%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : ITP089^2 : TPTP v9.2.1. Released v7.5.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 08:55:28 AM UTC 2026
% Result : Theorem 95.24s 15.12s
% Output : Refutation 95.24s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : ITP089^2 : TPTP v9.2.1. Released v7.5.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n020.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 08:25:57 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.25/0.49 ---- Original DTF file ---
% 0.25/0.49 thf(spec,logic,$$dhol).
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 % File : ITP089^2 : TPTP v9.2.1. Released v7.5.0.
% 0.25/0.49 % Domain : Interactive Theorem Proving
% 0.25/0.49 % Problem : Sledgehammer KnowledgeKeysSecrets problem prob_396__3295470_1
% 0.25/0.49 % Version : Especial.
% 0.25/0.49 % English :
% 0.25/0.49
% 0.25/0.49 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 0.25/0.49 % : [Des21] Desharnais (2021), Email to Geoff Sutcliffe
% 0.25/0.49 % Source : [Des21]
% 0.25/0.49 % Names : KnowledgeKeysSecrets/prob_396__3295470_1 [Des21]
% 0.25/0.49
% 0.25/0.49 % Status : Theorem
% 0.25/0.49 % Rating : 0.67 v9.1.0, 0.33 v8.2.0, 0.67 v8.1.0, 0.50 v7.5.0
% 0.25/0.49 % Syntax : Number of formulae : 347 ( 110 unt; 66 typ; 0 def)
% 0.25/0.49 % Number of atoms : 1068 ( 271 equ; 0 cnn)
% 0.25/0.49 % Maximal formula atoms : 13 ( 3 avg)
% 0.25/0.49 % Number of connectives : 4595 ( 222 ~; 34 |; 94 &;3688 @)
% 0.25/0.49 % ( 0 <=>; 557 =>; 0 <=; 0 <~>)
% 0.25/0.49 % Maximal formula depth : 20 ( 8 avg)
% 0.25/0.49 % Number of types : 8 ( 7 usr)
% 0.25/0.49 % Number of type conns : 128 ( 128 >; 0 *; 0 +; 0 <<)
% 0.25/0.49 % Number of symbols : 60 ( 59 usr; 5 con; 0-4 aty)
% 0.25/0.49 % Number of variables : 970 ( 59 ^; 862 !; 29 ?; 970 :)
% 0.25/0.49 % ( 20 !>; 0 ?*; 0 @-; 0 @+)
% 0.25/0.49 % SPC : TH1_THM_EQU_NAR
% 0.25/0.49
% 0.25/0.49 % Comments : This file was generated by Sledgehammer 2021-02-23 16:20:38.310
% 0.25/0.49 %------------------------------------------------------------------------------
% 0.25/0.49 % Could-be-implicit typings (9)
% 0.25/0.49 thf(ty_t_Secrecy__types_OExpression,type,
% 0.25/0.49 secrecy_Expression: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Secrecy__types_OSecrets,type,
% 0.25/0.49 secrecy_Secrets: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Secrecy__types_OspecID,type,
% 0.25/0.49 secrecy_specID: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Secrecy__types_OchanID,type,
% 0.25/0.49 secrecy_chanID: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Secrecy__types_OKeys,type,
% 0.25/0.49 secrecy_Keys: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Secrecy__types_OKS,type,
% 0.25/0.49 secrecy_KS: $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_List_Olist,type,
% 0.25/0.49 list: $tType > $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Set_Oset,type,
% 0.25/0.49 set: $tType > $tType ).
% 0.25/0.49
% 0.25/0.49 thf(ty_t_Nat_Onat,type,
% 0.25/0.49 nat: $tType ).
% 0.25/0.49
% 0.25/0.49 % Explicit typings (57)
% 0.25/0.49 thf(sy_cl_Lattices_Obounded__lattice,type,
% 0.25/0.49 bounded_lattice:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_HOL_Otype,type,
% 0.25/0.49 type:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_Orderings_Obot,type,
% 0.25/0.49 bot:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_Orderings_Oord,type,
% 0.25/0.49 ord:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_Orderings_Oorder,type,
% 0.25/0.49 order:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_Orderings_Olinorder,type,
% 0.25/0.49 linorder:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_Orderings_Opreorder,type,
% 0.25/0.49 preorder:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 0.25/0.49 bounde1808546759up_bot:
% 0.25/0.49 !>[A: $tType] : $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 0.25/0.49 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 0.25/0.49 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 0.25/0.49 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Lattices_Osup__class_Osup,type,
% 0.25/0.49 sup_sup:
% 0.25/0.49 !>[A: $tType] : ( A > A > A ) ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_ListExtras_Omem,type,
% 0.25/0.49 mem:
% 0.25/0.49 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Obot__class_Obot,type,
% 0.25/0.49 bot_bot:
% 0.25/0.49 !>[A: $tType] : A ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 0.25/0.49 ord_less_eq:
% 0.25/0.49 !>[A: $tType] : ( A > A > $o ) ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 0.25/0.49 correctCompositionKS: secrecy_specID > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_Oeout,type,
% 0.25/0.49 eout: secrecy_specID > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OeoutM,type,
% 0.25/0.49 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OexprChannel,type,
% 0.25/0.49 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_Oine,type,
% 0.25/0.49 ine: secrecy_specID > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OineM,type,
% 0.25/0.49 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 0.25/0.49 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 0.25/0.49 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 0.25/0.49 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 0.25/0.49 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 0.25/0.49 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OspecKeys,type,
% 0.25/0.49 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 0.25/0.49 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 0.25/0.49
% 0.25/0.49 thf(sy_c_Secrecy_OspecSecrets,type,
% 0.25/0.49 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 0.25/0.50 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 0.25/0.50 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 0.25/0.50 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 0.25/0.50 secrecy_case_KS:
% 0.25/0.50 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 0.25/0.50 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 0.25/0.50 secrecy_rec_KS:
% 0.25/0.50 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 0.25/0.50 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Set_OCollect,type,
% 0.25/0.50 collect:
% 0.25/0.50 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Set_Oinsert,type,
% 0.25/0.50 insert:
% 0.25/0.50 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Set_Ois__empty,type,
% 0.25/0.50 is_empty:
% 0.25/0.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Set_Ois__singleton,type,
% 0.25/0.50 is_singleton:
% 0.25/0.50 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_Set_Othe__elem,type,
% 0.25/0.50 the_elem:
% 0.25/0.50 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_OcorrectCompositionIn,type,
% 0.25/0.50 correctCompositionIn: secrecy_specID > $o ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 0.25/0.50 correc965049635ionLoc: secrecy_specID > $o ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_OcorrectCompositionOut,type,
% 0.25/0.50 correc990227761ionOut: secrecy_specID > $o ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_OinStream,type,
% 0.25/0.50 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_Oins,type,
% 0.25/0.50 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_Oloc,type,
% 0.25/0.50 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_OlocStream,type,
% 0.25/0.50 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_Oout,type,
% 0.25/0.50 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_OoutStream,type,
% 0.25/0.50 outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_inout_Osubcomponents,type,
% 0.25/0.50 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_c_member,type,
% 0.25/0.50 member:
% 0.25/0.50 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 0.25/0.50
% 0.25/0.50 thf(sy_v_P,type,
% 0.25/0.50 p: secrecy_specID ).
% 0.25/0.50
% 0.25/0.50 thf(sy_v_PQ,type,
% 0.25/0.50 pq: secrecy_specID ).
% 0.25/0.50
% 0.25/0.50 thf(sy_v_Q,type,
% 0.25/0.50 q: secrecy_specID ).
% 0.25/0.50
% 0.25/0.50 thf(sy_v_m,type,
% 0.25/0.50 m: secrecy_KS ).
% 0.25/0.50
% 0.25/0.50 thf(sy_v_secret____,type,
% 0.25/0.50 secret: secrecy_Secrets ).
% 0.25/0.50
% 0.25/0.50 % Relevant facts (256)
% 0.25/0.50 thf(fact_0_cCompLoc,axiom,
% 0.25/0.50 correc965049635ionLoc @ pq ).
% 0.25/0.50
% 0.25/0.50 % cCompLoc
% 0.25/0.50 thf(fact_1_sg1a,axiom,
% 0.25/0.50 ~ ( ine @ p @ ( secrecy_sE @ secret ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg1a
% 0.25/0.50 thf(fact_2_sg2a,axiom,
% 0.25/0.50 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg2a
% 0.25/0.50 thf(fact_3_sg1b,axiom,
% 0.25/0.50 ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg1b
% 0.25/0.50 thf(fact_4_sg2b,axiom,
% 0.25/0.50 ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg2b
% 0.25/0.50 thf(fact_5_subPQ,axiom,
% 0.25/0.50 ( ( subcomponents @ pq )
% 0.25/0.50 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % subPQ
% 0.25/0.50 thf(fact_6_a2,axiom,
% 0.25/0.50 ( m
% 0.25/0.50 = ( secrecy_sKS @ secret ) ) ).
% 0.25/0.50
% 0.25/0.50 % a2
% 0.25/0.50 thf(fact_7_cCompI,axiom,
% 0.25/0.50 correctCompositionIn @ pq ).
% 0.25/0.50
% 0.25/0.50 % cCompI
% 0.25/0.50 thf(fact_8_sg3,axiom,
% 0.25/0.50 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg3
% 0.25/0.50 thf(fact_9_KS_Oinject_I2_J,axiom,
% 0.25/0.50 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.25/0.50 ( ( ( secrecy_sKS @ X2 )
% 0.25/0.50 = ( secrecy_sKS @ Y2 ) )
% 0.25/0.50 = ( X2 = Y2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.inject(2)
% 0.25/0.50 thf(fact_10_sg1,axiom,
% 0.25/0.50 ~ ( knowle1437066798e_know @ p @ ( secrecy_sKS @ secret ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg1
% 0.25/0.50 thf(fact_11_sg2,axiom,
% 0.25/0.50 ~ ( knowle1437066798e_know @ q @ ( secrecy_sKS @ secret ) ) ).
% 0.25/0.50
% 0.25/0.50 % sg2
% 0.25/0.50 thf(fact_12_know_Osimps_I2_J,axiom,
% 0.25/0.50 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.25/0.50 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 0.25/0.50 | ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know.simps(2)
% 0.25/0.50 thf(fact_13_KS_Osimps_I8_J,axiom,
% 0.25/0.50 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 0.25/0.50 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 0.25/0.50 = ( F2 @ X2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.simps(8)
% 0.25/0.50 thf(fact_14_KS_Osimps_I6_J,axiom,
% 0.25/0.50 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 0.25/0.50 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 0.25/0.50 = ( F2 @ X2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.simps(6)
% 0.25/0.50 thf(fact_15_LocalSecretsComposition__ine1__s,axiom,
% 0.25/0.50 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.25/0.50 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_ine1_s
% 0.25/0.50 thf(fact_16_LocalSecretsComposition__ine2__s,axiom,
% 0.25/0.50 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.25/0.50 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_ine2_s
% 0.25/0.50 thf(fact_17_LocalSecretsComposition__neg1__s,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg1_s
% 0.25/0.50 thf(fact_18_KS2Expression_Osimps_I2_J,axiom,
% 0.25/0.50 ! [M: secrecy_Secrets] :
% 0.25/0.50 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 0.25/0.50 = ( secrecy_sE @ M ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS2Expression.simps(2)
% 0.25/0.50 thf(fact_19_LocalSecretsComposition1,axiom,
% 0.25/0.50 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition1
% 0.25/0.50 thf(fact_20_not__know__s__not__ine,axiom,
% 0.25/0.50 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 0.25/0.50 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 => ~ ( ine @ A2 @ ( secrecy_sE @ M ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % not_know_s_not_ine
% 0.25/0.50 thf(fact_21_notknowQ,axiom,
% 0.25/0.50 ~ ( knowle1437066798e_know @ q @ m ) ).
% 0.25/0.50
% 0.25/0.50 % notknowQ
% 0.25/0.50 thf(fact_22_notknowP,axiom,
% 0.25/0.50 ~ ( knowle1437066798e_know @ p @ m ) ).
