|)) (not (forall ((ii tptp.set_li849033543y_Keys)) (= (ho_234 v ii) (ite (= i ii) e (ho_234 u ii)))))))))) (let ((_let_138 (forall ((x |u_(-> tptp.set_li849033543y_Keys tptp.secrecy_Keys tptp.set_li849033543y_Keys)|) (y |u_(-> tptp.set_li849033543y_Keys tptp.secrecy_Keys tptp.set_li849033543y_Keys)|)) (or (not (forall ((z tptp.set_li849033543y_Keys)) (= (ho_234 x z) (ho_234 y z)))) (= x y))))) (let ((_let_139 (forall ((u |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression Bool)|) (e |u_(-> tptp.secrecy_Expression Bool)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression Bool)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_155 v ii) (ite (= i ii) e (ho_155 u ii)))))))))) (let ((_let_140 (forall ((x |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.list_S529945141ession tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_155 x z) (ho_155 y z)))) (= x y))))) (let ((_let_141 (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_61 v ii) (ite (= i ii) e (ho_61 u ii)))))))))) (let ((_let_142 (forall ((x |u_(-> tptp.set_Secrecy_Keys Bool)|) (y |u_(-> tptp.set_Secrecy_Keys Bool)|)) (or (not (forall ((z tptp.set_Secrecy_Keys)) (= (ho_61 x z) (ho_61 y z)))) (= x y))))) (let ((_let_143 (forall ((u |u_(-> tptp.set_list_Secrecy_KS Bool)|) (e Bool) (i tptp.set_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_list_Secrecy_KS Bool)|)) (not (forall ((ii tptp.set_list_Secrecy_KS)) (= (ho_218 v ii) (ite (= i ii) e (ho_218 u ii)))))))))) (let ((_let_144 (forall ((x |u_(-> tptp.set_list_Secrecy_KS Bool)|) (y |u_(-> tptp.set_list_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.set_list_Secrecy_KS)) (= (ho_218 x z) (ho_218 y z)))) (= x y))))) (let ((_let_145 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (i |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|)) (= (ho_51 v ii) (ite (= i ii) e (ho_51 u ii)))))))))) (let ((_let_146 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|)) (= (ho_51 x z) (ho_51 y z)))) (= x y))))) (let ((_let_147 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession Bool)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_52 v ii) (ite (= i ii) e (ho_52 u ii)))))))))) (let ((_let_148 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_52 x z) (ho_52 y z)))) (= x y))))) (let ((_let_149 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_40 v ii) (ite (= i ii) e (ho_40 u ii)))))))))) (let ((_let_150 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_40 x z) (ho_40 y z)))) (= x y))))) (let ((_let_151 (forall ((u |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|) (e tptp.secrecy_Expression) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_98 v ii) (ite (= i ii) e (ho_98 u ii)))))))))) (let ((_let_152 (forall ((x |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|) (y |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_98 x z) (ho_98 y z)))) (= x y))))) (let ((_let_153 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)_ tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|) (i |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)_ tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|)) (= (ho_46 v ii) (ite (= i ii) e (ho_46 u ii)))))))))) (let ((_let_154 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)_ tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)_ tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|)) (= (ho_46 x z) (ho_46 y z)))) (= x y))))) (let ((_let_155 (forall ((u |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|) (e |u_(-> tptp.secrecy_KS Bool)|) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_44 v ii) (ite (= i ii) e (ho_44 u ii)))))))))) (let ((_let_156 (forall ((x |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_44 x z) (ho_44 y z)))) (= x y))))) (let ((_let_157 (forall ((u |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_Secrecy_KS Bool)|) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_190 v ii) (ite (= i ii) e (ho_190 u ii)))))))))) (let ((_let_158 (forall ((x |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_190 x z) (ho_190 y z)))) (= x y))))) (let ((_let_159 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (i |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (= (ho_99 v ii) (ite (= i ii) e (ho_99 u ii)))))))))) (let ((_let_160 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (= (ho_99 x z) (ho_99 y z)))) (= x y))))) (let ((_let_161 (forall ((u |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (e |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (i tptp.list_Secrecy_Secrets)) (not (forall ((v |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|)) (not (forall ((ii tptp.list_Secrecy_Secrets)) (= (ho_198 v ii) (ite (= i ii) e (ho_198 u ii)))))))))) (let ((_let_162 (forall ((x |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|) (y |u_(-> tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets tptp.list_Secrecy_Secrets)|)) (or (not (forall ((z tptp.list_Secrecy_Secrets)) (= (ho_198 x z) (ho_198 y z)))) (= x y))))) (let ((_let_163 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_Secrecy_KS Bool)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_47 v ii) (ite (= i ii) e (ho_47 u ii)))))))))) (let ((_let_164 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|) (y |u_(-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_47 x z) (ho_47 y z)))) (= x y))))) (let ((_let_165 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession Bool)|) (i |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (= (ho_101 v ii) (ite (= i ii) e (ho_101 u ii)))))))))) (let ((_let_166 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (= (ho_101 x z) (ho_101 y z)))) (= x y))))) (let ((_let_167 (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_35 v ii) (ite (= i ii) e (ho_35 u ii)))))))))) (let ((_let_168 (forall ((x |u_(-> tptp.secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_35 x z) (ho_35 y z)))) (= x y))))) (let ((_let_169 (forall ((u |u_(-> tptp.secrecy_Keys tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_92 v ii) (ite (= i ii) e (ho_92 u ii)))))))))) (let ((_let_170 (forall ((x |u_(-> tptp.secrecy_Keys tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> tptp.secrecy_Keys tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_92 x z) (ho_92 y z)))) (= x y))))) (let ((_let_171 (forall ((u |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_37 v ii) (ite (= i ii) e (ho_37 u ii)))))))))) (let ((_let_172 (forall ((x |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_37 x z) (ho_37 y z)))) (= x y))))) (let ((_let_173 (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_58 v ii) (ite (= i ii) e (ho_58 u ii)))))))))) (let ((_let_174 (forall ((x |u_(-> tptp.secrecy_Keys Bool)|) (y |u_(-> tptp.secrecy_Keys Bool)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_58 x z) (ho_58 y z)))) (= x y))))) (let ((_let_175 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_38 v ii) (ite (= i ii) e (ho_38 u ii)))))))))) (let ((_let_176 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_38 x z) (ho_38 y z)))) (= x y))))) (let ((_let_177 (forall ((u |u_(-> tptp.secrecy_Keys tptp.set_li849033543y_Keys)|) (e tptp.set_li849033543y_Keys) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.set_li849033543y_Keys)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_235 v ii) (ite (= i ii) e (ho_235 u ii)))))))))) (let ((_let_178 (forall ((x |u_(-> tptp.secrecy_Keys tptp.set_li849033543y_Keys)|) (y |u_(-> tptp.secrecy_Keys tptp.set_li849033543y_Keys)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_235 x z) (ho_235 y z)))) (= x y))))) (let ((_let_179 (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_105 v ii) (ite (= i ii) e (ho_105 u ii)))))))))) (let ((_let_180 (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_105 x z) (ho_105 y z)))) (= x y))))) (let ((_let_181 (forall ((u |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|) (e |u_(-> tptp.secrecy_KS Bool)|) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_30 v ii) (ite (= i ii) e (ho_30 u ii)))))))))) (let ((_let_182 (forall ((x |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|) (y |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_30 x z) (ho_30 y z)))) (= x y))))) (let ((_let_183 (forall ((u |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|) (e |u_(-> tptp.secrecy_Expression Bool)|) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_49 v ii) (ite (= i ii) e (ho_49 u ii)))))))))) (let ((_let_184 (forall ((x |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_49 x z) (ho_49 y z)))) (= x y))))) (let ((_let_185 (forall ((u |u_(-> _u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (e |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (i |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (= (ho_170 v ii) (ite (= i ii) e (ho_170 u ii)))))))))) (let ((_let_186 (forall ((x |u_(-> _u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> _u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (= (ho_170 x z) (ho_170 y z)))) (= x y))))) (let ((_let_187 (forall ((u |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|) (e |u_(-> tptp.secrecy_Expression Bool)|) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_21 v ii) (ite (= i ii) e (ho_21 u ii)))))))))) (let ((_let_188 (forall ((x |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_21 x z) (ho_21 y z)))) (= x y))))) (let ((_let_189 (forall ((u |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (e |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (i tptp.list_Secrecy_Keys)) (not (forall ((v |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|)) (not (forall ((ii tptp.list_Secrecy_Keys)) (= (ho_209 v ii) (ite (= i ii) e (ho_209 u ii)))))))))) (let ((_let_190 (forall ((x |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (y |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|)) (or (not (forall ((z tptp.list_Secrecy_Keys)) (= (ho_209 x z) (ho_209 y z)))) (= x y))))) (let ((_let_191 (forall ((u |u_(-> tptp.secrecy_Keys tptp.secrecy_Keys Bool)|) (e |u_(-> tptp.secrecy_Keys Bool)|) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.secrecy_Keys Bool)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_95 v ii) (ite (= i ii) e (ho_95 u ii)))))))))) (let ((_let_192 (forall ((x |u_(-> tptp.secrecy_Keys tptp.secrecy_Keys Bool)|) (y |u_(-> tptp.secrecy_Keys tptp.secrecy_Keys Bool)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_95 x z) (ho_95 y z)))) (= x y))))) (let ((_let_193 (forall ((u |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (i tptp.list_l425507653ession)) (not (forall ((v |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_l425507653ession)) (= (ho_19 v ii) (ite (= i ii) e (ho_19 u ii)))))))))) (let ((_let_194 (forall ((x |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_l425507653ession)) (= (ho_19 x z) (ho_19 y z)))) (= x y))))) (let ((_let_195 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (i |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (= (ho_134 v ii) (ite (= i ii) e (ho_134 u ii)))))))))) (let ((_let_196 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)_ tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression)|)) (= (ho_134 x z) (ho_134 y z)))) (= x y))))) (let ((_let_197 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (i |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (= (ho_97 v ii) (ite (= i ii) e (ho_97 u ii)))))))))) (let ((_let_198 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_Expression)_ tptp.list_Secrecy_KS tptp.list_S529945141ession Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.secrecy_Expression)|)) (= (ho_97 x z) (ho_97 y z)))) (= x y))))) (let ((_let_199 (forall ((u |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (i |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (= (ho_23 v ii) (ite (= i ii) e (ho_23 u ii)))))))))) (let ((_let_200 (forall ((x |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|) (y |u_(-> _u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)_ tptp.list_S529945141ession tptp.list_S529945141ession Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|)) (= (ho_23 x z) (ho_23 y z)))) (= x y))))) (let ((_let_201 (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_60 v ii) (ite (= i ii) e (ho_60 u ii)))))))))) (let ((_let_202 (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_60 x z) (ho_60 y z)))) (= x y))))) (let ((_let_203 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_16 v ii) (ite (= i ii) e (ho_16 u ii)))))))))) (let ((_let_204 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_16 x z) (ho_16 y z)))) (= x y))))) (let ((_let_205 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (= (ho_150 v ii) (ite (= i ii) e (ho_150 u ii)))))))))) (let ((_let_206 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.list_Secrecy_KS)|)) (= (ho_150 x z) (ho_150 y z)))) (= x y))))) (let ((_let_207 (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_63 v ii) (ite (= i ii) e (ho_63 u ii)))))))))) (let ((_let_208 (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_63 x z) (ho_63 y z)))) (= x y))))) (let ((_let_209 (forall ((u |u_(-> tptp.list_S529945141ession Bool)|) (e Bool) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession Bool)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_25 v ii) (ite (= i ii) e (ho_25 u ii)))))))))) (let ((_let_210 (forall ((x |u_(-> tptp.list_S529945141ession Bool)|) (y |u_(-> tptp.list_S529945141ession Bool)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_25 x z) (ho_25 y z)))) (= x y))))) (let ((_let_211 (forall ((u |u_(-> tptp.secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (e |u_(-> tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (i tptp.secrecy_Keys)) (not (forall ((v |u_(-> tptp.secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|)) (not (forall ((ii tptp.secrecy_Keys)) (= (ho_206 v ii) (ite (= i ii) e (ho_206 u ii)))))))))) (let ((_let_212 (forall ((x |u_(-> tptp.secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|) (y |u_(-> tptp.secrecy_Keys tptp.list_Secrecy_Keys tptp.list_Secrecy_Keys)|)) (or (not (forall ((z tptp.secrecy_Keys)) (= (ho_206 x z) (ho_206 y z)))) (= x y))))) (let ((_let_213 (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_26 v ii) (ite (= i ii) e (ho_26 u ii)))))))))) (let ((_let_214 (forall ((x |u_(-> tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_26 x z) (ho_26 y z)))) (= x y))))) (let ((_let_215 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|) (i |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (= (ho_32 v ii) (ite (= i ii) e (ho_32 u ii)))))))))) (let ((_let_216 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (= (ho_32 x z) (ho_32 y z)))) (= x y))))) (let ((_let_217 (forall ((u |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession)|) (e tptp.set_li185139947ession) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_258 v ii) (ite (= i ii) e (ho_258 u ii)))))))))) (let ((_let_218 (forall ((x |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession)|) (y |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_258 x z) (ho_258 y z)))) (= x y))))) (let ((_let_219 (forall ((u |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i