% 0.25/0.50
% 0.25/0.50 % notknowP
% 0.25/0.50 thf(fact_23_Expression_Oinject_I2_J,axiom,
% 0.25/0.50 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 0.25/0.50 ( ( ( secrecy_sE @ X2 )
% 0.25/0.50 = ( secrecy_sE @ Y2 ) )
% 0.25/0.50 = ( X2 = Y2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % Expression.inject(2)
% 0.25/0.50 thf(fact_24_know__composition__neg__ine__s,axiom,
% 0.25/0.50 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_sKS @ Secret ) )
% 0.25/0.50 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know_composition_neg_ine_s
% 0.25/0.50 thf(fact_25_TBtheorem1a,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( ine @ PQ @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ine @ P @ E )
% 0.25/0.50 | ( ine @ Q @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem1a
% 0.25/0.50 thf(fact_26_TBtheorem3a,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( ine @ P @ E )
% 0.25/0.50 => ( ~ ( ine @ Q @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem3a
% 0.25/0.50 thf(fact_27_singletonI,axiom,
% 0.25/0.50 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % singletonI
% 0.25/0.50 thf(fact_28_insertCI,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 0.25/0.50 ( ( ~ ( member @ A @ A3 @ B )
% 0.25/0.50 => ( A3 = B2 ) )
% 0.25/0.50 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insertCI
% 0.25/0.50 thf(fact_29_insert__iff,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.25/0.50 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.25/0.50 = ( ( A3 = B2 )
% 0.25/0.50 | ( member @ A @ A3 @ A2 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_iff
% 0.25/0.50 thf(fact_30_insert__absorb2,axiom,
% 0.25/0.50 ! [A: $tType,X: A,A2: set @ A] :
% 0.25/0.50 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 0.25/0.50 = ( insert @ A @ X @ A2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_absorb2
% 0.25/0.50 thf(fact_31_empty__iff,axiom,
% 0.25/0.50 ! [A: $tType,C: A] :
% 0.25/0.50 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % empty_iff
% 0.25/0.50 thf(fact_32_all__not__in__conv,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( ! [X3: A] :
% 0.25/0.50 ~ ( member @ A @ X3 @ A2 ) )
% 0.25/0.50 = ( A2
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % all_not_in_conv
% 0.25/0.50 thf(fact_33_Collect__empty__eq,axiom,
% 0.25/0.50 ! [A: $tType,P: A > $o] :
% 0.25/0.50 ( ( ( collect @ A @ P )
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 = ( ! [X3: A] :
% 0.25/0.50 ~ ( P @ X3 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Collect_empty_eq
% 0.25/0.50 thf(fact_34_empty__Collect__eq,axiom,
% 0.25/0.50 ! [A: $tType,P: A > $o] :
% 0.25/0.50 ( ( ( bot_bot @ ( set @ A ) )
% 0.25/0.50 = ( collect @ A @ P ) )
% 0.25/0.50 = ( ! [X3: A] :
% 0.25/0.50 ~ ( P @ X3 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % empty_Collect_eq
% 0.25/0.50 thf(fact_35_ex__in__conv,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( ? [X3: A] : ( member @ A @ X3 @ A2 ) )
% 0.25/0.50 = ( A2
% 0.25/0.50 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ex_in_conv
% 0.25/0.50 thf(fact_36_equals0I,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ! [Y: A] :
% 0.25/0.50 ~ ( member @ A @ Y @ A2 )
% 0.25/0.50 => ( A2
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % equals0I
% 0.25/0.50 thf(fact_37_equals0D,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,A3: A] :
% 0.25/0.50 ( ( A2
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % equals0D
% 0.25/0.50 thf(fact_38_emptyE,axiom,
% 0.25/0.50 ! [A: $tType,A3: A] :
% 0.25/0.50 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % emptyE
% 0.25/0.50 thf(fact_39_mk__disjoint__insert,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,A2: set @ A] :
% 0.25/0.50 ( ( member @ A @ A3 @ A2 )
% 0.25/0.50 => ? [B3: set @ A] :
% 0.25/0.50 ( ( A2
% 0.25/0.50 = ( insert @ A @ A3 @ B3 ) )
% 0.25/0.50 & ~ ( member @ A @ A3 @ B3 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % mk_disjoint_insert
% 0.25/0.50 thf(fact_40_insert__commute,axiom,
% 0.25/0.50 ! [A: $tType,X: A,Y3: A,A2: set @ A] :
% 0.25/0.50 ( ( insert @ A @ X @ ( insert @ A @ Y3 @ A2 ) )
% 0.25/0.50 = ( insert @ A @ Y3 @ ( insert @ A @ X @ A2 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_commute
% 0.25/0.50 thf(fact_41_insert__eq__iff,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,A2: set @ A,B2: A,B: set @ A] :
% 0.25/0.50 ( ~ ( member @ A @ A3 @ A2 )
% 0.25/0.50 => ( ~ ( member @ A @ B2 @ B )
% 0.25/0.50 => ( ( ( insert @ A @ A3 @ A2 )
% 0.25/0.50 = ( insert @ A @ B2 @ B ) )
% 0.25/0.50 = ( ( ( A3 = B2 )
% 0.25/0.50 => ( A2 = B ) )
% 0.25/0.50 & ( ( A3 != B2 )
% 0.25/0.50 => ? [C2: set @ A] :
% 0.25/0.50 ( ( A2
% 0.25/0.50 = ( insert @ A @ B2 @ C2 ) )
% 0.25/0.50 & ~ ( member @ A @ B2 @ C2 )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( insert @ A @ A3 @ C2 ) )
% 0.25/0.50 & ~ ( member @ A @ A3 @ C2 ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_eq_iff
% 0.25/0.50 thf(fact_42_insert__absorb,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,A2: set @ A] :
% 0.25/0.50 ( ( member @ A @ A3 @ A2 )
% 0.25/0.50 => ( ( insert @ A @ A3 @ A2 )
% 0.25/0.50 = A2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_absorb
% 0.25/0.50 thf(fact_43_insert__ident,axiom,
% 0.25/0.50 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ~ ( member @ A @ X @ A2 )
% 0.25/0.50 => ( ~ ( member @ A @ X @ B )
% 0.25/0.50 => ( ( ( insert @ A @ X @ A2 )
% 0.25/0.50 = ( insert @ A @ X @ B ) )
% 0.25/0.50 = ( A2 = B ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_ident
% 0.25/0.50 thf(fact_44_Set_Oset__insert,axiom,
% 0.25/0.50 ! [A: $tType,X: A,A2: set @ A] :
% 0.25/0.50 ( ( member @ A @ X @ A2 )
% 0.25/0.50 => ~ ! [B3: set @ A] :
% 0.25/0.50 ( ( A2
% 0.25/0.50 = ( insert @ A @ X @ B3 ) )
% 0.25/0.50 => ( member @ A @ X @ B3 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Set.set_insert
% 0.25/0.50 thf(fact_45_mem__Collect__eq,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,P: A > $o] :
% 0.25/0.50 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 0.25/0.50 = ( P @ A3 ) ) ).
% 0.25/0.50
% 0.25/0.50 % mem_Collect_eq
% 0.25/0.50 thf(fact_46_Collect__mem__eq,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( collect @ A
% 0.25/0.50 @ ^ [X3: A] : ( member @ A @ X3 @ A2 ) )
% 0.25/0.50 = A2 ) ).
% 0.25/0.50
% 0.25/0.50 % Collect_mem_eq
% 0.25/0.50 thf(fact_47_Collect__cong,axiom,
% 0.25/0.50 ! [A: $tType,P: A > $o,Q: A > $o] :
% 0.25/0.50 ( ! [X4: A] :
% 0.25/0.50 ( ( P @ X4 )
% 0.25/0.50 = ( Q @ X4 ) )
% 0.25/0.50 => ( ( collect @ A @ P )
% 0.25/0.50 = ( collect @ A @ Q ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Collect_cong
% 0.25/0.50 thf(fact_48_ext,axiom,
% 0.25/0.50 ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 0.25/0.50 ( ! [X4: A] :
% 0.25/0.50 ( ( F @ X4 )
% 0.25/0.50 = ( G @ X4 ) )
% 0.25/0.50 => ( F = G ) ) ).
% 0.25/0.50
% 0.25/0.50 % ext
% 0.25/0.50 thf(fact_49_insertI2,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 0.25/0.50 ( ( member @ A @ A3 @ B )
% 0.25/0.50 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insertI2
% 0.25/0.50 thf(fact_50_insertI1,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B ) ) ).
% 0.25/0.50
% 0.25/0.50 % insertI1
% 0.25/0.50 thf(fact_51_insertE,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 0.25/0.50 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 0.25/0.50 => ( ( A3 != B2 )
% 0.25/0.50 => ( member @ A @ A3 @ A2 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insertE
% 0.25/0.50 thf(fact_52_singleton__inject,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B2: A] :
% 0.25/0.50 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 => ( A3 = B2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % singleton_inject
% 0.25/0.50 thf(fact_53_insert__not__empty,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,A2: set @ A] :
% 0.25/0.50 ( ( insert @ A @ A3 @ A2 )
% 0.25/0.50 != ( bot_bot @ ( set @ A ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_not_empty
% 0.25/0.50 thf(fact_54_doubleton__eq__iff,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B2: A,C: A,D: A] :
% 0.25/0.50 ( ( ( insert @ A @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.25/0.50 = ( ( ( A3 = C )
% 0.25/0.50 & ( B2 = D ) )
% 0.25/0.50 | ( ( A3 = D )
% 0.25/0.50 & ( B2 = C ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % doubleton_eq_iff
% 0.25/0.50 thf(fact_55_singleton__iff,axiom,
% 0.25/0.50 ! [A: $tType,B2: A,A3: A] :
% 0.25/0.50 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 = ( B2 = A3 ) ) ).
% 0.25/0.50
% 0.25/0.50 % singleton_iff
% 0.25/0.50 thf(fact_56_singletonD,axiom,
% 0.25/0.50 ! [A: $tType,B2: A,A3: A] :
% 0.25/0.50 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 => ( B2 = A3 ) ) ).
% 0.25/0.50
% 0.25/0.50 % singletonD
% 0.25/0.50 thf(fact_57_the__elem__eq,axiom,
% 0.25/0.50 ! [A: $tType,X: A] :
% 0.25/0.50 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 = X ) ).
% 0.25/0.50
% 0.25/0.50 % the_elem_eq
% 0.25/0.50 thf(fact_58_bot__apply,axiom,
% 0.25/0.50 ! [C3: $tType,D2: $tType] :
% 0.25/0.50 ( ( bot @ C3 )
% 0.25/0.50 => ( ( bot_bot @ ( D2 > C3 ) )
% 0.25/0.50 = ( ^ [X3: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % bot_apply
% 0.25/0.50 thf(fact_59_is__singletonI,axiom,
% 0.25/0.50 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % is_singletonI
% 0.25/0.50 thf(fact_60_TBtheorem4a__empty,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ( ine @ P @ E )
% 0.25/0.50 | ( ine @ Q @ E ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ( loc @ PQ )
% 0.25/0.50 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.25/0.50 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4a_empty
% 0.25/0.50 thf(fact_61_TBtheorem3b,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( ineM @ P @ M2 @ E )
% 0.25/0.50 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem3b
% 0.25/0.50 thf(fact_62_TBtheorem1b,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( ineM @ PQ @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ineM @ P @ M2 @ E )
% 0.25/0.50 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem1b
% 0.25/0.50 thf(fact_63_Set_Ois__empty__def,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( is_empty @ A )
% 0.25/0.50 = ( ^ [A4: set @ A] :
% 0.25/0.50 ( A4
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Set.is_empty_def
% 0.25/0.50 thf(fact_64_correctCompositionIn__prop1,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.25/0.50 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionIn_prop1
% 0.25/0.50 thf(fact_65_correctCompositionIn__L2,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionIn_L2
% 0.25/0.50 thf(fact_66_bot__set__def,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bot_bot @ ( set @ A ) )
% 0.25/0.50 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % bot_set_def
% 0.25/0.50 thf(fact_67_ineM__ine,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( ineM @ P @ M2 @ E )
% 0.25/0.50 => ( ine @ P @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % ineM_ine
% 0.25/0.50 thf(fact_68_not__ine__ineM,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 0.25/0.50 ( ~ ( ine @ P @ E )
% 0.25/0.50 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % not_ine_ineM
% 0.25/0.50 thf(fact_69_is__singleton__the__elem,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( is_singleton @ A )
% 0.25/0.50 = ( ^ [A4: set @ A] :
% 0.25/0.50 ( A4
% 0.25/0.50 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % is_singleton_the_elem
% 0.25/0.50 thf(fact_70_correctCompositionIn__L1,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionIn_L1
% 0.25/0.50 thf(fact_71_is__singletonI_H,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( A2
% 0.25/0.50 != ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 => ( ! [X4: A,Y: A] :
% 0.25/0.50 ( ( member @ A @ X4 @ A2 )
% 0.25/0.50 => ( ( member @ A @ Y @ A2 )
% 0.25/0.50 => ( X4 = Y ) ) )
% 0.25/0.50 => ( is_singleton @ A @ A2 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % is_singletonI'
% 0.25/0.50 thf(fact_72_bot__fun__def,axiom,
% 0.25/0.50 ! [B4: $tType,A: $tType] :
% 0.25/0.50 ( ( bot @ B4 )
% 0.25/0.50 => ( ( bot_bot @ ( A > B4 ) )
% 0.25/0.50 = ( ^ [X3: A] : ( bot_bot @ B4 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % bot_fun_def
% 0.25/0.50 thf(fact_73_is__singletonE,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( is_singleton @ A @ A2 )
% 0.25/0.50 => ~ ! [X4: A] :
% 0.25/0.50 ( A2
% 0.25/0.50 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % is_singletonE
% 0.25/0.50 thf(fact_74_is__singleton__def,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( is_singleton @ A )
% 0.25/0.50 = ( ^ [A4: set @ A] :
% 0.25/0.50 ? [X3: A] :
% 0.25/0.50 ( A4
% 0.25/0.50 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % is_singleton_def
% 0.25/0.50 thf(fact_75_subcomponents__loc,axiom,
% 0.25/0.50 ! [X: secrecy_specID] :
% 0.25/0.50 ( ( correc965049635ionLoc @ X )
% 0.25/0.50 => ( ( ( subcomponents @ X )
% 0.25/0.50 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 0.25/0.50 => ( ( loc @ X )
% 0.25/0.50 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % subcomponents_loc
% 0.25/0.50 thf(fact_76_TBtheorem4b__notP1,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ineM @ P @ M2 @ E )
% 0.25/0.50 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4b_notP1
% 0.25/0.50 thf(fact_77_TBtheorem4a__notP1,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ine @ P @ E )
% 0.25/0.50 => ( ~ ( ine @ Q @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4a_notP1
% 0.25/0.50 thf(fact_78_TBtheorem4b__notP2,axiom,
% 0.25/0.50 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.25/0.50 ( ~ ( ineM @ Q @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4b_notP2
% 0.25/0.50 thf(fact_79_TBtheorem4b__notPQ,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.25/0.50 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4b_notPQ
% 0.25/0.50 thf(fact_80_TBtheorem4a__notP2,axiom,
% 0.25/0.50 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.25/0.50 ( ~ ( ine @ Q @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4a_notP2
% 0.25/0.50 thf(fact_81_TBtheorem4a__notPQ,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 0.25/0.50 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4a_notPQ
% 0.25/0.50 thf(fact_82_ine__exprChannelSingle__Set,axiom,
% 0.25/0.50 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 0.25/0.50 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_exprChannelSingle_Set
% 0.25/0.50 thf(fact_83_ine__exprChannelSet__Single,axiom,
% 0.25/0.50 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.25/0.50 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_exprChannelSet_Single
% 0.25/0.50 thf(fact_84_ine__empty__exprChannelSet,axiom,
% 0.25/0.50 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.25/0.50 => ( ( ChSet
% 0.25/0.50 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.25/0.50 => ~ ( ine @ P @ E ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_empty_exprChannelSet
% 0.25/0.50 thf(fact_85_ine__nonempty__exprChannelSet,axiom,
% 0.25/0.50 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 0.25/0.50 => ( ( ChSet
% 0.25/0.50 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.25/0.50 => ( ine @ P @ E ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_nonempty_exprChannelSet
% 0.25/0.50 thf(fact_86_locStream__def,axiom,
% 0.25/0.50 ( locStream
% 0.25/0.50 = ( ^ [X3: secrecy_specID] :
% 0.25/0.50 ( ^ [Y4: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y4 = Z )
% 0.25/0.50 @ ( loc @ X3 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % locStream_def
% 0.25/0.50 thf(fact_87_inStream__def,axiom,
% 0.25/0.50 ( inStream
% 0.25/0.50 = ( ^ [X3: secrecy_specID] :
% 0.25/0.50 ( ^ [Y4: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y4 = Z )
% 0.25/0.50 @ ( ins @ X3 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % inStream_def
% 0.25/0.50 thf(fact_88_TBtheorem4b__PQ,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ( ineM @ P @ M2 @ E )
% 0.25/0.50 | ( ineM @ Q @ M2 @ E ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.25/0.50 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4b_PQ
% 0.25/0.50 thf(fact_89_TBtheorem4b__P,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( ineM @ P @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 0.25/0.50 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4b_P
% 0.25/0.50 thf(fact_90_TBtheorem4a__PQ,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ( ine @ P @ E )
% 0.25/0.50 | ( ine @ Q @ E ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.25/0.50 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4a_PQ
% 0.25/0.50 thf(fact_91_TBtheorem4a__P,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( ine @ P @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ine @ PQ @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem4a_P
% 0.25/0.50 thf(fact_92_ine__def,axiom,
% 0.25/0.50 ( ine
% 0.25/0.50 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.25/0.50 ? [Ch3: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.25/0.50 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_def
% 0.25/0.50 thf(fact_93_ine__ins__neg1,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 0.25/0.50 ( ~ ( ine @ P @ M )
% 0.25/0.50 => ( ( exprChannel @ X @ M )
% 0.25/0.50 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_ins_neg1
% 0.25/0.50 thf(fact_94_ineM__def,axiom,
% 0.25/0.50 ( ineM
% 0.25/0.50 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.25/0.50 ? [Ch3: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 0.25/0.50 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ineM_def
% 0.25/0.50 thf(fact_95_ineM__L1,axiom,
% 0.25/0.50 ! [Ch: secrecy_chanID,M2: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch @ M2 )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ E )
% 0.25/0.50 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ineM_L1
% 0.25/0.50 thf(fact_96_ine__exprChannelSet__def,axiom,
% 0.25/0.50 ( ine_exprChannelSet
% 0.25/0.50 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.25/0.50 ( ! [X3: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ X3 @ ( ins @ SP ) )
% 0.25/0.50 & ( exprChannel @ X3 @ E2 ) ) )
% 0.25/0.50 & ! [X3: secrecy_chanID] :
% 0.25/0.50 ( ( ~ ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 0.25/0.50 & ( member @ secrecy_chanID @ X3 @ ( ins @ SP ) ) )
% 0.25/0.50 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_exprChannelSet_def
% 0.25/0.50 thf(fact_97_ine__exprChannelSingle__def,axiom,
% 0.25/0.50 ( ine_ex1303305700Single
% 0.25/0.50 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 0.25/0.50 & ( exprChannel @ Ch3 @ E2 )
% 0.25/0.50 & ! [X3: secrecy_chanID,T: nat] :
% 0.25/0.50 ( ( ( member @ secrecy_chanID @ X3 @ ( ins @ SP ) )
% 0.25/0.50 & ( X3 != Ch3 ) )
% 0.25/0.50 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ine_exprChannelSingle_def
% 0.25/0.50 thf(fact_98_LocalSecretsComposition__exprChannel__s,axiom,
% 0.25/0.50 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_exprChannel_s
% 0.25/0.50 thf(fact_99_correctCompositionInLoc__exprChannel,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ M )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ( ins @ PQ ) )
% 0.25/0.50 => ~ ( exprChannel @ X4 @ M ) )
% 0.25/0.50 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionInLoc_exprChannel
% 0.25/0.50 thf(fact_100_TBlemma3b,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 0.25/0.50 ( ~ ( ineM @ P @ M2 @ E )
% 0.25/0.50 => ( ~ ( ineM @ Q @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ M2 )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.25/0.50 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBlemma3b
% 0.25/0.50 thf(fact_101_Collect__empty__eq__bot,axiom,
% 0.25/0.50 ! [A: $tType,P: A > $o] :
% 0.25/0.50 ( ( ( collect @ A @ P )
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 = ( P
% 0.25/0.50 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Collect_empty_eq_bot
% 0.25/0.50 thf(fact_102_bot__empty__eq,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bot_bot @ ( A > $o ) )
% 0.25/0.50 = ( ^ [X3: A] : ( member @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % bot_empty_eq
% 0.25/0.50 thf(fact_103_LocalSecretsComposition__neg__loc__s,axiom,
% 0.25/0.50 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.25/0.50 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg_loc_s
% 0.25/0.50 thf(fact_104_correctCompositionKS__exprChannel__s__P,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_s_P
% 0.25/0.50 thf(fact_105_correctCompositionKS__exprChannel__s__Q,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_s_Q
% 0.25/0.50 thf(fact_106_correctCompositionKS__negQ,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_negQ
% 0.25/0.50 thf(fact_107_correctCompositionKS__negP,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_negP
% 0.25/0.50 thf(fact_108_correctCompositionKS__neg1,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_neg1
% 0.25/0.50 thf(fact_109_correctCompositionKS__PQ,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.25/0.50 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_PQ
% 0.25/0.50 thf(fact_110_know__composition2,axiom,
% 0.25/0.50 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ( ( knowle1437066798e_know @ Q @ M )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know_composition2
% 0.25/0.50 thf(fact_111_know__composition1,axiom,
% 0.25/0.50 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ( ( knowle1437066798e_know @ P @ M )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know_composition1
% 0.25/0.50 thf(fact_112_know__composition,axiom,
% 0.25/0.50 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ( ( ( knowle1437066798e_know @ P @ M )
% 0.25/0.50 | ( knowle1437066798e_know @ Q @ M ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know_composition
% 0.25/0.50 thf(fact_113_correctCompositionKS__exprChannel__s__Qex,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ? [Ch4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_s_Qex
% 0.25/0.50 thf(fact_114_correctCompositionKS__exprChannel__s__Pex,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ? [Ch4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_s_Pex
% 0.25/0.50 thf(fact_115_LocalSecretsComposition__neg__s,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg_s
% 0.25/0.50 thf(fact_116_correctCompositionKS__exprChannel__k__Qex,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ? [Ch4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_k_Qex
% 0.25/0.50 thf(fact_117_correctCompositionKS__exprChannel__k__Pex,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ? [Ch4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_k_Pex
% 0.25/0.50 thf(fact_118_correctCompositionKS__exprChannel__k__Q,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_k_Q
% 0.25/0.50 thf(fact_119_correctCompositionKS__exprChannel__k__P,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 0.25/0.50 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_exprChannel_k_P
% 0.25/0.50 thf(fact_120_Un__iff,axiom,
% 0.25/0.50 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.50 = ( ( member @ A @ C @ A2 )
% 0.25/0.50 | ( member @ A @ C @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_iff
% 0.25/0.50 thf(fact_121_UnCI,axiom,
% 0.25/0.50 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 0.25/0.50 ( ( ~ ( member @ A @ C @ B )
% 0.25/0.50 => ( member @ A @ C @ A2 ) )
% 0.25/0.50 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % UnCI
% 0.25/0.50 thf(fact_122_KS_Oinject_I1_J,axiom,
% 0.25/0.50 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.25/0.50 ( ( ( secrecy_kKS @ X1 )
% 0.25/0.50 = ( secrecy_kKS @ Y1 ) )
% 0.25/0.50 = ( X1 = Y1 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.inject(1)
% 0.25/0.50 thf(fact_123_Expression_Oinject_I1_J,axiom,
% 0.25/0.50 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 0.25/0.50 ( ( ( secrecy_kE @ X1 )
% 0.25/0.50 = ( secrecy_kE @ Y1 ) )
% 0.25/0.50 = ( X1 = Y1 ) ) ).
% 0.25/0.50
% 0.25/0.50 % Expression.inject(1)
% 0.25/0.50 thf(fact_124_Un__empty,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 = ( ( A2
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_empty
% 0.25/0.50 thf(fact_125_Un__insert__left,axiom,
% 0.25/0.50 ! [A: $tType,A3: A,B: set @ A,C4: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B ) @ C4 )
% 0.25/0.50 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_insert_left
% 0.25/0.50 thf(fact_126_Un__insert__right,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,A3: A,B: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B ) )
% 0.25/0.50 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_insert_right
% 0.25/0.50 thf(fact_127_not__know__k__not__ine,axiom,
% 0.25/0.50 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.25/0.50 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.25/0.50 => ~ ( ine @ A2 @ ( secrecy_kE @ M ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % not_know_k_not_ine
% 0.25/0.50 thf(fact_128_Un__empty__right,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 = A2 ) ).
% 0.25/0.50
% 0.25/0.50 % Un_empty_right
% 0.25/0.50 thf(fact_129_Un__empty__left,axiom,
% 0.25/0.50 ! [A: $tType,B: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 0.25/0.50 = B ) ).
% 0.25/0.50
% 0.25/0.50 % Un_empty_left
% 0.25/0.50 thf(fact_130_KS2Expression_Osimps_I1_J,axiom,
% 0.25/0.50 ! [M: secrecy_Keys] :
% 0.25/0.50 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 0.25/0.50 = ( secrecy_kE @ M ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS2Expression.simps(1)
% 0.25/0.50 thf(fact_131_Un__left__commute,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 0.25/0.50 = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_left_commute
% 0.25/0.50 thf(fact_132_Un__left__absorb,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.50 = ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_left_absorb
% 0.25/0.50 thf(fact_133_Un__commute,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) )
% 0.25/0.50 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_commute
% 0.25/0.50 thf(fact_134_Un__absorb,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 0.25/0.50 = A2 ) ).
% 0.25/0.50
% 0.25/0.50 % Un_absorb
% 0.25/0.50 thf(fact_135_Un__assoc,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.25/0.50 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 0.25/0.50 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_assoc
% 0.25/0.50 thf(fact_136_ball__Un,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 0.25/0.50 ( ( ! [X3: A] :
% 0.25/0.50 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.50 => ( P @ X3 ) ) )
% 0.25/0.50 = ( ! [X3: A] :
% 0.25/0.50 ( ( member @ A @ X3 @ A2 )
% 0.25/0.50 => ( P @ X3 ) )
% 0.25/0.50 & ! [X3: A] :
% 0.25/0.50 ( ( member @ A @ X3 @ B )
% 0.25/0.50 => ( P @ X3 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % ball_Un
% 0.25/0.50 thf(fact_137_bex__Un,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 0.25/0.50 ( ( ? [X3: A] :
% 0.25/0.50 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.50 & ( P @ X3 ) ) )
% 0.25/0.50 = ( ? [X3: A] :
% 0.25/0.50 ( ( member @ A @ X3 @ A2 )
% 0.25/0.50 & ( P @ X3 ) )
% 0.25/0.50 | ? [X3: A] :
% 0.25/0.50 ( ( member @ A @ X3 @ B )
% 0.25/0.50 & ( P @ X3 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % bex_Un
% 0.25/0.50 thf(fact_138_UnI2,axiom,
% 0.25/0.50 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 0.25/0.50 ( ( member @ A @ C @ B )
% 0.25/0.50 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % UnI2
% 0.25/0.50 thf(fact_139_UnI1,axiom,
% 0.25/0.50 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ( member @ A @ C @ A2 )
% 0.25/0.50 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % UnI1
% 0.25/0.50 thf(fact_140_UnE,axiom,
% 0.25/0.50 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.50 => ( ~ ( member @ A @ C @ A2 )
% 0.25/0.50 => ( member @ A @ C @ B ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % UnE
% 0.25/0.50 thf(fact_141_KS_Oexhaust,axiom,
% 0.25/0.50 ! [Y3: secrecy_KS] :
% 0.25/0.50 ( ! [X12: secrecy_Keys] :
% 0.25/0.50 ( Y3
% 0.25/0.50 != ( secrecy_kKS @ X12 ) )
% 0.25/0.50 => ~ ! [X22: secrecy_Secrets] :
% 0.25/0.50 ( Y3
% 0.25/0.50 != ( secrecy_sKS @ X22 ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.exhaust
% 0.25/0.50 thf(fact_142_KS_Oinduct,axiom,
% 0.25/0.50 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 0.25/0.50 ( ! [X4: secrecy_Keys] : ( P @ ( secrecy_kKS @ X4 ) )
% 0.25/0.50 => ( ! [X4: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X4 ) )
% 0.25/0.50 => ( P @ KS ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.induct
% 0.25/0.50 thf(fact_143_KS_Odistinct_I1_J,axiom,
% 0.25/0.50 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.25/0.50 ( ( secrecy_kKS @ X1 )
% 0.25/0.50 != ( secrecy_sKS @ X2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.distinct(1)
% 0.25/0.50 thf(fact_144_Expression_Odistinct_I1_J,axiom,
% 0.25/0.50 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 0.25/0.50 ( ( secrecy_kE @ X1 )
% 0.25/0.50 != ( secrecy_sE @ X2 ) ) ).
% 0.25/0.50
% 0.25/0.50 % Expression.distinct(1)
% 0.25/0.50 thf(fact_145_KS_Osimps_I5_J,axiom,
% 0.25/0.50 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.25/0.50 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.25/0.50 = ( F1 @ X1 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.simps(5)
% 0.25/0.50 thf(fact_146_know_Osimps_I1_J,axiom,
% 0.25/0.50 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 0.25/0.50 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.25/0.50 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 0.25/0.50 | ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know.simps(1)
% 0.25/0.50 thf(fact_147_KS_Osimps_I7_J,axiom,
% 0.25/0.50 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 0.25/0.50 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 0.25/0.50 = ( F1 @ X1 ) ) ).