tptp.secrecy_KS)) (not (forall ((v |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (not (forall ((ii tptp.secrecy_KS)) (= (ho_143 v ii) (ite (= i ii) e (ho_143 u ii)))))))))) (let ((_let_220 (forall ((x |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|) (y |u_(-> tptp.secrecy_KS tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.secrecy_KS)) (= (ho_143 x z) (ho_143 y z)))) (= x y))))) (let ((_let_221 (forall ((u |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i tptp.list_l425507653ession)) (not (forall ((v |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_l425507653ession)) (= (ho_13 v ii) (ite (= i ii) e (ho_13 u ii)))))))))) (let ((_let_222 (forall ((x |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession)|) (y |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_l425507653ession)) (= (ho_13 x z) (ho_13 y z)))) (= x y))))) (let ((_let_223 (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_65 v ii) (ite (= i ii) e (ho_65 u ii)))))))))) (let ((_let_224 (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_65 x z) (ho_65 y z)))) (= x y))))) (let ((_let_225 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_Secrecy_KS Bool)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_33 v ii) (ite (= i ii) e (ho_33 u ii)))))))))) (let ((_let_226 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_33 x z) (ho_33 y z)))) (= x y))))) (let ((_let_227 (forall ((u |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (i tptp.secrecy_Expression)) (not (forall ((v |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.secrecy_Expression)) (= (ho_28 v ii) (ite (= i ii) e (ho_28 u ii)))))))))) (let ((_let_228 (forall ((x |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> tptp.secrecy_Expression tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.secrecy_Expression)) (= (ho_28 x z) (ho_28 y z)))) (= x y))))) (let ((_let_229 (forall ((u |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (e |u_(-> _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_141 v ii) (ite (= i ii) e (ho_141 u ii)))))))))) (let ((_let_230 (forall ((x |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_S529945141ession _u_(-> tptp.secrecy_Expression tptp.list_Secrecy_KS)_ tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_141 x z) (ho_141 y z)))) (= x y))))) (let ((_let_231 (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_68 v ii) (ite (= i ii) e (ho_68 u ii)))))))))) (let ((_let_232 (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_68 x z) (ho_68 y z)))) (= x y))))) (let ((_let_233 (forall ((u |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (e |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (i tptp.list_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_list_Secrecy_KS)) (= (ho_171 v ii) (ite (= i ii) e (ho_171 u ii)))))))))) (let ((_let_234 (forall ((x |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_list_Secrecy_KS)) (= (ho_171 x z) (ho_171 y z)))) (= x y))))) (let ((_let_235 (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_107 v ii) (ite (= i ii) e (ho_107 u ii)))))))))) (let ((_let_236 (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_107 x z) (ho_107 y z)))) (= x y))))) (let ((_let_237 (forall ((u |u_(-> tptp.list_Secrecy_KS Bool)|) (e Bool) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_34 v ii) (ite (= i ii) e (ho_34 u ii)))))))))) (let ((_let_238 (forall ((x |u_(-> tptp.list_Secrecy_KS Bool)|) (y |u_(-> tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_34 x z) (ho_34 y z)))) (= x y))))) (let ((_let_239 (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_94 v ii) (ite (= i ii) e (ho_94 u ii)))))))))) (let ((_let_240 (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_94 x z) (ho_94 y z)))) (= x y))))) (let ((_let_241 (forall ((u |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (e tptp.list_list_Secrecy_KS) (i tptp.list_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (not (forall ((ii tptp.list_list_Secrecy_KS)) (= (ho_110 v ii) (ite (= i ii) e (ho_110 u ii)))))))))) (let ((_let_242 (forall ((x |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (y |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_list_Secrecy_KS)) (= (ho_110 x z) (ho_110 y z)))) (= x y))))) (let ((_let_243 (forall ((u |u_(-> _u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)_ tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (i |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((v |u_(-> _u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)_ tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (= (ho_18 v ii) (ite (= i ii) e (ho_18 u ii)))))))))) (let ((_let_244 (forall ((x |u_(-> _u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)_ tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> _u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)_ tptp.list_l425507653ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.list_S529945141ession)|)) (= (ho_18 x z) (ho_18 y z)))) (= x y))))) (let ((_let_245 (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_82 v ii) (ite (= i ii) e (ho_82 u ii)))))))))) (let ((_let_246 (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_82 x z) (ho_82 y z)))) (= x y))))) (let ((_let_247 (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_72 v ii) (ite (= i ii) e (ho_72 u ii)))))))))) (let ((_let_248 (forall ((x |u_(-> tptp.set_Secrecy_Secrets Bool)|) (y |u_(-> tptp.set_Secrecy_Secrets Bool)|)) (or (not (forall ((z tptp.set_Secrecy_Secrets)) (= (ho_72 x z) (ho_72 y z)))) (= x y))))) (let ((_let_249 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (e tptp.list_S529945141ession) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_20 v ii) (ite (= i ii) e (ho_20 u ii)))))))))) (let ((_let_250 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_20 x z) (ho_20 y z)))) (= x y))))) (let ((_let_251 (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_74 v ii) (ite (= i ii) e (ho_74 u ii)))))))))) (let ((_let_252 (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_74 x z) (ho_74 y z)))) (= x y))))) (let ((_let_253 (forall ((u |u_(-> tptp.secrecy_specID tptp.list_S529945141ession Bool)|) (e |u_(-> tptp.list_S529945141ession Bool)|) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.list_S529945141ession Bool)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_76 v ii) (ite (= i ii) e (ho_76 u ii)))))))))) (let ((_let_254 (forall ((x |u_(-> tptp.secrecy_specID tptp.list_S529945141ession Bool)|) (y |u_(-> tptp.secrecy_specID tptp.list_S529945141ession Bool)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_76 x z) (ho_76 y z)))) (= x y))))) (let ((_let_255 (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_78 v ii) (ite (= i ii) e (ho_78 u ii)))))))))) (let ((_let_256 (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_78 x z) (ho_78 y z)))) (= x y))))) (let ((_let_257 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|) (e |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_132 v ii) (ite (= i ii) e (ho_132 u ii)))))))))) (let ((_let_258 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_S529945141ession tptp.list_S529945141ession)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_132 x z) (ho_132 y z)))) (= x y))))) (let ((_let_259 (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_80 v ii) (ite (= i ii) e (ho_80 u ii)))))))))) (let ((_let_260 (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_80 x z) (ho_80 y z)))) (= x y))))) (let ((_let_261 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession tptp.list_l425507653ession)|) (e |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession tptp.list_l425507653ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_112 v ii) (ite (= i ii) e (ho_112 u ii)))))))))) (let ((_let_262 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession tptp.list_l425507653ession)|) (y |u_(-> tptp.list_S529945141ession tptp.list_l425507653ession tptp.list_l425507653ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_112 x z) (ho_112 y z)))) (= x y))))) (let ((_let_263 (forall ((u |u_(-> tptp.secrecy_specID tptp.secrecy_Expression Bool)|) (e |u_(-> tptp.secrecy_Expression Bool)|) (i tptp.secrecy_specID)) (not (forall ((v |u_(-> tptp.secrecy_specID tptp.secrecy_Expression Bool)|)) (not (forall ((ii tptp.secrecy_specID)) (= (ho_86 v ii) (ite (= i ii) e (ho_86 u ii)))))))))) (let ((_let_264 (forall ((x |u_(-> tptp.secrecy_specID tptp.secrecy_Expression Bool)|) (y |u_(-> tptp.secrecy_specID tptp.secrecy_Expression Bool)|)) (or (not (forall ((z tptp.secrecy_specID)) (= (ho_86 x z) (ho_86 y z)))) (= x y))))) (let ((_let_265 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (e |u_(-> tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_109 v ii) (ite (= i ii) e (ho_109 u ii)))))))))) (let ((_let_266 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_list_Secrecy_KS tptp.list_list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_109 x z) (ho_109 y z)))) (= x y))))) (let ((_let_267 (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_268 (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_269 (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_103 v ii) (ite (= i ii) e (ho_103 u ii)))))))))) (let ((_let_270 (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_103 x z) (ho_103 y z)))) (= x y))))) (let ((_let_271 (forall ((u |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|) (e |u_(-> tptp.list_Secrecy_KS Bool)|) (i |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (not (forall ((v |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|)) (not (forall ((ii |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (= (ho_100 v ii) (ite (= i ii) e (ho_100 u ii)))))))))) (let ((_let_272 (forall ((x |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|) (y |u_(-> _u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)_ tptp.list_Secrecy_KS Bool)|)) (or (not (forall ((z |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|)) (= (ho_100 x z) (ho_100 y z)))) (= x y))))) (let ((_let_273 (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_66 v ii) (ite (= i ii) e (ho_66 u ii)))))))))) (let ((_let_274 (forall ((x |u_(-> tptp.set_Secrecy_KS Bool)|) (y |u_(-> tptp.set_Secrecy_KS Bool)|)) (or (not (forall ((z tptp.set_Secrecy_KS)) (= (ho_66 x z) (ho_66 y z)))) (= x y))))) (let ((_let_275 (forall ((u |u_(-> tptp.set_list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|) (e |u_(-> tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|) (i tptp.set_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|)) (not (forall ((ii tptp.set_list_Secrecy_KS)) (= (ho_214 v ii) (ite (= i ii) e (ho_214 u ii)))))))))) (let ((_let_276 (forall ((x |u_(-> tptp.set_list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|) (y |u_(-> tptp.set_list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_Secrecy_KS)|)) (or (not (forall ((z tptp.set_list_Secrecy_KS)) (= (ho_214 x z) (ho_214 y z)))) (= x y))))) (let ((_let_277 (forall ((u |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession)|) (e tptp.list_l425507653ession) (i tptp.list_l425507653ession)) (not (forall ((v |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession)|)) (not (forall ((ii tptp.list_l425507653ession)) (= (ho_113 v ii) (ite (= i ii) e (ho_113 u ii)))))))))) (let ((_let_278 (forall ((x |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession)|) (y |u_(-> tptp.list_l425507653ession tptp.list_l425507653ession)|)) (or (not (forall ((z tptp.list_l425507653ession)) (= (ho_113 x z) (ho_113 y z)))) (= x y))))) (let ((_let_279 (forall ((u |u_(-> tptp.set_list_Secrecy_KS tptp.secrecy_KS tptp.set_list_Secrecy_KS)|) (e |u_(-> tptp.secrecy_KS tptp.set_list_Secrecy_KS)|) (i tptp.set_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.set_list_Secrecy_KS tptp.secrecy_KS tptp.set_list_Secrecy_KS)|)) (not (forall ((ii tptp.set_list_Secrecy_KS)) (= (ho_240 v ii) (ite (= i ii) e (ho_240 u ii)))))))))) (let ((_let_280 (forall ((x |u_(-> tptp.set_list_Secrecy_KS tptp.secrecy_KS tptp.set_list_Secrecy_KS)|) (y |u_(-> tptp.set_list_Secrecy_KS tptp.secrecy_KS tptp.set_list_Secrecy_KS)|)) (or (not (forall ((z tptp.set_list_Secrecy_KS)) (= (ho_240 x z) (ho_240 y z)))) (= x y))))) (let ((_let_281 (forall ((u |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS)|) (e tptp.list_Secrecy_KS) (i tptp.list_list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS)|)) (not (forall ((ii tptp.list_list_Secrecy_KS)) (= (ho_246 v ii) (ite (= i ii) e (ho_246 u ii)))))))))) (let ((_let_282 (forall ((x |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS)|) (y |u_(-> tptp.list_list_Secrecy_KS tptp.list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_list_Secrecy_KS)) (= (ho_246 x z) (ho_246 y z)))) (= x y))))) (let ((_let_283 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|) (e tptp.set_list_Secrecy_KS) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_255 v ii) (ite (= i ii) e (ho_255 u ii)))))))))) (let ((_let_284 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_255 x z) (ho_255 y z)))) (= x y))))) (let ((_let_285 (forall ((u |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|) (e |u_(-> tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|) (i tptp.list_Secrecy_KS)) (not (forall ((v |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|)) (not (forall ((ii tptp.list_Secrecy_KS)) (= (ho_254 v ii) (ite (= i ii) e (ho_254 u ii)))))))))) (let ((_let_286 (forall ((x |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|) (y |u_(-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS tptp.set_list_Secrecy_KS)|)) (or (not (forall ((z tptp.list_Secrecy_KS)) (= (ho_254 x z) (ho_254 y z)))) (= x y))))) (let ((_let_287 (forall ((u |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.set_li185139947ession)|) (e |u_(-> tptp.list_S529945141ession tptp.set_li185139947ession)|) (i tptp.list_S529945141ession)) (not (forall ((v |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.set_li185139947ession)|)) (not (forall ((ii tptp.list_S529945141ession)) (= (ho_257 v ii) (ite (= i ii) e (ho_257 u ii)))))))))) (let ((_let_288 (forall ((x |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.set_li185139947ession)|) (y |u_(-> tptp.list_S529945141ession tptp.list_S529945141ession tptp.set_li185139947ession)|)) (or (not (forall ((z tptp.list_S529945141ession)) (= (ho_257 x z) (ho_257 y z)))) (= x y))))) (let ((_let_289 (forall ((BOUND_VARIABLE_13466 tptp.list_l425507653ession)) (= (ho_13 k_12 BOUND_VARIABLE_13466) (ho_20 (ho_19 (ho_18 k_17 k_15) BOUND_VARIABLE_13466) (ho_13 k_14 tptp.nil_li311616943ession)))))) (let ((_let_290 (forall ((BOUND_VARIABLE_13614 |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|) (BOUND_VARIABLE_13433 tptp.list_S529945141ession) (BOUND_VARIABLE_13434 tptp.list_S529945141ession)) (= (ho_25 (ho_24 (ho_23 k_29 BOUND_VARIABLE_13614) BOUND_VARIABLE_13433) BOUND_VARIABLE_13434) (or (= BOUND_VARIABLE_13433 (ho_13 k_14 tptp.nil_li311616943ession)) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (or (not (= BOUND_VARIABLE_13433 (ho_20 (ho_28 k_27 X4) Xs3))) (not (= BOUND_VARIABLE_13434 (ho_20 (ho_28 k_27 Y3) Ys))) (not (ho_26 (ho_21 