% 0.25/0.50
% 0.25/0.50 % KS.simps(7)
% 0.25/0.50 thf(fact_148_insert__is__Un,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( insert @ A )
% 0.25/0.50 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % insert_is_Un
% 0.25/0.50 thf(fact_149_Un__singleton__iff,axiom,
% 0.25/0.50 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 0.25/0.50 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 = ( ( ( A2
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.25/0.50 | ( ( A2
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 | ( ( A2
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % Un_singleton_iff
% 0.25/0.50 thf(fact_150_singleton__Un__iff,axiom,
% 0.25/0.50 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.25/0.50 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 = ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.50 = ( ( ( A2
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 0.25/0.50 | ( ( A2
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 | ( ( A2
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.50 & ( B
% 0.25/0.50 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % singleton_Un_iff
% 0.25/0.50 thf(fact_151_LocalSecretsComposition__neg__loc__k,axiom,
% 0.25/0.50 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 0.25/0.50 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg_loc_k
% 0.25/0.50 thf(fact_152_LocalSecretsComposition__neg__k,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg_k
% 0.25/0.50 thf(fact_153_know__composition__neg__ine__k,axiom,
% 0.25/0.50 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_kKS @ Key ) )
% 0.25/0.50 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ Key ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correctCompositionIn @ PQ )
% 0.25/0.50 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % know_composition_neg_ine_k
% 0.25/0.50 thf(fact_154_LocalSecretsComposition__ine1__k,axiom,
% 0.25/0.50 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.25/0.50 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_ine1_k
% 0.25/0.50 thf(fact_155_LocalSecretsComposition__ine2__k,axiom,
% 0.25/0.50 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 0.25/0.50 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_ine2_k
% 0.25/0.50 thf(fact_156_LocalSecretsComposition__neg1__k,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg1_k
% 0.25/0.50 thf(fact_157_LocalSecretsComposition__exprChannel__k,axiom,
% 0.25/0.50 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 0.25/0.50 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_exprChannel_k
% 0.25/0.50 thf(fact_158_LocalSecretsComposition__neg,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ( correctCompositionKS @ PQ )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 0.25/0.50 => ( ! [M4: secrecy_Keys] :
% 0.25/0.50 ( ( Ks
% 0.25/0.50 = ( secrecy_kKS @ M4 ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.25/0.50 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.25/0.50 => ( ! [M4: secrecy_Secrets] :
% 0.25/0.50 ( ( Ks
% 0.25/0.50 = ( secrecy_sKS @ M4 ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.25/0.50 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg
% 0.25/0.50 thf(fact_159_LocalSecretsComposition__neg1,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc965049635ionLoc @ PQ )
% 0.25/0.50 => ( ! [M4: secrecy_Keys] :
% 0.25/0.50 ( ( Ks
% 0.25/0.50 = ( secrecy_kKS @ M4 ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 0.25/0.50 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 0.25/0.50 => ( ! [M4: secrecy_Secrets] :
% 0.25/0.50 ( ( Ks
% 0.25/0.50 = ( secrecy_sKS @ M4 ) )
% 0.25/0.50 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 0.25/0.50 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 0.25/0.50 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % LocalSecretsComposition_neg1
% 0.25/0.50 thf(fact_160_sup__bot__left,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [X: A] :
% 0.25/0.50 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 0.25/0.50 = X ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_bot_left
% 0.25/0.50 thf(fact_161_sup__bot__right,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [X: A] :
% 0.25/0.50 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 0.25/0.50 = X ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_bot_right
% 0.25/0.50 thf(fact_162_bot__eq__sup__iff,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [X: A,Y3: A] :
% 0.25/0.50 ( ( ( bot_bot @ A )
% 0.25/0.50 = ( sup_sup @ A @ X @ Y3 ) )
% 0.25/0.50 = ( ( X
% 0.25/0.50 = ( bot_bot @ A ) )
% 0.25/0.50 & ( Y3
% 0.25/0.50 = ( bot_bot @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % bot_eq_sup_iff
% 0.25/0.50 thf(fact_163_sup__eq__bot__iff,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [X: A,Y3: A] :
% 0.25/0.50 ( ( ( sup_sup @ A @ X @ Y3 )
% 0.25/0.50 = ( bot_bot @ A ) )
% 0.25/0.50 = ( ( X
% 0.25/0.50 = ( bot_bot @ A ) )
% 0.25/0.50 & ( Y3
% 0.25/0.50 = ( bot_bot @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_eq_bot_iff
% 0.25/0.50 thf(fact_164_sup__bot_Oright__neutral,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [A3: A] :
% 0.25/0.50 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 0.25/0.50 = A3 ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_bot.right_neutral
% 0.25/0.50 thf(fact_165_sup__bot_Oneutr__eq__iff,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [A3: A,B2: A] :
% 0.25/0.50 ( ( ( bot_bot @ A )
% 0.25/0.50 = ( sup_sup @ A @ A3 @ B2 ) )
% 0.25/0.50 = ( ( A3
% 0.25/0.50 = ( bot_bot @ A ) )
% 0.25/0.50 & ( B2
% 0.25/0.50 = ( bot_bot @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_bot.neutr_eq_iff
% 0.25/0.50 thf(fact_166_sup__bot_Oleft__neutral,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [A3: A] :
% 0.25/0.50 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 0.25/0.50 = A3 ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_bot.left_neutral
% 0.25/0.50 thf(fact_167_sup__bot_Oeq__neutr__iff,axiom,
% 0.25/0.50 ! [A: $tType] :
% 0.25/0.50 ( ( bounde1808546759up_bot @ A )
% 0.25/0.50 => ! [A3: A,B2: A] :
% 0.25/0.50 ( ( ( sup_sup @ A @ A3 @ B2 )
% 0.25/0.50 = ( bot_bot @ A ) )
% 0.25/0.50 = ( ( A3
% 0.25/0.50 = ( bot_bot @ A ) )
% 0.25/0.50 & ( B2
% 0.25/0.50 = ( bot_bot @ A ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % sup_bot.eq_neutr_iff
% 0.25/0.50 thf(fact_168_ineM__Un1,axiom,
% 0.25/0.50 ! [P: secrecy_specID,A2: set @ secrecy_chanID,E: secrecy_Expression,B: set @ secrecy_chanID] :
% 0.25/0.50 ( ( ineM @ P @ A2 @ E )
% 0.25/0.50 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A2 @ B ) @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % ineM_Un1
% 0.25/0.50 thf(fact_169_notSpecKeysSecretsExpr__def,axiom,
% 0.25/0.50 ( notSpe1586871396tsExpr
% 0.25/0.50 = ( ^ [P2: secrecy_specID,E3: list @ secrecy_Expression] :
% 0.25/0.50 ( ! [X3: secrecy_Keys] :
% 0.25/0.50 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X3 ) @ E3 )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X3 ) @ ( specKeysSecrets @ P2 ) ) )
% 0.25/0.50 & ! [Y5: secrecy_Secrets] :
% 0.25/0.50 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y5 ) @ E3 )
% 0.25/0.50 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % notSpecKeysSecretsExpr_def
% 0.25/0.50 thf(fact_170_TBtheorem5a__empty,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ( eout @ P @ E )
% 0.25/0.50 | ( eout @ Q @ E ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( ( loc @ PQ )
% 0.25/0.50 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 0.25/0.50 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5a_empty
% 0.25/0.50 thf(fact_171_correctCompositionKS__subcomp4,axiom,
% 0.25/0.50 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.25/0.50 ( ( correctCompositionKS @ C4 )
% 0.25/0.50 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.25/0.50 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 0.25/0.50 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_subcomp4
% 0.25/0.50 thf(fact_172_TBtheorem2a,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( eout @ PQ @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( eout @ P @ E )
% 0.25/0.50 | ( eout @ Q @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem2a
% 0.25/0.50 thf(fact_173_correctCompositionKS__subcomp2,axiom,
% 0.25/0.50 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 0.25/0.50 ( ( correctCompositionKS @ C4 )
% 0.25/0.50 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.25/0.50 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 0.25/0.50 => ? [X4: secrecy_specID] :
% 0.25/0.50 ( ( member @ secrecy_specID @ X4 @ ( subcomponents @ C4 ) )
% 0.25/0.50 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X4 ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % correctCompositionKS_subcomp2
% 0.25/0.50 thf(fact_174_TBtheorem5a__notP1,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( eout @ P @ E )
% 0.25/0.50 => ( ~ ( eout @ Q @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5a_notP1
% 0.25/0.50 thf(fact_175_TBtheorem5a__notP2,axiom,
% 0.25/0.50 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.25/0.50 ( ~ ( eout @ Q @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5a_notP2
% 0.25/0.50 thf(fact_176_TBtheorem5a__notPQ,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.25/0.50 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5a_notPQ
% 0.25/0.50 thf(fact_177_out__exprChannelSingle__Set,axiom,
% 0.25/0.50 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( out_ex985543062Single @ P @ Ch @ E )
% 0.25/0.50 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % out_exprChannelSingle_Set
% 0.25/0.50 thf(fact_178_out__exprChannelSet__Single,axiom,
% 0.25/0.50 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 0.25/0.50 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % out_exprChannelSet_Single
% 0.25/0.50 thf(fact_179_TBtheorem5b__notPQ,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 0.25/0.50 ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 0.25/0.50 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 0.25/0.50 => ( ( M2
% 0.25/0.50 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5b_notPQ
% 0.25/0.50 thf(fact_180_eout__know__nonKS__s,axiom,
% 0.25/0.50 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 0.25/0.50 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 0.25/0.50 => ( ( eout @ A2 @ ( secrecy_sE @ M ) )
% 0.25/0.50 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 => ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % eout_know_nonKS_s
% 0.25/0.50 thf(fact_181_eoutKnowCorrect__L1s,axiom,
% 0.25/0.50 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 0.25/0.50 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 => ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 0.25/0.50 => ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 0.25/0.50 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % eoutKnowCorrect_L1s
% 0.25/0.50 thf(fact_182_eoutM__eout,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 0.25/0.50 ( ( eoutM @ P @ M2 @ E )
% 0.25/0.50 => ( eout @ P @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % eoutM_eout
% 0.25/0.50 thf(fact_183_not__eout__eoutM,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 0.25/0.50 ( ~ ( eout @ P @ E )
% 0.25/0.50 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 0.25/0.50
% 0.25/0.50 % not_eout_eoutM
% 0.25/0.50 thf(fact_184_TBtheorem2b,axiom,
% 0.25/0.50 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( eoutM @ PQ @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( eoutM @ P @ M2 @ E )
% 0.25/0.50 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem2b
% 0.25/0.50 thf(fact_185_TBtheorem5b__notP2,axiom,
% 0.25/0.50 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 0.25/0.50 ( ~ ( eoutM @ Q @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 0.25/0.50 => ( ! [X4: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 0.25/0.50 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5b_notP2
% 0.25/0.50 thf(fact_186_TBtheorem5b__notP1,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( eoutM @ P @ M2 @ E )
% 0.25/0.50 => ( ~ ( eoutM @ Q @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5b_notP1
% 0.25/0.50 thf(fact_187_eout__know__s,axiom,
% 0.25/0.50 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 0.25/0.50 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 = ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 0.25/0.50 = ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 0.25/0.50 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % eout_know_s
% 0.25/0.50 thf(fact_188_not__know__s__not__eout,axiom,
% 0.25/0.50 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 0.25/0.50 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 0.25/0.50 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 0.25/0.50 => ~ ( eout @ A2 @ ( secrecy_sE @ M ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % not_know_s_not_eout
% 0.25/0.50 thf(fact_189_TBtheore54b__P,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( eoutM @ P @ M2 @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 0.25/0.50 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheore54b_P
% 0.25/0.50 thf(fact_190_TBtheorem5b__PQ,axiom,
% 0.25/0.50 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.50 ( ( ( eoutM @ P @ M2 @ E )
% 0.25/0.50 | ( eoutM @ Q @ M2 @ E ) )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.25/0.50 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem5b_PQ
% 0.25/0.50 thf(fact_191_TBtheorem45a__P,axiom,
% 0.25/0.50 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 0.25/0.50 ( ( eout @ P @ E )
% 0.25/0.50 => ( ( ( subcomponents @ PQ )
% 0.25/0.50 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.50 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.50 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.25/0.50 & ( exprChannel @ Ch2 @ E )
% 0.25/0.50 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.50 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % TBtheorem45a_P
% 0.25/0.50 thf(fact_192_eout__def,axiom,
% 0.25/0.50 ( eout
% 0.25/0.50 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 0.25/0.50 ? [Ch3: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.25/0.50 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % eout_def
% 0.25/0.50 thf(fact_193_eoutM__def,axiom,
% 0.25/0.50 ( eoutM
% 0.25/0.50 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.25/0.50 ? [Ch3: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.25/0.50 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 0.25/0.50 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 0.25/0.50
% 0.25/0.50 % eoutM_def
% 0.25/0.50 thf(fact_194_out__exprChannelSet__def,axiom,
% 0.25/0.50 ( out_exprChannelSet
% 0.25/0.50 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 0.25/0.50 ( ! [X3: secrecy_chanID] :
% 0.25/0.50 ( ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 0.25/0.50 => ( ( member @ secrecy_chanID @ X3 @ ( out @ SP ) )
% 0.25/0.50 & ( exprChannel @ X3 @ E2 ) ) )
% 0.25/0.50 & ! [X3: secrecy_chanID] :
% 0.25/0.50 ( ( ~ ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 0.25/0.50 & ( member @ secrecy_chanID @ X3 @ ( out @ SP ) ) )
% 0.25/0.50 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % out_exprChannelSet_def
% 0.25/0.51 thf(fact_195_out__exprChannelSingle__def,axiom,
% 0.25/0.51 ( out_ex985543062Single
% 0.25/0.51 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 0.25/0.51 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 0.25/0.51 & ( exprChannel @ Ch3 @ E2 )
% 0.25/0.51 & ! [X3: secrecy_chanID,T: nat] :
% 0.25/0.51 ( ( ( member @ secrecy_chanID @ X3 @ ( out @ SP ) )
% 0.25/0.51 & ( X3 != Ch3 ) )
% 0.25/0.51 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % out_exprChannelSingle_def
% 0.25/0.51 thf(fact_196_correctCompositionOut__prop1,axiom,
% 0.25/0.51 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 0.25/0.51 ( ( ( subcomponents @ PQ )
% 0.25/0.51 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.51 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.51 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 0.25/0.51 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 0.25/0.51 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % correctCompositionOut_prop1
% 0.25/0.51 thf(fact_197_TBtheorem5a__PQ,axiom,
% 0.25/0.51 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 0.25/0.51 ( ( ( eout @ P @ E )
% 0.25/0.51 | ( eout @ Q @ E ) )
% 0.25/0.51 => ( ( ( subcomponents @ PQ )
% 0.25/0.51 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 0.25/0.51 => ( ( correc990227761ionOut @ PQ )
% 0.25/0.51 => ( ? [Ch2: secrecy_chanID] :
% 0.25/0.51 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 0.25/0.51 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 0.25/0.51 & ( exprChannel @ Ch2 @ E )
% 0.25/0.51 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 0.25/0.51 => ( eout @ PQ @ E ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % TBtheorem5a_PQ
% 0.25/0.51 thf(fact_198_outStream__def,axiom,
% 0.25/0.51 ( outStream
% 0.25/0.51 = ( ^ [X3: secrecy_specID] :
% 0.25/0.51 ( ^ [Y4: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y4 = Z )
% 0.25/0.51 @ ( out @ X3 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % outStream_def
% 0.25/0.51 thf(fact_199_eout__know__k,axiom,
% 0.25/0.51 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 0.25/0.51 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 0.25/0.51 = ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 0.25/0.51 = ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 0.25/0.51 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % eout_know_k
% 0.25/0.51 thf(fact_200_correctCompositionKS__subcomp1,axiom,
% 0.25/0.51 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.25/0.51 ( ( correctCompositionKS @ C4 )
% 0.25/0.51 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.25/0.51 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 0.25/0.51 => ? [X4: secrecy_specID] :
% 0.25/0.51 ( ( member @ secrecy_specID @ X4 @ ( subcomponents @ C4 ) )
% 0.25/0.51 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X4 ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % correctCompositionKS_subcomp1
% 0.25/0.51 thf(fact_201_correctCompositionKS__subcomp3,axiom,
% 0.25/0.51 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 0.25/0.51 ( ( correctCompositionKS @ C4 )
% 0.25/0.51 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 0.25/0.51 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 0.25/0.51 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % correctCompositionKS_subcomp3
% 0.25/0.51 thf(fact_202_eout__know__nonKS__k,axiom,
% 0.25/0.51 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 0.25/0.51 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 0.25/0.51 => ( ( eout @ A2 @ ( secrecy_kE @ M ) )
% 0.25/0.51 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 0.25/0.51 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % eout_know_nonKS_k
% 0.25/0.51 thf(fact_203_eoutKnowCorrect__L1k,axiom,
% 0.25/0.51 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 0.25/0.51 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 0.25/0.51 => ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 0.25/0.51 => ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 0.25/0.51 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % eoutKnowCorrect_L1k
% 0.25/0.51 thf(fact_204_not__know__k__not__eout,axiom,
% 0.25/0.51 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 0.25/0.51 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 0.25/0.51 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.25/0.51 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 0.25/0.51 => ~ ( eout @ A2 @ ( secrecy_kE @ M ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % not_know_k_not_eout
% 0.25/0.51 thf(fact_205_adv__not__know2,axiom,
% 0.25/0.51 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Secrets] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 0.25/0.51 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 0.25/0.51 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % adv_not_know2
% 0.25/0.51 thf(fact_206_adv__not__know1,axiom,
% 0.25/0.51 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Keys] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 0.25/0.51 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 0.25/0.51 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % adv_not_know1
% 0.25/0.51 thf(fact_207_order__refl,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( preorder @ A )
% 0.25/0.51 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 0.25/0.51
% 0.25/0.51 % order_refl
% 0.25/0.51 thf(fact_208_subsetI,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.25/0.51 ( ! [X4: A] :
% 0.25/0.51 ( ( member @ A @ X4 @ A2 )
% 0.25/0.51 => ( member @ A @ X4 @ B ) )
% 0.25/0.51 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 0.25/0.51
% 0.25/0.51 % subsetI
% 0.25/0.51 thf(fact_209_subset__antisym,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 => ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 0.25/0.51 => ( A2 = B ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_antisym
% 0.25/0.51 thf(fact_210_subset__empty,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 0.25/0.51 = ( A2
% 0.25/0.51 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_empty
% 0.25/0.51 thf(fact_211_empty__subsetI,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 0.25/0.51
% 0.25/0.51 % empty_subsetI
% 0.25/0.51 thf(fact_212_insert__subset,axiom,
% 0.25/0.51 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B )
% 0.25/0.51 = ( ( member @ A @ X @ B )
% 0.25/0.51 & ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % insert_subset
% 0.25/0.51 thf(fact_213_Un__subset__iff,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 0.25/0.51 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.25/0.51 & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_subset_iff
% 0.25/0.51 thf(fact_214_singleton__insert__inj__eq_H,axiom,
% 0.25/0.51 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 0.25/0.51 ( ( ( insert @ A @ A3 @ A2 )
% 0.25/0.51 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 0.25/0.51 = ( ( A3 = B2 )
% 0.25/0.51 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % singleton_insert_inj_eq'
% 0.25/0.51 thf(fact_215_singleton__insert__inj__eq,axiom,
% 0.25/0.51 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 0.25/0.51 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 0.25/0.51 = ( insert @ A @ A3 @ A2 ) )
% 0.25/0.51 = ( ( A3 = B2 )
% 0.25/0.51 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % singleton_insert_inj_eq
% 0.25/0.51 thf(fact_216_subset__Un__eq,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) )
% 0.25/0.51 = ( ^ [A4: set @ A,B5: set @ A] :
% 0.25/0.51 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 0.25/0.51 = B5 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_Un_eq
% 0.25/0.51 thf(fact_217_subset__UnE,axiom,
% 0.25/0.51 ! [A: $tType,C4: set @ A,A2: set @ A,B: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 0.25/0.51 => ~ ! [A6: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 0.25/0.51 => ! [B6: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B )
% 0.25/0.51 => ( C4
% 0.25/0.51 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_UnE
% 0.25/0.51 thf(fact_218_Un__absorb2,axiom,
% 0.25/0.51 ! [A: $tType,B: set @ A,A2: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 0.25/0.51 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 = A2 ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_absorb2
% 0.25/0.51 thf(fact_219_Un__absorb1,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 = B ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_absorb1
% 0.25/0.51 thf(fact_220_Un__upper2,axiom,
% 0.25/0.51 ! [A: $tType,B: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_upper2
% 0.25/0.51 thf(fact_221_Un__upper1,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_upper1
% 0.25/0.51 thf(fact_222_Un__least,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.25/0.51 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 0.25/0.51 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_least
% 0.25/0.51 thf(fact_223_Un__mono,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 0.25/0.51 => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 0.25/0.51 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % Un_mono
% 0.25/0.51 thf(fact_224_insert__mono,axiom,
% 0.25/0.51 ! [A: $tType,C4: set @ A,D3: set @ A,A3: A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 0.25/0.51 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C4 ) @ ( insert @ A @ A3 @ D3 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % insert_mono
% 0.25/0.51 thf(fact_225_subset__insert,axiom,
% 0.25/0.51 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 0.25/0.51 ( ~ ( member @ A @ X @ A2 )
% 0.25/0.51 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X @ B ) )
% 0.25/0.51 = ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_insert
% 0.25/0.51 thf(fact_226_subset__insertI,axiom,
% 0.25/0.51 ! [A: $tType,B: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A3 @ B ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_insertI
% 0.25/0.51 thf(fact_227_subset__insertI2,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A,B2: A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subset_insertI2
% 0.25/0.51 thf(fact_228_le__funD,axiom,
% 0.25/0.51 ! [B4: $tType,A: $tType] :
% 0.25/0.51 ( ( ord @ B4 )
% 0.25/0.51 => ! [F: A > B4,G: A > B4,X: A] :
% 0.25/0.51 ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 0.25/0.51 => ( ord_less_eq @ B4 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % le_funD
% 0.25/0.51 thf(fact_229_le__funE,axiom,
% 0.25/0.51 ! [B4: $tType,A: $tType] :
% 0.25/0.51 ( ( ord @ B4 )
% 0.25/0.51 => ! [F: A > B4,G: A > B4,X: A] :
% 0.25/0.51 ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 0.25/0.51 => ( ord_less_eq @ B4 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % le_funE
% 0.25/0.51 thf(fact_230_le__funI,axiom,
% 0.25/0.51 ! [B4: $tType,A: $tType] :
% 0.25/0.51 ( ( ord @ B4 )
% 0.25/0.51 => ! [F: A > B4,G: A > B4] :
% 0.25/0.51 ( ! [X4: A] : ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( G @ X4 ) )
% 0.25/0.51 => ( ord_less_eq @ ( A > B4 ) @ F @ G ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % le_funI
% 0.25/0.51 thf(fact_231_le__fun__def,axiom,
% 0.25/0.51 ! [B4: $tType,A: $tType] :
% 0.25/0.51 ( ( ord @ B4 )
% 0.25/0.51 => ( ( ord_less_eq @ ( A > B4 ) )
% 0.25/0.51 = ( ^ [F3: A > B4,G2: A > B4] :
% 0.25/0.51 ! [X3: A] : ( ord_less_eq @ B4 @ ( F3 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % le_fun_def
% 0.25/0.51 thf(fact_232_order__subst1,axiom,
% 0.25/0.51 ! [A: $tType,B4: $tType] :
% 0.25/0.51 ( ( ( order @ B4 )
% 0.25/0.51 & ( order @ A ) )
% 0.25/0.51 => ! [A3: A,F: B4 > A,B2: B4,C: B4] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A3 @ ( F @ B2 ) )
% 0.25/0.51 => ( ( ord_less_eq @ B4 @ B2 @ C )
% 0.25/0.51 => ( ! [X4: B4,Y: B4] :
% 0.25/0.51 ( ( ord_less_eq @ B4 @ X4 @ Y )
% 0.25/0.51 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y ) ) )
% 0.25/0.51 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % order_subst1
% 0.25/0.51 thf(fact_233_order__subst2,axiom,
% 0.25/0.51 ! [A: $tType,C3: $tType] :
% 0.25/0.51 ( ( ( order @ C3 )
% 0.25/0.51 & ( order @ A ) )
% 0.25/0.51 => ! [A3: A,B2: A,F: A > C3,C: C3] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.25/0.51 => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 0.25/0.51 => ( ! [X4: A,Y: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ X4 @ Y )
% 0.25/0.51 => ( ord_less_eq @ C3 @ ( F @ X4 ) @ ( F @ Y ) ) )
% 0.25/0.51 => ( ord_less_eq @ C3 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % order_subst2
% 0.25/0.51 thf(fact_234_ord__eq__le__subst,axiom,
% 0.25/0.51 ! [A: $tType,B4: $tType] :
% 0.25/0.51 ( ( ( ord @ B4 )
% 0.25/0.51 & ( ord @ A ) )
% 0.25/0.51 => ! [A3: A,F: B4 > A,B2: B4,C: B4] :
% 0.25/0.51 ( ( A3
% 0.25/0.51 = ( F @ B2 ) )
% 0.25/0.51 => ( ( ord_less_eq @ B4 @ B2 @ C )
% 0.25/0.51 => ( ! [X4: B4,Y: B4] :
% 0.25/0.51 ( ( ord_less_eq @ B4 @ X4 @ Y )
% 0.25/0.51 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y ) ) )
% 0.25/0.51 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % ord_eq_le_subst
% 0.25/0.51 thf(fact_235_ord__le__eq__subst,axiom,
% 0.25/0.51 ! [A: $tType,B4: $tType] :
% 0.25/0.51 ( ( ( ord @ B4 )
% 0.25/0.51 & ( ord @ A ) )
% 0.25/0.51 => ! [A3: A,B2: A,F: A > B4,C: B4] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.25/0.51 => ( ( ( F @ B2 )
% 0.25/0.51 = C )
% 0.25/0.51 => ( ! [X4: A,Y: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ X4 @ Y )
% 0.25/0.51 => ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( F @ Y ) ) )
% 0.25/0.51 => ( ord_less_eq @ B4 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % ord_le_eq_subst
% 0.25/0.51 thf(fact_236_eq__iff,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.25/0.51 = ( ^ [X3: A,Y5: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ X3 @ Y5 )
% 0.25/0.51 & ( ord_less_eq @ A @ Y5 @ X3 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % eq_iff
% 0.25/0.51 thf(fact_237_antisym,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [X: A,Y3: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ X @ Y3 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ Y3 @ X )
% 0.25/0.51 => ( X = Y3 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % antisym
% 0.25/0.51 thf(fact_238_linear,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( linorder @ A )
% 0.25/0.51 => ! [X: A,Y3: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ X @ Y3 )
% 0.25/0.51 | ( ord_less_eq @ A @ Y3 @ X ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % linear
% 0.25/0.51 thf(fact_239_eq__refl,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( preorder @ A )
% 0.25/0.51 => ! [X: A,Y3: A] :
% 0.25/0.51 ( ( X = Y3 )
% 0.25/0.51 => ( ord_less_eq @ A @ X @ Y3 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % eq_refl
% 0.25/0.51 thf(fact_240_le__cases,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( linorder @ A )
% 0.25/0.51 => ! [X: A,Y3: A] :
% 0.25/0.51 ( ~ ( ord_less_eq @ A @ X @ Y3 )
% 0.25/0.51 => ( ord_less_eq @ A @ Y3 @ X ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % le_cases
% 0.25/0.51 thf(fact_241_order_Otrans,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [A3: A,B2: A,C: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.25/0.51 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % order.trans
% 0.25/0.51 thf(fact_242_le__cases3,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( linorder @ A )
% 0.25/0.51 => ! [X: A,Y3: A,Z2: A] :
% 0.25/0.51 ( ( ( ord_less_eq @ A @ X @ Y3 )
% 0.25/0.51 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 0.25/0.51 => ( ( ( ord_less_eq @ A @ Y3 @ X )
% 0.25/0.51 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 0.25/0.51 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 0.25/0.51 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 0.25/0.51 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 0.25/0.51 => ~ ( ord_less_eq @ A @ Y3 @ X ) )
% 0.25/0.51 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.25/0.51 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 0.25/0.51 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 0.25/0.51 => ~ ( ord_less_eq @ A @ X @ Y3 ) ) ) ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % le_cases3
% 0.25/0.51 thf(fact_243_antisym__conv,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [Y3: A,X: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ Y3 @ X )
% 0.25/0.51 => ( ( ord_less_eq @ A @ X @ Y3 )
% 0.25/0.51 = ( X = Y3 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % antisym_conv
% 0.25/0.51 thf(fact_244_order__class_Oorder_Oeq__iff,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.25/0.51 = ( ^ [A5: A,B7: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A5 @ B7 )
% 0.25/0.51 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % order_class.order.eq_iff
% 0.25/0.51 thf(fact_245_ord__eq__le__trans,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( ord @ A )
% 0.25/0.51 => ! [A3: A,B2: A,C: A] :
% 0.25/0.51 ( ( A3 = B2 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ B2 @ C )
% 0.25/0.51 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % ord_eq_le_trans
% 0.25/0.51 thf(fact_246_ord__le__eq__trans,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( ord @ A )
% 0.25/0.51 => ! [A3: A,B2: A,C: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.25/0.51 => ( ( B2 = C )
% 0.25/0.51 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % ord_le_eq_trans
% 0.25/0.51 thf(fact_247_order__class_Oorder_Oantisym,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [A3: A,B2: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.25/0.51 => ( A3 = B2 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % order_class.order.antisym
% 0.25/0.51 thf(fact_248_order__trans,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( preorder @ A )
% 0.25/0.51 => ! [X: A,Y3: A,Z2: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ X @ Y3 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 0.25/0.51 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % order_trans
% 0.25/0.51 thf(fact_249_dual__order_Orefl,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 0.25/0.51
% 0.25/0.51 % dual_order.refl
% 0.25/0.51 thf(fact_250_linorder__wlog,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( linorder @ A )
% 0.25/0.51 => ! [P: A > A > $o,A3: A,B2: A] :
% 0.25/0.51 ( ! [A7: A,B8: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ A7 @ B8 )
% 0.25/0.51 => ( P @ A7 @ B8 ) )
% 0.25/0.51 => ( ! [A7: A,B8: A] :
% 0.25/0.51 ( ( P @ B8 @ A7 )
% 0.25/0.51 => ( P @ A7 @ B8 ) )
% 0.25/0.51 => ( P @ A3 @ B2 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % linorder_wlog
% 0.25/0.51 thf(fact_251_dual__order_Otrans,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [B2: A,A3: A,C: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ C @ B2 )
% 0.25/0.51 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % dual_order.trans
% 0.25/0.51 thf(fact_252_dual__order_Oeq__iff,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 0.25/0.51 = ( ^ [A5: A,B7: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ B7 @ A5 )
% 0.25/0.51 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % dual_order.eq_iff
% 0.25/0.51 thf(fact_253_dual__order_Oantisym,axiom,
% 0.25/0.51 ! [A: $tType] :
% 0.25/0.51 ( ( order @ A )
% 0.25/0.51 => ! [B2: A,A3: A] :
% 0.25/0.51 ( ( ord_less_eq @ A @ B2 @ A3 )
% 0.25/0.51 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 0.25/0.51 => ( A3 = B2 ) ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % dual_order.antisym
% 0.25/0.51 thf(fact_254_in__mono,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 => ( ( member @ A @ X @ A2 )
% 0.25/0.51 => ( member @ A @ X @ B ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % in_mono
% 0.25/0.51 thf(fact_255_subsetD,axiom,
% 0.25/0.51 ! [A: $tType,A2: set @ A,B: set @ A,C: A] :
% 0.25/0.51 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 0.25/0.51 => ( ( member @ A @ C @ A2 )
% 0.25/0.51 => ( member @ A @ C @ B ) ) ) ).