BOUND_VARIABLE_13614 X4) Y3))))) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (or (not (= BOUND_VARIABLE_13433 (ho_20 (ho_28 k_27 X4) Xs3))) (not (= BOUND_VARIABLE_13434 (ho_20 (ho_28 k_27 Y3) Ys))) (ho_26 (ho_21 BOUND_VARIABLE_13614 X4) Y3) (ho_26 (ho_21 BOUND_VARIABLE_13614 Y3) X4) (not (ho_25 (ho_24 (ho_23 k_22 BOUND_VARIABLE_13614) Xs3) Ys)))))))))) (let ((_let_291 (forall ((BOUND_VARIABLE_13681 |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|) (BOUND_VARIABLE_13399 tptp.list_Secrecy_KS) (BOUND_VARIABLE_13400 tptp.list_Secrecy_KS)) (= (ho_34 (ho_33 (ho_32 k_41 BOUND_VARIABLE_13681) BOUND_VARIABLE_13399) BOUND_VARIABLE_13400) (or (= BOUND_VARIABLE_13399 (ho_40 k_39 (ho_13 k_14 tptp.nil_li311616943ession))) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (or (not (= BOUND_VARIABLE_13399 (ho_38 (ho_37 k_36 X4) Xs3))) (not (= BOUND_VARIABLE_13400 (ho_38 (ho_37 k_36 Y3) Ys))) (not (ho_35 (ho_30 BOUND_VARIABLE_13681 X4) Y3))))) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (or (not (= BOUND_VARIABLE_13399 (ho_38 (ho_37 k_36 X4) Xs3))) (not (= BOUND_VARIABLE_13400 (ho_38 (ho_37 k_36 Y3) Ys))) (ho_35 (ho_30 BOUND_VARIABLE_13681 X4) Y3) (ho_35 (ho_30 BOUND_VARIABLE_13681 Y3) X4) (not (ho_34 (ho_33 (ho_32 k_31 BOUND_VARIABLE_13681) Xs3) Ys)))))))))) (let ((_let_292 (forall ((BOUND_VARIABLE_13755 |u_(-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)|) (BOUND_VARIABLE_13374 tptp.list_S529945141ession) (BOUND_VARIABLE_13375 tptp.list_S529945141ession)) (let ((_let_1 (ho_13 k_14 tptp.nil_li311616943ession))) (= (ho_25 (ho_24 (ho_23 k_43 BOUND_VARIABLE_13755) BOUND_VARIABLE_13374) BOUND_VARIABLE_13375) (or (and (= BOUND_VARIABLE_13374 _let_1) (= BOUND_VARIABLE_13375 _let_1)) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (or (not (= BOUND_VARIABLE_13374 (ho_20 (ho_28 k_27 X4) Xs3))) (not (= BOUND_VARIABLE_13375 (ho_20 (ho_28 k_27 Y3) Ys))) (not (ho_26 (ho_21 BOUND_VARIABLE_13755 X4) Y3)) (not (ho_25 (ho_24 (ho_23 k_42 BOUND_VARIABLE_13755) Xs3) Ys))))))))))) (let ((_let_293 (forall ((BOUND_VARIABLE_13790 |u_(-> tptp.secrecy_Expression tptp.secrecy_KS Bool)|) (BOUND_VARIABLE_13349 tptp.list_S529945141ession) (BOUND_VARIABLE_13350 tptp.list_Secrecy_KS)) (let ((_let_1 (ho_13 k_14 tptp.nil_li311616943ession))) (= (ho_34 (ho_47 (ho_46 k_48 BOUND_VARIABLE_13790) BOUND_VARIABLE_13349) BOUND_VARIABLE_13350) (or (and (= BOUND_VARIABLE_13349 _let_1) (= BOUND_VARIABLE_13350 (ho_40 k_39 _let_1))) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_Secrecy_KS)) (or (not (= BOUND_VARIABLE_13349 (ho_20 (ho_28 k_27 X4) Xs3))) (not (= BOUND_VARIABLE_13350 (ho_38 (ho_37 k_36 Y3) Ys))) (not (ho_35 (ho_44 BOUND_VARIABLE_13790 X4) Y3)) (not (ho_34 (ho_47 (ho_46 k_45 BOUND_VARIABLE_13790) Xs3) Ys))))))))))) (let ((_let_294 (forall ((BOUND_VARIABLE_13834 |u_(-> tptp.secrecy_KS tptp.secrecy_Expression Bool)|) (BOUND_VARIABLE_13324 tptp.list_Secrecy_KS) (BOUND_VARIABLE_13325 tptp.list_S529945141ession)) (let ((_let_1 (ho_13 k_14 tptp.nil_li311616943ession))) (= (ho_25 (ho_52 (ho_51 k_53 BOUND_VARIABLE_13834) BOUND_VARIABLE_13324) BOUND_VARIABLE_13325) (or (and (= BOUND_VARIABLE_13324 (ho_40 k_39 _let_1)) (= BOUND_VARIABLE_13325 _let_1)) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_S529945141ession)) (or (not (= BOUND_VARIABLE_13324 (ho_38 (ho_37 k_36 X4) Xs3))) (not (= BOUND_VARIABLE_13325 (ho_20 (ho_28 k_27 Y3) Ys))) (not (ho_26 (ho_49 BOUND_VARIABLE_13834 X4) Y3)) (not (ho_25 (ho_52 (ho_51 k_50 BOUND_VARIABLE_13834) Xs3) Ys))))))))))) (let ((_let_295 (forall ((BOUND_VARIABLE_13877 |u_(-> tptp.secrecy_KS tptp.secrecy_KS Bool)|) (BOUND_VARIABLE_13299 tptp.list_Secrecy_KS) (BOUND_VARIABLE_13300 tptp.list_Secrecy_KS)) (let ((_let_1 (ho_40 k_39 (ho_13 k_14 tptp.nil_li311616943ession)))) (= (ho_34 (ho_33 (ho_32 k_55 BOUND_VARIABLE_13877) BOUND_VARIABLE_13299) BOUND_VARIABLE_13300) (or (and (= BOUND_VARIABLE_13299 _let_1) (= BOUND_VARIABLE_13300 _let_1)) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (or (not (= BOUND_VARIABLE_13299 (ho_38 (ho_37 k_36 X4) Xs3))) (not (= BOUND_VARIABLE_13300 (ho_38 (ho_37 k_36 Y3) Ys))) (not (ho_35 (ho_30 BOUND_VARIABLE_13877 X4) Y3)) (not (ho_34 (ho_33 (ho_32 k_54 BOUND_VARIABLE_13877) Xs3) Ys))))))))))) (let ((_let_296 (forall ((BOUND_VARIABLE_13290 tptp.set_Secrecy_Keys) (BOUND_VARIABLE_13291 tptp.secrecy_Keys)) (= (ho_58 (ho_57 k_56 BOUND_VARIABLE_13290) BOUND_VARIABLE_13291) (ho_61 (ho_60 k_59 BOUND_VARIABLE_13291) BOUND_VARIABLE_13290))))) (let ((_let_297 (forall ((BOUND_VARIABLE_13282 tptp.set_Secrecy_KS) (BOUND_VARIABLE_13283 tptp.secrecy_KS)) (= (ho_35 (ho_63 k_62 BOUND_VARIABLE_13282) BOUND_VARIABLE_13283) (ho_66 (ho_65 k_64 BOUND_VARIABLE_13283) BOUND_VARIABLE_13282))))) (let ((_let_298 (forall ((BOUND_VARIABLE_13274 tptp.set_Secrecy_Secrets) (BOUND_VARIABLE_13275 tptp.secrecy_Secrets)) (= (ho_69 (ho_68 k_67 BOUND_VARIABLE_13274) BOUND_VARIABLE_13275) (ho_72 (ho_71 k_70 BOUND_VARIABLE_13275) BOUND_VARIABLE_13274))))) (let ((_let_299 (forall ((BOUND_VARIABLE_13466 tptp.list_l425507653ession)) (= (@ (@ (@ tptp.foldr_1531709715ession tptp.append2089414218ession) BOUND_VARIABLE_13466) (@ tptp.concat388015140ession tptp.nil_li311616943ession)) (ll_11 BOUND_VARIABLE_13466))))) (let ((_let_300 (forall ((BOUND_VARIABLE_13432 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (BOUND_VARIABLE_13433 tptp.list_S529945141ession) (BOUND_VARIABLE_13434 tptp.list_S529945141ession)) (= (ll_10 BOUND_VARIABLE_13432 BOUND_VARIABLE_13433 BOUND_VARIABLE_13434) (or (= (@ tptp.concat388015140ession tptp.nil_li311616943ession) BOUND_VARIABLE_13433) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (or (not (= (@ (@ tptp.cons_S112077679ession X4) Xs3) BOUND_VARIABLE_13433)) (not (= (@ (@ tptp.cons_S112077679ession Y3) Ys) BOUND_VARIABLE_13434)) (not (@ (@ BOUND_VARIABLE_13432 X4) Y3))))) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (or (not (= (@ (@ tptp.cons_S112077679ession X4) Xs3) BOUND_VARIABLE_13433)) (not (= (@ (@ tptp.cons_S112077679ession Y3) Ys) BOUND_VARIABLE_13434)) (@ (@ BOUND_VARIABLE_13432 X4) Y3) (@ (@ BOUND_VARIABLE_13432 Y3) X4) (not (@ (@ (@ tptp.lexord1123423577ession BOUND_VARIABLE_13432) Xs3) Ys)))))))))) (let ((_let_301 (forall ((BOUND_VARIABLE_13398 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (BOUND_VARIABLE_13399 tptp.list_Secrecy_KS) (BOUND_VARIABLE_13400 tptp.list_Secrecy_KS)) (= (ll_9 BOUND_VARIABLE_13398 BOUND_VARIABLE_13399 BOUND_VARIABLE_13400) (or (= (@ tptp.secrec1371625429on2KSL (@ tptp.concat388015140ession tptp.nil_li311616943ession)) BOUND_VARIABLE_13399) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (or (not (= (@ (@ tptp.cons_Secrecy_KS X4) Xs3) BOUND_VARIABLE_13399)) (not (= (@ (@ tptp.cons_Secrecy_KS Y3) Ys) BOUND_VARIABLE_13400)) (not (@ (@ BOUND_VARIABLE_13398 X4) Y3))))) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (or (not (= (@ (@ tptp.cons_Secrecy_KS X4) Xs3) BOUND_VARIABLE_13399)) (not (= (@ (@ tptp.cons_Secrecy_KS Y3) Ys) BOUND_VARIABLE_13400)) (@ (@ BOUND_VARIABLE_13398 X4) Y3) (@ (@ BOUND_VARIABLE_13398 Y3) X4) (not (@ (@ (@ tptp.lexord948960489ecy_KS BOUND_VARIABLE_13398) Xs3) Ys)))))))))) (let ((_let_302 (forall ((BOUND_VARIABLE_13373 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (BOUND_VARIABLE_13374 tptp.list_S529945141ession) (BOUND_VARIABLE_13375 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.concat388015140ession tptp.nil_li311616943ession))) (= (ll_8 BOUND_VARIABLE_13373 BOUND_VARIABLE_13374 BOUND_VARIABLE_13375) (or (and (= _let_1 BOUND_VARIABLE_13374) (= _let_1 BOUND_VARIABLE_13375)) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (or (not (= (@ (@ tptp.cons_S112077679ession X4) Xs3) BOUND_VARIABLE_13374)) (not (= (@ (@ tptp.cons_S112077679ession Y3) Ys) BOUND_VARIABLE_13375)) (not (@ (@ BOUND_VARIABLE_13373 X4) Y3)) (not (@ (@ (@ tptp.listre84909707ession BOUND_VARIABLE_13373) Xs3) Ys))))))))))) (let ((_let_303 (forall ((BOUND_VARIABLE_13348 (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (BOUND_VARIABLE_13349 tptp.list_S529945141ession) (BOUND_VARIABLE_13350 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.concat388015140ession tptp.nil_li311616943ession))) (= (ll_7 BOUND_VARIABLE_13348 BOUND_VARIABLE_13349 BOUND_VARIABLE_13350) (or (and (= _let_1 BOUND_VARIABLE_13349) (= (@ tptp.secrec1371625429on2KSL _let_1) BOUND_VARIABLE_13350)) (not (forall ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_Secrecy_KS)) (or (not (= (@ (@ tptp.cons_S112077679ession X4) Xs3) BOUND_VARIABLE_13349)) (not (= (@ (@ tptp.cons_Secrecy_KS Y3) Ys) BOUND_VARIABLE_13350)) (not (@ (@ BOUND_VARIABLE_13348 X4) Y3)) (not (@ (@ (@ tptp.listre565996059ecy_KS BOUND_VARIABLE_13348) Xs3) Ys))))))))))) (let ((_let_304 (forall ((BOUND_VARIABLE_13323 (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (BOUND_VARIABLE_13324 tptp.list_Secrecy_KS) (BOUND_VARIABLE_13325 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.concat388015140ession tptp.nil_li311616943ession))) (= (ll_6 BOUND_VARIABLE_13323 BOUND_VARIABLE_13324 BOUND_VARIABLE_13325) (or (and (= (@ tptp.secrec1371625429on2KSL _let_1) BOUND_VARIABLE_13324) (= _let_1 BOUND_VARIABLE_13325)) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_S529945141ession)) (or (not (= (@ (@ tptp.cons_Secrecy_KS X4) Xs3) BOUND_VARIABLE_13324)) (not (= (@ (@ tptp.cons_S112077679ession Y3) Ys) BOUND_VARIABLE_13325)) (not (@ (@ BOUND_VARIABLE_13323 X4) Y3)) (not (@ (@ (@ tptp.listre1601064475ession BOUND_VARIABLE_13323) Xs3) Ys))))))))))) (let ((_let_305 (forall ((BOUND_VARIABLE_13298 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (BOUND_VARIABLE_13299 tptp.list_Secrecy_KS) (BOUND_VARIABLE_13300 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.secrec1371625429on2KSL (@ tptp.concat388015140ession tptp.nil_li311616943ession)))) (= (ll_5 BOUND_VARIABLE_13298 BOUND_VARIABLE_13299 BOUND_VARIABLE_13300) (or (and (= _let_1 BOUND_VARIABLE_13299) (= _let_1 BOUND_VARIABLE_13300)) (not (forall ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (or (not (= (@ (@ tptp.cons_Secrecy_KS X4) Xs3) BOUND_VARIABLE_13299)) (not (= (@ (@ tptp.cons_Secrecy_KS Y3) Ys) BOUND_VARIABLE_13300)) (not (@ (@ BOUND_VARIABLE_13298 X4) Y3)) (not (@ (@ (@ tptp.listre788412843ecy_KS BOUND_VARIABLE_13298) Xs3) Ys))))))))))) (let ((_let_306 (forall ((BOUND_VARIABLE_13290 tptp.set_Secrecy_Keys) (BOUND_VARIABLE_13291 tptp.secrecy_Keys)) (= (@ (@ tptp.member_Secrecy_Keys BOUND_VARIABLE_13291) BOUND_VARIABLE_13290) (ll_4 BOUND_VARIABLE_13290 BOUND_VARIABLE_13291))))) (let ((_let_307 (forall ((BOUND_VARIABLE_13282 tptp.set_Secrecy_KS) (BOUND_VARIABLE_13283 tptp.secrecy_KS)) (= (@ (@ tptp.member_Secrecy_KS2 BOUND_VARIABLE_13283) BOUND_VARIABLE_13282) (ll_3 BOUND_VARIABLE_13282 BOUND_VARIABLE_13283))))) (let ((_let_308 (forall ((BOUND_VARIABLE_13274 tptp.set_Secrecy_Secrets) (BOUND_VARIABLE_13275 tptp.secrecy_Secrets)) (= (@ (@ tptp.member2138796287ecrets BOUND_VARIABLE_13275) BOUND_VARIABLE_13274) (ll_2 BOUND_VARIABLE_13274 BOUND_VARIABLE_13275))))) (let ((_let_309 (and (@ _let_13 (@ _let_12 _let_4)) _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299))) (let ((_let_310 (EQ_RESOLVE (ASSUME :args (_let_9)) (MACRO_SR_EQ_INTRO :args (_let_9 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_311 (SYMM (ASSUME :args (_let_6))))) (let ((_let_312 (SYMM (ASSUME :args (_let_5))))) (let ((_let_313 (EQ_RESOLVE (ASSUME :args (_let_3)) (MACRO_SR_EQ_INTRO :args (_let_3 SB_DEFAULT SBA_FIXPOINT))))) (let ((_let_314 (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_2)) (MACRO_SR_EQ_INTRO (AND_INTRO _let_313 _let_312 _let_311 _let_310) :args (_let_2 SB_DEFAULT SBA_FIXPOINT))) _let_313 _let_312 _let_311 _let_310))) (let ((_let_315 (forall ((M tptp.secrecy_Secrets)) (= (ho_74 k_73 M) (ho_82 k_81 (ho_78 k_77 M)))))) (let ((_let_316 (EQ_RESOLVE (ASSUME :args (_let_10)) (PREPROCESS :args ((= _let_10 _let_315)))))) (let ((_let_317 (ho_35 (ho_80 k_79 tptp.a) _let_19))) (let ((_let_318 (= _let_317 _let_22))) (let ((_let_319 (not _let_22))) (let ((_let_320 (forall ((C tptp.secrecy_specID) (M2 tptp.secrecy_Secrets)) (let ((_let_1 (ho_78 k_77 M2))) (= (ho_25 (ho_76 k_75 C) (ho_20 (ho_28 k_27 (ho_82 k_81 _let_1)) (ho_13 k_14 tptp.nil_li311616943ession))) (ho_35 (ho_80 k_79 C) _let_1)))))) (let ((_let_321 (EQ_RESOLVE (ASSUME :args (_let_11)) (TRANS (MACRO_SR_EQ_INTRO _let_314 :args (_let_11 SB_DEFAULT SBA_FIXPOINT)) (PREPROCESS :args ((= (forall ((C tptp.secrecy_specID) (M2 tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.secrecy_sKS M2))) (= (@ (@ tptp.knowle945212990e_know C) _let_1) (@ (@ tptp.knowle731562421_knows C) (@ (@ tptp.cons_S112077679ession (@ tptp.secrec1016742679ession _let_1)) (@ tptp.concat388015140ession tptp.nil_li311616943ession)))))) _let_320))))))) (let ((_let_322 (and _let_18 _let_21))) (let ((_let_323 (_let_18 _let_21))) (let ((_let_324 (ASSUME :args (_let_18)))) (let ((_let_325 (ASSUME :args (_let_21)))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (REORDERING (RESOLUTION (CNF_AND_NEG :args (_let_322)) (IMPLIES_ELIM (SCOPE (MODUS_PONENS (AND_INTRO _let_324 _let_325) (SCOPE (TRUE_ELIM (TRANS (CONG (REFL :args (_let_17)) (CONG (CONG (REFL :args (k_27)) (SYMM _let_325) :args (APPLY_UF ho_28)) (REFL :args (_let_15)) :args (APPLY_UF ho_20)) :args (APPLY_UF ho_25)) (TRUE_INTRO _let_324))) :args _let_323)) :args _let_323)) :args (true _let_322)) :args ((or (not _let_18) _let_22 (not _let_21)))) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_EQUIV_POS2 :args (_let_318)) :args ((or _let_317 _let_319 (not _let_318)))) (EQ_RESOLVE (ASSUME :args (_let_1)) (PREPROCESS :args ((= _let_1 (not _let_317))))) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (MACRO_SR_PRED_ELIM (SCOPE (INSTANTIATE _let_321 :args (tptp.a tptp.m QUANTIFIERS_INST_E_MATCHING ((ho_35 (ho_80 k_79 C) (ho_78 k_77 M2))))) :args (_let_320)))) _let_321 :args (_let_318 false _let_320)) :args (_let_319 true _let_317 false _let_318)) (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_316 :args (tptp.m QUANTIFIERS_INST_E_MATCHING_SIMPLE ((ho_74 k_73 M)))) :args (_let_315))) _let_316 :args (_let_21 false _let_315)) (AND_ELIM (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (MACRO_SR_PRED_TRANSFORM (AND_INTRO (EQ_RESOLVE (ASSUME :args (_let_14)) (MACRO_SR_EQ_INTRO _let_314 :args (_let_14 SB_DEFAULT SBA_FIXPOINT))) (PREPROCESS :args ((and _let_308 _let_307 _let_306 _let_305 _let_304 _let_303 _let_302 _let_301 _let_300 _let_299)))) :args (_let_309)) (PREPROCESS :args ((= _let_309 (and _let_18 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289))))) (PREPROCESS :args ((and _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 _let_274 _let_273 _let_272 _let_271 _let_270 _let_269 _let_268 _let_267 _let_266 _let_265 _let_264 _let_263 _let_262 _let_261 _let_260 _let_259 _let_258 _let_257 _let_256 _let_255 _let_254 _let_253 _let_252 _let_251 _let_250 _let_249 _let_248 _let_247 _let_246 _let_245 _let_244 _let_243 _let_242 _let_241 _let_240 _let_239 _let_238 _let_237 _let_236 _let_235 _let_234 _let_233 _let_232 _let_231 _let_230 _let_229 _let_228 _let_227 _let_226 _let_225 _let_224 _let_223 _let_222 _let_221 _let_220 _let_219 _let_218 _let_217 _let_216 _let_215 _let_214 _let_213 _let_212 _let_211 _let_210 _let_209 _let_208 _let_207 _let_206 _let_205 _let_204 _let_203 _let_202 _let_201 _let_200 _let_199 _let_198 _let_197 _let_196 _let_195 _let_194 _let_193 _let_192 _let_191 _let_190 _let_189 _let_188 _let_187 _let_186 _let_185 _let_184 _let_183 _let_182 _let_181 _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_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 _let_35 _let_34 _let_33 _let_32 _let_31 _let_30 _let_29 _let_28 _let_27 _let_26 _let_25 _let_24 _let_23)))) :args ((and _let_18 _let_298 _let_297 _let_296 _let_295 _let_294 _let_293 _let_292 _let_291 _let_290 _let_289 _let_288 _let_287 _let_286 _let_285 _let_284 _let_283 _let_282 _let_281 _let_280 _let_279 _let_278 _let_277 _let_276 _let_275 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(forall ((P (-> (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession Bool)) (A0 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ P P2) tptp.nil_Se901661471ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X tptp.secrecy_Expression)) (@ (@ P P2) (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (let ((_let_2 (@ P P2))) (=> (@ _let_2 _let_1) (@ _let_2 (@ (@ tptp.cons_S112077679ession X) _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_Secrecy_KS Bool)) (A0 tptp.list_Secrecy_KS)) (=> (@ P tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS)) (@ P (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (let ((_let_2 (@ tptp.cons_Secrecy_KS X))) (let ((_let_3 (= X Y4))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> tptp.list_S529945141ession Bool)) (A0 tptp.list_S529945141ession)) (=> (@ P tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression)) (@ P (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (let ((_let_2 (@ tptp.cons_S112077679ession X))) (let ((_let_3 (= X Y4))) (=> (=> _let_3 (@ P (@ _let_2 Xs2))) (=> (=> (not _let_3) (@ P _let_1)) (@ P (@ _let_2 _let_1)))))))) (@ P A0))))) (forall ((P (-> (-> tptp.secrecy_KS tptp.secrecy_KS Bool) tptp.list_Secrecy_KS Bool)) (A0 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS)) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ P P2) tptp.nil_Secrecy_KS)) (=> (forall ((P2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_Secrecy_KS X) Ys3))))) (@ (@ P A0) A1)))) (forall ((P (-> (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool) tptp.list_S529945141ession Bool)) (A0 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ P P2) tptp.nil_Se901661471ession)) (=> (forall ((P2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (let ((_let_1 (@ P P2))) (=> (@ _let_1 Ys3) (@ _let_1 (@ (@ tptp.cons_S112077679ession X) Ys3))))) (@ (@ P A0) A1)))) (forall ((X3 tptp.list_Secrecy_KS)) (=> (not (= X3 tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (not (= X3 (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS)))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (not (= X3 (@ (@ tptp.cons_Secrecy_KS X) (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))))))))) (forall ((X3 tptp.list_S529945141ession)) (=> (not (= X3 tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (not (= X3 (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession)))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (not (= X3 (@ (@ tptp.cons_S112077679ession X) (@ (@ tptp.cons_S112077679ession Y4) Xs2))))))))) (forall ((A4 tptp.secrecy_Secrets) (P (-> tptp.secrecy_Secrets Bool))) (= (@ (@ tptp.member2138796287ecrets A4) (@ tptp.collec836099393ecrets P)) (@ P A4))) (forall ((A4 tptp.secrecy_KS) (P (-> tptp.secrecy_KS Bool))) (= (@ (@ tptp.member_Secrecy_KS2 A4) (@ tptp.collect_Secrecy_KS P)) (@ P A4))) (forall ((A4 tptp.secrecy_Keys) (P (-> tptp.secrecy_Keys Bool))) (= (@ (@ tptp.member_Secrecy_Keys A4) (@ tptp.collect_Secrecy_Keys P)) (@ P A4))) (forall ((A tptp.set_Secrecy_Secrets)) (= (@ tptp.collec836099393ecrets (lambda ((X4 tptp.secrecy_Secrets)) (@ (@ tptp.member2138796287ecrets X4) A))) A)) (forall ((A tptp.set_Secrecy_KS)) (= (@ tptp.collect_Secrecy_KS (lambda ((X4 tptp.secrecy_KS)) (@ (@ tptp.member_Secrecy_KS2 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 ((X3 tptp.list_list_Secrecy_KS)) (=> (not (= X3 tptp.nil_list_Secrecy_KS)) (=> (forall ((Xss tptp.list_list_Secrecy_KS)) (not (= X3 (@ (@ tptp.cons_list_Secrecy_KS tptp.nil_Secrecy_KS) Xss)))) (not (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Xss tptp.list_list_Secrecy_KS)) (not (= X3 (@ (@ tptp.cons_list_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X) Xs2)) Xss)))))))) (forall ((X3 tptp.list_l425507653ession)) (=> (not (= X3 tptp.nil_li311616943ession)) (=> (forall ((Xss tptp.list_l425507653ession)) (not (= X3 (@ (@ tptp.cons_l533358079ession tptp.nil_Se901661471ession) Xss)))) (not (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Xss tptp.list_l425507653ession)) (not (= X3 (@ (@ tptp.cons_l533358079ession (@ (@ tptp.cons_S112077679ession X) Xs2)) Xss)))))))) (forall ((P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool)) (A0 tptp.list_Secrecy_KS) (A1 tptp.list_Secrecy_KS)) (=> (forall ((X_1 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Secrecy_KS) X_1)) (=> (forall ((Xs2 tptp.list_Secrecy_KS)) (@ (@ P Xs2) tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Y4 tptp.secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool)) (A0 tptp.list_S529945141ession) (A1 tptp.list_S529945141ession)) (=> (forall ((X_1 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Se901661471ession) X_1)) (=> (forall ((Xs2 tptp.list_S529945141ession)) (@ (@ P Xs2) tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Y4 tptp.secrecy_Expression) (Ys3 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Ys3))) (let ((_let_2 (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)))) (=> (@ (@ P Xs2) _let_1) (=> (@ _let_2 Ys3) (@ _let_2 _let_1)))))) (@ (@ P A0) A1))))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (= (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M)) (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession)))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M)) (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession)))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession)) (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M)))) (forall ((P tptp.secrecy_specID) (M tptp.secrecy_Keys) (Q tptp.secrecy_specID)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))) (let ((_let_2 (@ tptp.secrecy_kKS M))) (=> (or (@ (@ tptp.knowle945212990e_know P) _let_2) (@ (@ tptp.knowle945212990e_know Q) _let_2)) (or (@ (@ tptp.knowle731562421_knows P) _let_1) (@ (@ tptp.knowle731562421_knows Q) _let_1)))))) (forall ((P tptp.secrecy_specID) (M tptp.secrecy_Keys) (Q tptp.secrecy_specID)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (let ((_let_2 (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))) (=> (or (@ (@ tptp.knowle731562421_knows P) _let_2) (@ (@ tptp.knowle731562421_knows Q) _let_2)) (or (@ (@ tptp.knowle945212990e_know P) _let_1) (@ (@ tptp.knowle945212990e_know Q) _let_1)))))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M))) (not (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))))) (forall ((A tptp.secrecy_specID) (M tptp.secrecy_Keys)) (=> (not (@ (@ tptp.knowle731562421_knows A) (@ (@ tptp.cons_S112077679ession (@ tptp.secrecy_kE M)) tptp.nil_Se901661471ession))) (not (@ (@ tptp.knowle945212990e_know A) (@ tptp.secrecy_kKS M))))) (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_KS2 _let_1) (@ tptp.localSecrets A)))))) (forall ((X3 tptp.secrecy_KS)) (= (@ (@ tptp.insert_Secrecy_KS X3) tptp.nil_Secrecy_KS) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (forall ((X3 tptp.secrecy_Expression)) (= (@ (@ tptp.insert1173886601ession X3) tptp.nil_Se901661471ession) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (forall ((X1 tptp.secrecy_Keys) (Y1 tptp.secrecy_Keys)) (= (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_kE Y1)) (= X1 Y1))) (forall ((X1 tptp.secrecy_Keys) (X2 tptp.secrecy_Secrets)) (not (= (@ tptp.secrecy_kE X1) (@ tptp.secrecy_sE X2)))) (forall ((M tptp.secrecy_Keys)) (= (@ tptp.secrec1016742679ession (@ tptp.secrecy_kKS M)) (@ tptp.secrecy_kE M))) (forall ((C tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (=> (@ (@ tptp.knowle233900195orrect C) _let_1) (=> (@ (@ tptp.eout C) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))) (forall ((C tptp.secrecy_specID) (M tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.secrecy_kKS M))) (= (@ (@ tptp.knowle233900195orrect C) _let_1) (= (@ (@ tptp.eout C) (@ tptp.secrecy_kE M)) (or (@ (@ tptp.member_Secrecy_Keys M) (@ tptp.specKeys C)) (@ (@ tptp.knowle945212990e_know C) _let_1)))))) (forall ((C tptp.secrecy_specID) (E tptp.secrecy_Expression)) (=> (@ (@ tptp.knowle1268625169orrect C) E) (=> (@ (@ tptp.eout C) E) (or (exists ((K3 tptp.secrecy_Keys)) (and (= E (@ tptp.secrecy_kE K3)) (@ (@ tptp.member_Secrecy_Keys K3) (@ tptp.specKeys C)))) (exists ((S tptp.secrecy_Secrets)) (and (= E (@ tptp.secrecy_sE S)) (@ (@ tptp.member2138796287ecrets S) (@ tptp.specSecrets C)))) (@ (@ tptp.knowle731562421_knows C) (@ (@ tptp.cons_S112077679ession E) tptp.nil_Se901661471ession)))))) _let_9 (= (@ tptp.produc1450295286ession tptp.nil_li311616943ession) _let_8) (= (@ tptp.produc713695622ecy_KS tptp.nil_list_Secrecy_KS) _let_7) (= (@ tptp.subseq348280080ession tptp.nil_Se901661471ession) _let_8) (= (@ tptp.subseqs_Secrecy_KS tptp.nil_Secrecy_KS) _let_7) _let_6 (forall ((P (-> tptp.secrecy_Expression Bool))) (not (@ (@ tptp.list_e1486860828ession P) tptp.nil_Se901661471ession))) (forall ((P (-> tptp.secrecy_KS Bool))) (not (@ (@ tptp.list_ex1_Secrecy_KS P) tptp.nil_Secrecy_KS))) (forall ((X3 (-> tptp.secrecy_KS tptp.secrecy_Expression)) (Xa tptp.list_Secrecy_KS) (Xb tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ (@ (@ tptp.map_ta623472337ession X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_Secrecy_KS) (not (= Y Xb))) (not (forall ((A3 tptp.secrecy_KS) (As tptp.list_Secrecy_KS)) (=> (= Xa (@ (@ tptp.cons_Secrecy_KS A3) As)) (not (= Y (@ (@ (@ tptp.map_ta623472337ession X3) As) (@ (@ tptp.cons_S112077679ession (@ X3 A3)) Xb)))))))))) (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (Xa tptp.list_S529945141ession) (Xb tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ (@ (@ tptp.map_ta1624757057ession X3) Xa) Xb) Y) (=> (=> (= Xa tptp.nil_Se901661471ession) (not (= Y Xb))) (not (forall ((A3 tptp.secrecy_Expression) (As tptp.list_S529945141ession)) (=> (= Xa (@ (@ tptp.cons_S112077679ession A3) As)) (not (= Y (@ (@ (@ tptp.map_ta1624757057ession X3) As) (@ (@ tptp.cons_S112077679ession (@ X3 A3)) Xb)))))))))) (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (not (@ (@ (@ tptp.lexord948960489ecy_KS Less) (@ (@ tptp.cons_Secrecy_KS X3) Xs)) tptp.nil_Secrecy_KS))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (not (@ (@ (@ tptp.lexord1123423577ession Less) (@ (@ tptp.cons_S112077679ession X3) Xs)) tptp.nil_Se901661471ession))) (forall ((F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession))) (= (@ (@ tptp.bind_S815874003ession tptp.nil_Se901661471ession) F2) tptp.nil_Se901661471ession)) (forall ((F2 (-> tptp.secrecy_Expression tptp.list_Secrecy_KS))) (= (@ (@ tptp.bind_S1823644515ecy_KS tptp.nil_Se901661471ession) F2) tptp.nil_Secrecy_KS)) (forall ((F2 (-> tptp.secrecy_KS tptp.list_S529945141ession))) (= (@ (@ tptp.bind_S711229283ession tptp.nil_Secrecy_KS) F2) tptp.nil_Se901661471ession)) (forall ((F2 (-> tptp.secrecy_KS tptp.list_Secrecy_KS))) (= (@ (@ tptp.bind_S645462771ecy_KS tptp.nil_Secrecy_KS) F2) tptp.nil_Secrecy_KS)) (forall ((R (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X1 tptp.list_Secrecy_KS) (X2 tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool))) (=> (@ (@ (@ tptp.listre788412843ecy_KS R) X1) X2) (=> (@ (@ P tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre788412843ecy_KS R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))))) (@ (@ P X1) X2))))) (forall ((R (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (X1 tptp.list_Secrecy_KS) (X2 tptp.list_S529945141ession) (P (-> tptp.list_Secrecy_KS tptp.list_S529945141ession Bool))) (=> (@ (@ (@ tptp.listre1601064475ession R) X1) X2) (=> (@ (@ P tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre1601064475ession R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))))) (@ (@ P X1) X2))))) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (X1 tptp.list_S529945141ession) (X2 tptp.list_Secrecy_KS) (P (-> tptp.list_S529945141ession tptp.list_Secrecy_KS Bool))) (=> (@ (@ (@ tptp.listre565996059ecy_KS R) X1) X2) (=> (@ (@ P tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre565996059ecy_KS R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))))) (@ (@ P X1) X2))))) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X1 tptp.list_S529945141ession) (X2 tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool))) (=> (@ (@ (@ tptp.listre84909707ession R) X1) X2) (=> (@ (@ P tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ R X) Y4) (=> (@ (@ (@ tptp.listre84909707ession R) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))))) (@ (@ P X1) X2))))) (= tptp.listre788412843ecy_KS (lambda ((R2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A12 tptp.list_Secrecy_KS) (A22 tptp.list_Secrecy_KS)) (or (and (= A12 tptp.nil_Secrecy_KS) (= A22 tptp.nil_Secrecy_KS)) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre788412843ecy_KS R2) Xs3) Ys)))))) (= tptp.listre1601064475ession (lambda ((R2 (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (A12 tptp.list_Secrecy_KS) (A22 tptp.list_S529945141ession)) (or (and (= A12 tptp.nil_Secrecy_KS) (= A22 tptp.nil_Se901661471ession)) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre1601064475ession R2) Xs3) Ys)))))) (= tptp.listre565996059ecy_KS (lambda ((R2 (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (A12 tptp.list_S529945141ession) (A22 tptp.list_Secrecy_KS)) (or (and (= A12 tptp.nil_Se901661471ession) (= A22 tptp.nil_Secrecy_KS)) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre565996059ecy_KS R2) Xs3) Ys)))))) (= tptp.listre84909707ession (lambda ((R2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A12 tptp.list_S529945141ession) (A22 tptp.list_S529945141ession)) (or (and (= A12 tptp.nil_Se901661471ession) (= A22 tptp.nil_Se901661471ession)) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (@ (@ R2 X4) Y3) (@ (@ (@ tptp.listre84909707ession R2) Xs3) Ys)))))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Y tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.lexord1123423577ession Less))) (= (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2)) (or (@ (@ Less X3) Y) (and (not (@ (@ Less Y) X3)) (@ (@ _let_1 Xs) Ys2)))))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xs tptp.list_S529945141ession)) (= (@ (@ (@ tptp.lexord1123423577ession Less) Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))) (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS)) (= (@ (@ (@ tptp.lexord948960489ecy_KS Less) Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Ys2 tptp.list_S529945141ession)) (@ (@ (@ tptp.lexord1123423577ession Less) tptp.nil_Se901661471ession) Ys2)) (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Ys2 tptp.list_Secrecy_KS)) (@ (@ (@ tptp.lexord948960489ecy_KS Less) tptp.nil_Secrecy_KS) Ys2)) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ (@ Less X3) Y) (@ (@ (@ tptp.lexord1123423577ession Less) (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2)))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.lexord1123423577ession Less))) (=> (not (@ (@ Less X3) Y)) (=> (not (@ (@ Less Y) X3)) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2))))))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Ys2 tptp.list_S529945141ession)) (@ (@ (@ tptp.lexord1123423577ession Less) tptp.nil_Se901661471ession) Ys2)) (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Ys2 tptp.list_Secrecy_KS)) (@ (@ (@ tptp.lexord948960489ecy_KS Less) tptp.nil_Secrecy_KS) Ys2)) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.listre84909707ession R))) (=> (@ (@ R X3) Y) (=> (@ (@ _let_1 Xs) Ys2) (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.cons_S112077679ession Y) Ys2)))))) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ (@ tptp.listre84909707ession R) tptp.nil_Se901661471ession) tptp.nil_Se901661471ession)) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_KS Bool))) (@ (@ (@ tptp.listre565996059ecy_KS R) tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS)) (forall ((R (-> tptp.secrecy_KS tptp.secrecy_Expression Bool))) (@ (@ (@ tptp.listre1601064475ession R) tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession)) (forall ((R (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ (@ tptp.listre788412843ecy_KS R) tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS)) (forall ((F2 (-> tptp.secrecy_Expression tptp.secrecy_Expression)) (A4 tptp.secrecy_Expression) (As2 tptp.list_S529945141ession) (Bs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.map_ta1624757057ession F2))) (= (@ (@ _let_1 (@ (@ tptp.cons_S112077679ession A4) As2)) Bs2) (@ (@ _let_1 As2) (@ (@ tptp.cons_S112077679ession (@ F2 A4)) Bs2))))) (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_Secrecy_KS)) (=> (@ (@ (@ tptp.lexord948960489ecy_KS Less) A1) A2) (=> (not (= A1 tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (=> (exists ((Xs2 tptp.list_Secrecy_KS)) (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2))) (forall ((Y4 tptp.secrecy_KS)) (=> (exists ((Ys3 tptp.list_Secrecy_KS)) (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))) (not (@ (@ Less X) Y4)))))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (forall ((Ys3 tptp.list_Secrecy_KS)) (=> (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (not (@ (@ (@ tptp.lexord948960489ecy_KS Less) Xs2) Ys3))))))))))))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession) (A2 tptp.list_S529945141ession)) (=> (@ (@ (@ tptp.lexord1123423577ession Less) A1) A2) (=> (not (= A1 tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (=> (exists ((Xs2 tptp.list_S529945141ession)) (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2))) (forall ((Y4 tptp.secrecy_Expression)) (=> (exists ((Ys3 tptp.list_S529945141ession)) (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3))) (not (@ (@ Less X) Y4)))))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2)) (forall ((Ys3 tptp.list_S529945141ession)) (=> (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (not (@ (@ (@ tptp.lexord1123423577ession Less) Xs2) Ys3))))))))))))) (= tptp.lexord948960489ecy_KS (lambda ((Less2 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A12 tptp.list_Secrecy_KS) (A22 tptp.list_Secrecy_KS)) (or (exists ((Ys tptp.list_Secrecy_KS)) (and (= A12 tptp.nil_Secrecy_KS) (= A22 Ys))) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (@ (@ Less2 X4) Y3))) (exists ((X4 tptp.secrecy_KS) (Y3 tptp.secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Ys tptp.list_Secrecy_KS)) (and (= A12 (@ (@ tptp.cons_Secrecy_KS X4) Xs3)) (= A22 (@ (@ tptp.cons_Secrecy_KS Y3) Ys)) (not (@ (@ Less2 X4) Y3)) (not (@ (@ Less2 Y3) X4)) (@ (@ (@ tptp.lexord948960489ecy_KS Less2) Xs3) Ys)))))) (= tptp.lexord1123423577ession (lambda ((Less2 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A12 tptp.list_S529945141ession) (A22 tptp.list_S529945141ession)) (or (exists ((Ys tptp.list_S529945141ession)) (and (= A12 tptp.nil_Se901661471ession) (= A22 Ys))) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (@ (@ Less2 X4) Y3))) (exists ((X4 tptp.secrecy_Expression) (Y3 tptp.secrecy_Expression) (Xs3 tptp.list_S529945141ession) (Ys tptp.list_S529945141ession)) (and (= A12 (@ (@ tptp.cons_S112077679ession X4) Xs3)) (= A22 (@ (@ tptp.cons_S112077679ession Y3) Ys)) (not (@ (@ Less2 X4) Y3)) (not (@ (@ Less2 Y3) X4)) (@ (@ (@ tptp.lexord1123423577ession Less2) Xs3) Ys)))))) (forall ((Less (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X1 tptp.list_Secrecy_KS) (X2 tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS tptp.list_Secrecy_KS Bool))) (=> (@ (@ (@ tptp.lexord948960489ecy_KS Less) X1) X2) (=> (forall ((X_1 tptp.list_Secrecy_KS)) (@ (@ P tptp.nil_Secrecy_KS) X_1)) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (@ (@ Less X) Y4) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)))) (=> (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS) (Ys3 tptp.list_Secrecy_KS)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (=> (@ (@ (@ tptp.lexord948960489ecy_KS Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (@ (@ tptp.cons_Secrecy_KS Y4) Ys3))))))) (@ (@ P X1) X2)))))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X1 tptp.list_S529945141ession) (X2 tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession tptp.list_S529945141ession Bool))) (=> (@ (@ (@ tptp.lexord1123423577ession Less) X1) X2) (=> (forall ((X_1 tptp.list_S529945141ession)) (@ (@ P tptp.nil_Se901661471ession) X_1)) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (@ (@ Less X) Y4) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3)))) (=> (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession) (Ys3 tptp.list_S529945141ession)) (=> (not (@ (@ Less X) Y4)) (=> (not (@ (@ Less Y4) X)) (=> (@ (@ (@ tptp.lexord1123423577ession Less) Xs2) Ys3) (=> (@ (@ P Xs2) Ys3) (@ (@ P (@ (@ tptp.cons_S112077679ession X) Xs2)) (@ (@ tptp.cons_S112077679ession Y4) Ys3))))))) (@ (@ P X1) X2)))))) (forall ((R (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_Secrecy_KS)) (=> (@ (@ (@ tptp.listre788412843ecy_KS R) A1) A2) (=> (=> (= A1 tptp.nil_Secrecy_KS) (not (= A2 tptp.nil_Secrecy_KS))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (forall ((Ys3 tptp.list_Secrecy_KS)) (=> (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre788412843ecy_KS R) Xs2) Ys3))))))))))) (forall ((R (-> tptp.secrecy_KS tptp.secrecy_Expression Bool)) (A1 tptp.list_Secrecy_KS) (A2 tptp.list_S529945141ession)) (=> (@ (@ (@ tptp.listre1601064475ession R) A1) A2) (=> (=> (= A1 tptp.nil_Secrecy_KS) (not (= A2 tptp.nil_Se901661471ession))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_Secrecy_KS)) (=> (= A1 (@ (@ tptp.cons_Secrecy_KS X) Xs2)) (forall ((Ys3 tptp.list_S529945141ession)) (=> (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre1601064475ession R) Xs2) Ys3))))))))))) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_KS Bool)) (A1 tptp.list_S529945141ession) (A2 tptp.list_Secrecy_KS)) (=> (@ (@ (@ tptp.listre565996059ecy_KS R) A1) A2) (=> (=> (= A1 tptp.nil_Se901661471ession) (not (= A2 tptp.nil_Secrecy_KS))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_S529945141ession)) (=> (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2)) (forall ((Ys3 tptp.list_Secrecy_KS)) (=> (= A2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre565996059ecy_KS R) Xs2) Ys3))))))))))) (forall ((R (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (A1 tptp.list_S529945141ession) (A2 tptp.list_S529945141ession)) (=> (@ (@ (@ tptp.listre84909707ession R) A1) A2) (=> (=> (= A1 tptp.nil_Se901661471ession) (not (= A2 tptp.nil_Se901661471ession))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (= A1 (@ (@ tptp.cons_S112077679ession X) Xs2)) (forall ((Ys3 tptp.list_S529945141ession)) (=> (= A2 (@ (@ tptp.cons_S112077679ession Y4) Ys3)) (=> (@ (@ R X) Y4) (not (@ (@ (@ tptp.listre84909707ession R) Xs2) Ys3))))))))))) (forall ((P tptp.secrecy_specID) (A4 tptp.secrecy_Expression) (L tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession A4))) (let ((_let_2 (@ tptp.notSpe1586871396tsExpr P))) (=> (@ _let_2 (@ _let_1 L)) (@ _let_2 (@ _let_1 tptp.nil_Se901661471ession)))))) (forall ((Y tptp.secrecy_Expression)) (not (@ (@ tptp.member2020590922ession tptp.nil_Se901661471ession) Y))) (forall ((Y tptp.secrecy_KS)) (not (@ (@ tptp.member_Secrecy_KS tptp.nil_Secrecy_KS) Y))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Y tptp.secrecy_Expression)) (= (@ (@ tptp.member2020590922ession (@ (@ tptp.cons_S112077679ession X3) Xs)) Y) (or (= X3 Y) (@ (@ tptp.member2020590922ession Xs) Y)))) (forall ((X3 tptp.list_Secrecy_KS) (Xa tptp.list_Secrecy_KS) (Y tptp.list_Secrecy_KS)) (=> (= (@ (@ tptp.splice_Secrecy_KS X3) Xa) Y) (=> (=> (= X3 tptp.nil_Secrecy_KS) (not (= Y Xa))) (not (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice_Secrecy_KS Xa) Xs2))))))))))) (forall ((X3 tptp.list_S529945141ession) (Xa tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ (@ tptp.splice1390717708ession X3) Xa) Y) (=> (=> (= X3 tptp.nil_Se901661471ession) (not (= Y Xa))) (not (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X))) (=> (= X3 (@ _let_1 Xs2)) (not (= Y (@ _let_1 (@ (@ tptp.splice1390717708ession Xa) Xs2))))))))))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession))) (= (@ (@ tptp.bind_S815874003ession (@ (@ tptp.cons_S112077679ession X3) Xs)) F2) (@ (@ tptp.append2089414218ession (@ F2 X3)) (@ (@ tptp.bind_S815874003ession Xs) F2)))) (forall ((A4 tptp.list_S529945141ession) (B tptp.list_S529945141ession) (C3 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession A4))) (= (@ (@ tptp.append2089414218ession (@ _let_1 B)) C3) (@ _let_1 (@ (@ tptp.append2089414218ession B) C3))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (= (@ (@ tptp.append2089414218ession (@ _let_1 Ys2)) Zs2) (@ _let_1 (@ (@ tptp.append2089414218ession Ys2) Zs2))))) (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Ys2) Xs) (@ (@ tptp.append2089414218ession Zs2) Xs)) (= Ys2 Zs2))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (= (= (@ _let_1 Ys2) (@ _let_1 Zs2)) (= Ys2 Zs2)))) (forall ((A4 tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession A4) tptp.nil_Se901661471ession) A4)) (forall ((A4 tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS A4) tptp.nil_Secrecy_KS) A4)) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) tptp.nil_Se901661471ession) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) Ys2) tptp.nil_Secrecy_KS) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= tptp.nil_Se901661471ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= tptp.nil_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))) (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (= (= Ys2 (@ (@ tptp.append2089414218ession Xs) Ys2)) (= Xs tptp.nil_Se901661471ession))) (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (= (= Ys2 (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (= Xs tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) Ys2) (= Xs tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) Ys2) Ys2) (= Xs tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= Xs (@ (@ tptp.append2089414218ession Xs) Ys2)) (= Ys2 tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= Xs (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (= Ys2 tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) Xs) (= Ys2 tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) Ys2) Xs) (= Ys2 tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession Xs) tptp.nil_Se901661471ession) Xs)) (forall ((Xs tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS Xs) tptp.nil_Secrecy_KS) Xs)) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.splice1390717708ession Xs) Ys2) tptp.nil_Se901661471ession) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.splice_Secrecy_KS Xs) Ys2) tptp.nil_Secrecy_KS) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))) (forall ((Xs tptp.list_S529945141ession)) (= (@ (@ tptp.splice1390717708ession Xs) tptp.nil_Se901661471ession) Xs)) (forall ((Xs tptp.list_Secrecy_KS)) (= (@ (@ tptp.splice_Secrecy_KS Xs) tptp.nil_Secrecy_KS) Xs)) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Ys2 tptp.list_Secrecy_KS) (Y tptp.secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS)) (@ (@ tptp.append_Secrecy_KS Ys2) (@ (@ tptp.cons_Secrecy_KS Y) tptp.nil_Secrecy_KS))) (and (= Xs Ys2) (= X3 Y)))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession) (Y tptp.secrecy_Expression)) (= (= (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession)) (@ (@ tptp.append2089414218ession Ys2) (@ (@ tptp.cons_S112077679ession Y) tptp.nil_Se901661471ession))) (and (= Xs Ys2) (= X3 Y)))) (forall ((Xs tptp.list_S529945141ession) (Xs1 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Us tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (=> (= (@ _let_1 Xs1) Zs2) (=> (= Ys2 (@ (@ tptp.append2089414218ession Xs1) Us)) (= (@ _let_1 Ys2) (@ (@ tptp.append2089414218ession Zs2) Us)))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession) (Ts tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) Ys2) (@ (@ tptp.append2089414218ession Zs2) Ts)) (exists ((Us2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Us2))) (or (and (= Xs (@ (@ tptp.append2089414218ession Zs2) Us2)) (= (@ _let_1 Ys2) Ts)) (and (= (@ (@ tptp.append2089414218ession Xs) Us2) Zs2) (= Ys2 (@ _let_1 Ts)))))))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ (@ tptp.append2089414218ession (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.append2089414218ession Xs) Ys2))))) (forall ((X3 tptp.secrecy_Expression) (Xs1 tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (=> (= (@ _let_1 Xs1) Ys2) (=> (= Xs (@ (@ tptp.append2089414218ession Xs1) Zs2)) (= (@ _let_1 Xs) (@ (@ tptp.append2089414218ession Ys2) Zs2)))))) (forall ((A4 tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession tptp.nil_Se901661471ession) A4) A4)) (forall ((A4 tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS tptp.nil_Secrecy_KS) A4) A4)) (forall ((Ys2 tptp.list_S529945141ession)) (= (@ (@ tptp.append2089414218ession tptp.nil_Se901661471ession) Ys2) Ys2)) (forall ((Ys2 tptp.list_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS tptp.nil_Secrecy_KS) Ys2) Ys2)) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append2089414218ession tptp.nil_Se901661471ession) Ys2)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (= Xs Ys2) (= Xs (@ (@ tptp.append_Secrecy_KS tptp.nil_Secrecy_KS) Ys2)))) (forall ((A tptp.secrecy_specID) (E tptp.list_S529945141ession) (E1 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (@ _let_1 (@ (@ tptp.append2089414218ession E) E1)) (@ _let_1 E)))) (forall ((A tptp.secrecy_specID) (E1 tptp.list_S529945141ession) (E tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (@ _let_1 (@ (@ tptp.append2089414218ession E1) E)) (@ _let_1 E)))) (forall ((A tptp.secrecy_specID) (E1 tptp.list_S529945141ession) (E22 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.knowle731562421_knows A))) (=> (and (@ _let_1 E1) (@ _let_1 E22)) (@ _let_1 (@ (@ tptp.append2089414218ession E1) E22))))) (forall ((Less (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (U tptp.list_S529945141ession) (V tptp.list_S529945141ession)) (@ (@ (@ tptp.lexord1123423577ession Less) U) (@ (@ tptp.append2089414218ession U) V))) (forall ((P tptp.secrecy_specID) (A4 tptp.secrecy_Expression) (L tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.notSpe1586871396tsExpr P))) (=> (@ _let_1 (@ (@ tptp.cons_S112077679ession A4) L)) (@ _let_1 L)))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ (@ tptp.splice1390717708ession (@ _let_1 Xs)) Ys2) (@ _let_1 (@ (@ tptp.splice1390717708ession Ys2) Xs))))) (forall ((Ys2 tptp.list_S529945141ession)) (= (@ (@ tptp.splice1390717708ession tptp.nil_Se901661471ession) Ys2) Ys2)) (forall ((Ys2 tptp.list_Secrecy_KS)) (= (@ (@ tptp.splice_Secrecy_KS tptp.nil_Secrecy_KS) Ys2) Ys2)) (forall ((Xs tptp.list_Secrecy_KS) (P (-> tptp.list_Secrecy_KS Bool))) (=> (not (= Xs tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (@ P (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (not (= Xs2 tptp.nil_Secrecy_KS)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_Secrecy_KS Xs2) (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS)))))) (@ P Xs))))) (forall ((Xs tptp.list_S529945141ession) (P (-> tptp.list_S529945141ession Bool))) (=> (not (= Xs tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (@ P (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (not (= Xs2 tptp.nil_Se901661471ession)) (=> (@ P Xs2) (@ P (@ (@ tptp.append2089414218ession Xs2) (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession)))))) (@ P Xs))))) (forall ((Ys2 tptp.list_Secrecy_KS) (Zs2 tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) Xs))) (= (= (@ (@ tptp.append_Secrecy_KS Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_Secrecy_KS) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_Secrecy_KS)) (and (= Ys2 (@ (@ tptp.cons_Secrecy_KS X3) Ys4)) (= (@ (@ tptp.append_Secrecy_KS Ys4) Zs2) Xs))))))) (forall ((Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) Xs))) (= (= (@ (@ tptp.append2089414218ession Ys2) Zs2) _let_1) (or (and (= Ys2 tptp.nil_Se901661471ession) (= Zs2 _let_1)) (exists ((Ys4 tptp.list_S529945141ession)) (and (= Ys2 (@ (@ tptp.cons_S112077679ession X3) Ys4)) (= (@ (@ tptp.append2089414218ession Ys4) Zs2) Xs))))))) (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS) (Zs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) Xs))) (= (= _let_1 (@ (@ tptp.append_Secrecy_KS Ys2) Zs2)) (or (and (= Ys2 tptp.nil_Secrecy_KS) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_Secrecy_KS)) (and (= (@ (@ tptp.cons_Secrecy_KS X3) Ys4) Ys2) (= Xs (@ (@ tptp.append_Secrecy_KS Ys4) Zs2)))))))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) Xs))) (= (= _let_1 (@ (@ tptp.append2089414218ession Ys2) Zs2)) (or (and (= Ys2 tptp.nil_Se901661471ession) (= _let_1 Zs2)) (exists ((Ys4 tptp.list_S529945141ession)) (and (= (@ (@ tptp.cons_S112077679ession X3) Ys4) Ys2) (= Xs (@ (@ tptp.append2089414218ession Ys4) Zs2)))))))) (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (not (forall ((Ys3 tptp.list_Secrecy_KS) (Y4 tptp.secrecy_KS)) (not (= Xs (@ (@ tptp.append_Secrecy_KS Ys3) (@ (@ tptp.cons_Secrecy_KS Y4) tptp.nil_Secrecy_KS)))))))) (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (not (forall ((Ys3 tptp.list_S529945141ession) (Y4 tptp.secrecy_Expression)) (not (= Xs (@ (@ tptp.append2089414218ession Ys3) (@ (@ tptp.cons_S112077679ession Y4) tptp.nil_Se901661471ession)))))))) (forall ((P (-> tptp.list_Secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS)) (=> (@ P tptp.nil_Secrecy_KS) (=> (forall ((X tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (=> (@ P Xs2) (@ P (@ (@ tptp.append_Secrecy_KS Xs2) (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))))) (@ P Xs)))) (forall ((P (-> tptp.list_S529945141ession Bool)) (Xs tptp.list_S529945141ession)) (=> (@ P tptp.nil_Se901661471ession) (=> (forall ((X tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (=> (@ P Xs2) (@ P (@ (@ tptp.append2089414218ession Xs2) (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))))) (@ P Xs)))) (forall ((F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.maps_S599402637ession F2))) (= (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ (@ tptp.append2089414218ession (@ F2 X3)) (@ _let_1 Xs))))) (forall ((K12 tptp.secrecy_Keys) (K22 tptp.secrecy_Keys) (E3 tptp.list_S529945141ession)) (=> (@ (@ tptp.encrDecrKeys K12) K22) (= (@ (@ tptp.ext K12) (@ (@ tptp.sign K22) E3)) E3))) (forall ((K12 tptp.secrecy_Keys) (K22 tptp.secrecy_Keys) (E3 tptp.list_S529945141ession)) (=> (@ (@ tptp.encrDecrKeys K12) K22) (= (@ (@ tptp.decr K22) (@ (@ tptp.enc K12) E3)) E3))) (forall ((Xss2 tptp.list_l425507653ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (let ((_let_1 (= Xss2 tptp.nil_li311616943ession))) (= (= (@ tptp.concat388015140ession Xss2) (@ (@ tptp.append2089414218ession Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_Se901661471ession) (= Zs2 tptp.nil_Se901661471ession))) (=> (not _let_1) (exists ((Xss1 tptp.list_l425507653ession) (Xs3 tptp.list_S529945141ession) (Xs4 tptp.list_S529945141ession) (Xss22 tptp.list_l425507653ession)) (and (= Xss2 (@ (@ tptp.append1105297242ession Xss1) (@ (@ tptp.cons_l533358079ession (@ (@ tptp.append2089414218ession Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append2089414218ession (@ tptp.concat388015140ession Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append2089414218ession Xs4) (@ tptp.concat388015140ession Xss22)))))))))) (forall ((Xss2 tptp.list_list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS) (Zs2 tptp.list_Secrecy_KS)) (let ((_let_1 (= Xss2 tptp.nil_list_Secrecy_KS))) (= (= (@ tptp.concat_Secrecy_KS Xss2) (@ (@ tptp.append_Secrecy_KS Ys2) Zs2)) (and (=> _let_1 (and (= Ys2 tptp.nil_Secrecy_KS) (= Zs2 tptp.nil_Secrecy_KS))) (=> (not _let_1) (exists ((Xss1 tptp.list_list_Secrecy_KS) (Xs3 tptp.list_Secrecy_KS) (Xs4 tptp.list_Secrecy_KS) (Xss22 tptp.list_list_Secrecy_KS)) (and (= Xss2 (@ (@ tptp.append1376766698ecy_KS Xss1) (@ (@ tptp.cons_list_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs3) Xs4)) Xss22))) (= Ys2 (@ (@ tptp.append_Secrecy_KS (@ tptp.concat_Secrecy_KS Xss1)) Xs3)) (= Zs2 (@ (@ tptp.append_Secrecy_KS Xs4) (@ tptp.concat_Secrecy_KS Xss22)))))))))) (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (= (@ tptp.rotate1_Secrecy_KS (@ _let_1 Xs)) (@ (@ tptp.append_Secrecy_KS Xs) (@ _let_1 tptp.nil_Secrecy_KS))))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ tptp.rotate1237234450ession (@ _let_1 Xs)) (@ (@ tptp.append2089414218ession Xs) (@ _let_1 tptp.nil_Se901661471ession))))) (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.rotate1237234450ession Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.rotate1_Secrecy_KS Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_l425507653ession) (Ys2 tptp.list_l425507653ession)) (= (@ tptp.concat388015140ession (@ (@ tptp.append1105297242ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.concat388015140ession Xs)) (@ tptp.concat388015140ession Ys2)))) (= (@ tptp.rotate1237234450ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (= (@ tptp.rotate1_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) _let_5 (= (@ tptp.concat_Secrecy_KS tptp.nil_list_Secrecy_KS) tptp.nil_Secrecy_KS) (forall ((X3 tptp.list_S529945141ession) (Xs tptp.list_l425507653ession)) (= (@ tptp.concat388015140ession (@ (@ tptp.cons_l533358079ession X3) Xs)) (@ (@ tptp.append2089414218ession X3) (@ tptp.concat388015140ession Xs)))) (forall ((F2 (-> tptp.secrecy_Expression tptp.list_S529945141ession))) (= (@ (@ tptp.maps_S599402637ession F2) tptp.nil_Se901661471ession) tptp.nil_Se901661471ession)) (forall ((F2 (-> tptp.secrecy_Expression tptp.list_Secrecy_KS))) (= (@ (@ tptp.maps_S399472669ecy_KS F2) tptp.nil_Se901661471ession) tptp.nil_Secrecy_KS)) (forall ((F2 (-> tptp.secrecy_KS tptp.list_S529945141ession))) (= (@ (@ tptp.maps_S1434541085ession F2) tptp.nil_Secrecy_KS) tptp.nil_Se901661471ession)) (forall ((F2 (-> tptp.secrecy_KS tptp.list_Secrecy_KS))) (= (@ (@ tptp.maps_S377605037ecy_KS F2) tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS)) (forall ((Xss2 tptp.list_l425507653ession) (Ys2 tptp.list_S529945141ession) (Zs2 tptp.list_S529945141ession)) (=> (= (@ tptp.concat388015140ession Xss2) (@ (@ tptp.append2089414218ession Ys2) Zs2)) (=> (not (= Xss2 tptp.nil_li311616943ession)) (exists ((Xss12 tptp.list_l425507653ession) (Xs2 tptp.list_S529945141ession) (Xs5 tptp.list_S529945141ession) (Xss23 tptp.list_l425507653ession)) (and (= Xss2 (@ (@ tptp.append1105297242ession Xss12) (@ (@ tptp.cons_l533358079ession (@ (@ tptp.append2089414218ession Xs2) Xs5)) Xss23))) (= Ys2 (@ (@ tptp.append2089414218ession (@ tptp.concat388015140ession Xss12)) Xs2)) (= Zs2 (@ (@ tptp.append2089414218ession Xs5) (@ tptp.concat388015140ession Xss23)))))))) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (= (@ tptp.butlast_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) Xs)) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (= (@ tptp.butlas171474643ession (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) Xs)) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) X3)) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (= (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) X3)) _let_3 (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (=> (not (= Ys2 tptp.nil_Se901661471ession)) (= (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.last_S1532390982ession Ys2)))) (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (=> (not (= Ys2 tptp.nil_Secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ tptp.last_Secrecy_KS Ys2)))) (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (=> (= Ys2 tptp.nil_Se901661471ession) (= (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.last_S1532390982ession Xs)))) (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (=> (= Ys2 tptp.nil_Secrecy_KS) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ tptp.last_Secrecy_KS Xs)))) (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ (@ tptp.append_Secrecy_KS (@ tptp.butlast_Secrecy_KS Xs)) (@ (@ tptp.cons_Secrecy_KS (@ tptp.last_Secrecy_KS Xs)) tptp.nil_Secrecy_KS)) Xs))) (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ (@ tptp.append2089414218ession (@ tptp.butlas171474643ession Xs)) (@ (@ tptp.cons_S112077679ession (@ tptp.last_S1532390982ession Xs)) tptp.nil_Se901661471ession)) Xs))) (= (@ tptp.butlas171474643ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (= (@ tptp.butlast_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (= (@ (@ tptp.append_Secrecy_KS Xs) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS)) Ys2) (and (not (= Ys2 tptp.nil_Secrecy_KS)) (= (@ tptp.butlast_Secrecy_KS Ys2) Xs) (= (@ tptp.last_Secrecy_KS Ys2) X3)))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession)) (= (= (@ (@ tptp.append2089414218ession Xs) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession)) Ys2) (and (not (= Ys2 tptp.nil_Se901661471ession)) (= (@ tptp.butlas171474643ession Ys2) Xs) (= (@ tptp.last_S1532390982ession Ys2) X3)))) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)) (@ tptp.last_Secrecy_KS Xs)))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.last_S1532390982ession (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ tptp.last_S1532390982ession Xs)))) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (=> (= Xs tptp.nil_Secrecy_KS) (= (@ tptp.last_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)) X3))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (=> (= Xs tptp.nil_Se901661471ession) (= (@ tptp.last_S1532390982ession (@ (@ tptp.cons_S112077679ession X3) Xs)) X3))) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.last_Secrecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_Secrecy_KS))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_Secrecy_KS Xs))))))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.last_S1532390982ession (@ (@ tptp.cons_S112077679ession X3) Xs)))) (let ((_let_2 (= Xs tptp.nil_Se901661471ession))) (and (=> _let_2 (= _let_1 X3)) (=> (not _let_2) (= _let_1 (@ tptp.last_S1532390982ession Xs))))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (exists ((Ss tptp.list_S529945141ession) (Xs5 tptp.list_S529945141ession) (Ys5 tptp.list_S529945141ession)) (and (= Xs (@ (@ tptp.append2089414218ession Xs5) Ss)) (= Ys2 (@ (@ tptp.append2089414218ession Ys5) Ss)) (or (= Xs5 tptp.nil_Se901661471ession) (= Ys5 tptp.nil_Se901661471ession) (not (= (@ tptp.last_S1532390982ession Xs5) (@ tptp.last_S1532390982ession Ys5))))))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (exists ((Ss tptp.list_Secrecy_KS) (Xs5 tptp.list_Secrecy_KS) (Ys5 tptp.list_Secrecy_KS)) (and (= Xs (@ (@ tptp.append_Secrecy_KS Xs5) Ss)) (= Ys2 (@ (@ tptp.append_Secrecy_KS Ys5) Ss)) (or (= Xs5 tptp.nil_Secrecy_KS) (= Ys5 tptp.nil_Secrecy_KS) (not (= (@ tptp.last_Secrecy_KS Xs5) (@ tptp.last_Secrecy_KS Ys5))))))) (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.last_S1532390982ession (@ (@ tptp.append2089414218ession Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_Se901661471ession))) (and (=> _let_2 (= _let_1 (@ tptp.last_S1532390982ession Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_S1532390982ession Ys2))))))) (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.last_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)))) (let ((_let_2 (= Ys2 tptp.nil_Secrecy_KS))) (and (=> _let_2 (= _let_1 (@ tptp.last_Secrecy_KS Xs))) (=> (not _let_2) (= _let_1 (@ tptp.last_Secrecy_KS Ys2))))))) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (let ((_let_2 (@ tptp.butlast_Secrecy_KS (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_Secrecy_KS))) (and (=> _let_3 (= _let_2 tptp.nil_Secrecy_KS)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_Secrecy_KS Xs))))))))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (let ((_let_2 (@ tptp.butlas171474643ession (@ _let_1 Xs)))) (let ((_let_3 (= Xs tptp.nil_Se901661471ession))) (and (=> _let_3 (= _let_2 tptp.nil_Se901661471ession)) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas171474643ession Xs))))))))) (forall ((Ys2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Xs))) (let ((_let_2 (@ tptp.butlas171474643ession (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_Se901661471ession))) (and (=> _let_3 (= _let_2 (@ tptp.butlas171474643ession Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlas171474643ession Ys2))))))))) (forall ((Ys2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.append_Secrecy_KS Xs))) (let ((_let_2 (@ tptp.butlast_Secrecy_KS (@ _let_1 Ys2)))) (let ((_let_3 (= Ys2 tptp.nil_Secrecy_KS))) (and (=> _let_3 (= _let_2 (@ tptp.butlast_Secrecy_KS Xs))) (=> (not _let_3) (= _let_2 (@ _let_1 (@ tptp.butlast_Secrecy_KS Ys2))))))))) (forall ((X3 tptp.secrecy_KS)) (not (@ (@ tptp.mem_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (forall ((X3 tptp.secrecy_Expression)) (not (@ (@ tptp.mem_Se1967555118ession X3) tptp.nil_Se901661471ession))) (forall ((X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (L tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.mem_Se1967555118ession X3))) (= (@ _let_1 (@ (@ tptp.cons_S112077679ession Y) L)) (or (= X3 Y) (@ _let_1 L))))) (= tptp.concat388015140ession (lambda ((Xss3 tptp.list_l425507653ession)) (@ (@ (@ tptp.foldr_1531709715ession tptp.append2089414218ession) Xss3) tptp.nil_Se901661471ession))) _let_2 (forall ((Kl tptp.list_Secrecy_Secrets) (K tptp.secrecy_Secrets) (Kl2 tptp.set_li2007071804ecrets)) (=> (@ (@ tptp.member1138497285ecrets (@ (@ tptp.append186372209ecrets Kl) (@ (@ tptp.cons_Secrecy_Secrets K) tptp.nil_Secrecy_Secrets))) Kl2) (@ (@ tptp.member2138796287ecrets K) (@ (@ tptp.bNF_Gr957048817ecrets Kl2) Kl)))) (forall ((Kl tptp.list_Secrecy_Keys) (K tptp.secrecy_Keys) (Kl2 tptp.set_li849033543y_Keys)) (=> (@ (@ tptp.member341114536y_Keys (@ (@ tptp.append_Secrecy_Keys Kl) (@ (@ tptp.cons_Secrecy_Keys K) tptp.nil_Secrecy_Keys))) Kl2) (@ (@ tptp.member_Secrecy_Keys K) (@ (@ tptp.bNF_Gr344893606y_Keys Kl2) Kl)))) (forall ((Kl tptp.list_Secrecy_KS) (K tptp.secrecy_KS) (Kl2 tptp.set_list_Secrecy_KS)) (=> (@ (@ tptp.member193705948ecy_KS (@ (@ tptp.append_Secrecy_KS Kl) (@ (@ tptp.cons_Secrecy_KS K) tptp.nil_Secrecy_KS))) Kl2) (@ (@ tptp.member_Secrecy_KS2 K) (@ (@ tptp.bNF_Gr577175642ecy_KS Kl2) Kl)))) (forall ((Kl tptp.list_S529945141ession) (K tptp.secrecy_Expression) (Kl2 tptp.set_li185139947ession)) (=> (@ (@ tptp.member249235532ession (@ (@ tptp.append2089414218ession Kl) (@ (@ tptp.cons_S112077679ession K) tptp.nil_Se901661471ession))) Kl2) (@ (@ tptp.member279582780ession K) (@ (@ tptp.bNF_Gr979629770ession Kl2) Kl)))) (forall ((K tptp.secrecy_Secrets) (Kl2 tptp.set_li2007071804ecrets) (Kl tptp.list_Secrecy_Secrets)) (=> (@ (@ tptp.member2138796287ecrets K) (@ (@ tptp.bNF_Gr957048817ecrets Kl2) Kl)) (@ (@ tptp.member1138497285ecrets (@ (@ tptp.append186372209ecrets Kl) (@ (@ tptp.cons_Secrecy_Secrets K) tptp.nil_Secrecy_Secrets))) Kl2))) (forall ((K tptp.secrecy_Keys) (Kl2 tptp.set_li849033543y_Keys) (Kl tptp.list_Secrecy_Keys)) (=> (@ (@ tptp.member_Secrecy_Keys K) (@ (@ tptp.bNF_Gr344893606y_Keys Kl2) Kl)) (@ (@ tptp.member341114536y_Keys (@ (@ tptp.append_Secrecy_Keys Kl) (@ (@ tptp.cons_Secrecy_Keys K) tptp.nil_Secrecy_Keys))) Kl2))) (forall ((K tptp.secrecy_KS) (Kl2 tptp.set_list_Secrecy_KS) (Kl tptp.list_Secrecy_KS)) (=> (@ (@ tptp.member_Secrecy_KS2 K) (@ (@ tptp.bNF_Gr577175642ecy_KS Kl2) Kl)) (@ (@ tptp.member193705948ecy_KS (@ (@ tptp.append_Secrecy_KS Kl) (@ (@ tptp.cons_Secrecy_KS K) tptp.nil_Secrecy_KS))) Kl2))) (forall ((K tptp.secrecy_Expression) (Kl2 tptp.set_li185139947ession) (Kl tptp.list_S529945141ession)) (=> (@ (@ tptp.member279582780ession K) (@ (@ tptp.bNF_Gr979629770ession Kl2) Kl)) (@ (@ tptp.member249235532ession (@ (@ tptp.append2089414218ession Kl) (@ (@ tptp.cons_S112077679ession K) tptp.nil_Se901661471ession))) Kl2))) (forall ((Xs tptp.list_Secrecy_KS) (Y tptp.secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS Y))) (= (= (@ tptp.rev_Secrecy_KS Xs) (@ _let_1 Ys2)) (= Xs (@ (@ tptp.append_Secrecy_KS (@ tptp.rev_Secrecy_KS Ys2)) (@ _let_1 tptp.nil_Secrecy_KS)))))) (forall ((Xs tptp.list_S529945141ession) (Y tptp.secrecy_Expression) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession Y))) (= (= (@ tptp.rev_Se1073238207ession Xs) (@ _let_1 Ys2)) (= Xs (@ (@ tptp.append2089414218ession (@ tptp.rev_Se1073238207ession Ys2)) (@ _let_1 tptp.nil_Se901661471ession)))))) (forall ((Xs tptp.list_S529945141ession)) (= (= tptp.nil_Se901661471ession (@ tptp.rev_Se1073238207ession Xs)) (= Xs tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS)) (= (= tptp.nil_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (= Xs tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.rev_Se1073238207ession Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.rev_Secrecy_KS Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (@ tptp.rev_Se1073238207ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.rev_Se1073238207ession Ys2)) (@ tptp.rev_Se1073238207ession Xs)))) (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (= (= _let_1 (@ tptp.rev_Secrecy_KS Xs)) (= Xs _let_1)))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (= (= _let_1 (@ tptp.rev_Se1073238207ession Xs)) (= Xs _let_1)))) (forall ((Xs tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (= (= (@ tptp.rev_Secrecy_KS Xs) _let_1) (= Xs _let_1)))) (forall ((Xs tptp.list_S529945141ession) (X3 tptp.secrecy_Expression)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (= (= (@ tptp.rev_Se1073238207ession Xs) _let_1) (= Xs _let_1)))) (= (@ tptp.rev_Se1073238207ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (= (@ tptp.rev_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (= (@ tptp.rev_Secrecy_KS (@ _let_1 Xs)) (@ (@ tptp.append_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (@ _let_1 tptp.nil_Secrecy_KS))))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (= (@ tptp.rev_Se1073238207ession (@ _let_1 Xs)) (@ (@ tptp.append2089414218ession (@ tptp.rev_Se1073238207ession Xs)) (@ _let_1 tptp.nil_Se901661471ession))))) (forall ((Kl2 tptp.set_li2007071804ecrets) (K tptp.secrecy_Secrets)) (let ((_let_1 (@ tptp.member1138497285ecrets tptp.nil_Secrecy_Secrets))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member2138796287ecrets K) (@ (@ tptp.bNF_Gr957048817ecrets Kl2) tptp.nil_Secrecy_Secrets)) (@ _let_1 (@ (@ tptp.bNF_Gr28627573ecrets Kl2) K)))))) (forall ((Kl2 tptp.set_li849033543y_Keys) (K tptp.secrecy_Keys)) (let ((_let_1 (@ tptp.member341114536y_Keys tptp.nil_Secrecy_Keys))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_Secrecy_Keys K) (@ (@ tptp.bNF_Gr344893606y_Keys Kl2) tptp.nil_Secrecy_Keys)) (@ _let_1 (@ (@ tptp.bNF_Gr414702370y_Keys Kl2) K)))))) (forall ((Kl2 tptp.set_li185139947ession) (K tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.member249235532ession tptp.nil_Se901661471ession))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member279582780ession K) (@ (@ tptp.bNF_Gr979629770ession Kl2) tptp.nil_Se901661471ession)) (@ _let_1 (@ (@ tptp.bNF_Gr275623750ession Kl2) K)))))) (forall ((Kl2 tptp.set_list_Secrecy_KS) (K tptp.secrecy_KS)) (let ((_let_1 (@ tptp.member193705948ecy_KS tptp.nil_Secrecy_KS))) (=> (@ _let_1 Kl2) (=> (@ (@ tptp.member_Secrecy_KS2 K) (@ (@ tptp.bNF_Gr577175642ecy_KS Kl2) tptp.nil_Secrecy_KS)) (@ _let_1 (@ (@ tptp.bNF_Gr660123862ecy_KS Kl2) K)))))) (forall ((Kl tptp.list_S529945141ession) (Kl2 tptp.set_li185139947ession) (K tptp.secrecy_Expression)) (=> (@ (@ tptp.member249235532ession Kl) (@ (@ tptp.bNF_Gr275623750ession Kl2) K)) (@ (@ tptp.member249235532ession (@ (@ tptp.cons_S112077679ession K) Kl)) Kl2))) (forall ((Kl2 tptp.set_li185139947ession) (K tptp.secrecy_Expression) (Kl tptp.list_S529945141ession)) (= (@ (@ tptp.bNF_Gr979629770ession (@ (@ tptp.bNF_Gr275623750ession Kl2) K)) Kl) (@ (@ tptp.bNF_Gr979629770ession Kl2) (@ (@ tptp.cons_S112077679ession K) Kl)))) (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.last_S1532390982ession (@ tptp.rev_Se1073238207ession Xs)) (@ tptp.hd_Sec357328890ession Xs)))) (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.last_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (@ tptp.hd_Secrecy_KS Xs)))) (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession (@ tptp.rev_Se1073238207ession Xs)) (@ tptp.last_S1532390982ession Xs)))) (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS (@ tptp.rev_Secrecy_KS Xs)) (@ tptp.last_Secrecy_KS Xs)))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.hd_Sec357328890ession Xs)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ tptp.hd_Secrecy_KS Xs)))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.hd_Sec357328890ession (@ (@ tptp.append2089414218ession Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_Se901661471ession))) (and (=> _let_2 (= _let_1 (@ tptp.hd_Sec357328890ession Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_Sec357328890ession Xs))))))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.hd_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)))) (let ((_let_2 (= Xs tptp.nil_Secrecy_KS))) (and (=> _let_2 (= _let_1 (@ tptp.hd_Secrecy_KS Ys2))) (=> (not _let_2) (= _let_1 (@ tptp.hd_Secrecy_KS Xs))))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (exists ((Ps tptp.list_S529945141ession) (Xs5 tptp.list_S529945141ession) (Ys5 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.append2089414218ession Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_Se901661471ession) (= Ys5 tptp.nil_Se901661471ession) (not (= (@ tptp.hd_Sec357328890ession Xs5) (@ tptp.hd_Sec357328890ession Ys5)))))))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (exists ((Ps tptp.list_Secrecy_KS) (Xs5 tptp.list_Secrecy_KS) (Ys5 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.append_Secrecy_KS Ps))) (and (= Xs (@ _let_1 Xs5)) (= Ys2 (@ _let_1 Ys5)) (or (= Xs5 tptp.nil_Secrecy_KS) (= Ys5 tptp.nil_Secrecy_KS) (not (= (@ tptp.hd_Secrecy_KS Xs5) (@ tptp.hd_Secrecy_KS Ys5)))))))) (forall ((Xs tptp.list_l425507653ession)) (let ((_let_1 (@ tptp.hd_lis1623417098ession Xs))) (=> (not (= Xs tptp.nil_li311616943ession)) (=> (not (= _let_1 tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession (@ tptp.concat388015140ession Xs)) (@ tptp.hd_Sec357328890ession _let_1)))))) (forall ((Xs tptp.list_list_Secrecy_KS)) (let ((_let_1 (@ tptp.hd_list_Secrecy_KS Xs))) (=> (not (= Xs tptp.nil_list_Secrecy_KS)) (=> (not (= _let_1 tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS (@ tptp.concat_Secrecy_KS Xs)) (@ tptp.hd_Secrecy_KS _let_1)))))) (forall ((X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession)) (= (@ tptp.hd_Sec357328890ession (@ (@ tptp.cons_S112077679ession X21) X222)) X21)) (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.rotate1_Secrecy_KS Xs) (@ (@ tptp.append_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS Xs)) tptp.nil_Secrecy_KS))))) (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.rotate1237234450ession Xs) (@ (@ tptp.append2089414218ession (@ tptp.tl_Sec1905266422ession Xs)) (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession Xs)) tptp.nil_Se901661471ession))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (@ tptp.distin1076152135ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (and (@ tptp.distin1076152135ession Xs) (@ tptp.distin1076152135ession Ys2) (or (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession) (not (= (@ tptp.last_S1532390982ession Xs) (@ tptp.hd_Sec357328890ession Ys2))))))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (@ tptp.distin1495927511ecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (and (@ tptp.distin1495927511ecy_KS Xs) (@ tptp.distin1495927511ecy_KS Ys2) (or (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS) (not (= (@ tptp.last_Secrecy_KS Xs) (@ tptp.hd_Secrecy_KS Ys2))))))) (forall ((X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y) Xs))) (= (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) _let_1)) (and (not (= X3 Y)) (@ tptp.distin1076152135ession _let_1))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.tl_Sec1905266422ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.tl_Sec1905266422ession Xs)) Ys2)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.tl_Secrecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ (@ tptp.append_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) Ys2)))) (forall ((List tptp.list_Secrecy_KS)) (=> (not (= List tptp.nil_Secrecy_KS)) (= (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS List)) (@ tptp.tl_Secrecy_KS List)) List))) (forall ((List tptp.list_S529945141ession)) (=> (not (= List tptp.nil_Se901661471ession)) (= (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession List)) (@ tptp.tl_Sec1905266422ession List)) List))) (forall ((Xs tptp.list_Secrecy_KS)) (=> (not (= Xs tptp.nil_Secrecy_KS)) (= (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS Xs)) (@ tptp.tl_Secrecy_KS Xs)) Xs))) (forall ((Xs tptp.list_S529945141ession)) (=> (not (= Xs tptp.nil_Se901661471ession)) (= (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession Xs)) (@ tptp.tl_Sec1905266422ession Xs)) Xs))) (forall ((List tptp.list_S529945141ession) (List2 tptp.list_S529945141ession)) (let ((_let_1 (= List2 tptp.nil_Se901661471ession))) (let ((_let_2 (= List tptp.nil_Se901661471ession))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_Sec357328890ession List) (@ tptp.hd_Sec357328890ession List2)) (= (@ tptp.tl_Sec1905266422ession List) (@ tptp.tl_Sec1905266422ession List2))))) (= List List2)))))) (forall ((List tptp.list_Secrecy_KS) (List2 tptp.list_Secrecy_KS)) (let ((_let_1 (= List2 tptp.nil_Secrecy_KS))) (let ((_let_2 (= List tptp.nil_Secrecy_KS))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (and (= (@ tptp.hd_Secrecy_KS List) (@ tptp.hd_Secrecy_KS List2)) (= (@ tptp.tl_Secrecy_KS List) (@ tptp.tl_Secrecy_KS List2))))) (= List List2)))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ tptp.distin1076152135ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.distin1076152135ession Xs))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ tptp.distin1076152135ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ tptp.distin1076152135ession Ys2))) (@ tptp.distin1076152135ession tptp.nil_Se901661471ession) (@ tptp.distin1495927511ecy_KS tptp.nil_Secrecy_KS) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (=> (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) Xs)) (@ tptp.distin1076152135ession Xs))) (= (@ tptp.tl_Sec1905266422ession tptp.nil_Se901661471ession) tptp.nil_Se901661471ession) (= (@ tptp.tl_Secrecy_KS tptp.nil_Secrecy_KS) tptp.nil_Secrecy_KS) (forall ((X21 tptp.secrecy_Expression) (X222 tptp.list_S529945141ession)) (= (@ tptp.tl_Sec1905266422ession (@ (@ tptp.cons_S112077679ession X21) X222)) X222)) (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.tl_Secrecy_KS Xs) tptp.nil_Secrecy_KS) (or (= Xs tptp.nil_Secrecy_KS) (exists ((X4 tptp.secrecy_KS)) (= Xs (@ (@ tptp.cons_Secrecy_KS X4) tptp.nil_Secrecy_KS)))))) (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.tl_Sec1905266422ession Xs) tptp.nil_Se901661471ession) (or (= Xs tptp.nil_Se901661471ession) (exists ((X4 tptp.secrecy_Expression)) (= Xs (@ (@ tptp.cons_S112077679ession X4) tptp.nil_Se901661471ession)))))) (forall ((Xs tptp.list_Secrecy_KS)) (= (= tptp.nil_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) (or (= Xs tptp.nil_Secrecy_KS) (exists ((X4 tptp.secrecy_KS)) (= Xs (@ (@ tptp.cons_Secrecy_KS X4) tptp.nil_Secrecy_KS)))))) (forall ((Xs tptp.list_S529945141ession)) (= (= tptp.nil_Se901661471ession (@ tptp.tl_Sec1905266422ession Xs)) (or (= Xs tptp.nil_Se901661471ession) (exists ((X4 tptp.secrecy_Expression)) (= Xs (@ (@ tptp.cons_S112077679ession X4) tptp.nil_Se901661471ession)))))) (forall ((Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.tl_Sec1905266422ession Xs))) (=> (or (= Xs tptp.nil_Se901661471ession) (not (= _let_1 tptp.nil_Se901661471ession))) (= (@ tptp.last_S1532390982ession _let_1) (@ tptp.last_S1532390982ession Xs))))) (forall ((Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.tl_Secrecy_KS Xs))) (=> (or (= Xs tptp.nil_Secrecy_KS) (not (= _let_1 tptp.nil_Secrecy_KS))) (= (@ tptp.last_Secrecy_KS _let_1) (@ tptp.last_Secrecy_KS Xs))))) (forall ((X3 tptp.secrecy_KS)) (@ tptp.distin1495927511ecy_KS (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (forall ((X3 tptp.secrecy_Expression)) (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (forall ((List tptp.list_Secrecy_KS)) (=> (not (= List tptp.nil_Secrecy_KS)) (= List (@ (@ tptp.cons_Secrecy_KS (@ tptp.hd_Secrecy_KS List)) (@ tptp.tl_Secrecy_KS List))))) (forall ((List tptp.list_S529945141ession)) (=> (not (= List tptp.nil_Se901661471ession)) (= List (@ (@ tptp.cons_S112077679ession (@ tptp.hd_Sec357328890ession List)) (@ tptp.tl_Sec1905266422ession List))))) (forall ((X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (= (@ tptp.distin1495927511ecy_KS (@ (@ tptp.cons_Secrecy_KS X3) Xs)) (or (= Xs tptp.nil_Secrecy_KS) (and (not (= X3 (@ tptp.hd_Secrecy_KS Xs))) (@ tptp.distin1495927511ecy_KS Xs))))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (= (@ tptp.distin1076152135ession (@ (@ tptp.cons_S112077679ession X3) Xs)) (or (= Xs tptp.nil_Se901661471ession) (and (not (= X3 (@ tptp.hd_Sec357328890ession Xs))) (@ tptp.distin1076152135ession Xs))))) (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.succes1388047762ession P))) (= (@ _let_1 (@ (@ tptp.append2089414218ession Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession) (@ (@ P (@ tptp.last_S1532390982ession Xs)) (@ tptp.hd_Sec357328890ession Ys2))))))) (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.succes590251810ecy_KS P))) (= (@ _let_1 (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (and (@ _let_1 Xs) (@ _let_1 Ys2) (or (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS) (@ (@ P (@ tptp.last_Secrecy_KS Xs)) (@ tptp.hd_Secrecy_KS Ys2))))))) (forall ((Z tptp.secrecy_KS) (Zs2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.shuffles_Secrecy_KS Xs))) (let ((_let_2 (@ tptp.member193705948ecy_KS Zs2))) (= (@ (@ tptp.member193705948ecy_KS (@ (@ tptp.cons_Secrecy_KS Z) Zs2)) (@ _let_1 Ys2)) (or (and (not (= Xs tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS Xs) Z) (@ _let_2 (@ (@ tptp.shuffles_Secrecy_KS (@ tptp.tl_Secrecy_KS Xs)) Ys2))) (and (not (= Ys2 tptp.nil_Secrecy_KS)) (= (@ tptp.hd_Secrecy_KS Ys2) Z) (@ _let_2 (@ _let_1 (@ tptp.tl_Secrecy_KS Ys2))))))))) (forall ((Z tptp.secrecy_Expression) (Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.shuffl552897610ession Xs))) (let ((_let_2 (@ tptp.member249235532ession Zs2))) (= (@ (@ tptp.member249235532ession (@ (@ tptp.cons_S112077679ession Z) Zs2)) (@ _let_1 Ys2)) (or (and (not (= Xs tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession Xs) Z) (@ _let_2 (@ (@ tptp.shuffl552897610ession (@ tptp.tl_Sec1905266422ession Xs)) Ys2))) (and (not (= Ys2 tptp.nil_Se901661471ession)) (= (@ tptp.hd_Sec357328890ession Ys2) Z) (@ _let_2 (@ _let_1 (@ tptp.tl_Sec1905266422ession Ys2))))))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (= (@ (@ tptp.member249235532ession tptp.nil_Se901661471ession) (@ (@ tptp.shuffl552897610ession Xs) Ys2)) (and (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession)))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (= (@ (@ tptp.member193705948ecy_KS tptp.nil_Secrecy_KS) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys2)) (and (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS)))) (forall ((Zs2 tptp.list_Secrecy_KS) (Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (@ (@ tptp.member193705948ecy_KS Zs2) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys2)) (=> (=> (= Zs2 Xs) (not (= Ys2 tptp.nil_Secrecy_KS))) (=> (=> (= Zs2 Ys2) (not (= Xs tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS) (Xs5 tptp.list_Secrecy_KS)) (=> (= Xs (@ (@ tptp.cons_Secrecy_KS X) Xs5)) (forall ((Z2 tptp.secrecy_KS) (Zs3 tptp.list_Secrecy_KS)) (=> (= Zs2 (@ (@ tptp.cons_Secrecy_KS Z2) Zs3)) (=> (= X Z2) (not (@ (@ tptp.member193705948ecy_KS Zs3) (@ (@ tptp.shuffles_Secrecy_KS Xs5) Ys2)))))))) (not (forall ((Y4 tptp.secrecy_KS) (Ys5 tptp.list_Secrecy_KS)) (=> (= Ys2 (@ (@ tptp.cons_Secrecy_KS Y4) Ys5)) (forall ((Z2 tptp.secrecy_KS) (Zs3 tptp.list_Secrecy_KS)) (=> (= Zs2 (@ (@ tptp.cons_Secrecy_KS Z2) Zs3)) (=> (= Y4 Z2) (not (@ (@ tptp.member193705948ecy_KS Zs3) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys5)))))))))))))) (forall ((Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (@ (@ tptp.member249235532ession Zs2) (@ (@ tptp.shuffl552897610ession Xs) Ys2)) (=> (=> (= Zs2 Xs) (not (= Ys2 tptp.nil_Se901661471ession))) (=> (=> (= Zs2 Ys2) (not (= Xs tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression) (Xs5 tptp.list_S529945141ession)) (=> (= Xs (@ (@ tptp.cons_S112077679ession X) Xs5)) (forall ((Z2 tptp.secrecy_Expression) (Zs3 tptp.list_S529945141ession)) (=> (= Zs2 (@ (@ tptp.cons_S112077679ession Z2) Zs3)) (=> (= X Z2) (not (@ (@ tptp.member249235532ession Zs3) (@ (@ tptp.shuffl552897610ession Xs5) Ys2)))))))) (not (forall ((Y4 tptp.secrecy_Expression) (Ys5 tptp.list_S529945141ession)) (=> (= Ys2 (@ (@ tptp.cons_S112077679ession Y4) Ys5)) (forall ((Z2 tptp.secrecy_Expression) (Zs3 tptp.list_S529945141ession)) (=> (= Zs2 (@ (@ tptp.cons_S112077679ession Z2) Zs3)) (=> (= Y4 Z2) (not (@ (@ tptp.member249235532ession Zs3) (@ (@ tptp.shuffl552897610ession Xs) Ys5)))))))))))))) (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X3 tptp.secrecy_KS)) (@ (@ tptp.succes590251810ecy_KS P) (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression)) (@ (@ tptp.succes1388047762ession P) (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (forall ((X3 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xa tptp.list_Secrecy_KS) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.succes590251810ecy_KS X3) Xa) Y) (=> (=> (= Xa tptp.nil_Secrecy_KS) _let_1) (=> (=> (exists ((X tptp.secrecy_KS)) (= Xa (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) _let_1) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_Secrecy_KS X) _let_1)) (= Y (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes590251810ecy_KS X3) _let_1))))))))))))) (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xa tptp.list_S529945141ession) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ (@ tptp.succes1388047762ession X3) Xa) Y) (=> (=> (= Xa tptp.nil_Se901661471ession) _let_1) (=> (=> (exists ((X tptp.secrecy_Expression)) (= Xa (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) _let_1) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_S112077679ession X) _let_1)) (= Y (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes1388047762ession X3) _let_1))))))))))))) (forall ((X3 (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (Xa tptp.list_Secrecy_KS)) (=> (@ (@ tptp.succes590251810ecy_KS X3) Xa) (=> (not (= Xa tptp.nil_Secrecy_KS)) (=> (forall ((X tptp.secrecy_KS)) (not (= Xa (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS)))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_Secrecy_KS X) _let_1)) (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes590251810ecy_KS X3) _let_1))))))))))) (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xa tptp.list_S529945141ession)) (=> (@ (@ tptp.succes1388047762ession X3) Xa) (=> (not (= Xa tptp.nil_Se901661471ession)) (=> (forall ((X tptp.secrecy_Expression)) (not (= Xa (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession)))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_S112077679ession X) _let_1)) (not (and (@ (@ X3 X) Y4) (@ (@ tptp.succes1388047762ession X3) _let_1))))))))))) (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool))) (@ (@ tptp.succes1388047762ession P) tptp.nil_Se901661471ession)) (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool))) (@ (@ tptp.succes590251810ecy_KS P) tptp.nil_Secrecy_KS)) (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y) Xs))) (let ((_let_2 (@ tptp.succes1388047762ession P))) (= (@ _let_2 (@ (@ tptp.cons_S112077679ession X3) _let_1)) (and (@ (@ P X3) Y) (@ _let_2 _let_1)))))) (forall ((X3 (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (Xa tptp.list_S529945141ession)) (=> (not (@ (@ tptp.succes1388047762ession X3) Xa)) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (=> (= Xa (@ (@ tptp.cons_S112077679ession X) _let_1)) (and (@ (@ X3 X) Y4) (@ (@ tptp.succes1388047762ession X3) _let_1)))))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (= Xs tptp.nil_Se901661471ession) (=> (= Ys2 tptp.nil_Se901661471ession) (@ (@ tptp.member249235532ession tptp.nil_Se901661471ession) (@ (@ tptp.shuffl552897610ession Xs) Ys2))))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (= Xs tptp.nil_Secrecy_KS) (=> (= Ys2 tptp.nil_Secrecy_KS) (@ (@ tptp.member193705948ecy_KS tptp.nil_Secrecy_KS) (@ (@ tptp.shuffles_Secrecy_KS Xs) Ys2))))) (forall ((Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Z tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.cons_S112077679ession Z))) (let ((_let_2 (@ tptp.shuffl552897610ession Xs))) (=> (@ (@ tptp.member249235532ession Zs2) (@ _let_2 Ys2)) (@ (@ tptp.member249235532ession (@ _let_1 Zs2)) (@ _let_2 (@ _let_1 Ys2))))))) (forall ((Zs2 tptp.list_S529945141ession) (Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession) (Z tptp.secrecy_Expression)) (let ((_let_1 (@ tptp.cons_S112077679ession Z))) (=> (@ (@ tptp.member249235532ession Zs2) (@ (@ tptp.shuffl552897610ession Xs) Ys2)) (@ (@ tptp.member249235532ession (@ _let_1 Zs2)) (@ (@ tptp.shuffl552897610ession (@ _let_1 Xs)) Ys2))))) (forall ((P (-> tptp.secrecy_KS tptp.secrecy_KS Bool)) (X3 tptp.secrecy_KS) (Xs tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.succes590251810ecy_KS P))) (= (@ _let_1 (@ (@ tptp.cons_Secrecy_KS X3) Xs)) (or (= Xs tptp.nil_Secrecy_KS) (and (@ (@ P X3) (@ tptp.hd_Secrecy_KS Xs)) (@ _let_1 Xs)))))) (forall ((P (-> tptp.secrecy_Expression tptp.secrecy_Expression Bool)) (X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.succes1388047762ession P))) (= (@ _let_1 (@ (@ tptp.cons_S112077679ession X3) Xs)) (or (= Xs tptp.nil_Se901661471ession) (and (@ (@ P X3) (@ tptp.hd_Sec357328890ession Xs)) (@ _let_1 Xs)))))) (forall ((Xs tptp.list_S529945141ession) (Ys2 tptp.list_S529945141ession)) (=> (or (= Xs tptp.nil_Se901661471ession) (= Ys2 tptp.nil_Se901661471ession) (not (= (@ tptp.last_S1532390982ession Xs) (@ tptp.hd_Sec357328890ession Ys2)))) (= (@ tptp.remdup484344169ession (@ (@ tptp.append2089414218ession Xs) Ys2)) (@ (@ tptp.append2089414218ession (@ tptp.remdup484344169ession Xs)) (@ tptp.remdup484344169ession Ys2))))) (forall ((Xs tptp.list_Secrecy_KS) (Ys2 tptp.list_Secrecy_KS)) (=> (or (= Xs tptp.nil_Secrecy_KS) (= Ys2 tptp.nil_Secrecy_KS) (not (= (@ tptp.last_Secrecy_KS Xs) (@ tptp.hd_Secrecy_KS Ys2)))) (= (@ tptp.remdup351570169ecy_KS (@ (@ tptp.append_Secrecy_KS Xs) Ys2)) (@ (@ tptp.append_Secrecy_KS (@ tptp.remdup351570169ecy_KS Xs)) (@ tptp.remdup351570169ecy_KS Ys2))))) (forall ((Xs_1 tptp.list_Secrecy_KS) (X3 tptp.secrecy_KS) (Xs_2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ tptp.cons_Secrecy_KS X3))) (let ((_let_2 (@ _let_1 Xs_2))) (let ((_let_3 (@ tptp.append_Secrecy_KS Xs_1))) (= (@ tptp.remdup351570169ecy_KS (@ _let_3 _let_2)) (@ (@ tptp.append_Secrecy_KS (@ tptp.remdup351570169ecy_KS (@ _let_3 (@ _let_1 tptp.nil_Secrecy_KS)))) (@ tptp.tl_Secrecy_KS (@ tptp.remdup351570169ecy_KS _let_2)))))))) (forall ((Xs_1 tptp.list_S529945141ession) (X3 tptp.secrecy_Expression) (Xs_2 tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (let ((_let_2 (@ _let_1 Xs_2))) (let ((_let_3 (@ tptp.append2089414218ession Xs_1))) (= (@ tptp.remdup484344169ession (@ _let_3 _let_2)) (@ (@ tptp.append2089414218ession (@ tptp.remdup484344169ession (@ _let_3 (@ _let_1 tptp.nil_Se901661471ession)))) (@ tptp.tl_Sec1905266422ession (@ tptp.remdup484344169ession _let_2)))))))) (forall ((Xs tptp.list_S529945141ession)) (= (= (@ tptp.remdup484344169ession Xs) tptp.nil_Se901661471ession) (= Xs tptp.nil_Se901661471ession))) (forall ((Xs tptp.list_Secrecy_KS)) (= (= (@ tptp.remdup351570169ecy_KS Xs) tptp.nil_Secrecy_KS) (= Xs tptp.nil_Secrecy_KS))) (forall ((X3 tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ tptp.cons_S112077679ession X3))) (let ((_let_2 (@ tptp.remdup484344169ession (@ _let_1 Xs)))) (= (@ _let_1 (@ tptp.tl_Sec1905266422ession _let_2)) _let_2)))) (forall ((X3 tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X3) tptp.nil_Secrecy_KS))) (= (@ tptp.remdup351570169ecy_KS _let_1) _let_1))) (forall ((X3 tptp.secrecy_Expression)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X3) tptp.nil_Se901661471ession))) (= (@ tptp.remdup484344169ession _let_1) _let_1))) (forall ((X3 tptp.list_Secrecy_KS) (Y tptp.list_Secrecy_KS)) (=> (= (@ tptp.remdup351570169ecy_KS X3) Y) (=> (=> (= X3 tptp.nil_Secrecy_KS) (not (= Y tptp.nil_Secrecy_KS))) (=> (forall ((X tptp.secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS X) tptp.nil_Secrecy_KS))) (=> (= X3 _let_1) (not (= Y _let_1))))) (not (forall ((X tptp.secrecy_KS) (Y4 tptp.secrecy_KS) (Xs2 tptp.list_Secrecy_KS)) (let ((_let_1 (@ (@ tptp.cons_Secrecy_KS Y4) Xs2))) (let ((_let_2 (@ tptp.cons_Secrecy_KS X))) (let ((_let_3 (= X Y4))) (=> (= X3 (@ _let_2 _let_1)) (not (and (=> _let_3 (= Y (@ tptp.remdup351570169ecy_KS (@ _let_2 Xs2)))) (=> (not _let_3) (= Y (@ _let_2 (@ tptp.remdup351570169ecy_KS _let_1)))))))))))))))) (forall ((X3 tptp.list_S529945141ession) (Y tptp.list_S529945141ession)) (=> (= (@ tptp.remdup484344169ession X3) Y) (=> (=> (= X3 tptp.nil_Se901661471ession) (not (= Y tptp.nil_Se901661471ession))) (=> (forall ((X tptp.secrecy_Expression)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession X) tptp.nil_Se901661471ession))) (=> (= X3 _let_1) (not (= Y _let_1))))) (not (forall ((X tptp.secrecy_Expression) (Y4 tptp.secrecy_Expression) (Xs2 tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y4) Xs2))) (let ((_let_2 (@ tptp.cons_S112077679ession X))) (let ((_let_3 (= X Y4))) (=> (= X3 (@ _let_2 _let_1)) (not (and (=> _let_3 (= Y (@ tptp.remdup484344169ession (@ _let_2 Xs2)))) (=> (not _let_3) (= Y (@ _let_2 (@ tptp.remdup484344169ession _let_1)))))))))))))))) (forall ((X3 tptp.secrecy_Expression) (Y tptp.secrecy_Expression) (Xs tptp.list_S529945141ession)) (let ((_let_1 (@ (@ tptp.cons_S112077679ession Y) Xs))) (let ((_let_2 (@ tptp.cons_S112077679ession X3))) (let ((_let_3 (@ tptp.remdup484344169ession (@ _let_2 _let_1)))) (let ((_let_4 (= X3 Y))) (and (=> _let_4 (= _let_3 (@ tptp.remdup484344169ession (@ _let_2 Xs)))) (=> (not _let_4) (= _let_3 (@ _let_2 (@ tptp.remdup484344169ession _let_1)))))))))) _let_1 true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))
% 0.56/1.12 )
% 0.56/1.12 % SZS output end Proof for ITP085^1
% 0.56/1.12 % cvc5---1.0.5 exiting
% 0.56/1.13 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------