% 0.25/0.51
% 0.25/0.51 % subsetD
% 0.25/0.51
% 0.25/0.51 % Type constructors (24)
% 0.25/0.51 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 0.25/0.51 bounded_lattice @ $o ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 0.25/0.51 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 0.25/0.51 ! [A8: $tType,A9: $tType] :
% 0.25/0.51 ( ( bounded_lattice @ A9 )
% 0.25/0.51 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 0.25/0.51 ! [A8: $tType,A9: $tType] :
% 0.25/0.51 ( ( bounded_lattice @ A9 )
% 0.25/0.51 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_fun___Orderings_Opreorder,axiom,
% 0.25/0.51 ! [A8: $tType,A9: $tType] :
% 0.25/0.51 ( ( preorder @ A9 )
% 0.25/0.51 => ( preorder @ ( A8 > A9 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_fun___Orderings_Oorder,axiom,
% 0.25/0.51 ! [A8: $tType,A9: $tType] :
% 0.25/0.51 ( ( order @ A9 )
% 0.25/0.51 => ( order @ ( A8 > A9 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_fun___Orderings_Oord,axiom,
% 0.25/0.51 ! [A8: $tType,A9: $tType] :
% 0.25/0.51 ( ( ord @ A9 )
% 0.25/0.51 => ( ord @ ( A8 > A9 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_fun___Orderings_Obot,axiom,
% 0.25/0.51 ! [A8: $tType,A9: $tType] :
% 0.25/0.51 ( ( bot @ A9 )
% 0.25/0.51 => ( bot @ ( A8 > A9 ) ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 0.25/0.51 preorder @ nat ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 0.25/0.51 linorder @ nat ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 0.25/0.51 order @ nat ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 0.25/0.51 ord @ nat ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Nat_Onat___Orderings_Obot_6,axiom,
% 0.25/0.51 bot @ nat ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 0.25/0.51 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 0.25/0.51 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 0.25/0.51 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 0.25/0.51 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 0.25/0.51 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 0.25/0.51 bounde1808546759up_bot @ $o ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 0.25/0.51 preorder @ $o ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 0.25/0.51 linorder @ $o ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 0.25/0.51 order @ $o ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 0.25/0.51 ord @ $o ).
% 0.25/0.51
% 0.25/0.51 thf(tcon_HOL_Obool___Orderings_Obot_17,axiom,
% 0.25/0.51 bot @ $o ).
% 0.25/0.51
% 0.25/0.51 % Conjectures (1)
% 0.25/0.51 thf(conj_0,conjecture,
% 0.25/0.51 ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ) ).
% 0.25/0.51
% 0.25/0.51 %------------------------------------------------------------------------------
% 0.25/0.51 ------------------------
% 3.13/1.87 ---- Embedded in THF ---
% 3.13/1.87 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 3.13/1.87 %%% Generated on Tue Feb 24 08:25:58 EST 2026
% 3.13/1.87 %%% using '$$dhol' embedding, version 1.3.0.
% 3.13/1.87 %%% Logic specification used:
% 3.13/1.87 %%% thf(spec, logic, $$dhol).
% 3.13/1.87
% 3.13/1.87 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2DTF3672.p
% 3.13/1.87 thf(ty_t_Secrecy__types_OExpression, type, secrecy_Expression: $tType).
% 3.13/1.87 thf(ty_t_Secrecy__types_OSecrets, type, secrecy_Secrets: $tType).
% 3.13/1.87 thf(ty_t_Secrecy__types_OspecID, type, secrecy_specID: $tType).
% 3.13/1.87 thf(ty_t_Secrecy__types_OchanID, type, secrecy_chanID: $tType).
% 3.13/1.87 thf(ty_t_Secrecy__types_OKeys, type, secrecy_Keys: $tType).
% 3.13/1.87 thf(ty_t_Secrecy__types_OKS, type, secrecy_KS: $tType).
% 3.13/1.87 thf(ty_t_List_Olist, type, list: ($tType > $tType)).
% 3.13/1.87 thf(ty_t_Set_Oset, type, set: ($tType > $tType)).
% 3.13/1.87 thf(ty_t_Nat_Onat, type, nat: $tType).
% 3.13/1.87 thf(sy_cl_Lattices_Obounded__lattice, type, bounded_lattice: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_HOL_Otype, type, type: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_Orderings_Obot, type, bot: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_Orderings_Oord, type, ord: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_Orderings_Oorder, type, order: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_Orderings_Olinorder, type, linorder: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_Orderings_Opreorder, type, preorder: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot, type, bounde1808546759up_bot: (!> [A:$tType]: ($o))).
% 3.13/1.87 thf(sy_c_CompLocalSecrets_OLocalSecrets, type, localSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 3.13/1.87 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect, type, knowle1667810483orrect: (secrecy_specID > (secrecy_KS > $o))).
% 3.13/1.87 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow, type, knowle1437066798e_know: (secrecy_specID > (secrecy_KS > $o))).
% 3.13/1.87 thf(sy_c_Lattices_Osup__class_Osup, type, sup_sup: (!> [A:$tType]: ((A > (A > A))))).
% 3.13/1.87 thf(sy_c_ListExtras_Omem, type, mem: (!> [A:$tType]: ((A > ((list @ A) > $o))))).
% 3.13/1.87 thf(sy_c_Orderings_Obot__class_Obot, type, bot_bot: (!> [A:$tType]: (A))).
% 3.13/1.87 thf(sy_c_Orderings_Oord__class_Oless__eq, type, ord_less_eq: (!> [A:$tType]: ((A > (A > $o))))).
% 3.13/1.87 thf(sy_c_Secrecy_OcorrectCompositionKS, type, correctCompositionKS: (secrecy_specID > $o)).
% 3.13/1.87 thf(sy_c_Secrecy_Oeout, type, eout: (secrecy_specID > (secrecy_Expression > $o))).
% 3.13/1.87 thf(sy_c_Secrecy_OeoutM, type, eoutM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.13/1.87 thf(sy_c_Secrecy_OexprChannel, type, exprChannel: (secrecy_chanID > (secrecy_Expression > $o))).
% 3.13/1.87 thf(sy_c_Secrecy_Oine, type, ine: (secrecy_specID > (secrecy_Expression > $o))).
% 3.13/1.87 thf(sy_c_Secrecy_OineM, type, ineM: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.13/1.87 thf(sy_c_Secrecy_Oine__exprChannelSet, type, ine_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.13/1.87 thf(sy_c_Secrecy_Oine__exprChannelSingle, type, ine_ex1303305700Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 3.13/1.87 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr, type, notSpe1586871396tsExpr: (secrecy_specID > ((list @ secrecy_Expression) > $o))).
% 3.13/1.87 thf(sy_c_Secrecy_Oout__exprChannelSet, type, out_exprChannelSet: (secrecy_specID > ((set @ secrecy_chanID) > (secrecy_Expression > $o)))).
% 3.13/1.87 thf(sy_c_Secrecy_Oout__exprChannelSingle, type, out_ex985543062Single: (secrecy_specID > (secrecy_chanID > (secrecy_Expression > $o)))).
% 3.13/1.87 thf(sy_c_Secrecy_OspecKeys, type, specKeys: (secrecy_specID > (set @ secrecy_Keys))).
% 3.13/1.87 thf(sy_c_Secrecy_OspecKeysSecrets, type, specKeysSecrets: (secrecy_specID > (set @ secrecy_KS))).
% 3.13/1.87 thf(sy_c_Secrecy_OspecSecrets, type, specSecrets: (secrecy_specID > (set @ secrecy_Secrets))).
% 3.13/1.87 thf(sy_c_Secrecy__types_OExpression_OkE, type, secrecy_kE: (secrecy_Keys > secrecy_Expression)).
% 3.13/1.87 thf(sy_c_Secrecy__types_OExpression_OsE, type, secrecy_sE: (secrecy_Secrets > secrecy_Expression)).
% 3.13/1.87 thf(sy_c_Secrecy__types_OKS2Expression, type, secrec1016742679ession: (secrecy_KS > secrecy_Expression)).
% 3.13/1.87 thf(sy_c_Secrecy__types_OKS_Ocase__KS, type, secrecy_case_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 3.13/1.87 thf(sy_c_Secrecy__types_OKS_OkKS, type, secrecy_kKS: (secrecy_Keys > secrecy_KS)).
% 3.13/1.87 thf(sy_c_Secrecy__types_OKS_Orec__KS, type, secrecy_rec_KS: (!> [A:$tType]: (((secrecy_Keys > A) > ((secrecy_Secrets > A) > (secrecy_KS > A)))))).
% 3.13/1.87 thf(sy_c_Secrecy__types_OKS_OsKS, type, secrecy_sKS: (secrecy_Secrets > secrecy_KS)).
% 3.13/1.87 thf(sy_c_Set_OCollect, type, collect: (!> [A:$tType]: (((A > $o) > (set @ A))))).
% 3.13/1.87 thf(sy_c_Set_Oinsert, type, insert: (!> [A:$tType]: ((A > ((set @ A) > (set @ A)))))).
% 3.13/1.87 thf(sy_c_Set_Ois__empty, type, is_empty: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.13/1.87 thf(sy_c_Set_Ois__singleton, type, is_singleton: (!> [A:$tType]: (((set @ A) > $o)))).
% 3.13/1.87 thf(sy_c_Set_Othe__elem, type, the_elem: (!> [A:$tType]: (((set @ A) > A)))).
% 3.13/1.87 thf(sy_c_inout_OcorrectCompositionIn, type, correctCompositionIn: (secrecy_specID > $o)).
% 3.13/1.87 thf(sy_c_inout_OcorrectCompositionLoc, type, correc965049635ionLoc: (secrecy_specID > $o)).
% 3.13/1.87 thf(sy_c_inout_OcorrectCompositionOut, type, correc990227761ionOut: (secrecy_specID > $o)).
% 3.13/1.87 thf(sy_c_inout_OinStream, type, inStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 3.13/1.87 thf(sy_c_inout_Oins, type, ins: (secrecy_specID > (set @ secrecy_chanID))).
% 3.13/1.87 thf(sy_c_inout_Oloc, type, loc: (secrecy_specID > (set @ secrecy_chanID))).
% 3.13/1.87 thf(sy_c_inout_OlocStream, type, locStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 3.13/1.87 thf(sy_c_inout_Oout, type, out: (secrecy_specID > (set @ secrecy_chanID))).
% 3.13/1.87 thf(sy_c_inout_OoutStream, type, outStream: (secrecy_specID > ((set @ secrecy_chanID) > $o))).
% 3.13/1.87 thf(sy_c_inout_Osubcomponents, type, subcomponents: (secrecy_specID > (set @ secrecy_specID))).
% 3.13/1.87 thf(sy_c_member, type, member: (!> [A:$tType]: ((A > ((set @ A) > $o))))).
% 3.13/1.87 thf(sy_v_P, type, p: secrecy_specID).
% 3.13/1.87 thf(sy_v_PQ, type, pq: secrecy_specID).
% 3.13/1.87 thf(sy_v_Q, type, q: secrecy_specID).
% 3.13/1.87 thf(sy_v_m, type, m: secrecy_KS).
% 3.13/1.87 thf(sy_v_secret____, type, secret: secrecy_Secrets).
% 3.13/1.87 thf(fact_0_cCompLoc, axiom, (correc965049635ionLoc @ pq)).
% 3.13/1.87 thf(fact_1_sg1a, axiom, (~ (((ine @ p) @ (secrecy_sE @ secret))))).
% 3.13/1.87 thf(fact_2_sg2a, axiom, (~ (((ine @ q) @ (secrecy_sE @ secret))))).
% 3.13/1.87 thf(fact_3_sg1b, axiom, (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ secret)) @ (localSecrets @ p))))).
% 3.13/1.87 thf(fact_4_sg2b, axiom, (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ secret)) @ (localSecrets @ q))))).
% 3.13/1.87 thf(fact_5_subPQ, axiom, ((subcomponents @ pq) = (((insert @ secrecy_specID) @ p) @ (((insert @ secrecy_specID) @ q) @ (bot_bot @ (set @ secrecy_specID)))))).
% 3.13/1.87 thf(fact_6_a2, axiom, (m = (secrecy_sKS @ secret))).
% 3.13/1.87 thf(fact_7_cCompI, axiom, (correctCompositionIn @ pq)).
% 3.13/1.87 thf(fact_8_sg3, axiom, (~ (((ine @ pq) @ (secrecy_sE @ secret))))).
% 3.13/1.87 thf(fact_9_KS_Oinject_I2_J, axiom, (! [X2:secrecy_Secrets,Y2:secrecy_Secrets]: ((((secrecy_sKS @ X2) = (secrecy_sKS @ Y2)) = (X2 = Y2))))).
% 3.13/1.87 thf(fact_10_sg1, axiom, (~ (((knowle1437066798e_know @ p) @ (secrecy_sKS @ secret))))).
% 3.13/1.87 thf(fact_11_sg2, axiom, (~ (((knowle1437066798e_know @ q) @ (secrecy_sKS @ secret))))).
% 3.13/1.87 thf(fact_12_know_Osimps_I2_J, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: ((((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)) = (((ine @ A2) @ (secrecy_sE @ M)) | (((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (localSecrets @ A2))))))).
% 3.13/1.87 thf(fact_13_KS_Osimps_I8_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X2:secrecy_Secrets]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X2)) = (F2 @ X2))))).
% 3.13/1.87 thf(fact_14_KS_Osimps_I6_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X2:secrecy_Secrets]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_sKS @ X2)) = (F2 @ X2))))).
% 3.13/1.87 thf(fact_15_LocalSecretsComposition__ine1__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_sE @ S))))))))))).
% 3.13/1.87 thf(fact_16_LocalSecretsComposition__ine2__s, axiom, (! [S:secrecy_Secrets,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_sE @ S))))))))))).
% 3.13/1.87 thf(fact_17_LocalSecretsComposition__neg1__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,S:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_sE @ S)))) => ((~ (((ine @ Q) @ (secrecy_sE @ S)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ S)) @ (localSecrets @ PQ))))))))))))).
% 3.13/1.87 thf(fact_18_KS2Expression_Osimps_I2_J, axiom, (! [M:secrecy_Secrets]: (((secrec1016742679ession @ (secrecy_sKS @ M)) = (secrecy_sE @ M))))).
% 3.13/1.87 thf(fact_19_LocalSecretsComposition1, axiom, (! [Ls:secrecy_KS,P:secrecy_specID,PQ:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ Ls) @ (localSecrets @ P)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => (((member @ secrecy_KS) @ Ls) @ (localSecrets @ PQ))))))).
% 3.13/1.87 thf(fact_20_not__know__s__not__ine, axiom, (! [A2:secrecy_specID,M:secrecy_Secrets]: (((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (~ (((ine @ A2) @ (secrecy_sE @ M)))))))).
% 3.13/1.87 thf(fact_21_notknowQ, axiom, (~ (((knowle1437066798e_know @ q) @ m)))).
% 3.13/1.87 thf(fact_22_notknowP, axiom, (~ (((knowle1437066798e_know @ p) @ m)))).
% 3.13/1.87 thf(fact_23_Expression_Oinject_I2_J, axiom, (! [X2:secrecy_Secrets,Y2:secrecy_Secrets]: ((((secrecy_sE @ X2) = (secrecy_sE @ Y2)) = (X2 = Y2))))).
% 3.13/1.87 thf(fact_24_know__composition__neg__ine__s, axiom, (! [P:secrecy_specID,Secret:secrecy_Secrets,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((knowle1437066798e_know @ P) @ (secrecy_sKS @ Secret)))) => ((~ (((knowle1437066798e_know @ Q) @ (secrecy_sKS @ Secret)))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ (secrecy_sE @ Secret))))))))))).
% 3.13/1.87 thf(fact_25_TBtheorem1a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((ine @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((ine @ P) @ E) | ((ine @ Q) @ E)))))))).
% 3.13/1.87 thf(fact_26_TBtheorem3a, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((ine @ P) @ E))) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ E)))))))))).
% 3.13/1.87 thf(fact_27_singletonI, axiom, (! [A:$tType,A3:A]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A))))))).
% 3.13/1.87 thf(fact_28_insertCI, axiom, (! [A:$tType,A3:A,B:(set @ A),B2:A]: ((((~ ((((member @ A) @ A3) @ B))) => (A3 = B2)) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B)))))).
% 3.13/1.87 thf(fact_29_insert__iff, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) = ((A3 = B2) | (((member @ A) @ A3) @ A2)))))).
% 3.13/1.87 thf(fact_30_insert__absorb2, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ X) @ A2)) = (((insert @ A) @ X) @ A2))))).
% 3.13/1.87 thf(fact_31_empty__iff, axiom, (! [A:$tType,C:A]: ((~ ((((member @ A) @ C) @ (bot_bot @ (set @ A)))))))).
% 3.13/1.87 thf(fact_32_all__not__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((! [X3:A]: ((~ ((((member @ A) @ X3) @ A2))))) = (A2 = (bot_bot @ (set @ A))))))).
% 3.13/1.87 thf(fact_33_Collect__empty__eq, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (! [X3:A]: ((~ ((P @ X3))))))))).
% 3.13/1.87 thf(fact_34_empty__Collect__eq, axiom, (! [A:$tType,P:(A > $o)]: ((((bot_bot @ (set @ A)) = ((collect @ A) @ P)) = (! [X3:A]: ((~ ((P @ X3))))))))).
% 3.13/1.87 thf(fact_35_ex__in__conv, axiom, (! [A:$tType,A2:(set @ A)]: (((? [X3:A]: ((((member @ A) @ X3) @ A2))) = (A2 != (bot_bot @ (set @ A))))))).
% 3.13/1.87 thf(fact_36_equals0I, axiom, (! [A:$tType,A2:(set @ A)]: (((! [Y:A]: ((~ ((((member @ A) @ Y) @ A2))))) => (A2 = (bot_bot @ (set @ A))))))).
% 3.13/1.87 thf(fact_37_equals0D, axiom, (! [A:$tType,A2:(set @ A),A3:A]: (((A2 = (bot_bot @ (set @ A))) => (~ ((((member @ A) @ A3) @ A2))))))).
% 3.13/1.87 thf(fact_38_emptyE, axiom, (! [A:$tType,A3:A]: ((~ ((((member @ A) @ A3) @ (bot_bot @ (set @ A)))))))).
% 3.13/1.87 thf(fact_39_mk__disjoint__insert, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => (? [B3:(set @ A)]: (((A2 = (((insert @ A) @ A3) @ B3)) & (~ ((((member @ A) @ A3) @ B3)))))))))).
% 3.13/1.87 thf(fact_40_insert__commute, axiom, (! [A:$tType,X:A,Y3:A,A2:(set @ A)]: (((((insert @ A) @ X) @ (((insert @ A) @ Y3) @ A2)) = (((insert @ A) @ Y3) @ (((insert @ A) @ X) @ A2)))))).
% 3.13/1.87 thf(fact_41_insert__eq__iff, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A,B:(set @ A)]: (((~ ((((member @ A) @ A3) @ A2))) => ((~ ((((member @ A) @ B2) @ B))) => (((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ B)) = (((A3 = B2) => (A2 = B)) & ((A3 != B2) => (? [C2:(set @ A)]: (((A2 = (((insert @ A) @ B2) @ C2)) & ((~ ((((member @ A) @ B2) @ C2))) & ((B = (((insert @ A) @ A3) @ C2)) & (~ ((((member @ A) @ A3) @ C2)))))))))))))))).
% 3.13/1.87 thf(fact_42_insert__absorb, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((member @ A) @ A3) @ A2) => ((((insert @ A) @ A3) @ A2) = A2))))).
% 3.13/1.87 thf(fact_43_insert__ident, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((~ ((((member @ A) @ X) @ B))) => (((((insert @ A) @ X) @ A2) = (((insert @ A) @ X) @ B)) = (A2 = B))))))).
% 3.13/1.87 thf(fact_44_Set_Oset__insert, axiom, (! [A:$tType,X:A,A2:(set @ A)]: (((((member @ A) @ X) @ A2) => (~ ((! [B3:(set @ A)]: (((A2 = (((insert @ A) @ X) @ B3)) => (((member @ A) @ X) @ B3)))))))))).
% 3.13/1.87 thf(fact_45_mem__Collect__eq, axiom, (! [A:$tType,A3:A,P:(A > $o)]: (((((member @ A) @ A3) @ ((collect @ A) @ P)) = (P @ A3))))).
% 3.13/1.87 thf(fact_46_Collect__mem__eq, axiom, (! [A:$tType,A2:(set @ A)]: ((((collect @ A) @ (^ [X3:A]: ((((member @ A) @ X3) @ A2)))) = A2)))).
% 3.13/1.87 thf(fact_47_Collect__cong, axiom, (! [A:$tType,P:(A > $o),Q:(A > $o)]: (((! [X4:A]: (((P @ X4) = (Q @ X4)))) => (((collect @ A) @ P) = ((collect @ A) @ Q)))))).
% 3.13/1.87 thf(fact_48_ext, axiom, (! [B4:$tType,A:$tType,F:(A > B4),G:(A > B4)]: (((! [X4:A]: (((F @ X4) = (G @ X4)))) => (F = G))))).
% 3.13/1.87 thf(fact_49_insertI2, axiom, (! [A:$tType,A3:A,B:(set @ A),B2:A]: (((((member @ A) @ A3) @ B) => (((member @ A) @ A3) @ (((insert @ A) @ B2) @ B)))))).
% 3.13/1.87 thf(fact_50_insertI1, axiom, (! [A:$tType,A3:A,B:(set @ A)]: ((((member @ A) @ A3) @ (((insert @ A) @ A3) @ B))))).
% 3.13/1.87 thf(fact_51_insertE, axiom, (! [A:$tType,A3:A,B2:A,A2:(set @ A)]: (((((member @ A) @ A3) @ (((insert @ A) @ B2) @ A2)) => ((A3 != B2) => (((member @ A) @ A3) @ A2)))))).
% 3.13/1.87 thf(fact_52_singleton__inject, axiom, (! [A:$tType,A3:A,B2:A]: ((((((insert @ A) @ A3) @ (bot_bot @ (set @ A))) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) => (A3 = B2))))).
% 3.13/1.87 thf(fact_53_insert__not__empty, axiom, (! [A:$tType,A3:A,A2:(set @ A)]: (((((insert @ A) @ A3) @ A2) != (bot_bot @ (set @ A)))))).
% 3.13/1.87 thf(fact_54_doubleton__eq__iff, axiom, (! [A:$tType,A3:A,B2:A,C:A,D:A]: ((((((insert @ A) @ A3) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = (((insert @ A) @ C) @ (((insert @ A) @ D) @ (bot_bot @ (set @ A))))) = (((A3 = C) & (B2 = D)) | ((A3 = D) & (B2 = C))))))).
% 3.13/1.87 thf(fact_55_singleton__iff, axiom, (! [A:$tType,B2:A,A3:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) = (B2 = A3))))).
% 3.13/1.87 thf(fact_56_singletonD, axiom, (! [A:$tType,B2:A,A3:A]: (((((member @ A) @ B2) @ (((insert @ A) @ A3) @ (bot_bot @ (set @ A)))) => (B2 = A3))))).
% 3.13/1.87 thf(fact_57_the__elem__eq, axiom, (! [A:$tType,X:A]: ((((the_elem @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = X)))).
% 3.13/1.87 thf(fact_58_bot__apply, axiom, (! [C3:$tType,D2:$tType]: (((bot @ C3) => ((bot_bot @ (D2 > C3)) = (^ [X3:D2]: ((bot_bot @ C3)))))))).
% 3.13/1.87 thf(fact_59_is__singletonI, axiom, (! [A:$tType,X:A]: (((is_singleton @ A) @ (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))).
% 3.13/1.87 thf(fact_60_TBtheorem4a__empty, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E) | ((ine @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (((loc @ PQ) = (bot_bot @ (set @ secrecy_chanID))) => ((ine @ PQ) @ E)))))))).
% 3.13/1.87 thf(fact_61_TBtheorem3b, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((ineM @ P) @ M2) @ E))) => ((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ ((((ineM @ PQ) @ M2) @ E)))))))))).
% 3.13/1.87 thf(fact_62_TBtheorem1b, axiom, (! [PQ:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((ineM @ PQ) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ineM @ P) @ M2) @ E) | (((ineM @ Q) @ M2) @ E)))))))).
% 3.13/1.87 thf(fact_63_Set_Ois__empty__def, axiom, (! [A:$tType]: (((is_empty @ A) = (^ [A4:(set @ A)]: ((A4 = (bot_bot @ (set @ A))))))))).
% 3.13/1.87 thf(fact_64_correctCompositionIn__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ X) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ X) @ (ins @ P)) | (((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))).
% 3.13/1.87 thf(fact_65_correctCompositionIn__L2, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch) @ (ins @ Q))))))))).
% 3.13/1.87 thf(fact_66_bot__set__def, axiom, (! [A:$tType]: (((bot_bot @ (set @ A)) = ((collect @ A) @ (bot_bot @ (A > $o))))))).
% 3.13/1.87 thf(fact_67_ineM__ine, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ineM @ P) @ M2) @ E) => ((ine @ P) @ E))))).
% 3.13/1.87 thf(fact_68_not__ine__ineM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M2:(set @ secrecy_chanID)]: (((~ (((ine @ P) @ E))) => (~ ((((ineM @ P) @ M2) @ E))))))).
% 3.13/1.87 thf(fact_69_is__singleton__the__elem, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((A4 = (((insert @ A) @ ((the_elem @ A) @ A4)) @ (bot_bot @ (set @ A)))))))))).
% 3.13/1.87 thf(fact_70_correctCompositionIn__L1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((member @ secrecy_chanID) @ Ch) @ (ins @ PQ))))))))).
% 3.13/1.87 thf(fact_71_is__singletonI_H, axiom, (! [A:$tType,A2:(set @ A)]: (((A2 != (bot_bot @ (set @ A))) => ((! [X4:A,Y:A]: (((((member @ A) @ X4) @ A2) => ((((member @ A) @ Y) @ A2) => (X4 = Y))))) => ((is_singleton @ A) @ A2)))))).
% 3.13/1.87 thf(fact_72_bot__fun__def, axiom, (! [B4:$tType,A:$tType]: (((bot @ B4) => ((bot_bot @ (A > B4)) = (^ [X3:A]: ((bot_bot @ B4)))))))).
% 3.13/1.87 thf(fact_73_is__singletonE, axiom, (! [A:$tType,A2:(set @ A)]: ((((is_singleton @ A) @ A2) => (~ ((! [X4:A]: ((A2 != (((insert @ A) @ X4) @ (bot_bot @ (set @ A)))))))))))).
% 3.13/1.87 thf(fact_74_is__singleton__def, axiom, (! [A:$tType]: (((is_singleton @ A) = (^ [A4:(set @ A)]: ((? [X3:A]: ((A4 = (((insert @ A) @ X3) @ (bot_bot @ (set @ A)))))))))))).
% 3.13/1.87 thf(fact_75_subcomponents__loc, axiom, (! [X:secrecy_specID]: (((correc965049635ionLoc @ X) => (((subcomponents @ X) = (bot_bot @ (set @ secrecy_specID))) => ((loc @ X) = (bot_bot @ (set @ secrecy_chanID)))))))).
% 3.13/1.87 thf(fact_76_TBtheorem4b__notP1, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ineM @ P) @ M2) @ E) => ((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch2) @ E) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))) => (~ ((((ineM @ PQ) @ M2) @ E))))))))))).
% 3.13/1.87 thf(fact_77_TBtheorem4a__notP1, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((ine @ P) @ E) => ((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((ine_ex1303305700Single @ P) @ Ch2) @ E) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E))))))))))).
% 3.13/1.87 thf(fact_78_TBtheorem4b__notP2, axiom, (! [Q:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSet) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M2) @ E))))))))))).
% 3.13/1.87 thf(fact_79_TBtheorem4b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M2:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetP) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetQ) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ ((((ineM @ PQ) @ M2) @ E)))))))))))).
% 3.13/1.87 thf(fact_80_TBtheorem4a__notP2, axiom, (! [Q:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((ine @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSet) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E))))))))))).
% 3.13/1.87 thf(fact_81_TBtheorem4a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((ine_exprChannelSet @ P) @ ChSetP) @ E) => ((((ine_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetP) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetQ) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ (((ine @ PQ) @ E)))))))))))).
% 3.13/1.87 thf(fact_82_ine__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((ine_ex1303305700Single @ P) @ Ch) @ E) => (((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E))))).
% 3.13/1.87 thf(fact_83_ine__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E) => (((ine_ex1303305700Single @ P) @ Ch) @ E))))).
% 3.13/1.87 thf(fact_84_ine__empty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((ChSet = (bot_bot @ (set @ secrecy_chanID))) => (~ (((ine @ P) @ E)))))))).
% 3.13/1.87 thf(fact_85_ine__nonempty__exprChannelSet, axiom, (! [P:secrecy_specID,ChSet:(set @ secrecy_chanID),E:secrecy_Expression]: (((((ine_exprChannelSet @ P) @ ChSet) @ E) => ((ChSet != (bot_bot @ (set @ secrecy_chanID))) => ((ine @ P) @ E)))))).
% 3.13/1.87 thf(fact_86_locStream__def, axiom, (locStream = (^ [X3:secrecy_specID]: (((^ [Y4:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y4 = Z))) @ (loc @ X3)))))).
% 3.13/1.87 thf(fact_87_inStream__def, axiom, (inStream = (^ [X3:secrecy_specID]: (((^ [Y4:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y4 = Z))) @ (ins @ X3)))))).
% 3.13/1.87 thf(fact_88_TBtheorem4b__PQ, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((ineM @ P) @ M2) @ E) | (((ineM @ Q) @ M2) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (ins @ Q))) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))))))) => (((ineM @ PQ) @ M2) @ E)))))))).
% 3.13/1.87 thf(fact_89_TBtheorem4b__P, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((ineM @ P) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ Q)) & (((exprChannel @ Ch2) @ E) & ((~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch2) @ M2)))))) => (((ineM @ PQ) @ M2) @ E)))))))).
% 3.13/1.87 thf(fact_90_TBtheorem4a__PQ, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((ine @ P) @ E) | ((ine @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (ins @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (ins @ Q))) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E)))))))).
% 3.13/1.87 thf(fact_91_TBtheorem4a__P, axiom, (! [P:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((ine @ P) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (ins @ P)) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((ine @ PQ) @ E)))))))).
% 3.13/1.87 thf(fact_92_ine__def, axiom, (ine = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & ((exprChannel @ Ch3) @ E2)))))))).
% 3.13/1.87 thf(fact_93_ine__ins__neg1, axiom, (! [P:secrecy_specID,M:secrecy_Expression,X:secrecy_chanID]: (((~ (((ine @ P) @ M))) => (((exprChannel @ X) @ M) => (~ ((((member @ secrecy_chanID) @ X) @ (ins @ P))))))))).
% 3.13/1.87 thf(fact_94_ineM__def, axiom, (ineM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & ((((member @ secrecy_chanID) @ Ch3) @ M3) & ((exprChannel @ Ch3) @ E2))))))))).
% 3.13/1.87 thf(fact_95_ineM__L1, axiom, (! [Ch:secrecy_chanID,M2:(set @ secrecy_chanID),P:secrecy_specID,E:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch) @ M2) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ E) => (((ineM @ P) @ M2) @ E))))))).
% 3.13/1.87 thf(fact_96_ine__exprChannelSet__def, axiom, (ine_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet2) => ((((member @ secrecy_chanID) @ X3) @ (ins @ SP)) & ((exprChannel @ X3) @ E2))))) & (! [X3:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X3) @ ChSet2))) & (((member @ secrecy_chanID) @ X3) @ (ins @ SP))) => (~ (((exprChannel @ X3) @ E2))))))))))).
% 3.13/1.87 thf(fact_97_ine__exprChannelSingle__def, axiom, (ine_ex1303305700Single = (^ [SP:secrecy_specID,Ch3:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch3) @ (ins @ SP)) & (((exprChannel @ Ch3) @ E2) & (! [X3:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X3) @ (ins @ SP)) & (X3 != Ch3)) => (~ (((exprChannel @ X3) @ E2)))))))))))).
% 3.13/1.87 thf(fact_98_LocalSecretsComposition__exprChannel__s, axiom, (! [X:secrecy_chanID,Secrets:secrecy_Secrets,P:secrecy_specID,Q:secrecy_specID]: ((((exprChannel @ X) @ (secrecy_sE @ Secrets)) => ((~ (((ine @ P) @ (secrecy_sE @ Secrets)))) => ((~ (((ine @ Q) @ (secrecy_sE @ Secrets)))) => ((~ ((((member @ secrecy_chanID) @ X) @ (ins @ P)))) & (~ ((((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))))).
% 3.13/1.87 thf(fact_99_correctCompositionInLoc__exprChannel, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ch:secrecy_chanID,M:secrecy_Expression]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ M) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ (ins @ PQ)) => (~ (((exprChannel @ X4) @ M)))))) => (((member @ secrecy_chanID) @ Ch) @ (loc @ PQ)))))))))).
% 3.13/1.87 thf(fact_100_TBlemma3b, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((ineM @ P) @ M2) @ E))) => ((~ ((((ineM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ M2) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) => (~ (((exprChannel @ Ch) @ E)))))))))))).
% 3.13/1.87 thf(fact_101_Collect__empty__eq__bot, axiom, (! [A:$tType,P:(A > $o)]: (((((collect @ A) @ P) = (bot_bot @ (set @ A))) = (P = (bot_bot @ (A > $o))))))).
% 3.13/1.87 thf(fact_102_bot__empty__eq, axiom, (! [A:$tType]: (((bot_bot @ (A > $o)) = (^ [X3:A]: ((((member @ A) @ X3) @ (bot_bot @ (set @ A))))))))).
% 3.13/1.87 thf(fact_103_LocalSecretsComposition__neg__loc__s, axiom, (! [Secret:secrecy_Secrets,P:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ P)))) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ P)))) => (~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ P)))))))))).
% 3.13/1.87 thf(fact_104_correctCompositionKS__exprChannel__s__P, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_sE @ Secret))))))))))))).
% 3.13/1.87 thf(fact_105_correctCompositionKS__exprChannel__s__Q, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_sE @ Secret))))))))))))).
% 3.13/1.87 thf(fact_106_correctCompositionKS__negQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))))))))).
% 3.13/1.87 thf(fact_107_correctCompositionKS__negP, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))))))))).
% 3.13/1.87 thf(fact_108_correctCompositionKS__neg1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ))))))))))).
% 3.13/1.87 thf(fact_109_correctCompositionKS__PQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ PQ)) => ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)) | (((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q))))))))).
% 3.13/1.87 thf(fact_110_know__composition2, axiom, (! [M:secrecy_KS,P:secrecy_specID,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ Q)))) => (((knowle1437066798e_know @ Q) @ M) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((correctCompositionKS @ PQ) => ((knowle1437066798e_know @ PQ) @ M)))))))))).
% 3.13/1.87 thf(fact_111_know__composition1, axiom, (! [M:secrecy_KS,P:secrecy_specID,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ Q)))) => (((knowle1437066798e_know @ P) @ M) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((correctCompositionKS @ PQ) => ((knowle1437066798e_know @ PQ) @ M)))))))))).
% 3.13/1.87 thf(fact_112_know__composition, axiom, (! [M:secrecy_KS,P:secrecy_specID,Q:secrecy_specID,PQ:secrecy_specID]: (((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ M) @ (specKeysSecrets @ Q)))) => ((((knowle1437066798e_know @ P) @ M) | ((knowle1437066798e_know @ Q) @ M)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => ((correctCompositionKS @ PQ) => ((knowle1437066798e_know @ PQ) @ M)))))))))).
% 3.13/1.87 thf(fact_113_correctCompositionKS__exprChannel__s__Qex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_sE @ Secret))))))))))))))).
% 3.13/1.87 thf(fact_114_correctCompositionKS__exprChannel__s__Pex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Secret:secrecy_Secrets,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_sE @ Secret)) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Secret)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_sE @ Secret))))))))))))))).
% 3.13/1.87 thf(fact_115_LocalSecretsComposition__neg__s, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,M:secrecy_Secrets]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (specKeysSecrets @ Q)))) => ((~ (((ine @ P) @ (secrecy_sE @ M)))) => ((~ (((ine @ Q) @ (secrecy_sE @ M)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ M)) @ (localSecrets @ PQ))))))))))))))).
% 3.13/1.87 thf(fact_116_correctCompositionKS__exprChannel__k__Qex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_kE @ Key))))))))))))))).
% 3.13/1.87 thf(fact_117_correctCompositionKS__exprChannel__k__Pex, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => (? [Ch4:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch4) @ (ins @ PQ)) & ((exprChannel @ Ch4) @ (secrecy_kE @ Key))))))))))))))).
% 3.13/1.87 thf(fact_118_correctCompositionKS__exprChannel__k__Q, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ Q)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_kE @ Key))))))))))))).
% 3.13/1.87 thf(fact_119_correctCompositionKS__exprChannel__k__P, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Key:secrecy_Keys,Ch:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ PQ)))) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ P)) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ PQ)))) => ((correctCompositionIn @ PQ) => ((((member @ secrecy_chanID) @ Ch) @ (ins @ PQ)) & ((exprChannel @ Ch) @ (secrecy_kE @ Key))))))))))))).
% 3.13/1.87 thf(fact_120_Un__iff, axiom, (! [A:$tType,C:A,A2:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)) = ((((member @ A) @ C) @ A2) | (((member @ A) @ C) @ B)))))).
% 3.13/1.87 thf(fact_121_UnCI, axiom, (! [A:$tType,C:A,B:(set @ A),A2:(set @ A)]: ((((~ ((((member @ A) @ C) @ B))) => (((member @ A) @ C) @ A2)) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 3.13/1.87 thf(fact_122_KS_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kKS @ X1) = (secrecy_kKS @ Y1)) = (X1 = Y1))))).
% 3.13/1.87 thf(fact_123_Expression_Oinject_I1_J, axiom, (! [X1:secrecy_Keys,Y1:secrecy_Keys]: ((((secrecy_kE @ X1) = (secrecy_kE @ Y1)) = (X1 = Y1))))).
% 3.13/1.87 thf(fact_124_Un__empty, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: ((((((sup_sup @ (set @ A)) @ A2) @ B) = (bot_bot @ (set @ A))) = ((A2 = (bot_bot @ (set @ A))) & (B = (bot_bot @ (set @ A)))))))).
% 3.13/1.87 thf(fact_125_Un__insert__left, axiom, (! [A:$tType,A3:A,B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((insert @ A) @ A3) @ B)) @ C4) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 3.13/1.87 thf(fact_126_Un__insert__right, axiom, (! [A:$tType,A2:(set @ A),A3:A,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((insert @ A) @ A3) @ B)) = (((insert @ A) @ A3) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 3.13/1.87 thf(fact_127_not__know__k__not__ine, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: (((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (~ (((ine @ A2) @ (secrecy_kE @ M)))))))).
% 3.13/1.87 thf(fact_128_Un__empty__right, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = A2)))).
% 3.13/1.87 thf(fact_129_Un__empty__left, axiom, (! [A:$tType,B:(set @ A)]: (((((sup_sup @ (set @ A)) @ (bot_bot @ (set @ A))) @ B) = B)))).
% 3.13/1.87 thf(fact_130_KS2Expression_Osimps_I1_J, axiom, (! [M:secrecy_Keys]: (((secrec1016742679ession @ (secrecy_kKS @ M)) = (secrecy_kE @ M))))).
% 3.13/1.87 thf(fact_131_Un__left__commute, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B) @ C4)) = (((sup_sup @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A2) @ C4)))))).
% 3.13/1.87 thf(fact_132_Un__left__absorb, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B)) = (((sup_sup @ (set @ A)) @ A2) @ B))))).
% 3.13/1.87 thf(fact_133_Un__commute, axiom, (! [A:$tType]: (((sup_sup @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: ((((sup_sup @ (set @ A)) @ B5) @ A4))))))).
% 3.13/1.87 thf(fact_134_Un__absorb, axiom, (! [A:$tType,A2:(set @ A)]: (((((sup_sup @ (set @ A)) @ A2) @ A2) = A2)))).
% 3.13/1.87 thf(fact_135_Un__assoc, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((sup_sup @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ C4) = (((sup_sup @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ B) @ C4)))))).
% 3.13/1.87 thf(fact_136_ball__Un, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),P:(A > $o)]: (((! [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A2) @ B)) => (P @ X3)))) = ((! [X3:A]: (((((member @ A) @ X3) @ A2) => (P @ X3)))) & (! [X3:A]: (((((member @ A) @ X3) @ B) => (P @ X3))))))))).
% 3.13/1.87 thf(fact_137_bex__Un, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),P:(A > $o)]: (((? [X3:A]: (((((member @ A) @ X3) @ (((sup_sup @ (set @ A)) @ A2) @ B)) & (P @ X3)))) = ((? [X3:A]: (((((member @ A) @ X3) @ A2) & (P @ X3)))) | (? [X3:A]: (((((member @ A) @ X3) @ B) & (P @ X3))))))))).
% 3.13/1.87 thf(fact_138_UnI2, axiom, (! [A:$tType,C:A,B:(set @ A),A2:(set @ A)]: (((((member @ A) @ C) @ B) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 3.13/1.87 thf(fact_139_UnI1, axiom, (! [A:$tType,C:A,A2:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)))))).
% 3.13/1.87 thf(fact_140_UnE, axiom, (! [A:$tType,C:A,A2:(set @ A),B:(set @ A)]: (((((member @ A) @ C) @ (((sup_sup @ (set @ A)) @ A2) @ B)) => ((~ ((((member @ A) @ C) @ A2))) => (((member @ A) @ C) @ B)))))).
% 3.13/1.87 thf(fact_141_KS_Oexhaust, axiom, (! [Y3:secrecy_KS]: (((! [X12:secrecy_Keys]: ((Y3 != (secrecy_kKS @ X12)))) => (~ ((! [X22:secrecy_Secrets]: ((Y3 != (secrecy_sKS @ X22)))))))))).
% 3.13/1.87 thf(fact_142_KS_Oinduct, axiom, (! [P:(secrecy_KS > $o),KS:secrecy_KS]: (((! [X4:secrecy_Keys]: ((P @ (secrecy_kKS @ X4)))) => ((! [X4:secrecy_Secrets]: ((P @ (secrecy_sKS @ X4)))) => (P @ KS)))))).
% 3.13/1.87 thf(fact_143_KS_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X2:secrecy_Secrets]: (((secrecy_kKS @ X1) != (secrecy_sKS @ X2))))).
% 3.13/1.87 thf(fact_144_Expression_Odistinct_I1_J, axiom, (! [X1:secrecy_Keys,X2:secrecy_Secrets]: (((secrecy_kE @ X1) != (secrecy_sE @ X2))))).
% 3.13/1.87 thf(fact_145_KS_Osimps_I5_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_case_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 3.13/1.87 thf(fact_146_know_Osimps_I1_J, axiom, (! [A2:secrecy_specID,M:secrecy_Keys]: ((((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)) = (((ine @ A2) @ (secrecy_kE @ M)) | (((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (localSecrets @ A2))))))).
% 3.13/1.87 thf(fact_147_KS_Osimps_I7_J, axiom, (! [A:$tType,F1:(secrecy_Keys > A),F2:(secrecy_Secrets > A),X1:secrecy_Keys]: ((((((secrecy_rec_KS @ A) @ F1) @ F2) @ (secrecy_kKS @ X1)) = (F1 @ X1))))).
% 3.13/1.87 thf(fact_148_insert__is__Un, axiom, (! [A:$tType]: (((insert @ A) = (^ [A5:A]: (((sup_sup @ (set @ A)) @ (((insert @ A) @ A5) @ (bot_bot @ (set @ A)))))))))).
% 3.13/1.87 thf(fact_149_Un__singleton__iff, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),X:A]: ((((((sup_sup @ (set @ A)) @ A2) @ B) = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) = (((A2 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 3.13/1.87 thf(fact_150_singleton__Un__iff, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: ((((((insert @ A) @ X) @ (bot_bot @ (set @ A))) = (((sup_sup @ (set @ A)) @ A2) @ B)) = (((A2 = (bot_bot @ (set @ A))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))) | (((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (bot_bot @ (set @ A)))) | ((A2 = (((insert @ A) @ X) @ (bot_bot @ (set @ A)))) & (B = (((insert @ A) @ X) @ (bot_bot @ (set @ A))))))))))).
% 3.13/1.87 thf(fact_151_LocalSecretsComposition__neg__loc__k, axiom, (! [Key:secrecy_Keys,P:secrecy_specID,Ch:secrecy_chanID]: (((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (localSecrets @ P)))) => (((exprChannel @ Ch) @ (secrecy_kE @ Key)) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Key)) @ (specKeysSecrets @ P)))) => (~ ((((member @ secrecy_chanID) @ Ch) @ (loc @ P)))))))))).
% 3.13/1.87 thf(fact_152_LocalSecretsComposition__neg__k, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,M:secrecy_Keys]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (specKeysSecrets @ Q)))) => ((~ (((ine @ P) @ (secrecy_kE @ M)))) => ((~ (((ine @ Q) @ (secrecy_kE @ M)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ M)) @ (localSecrets @ PQ))))))))))))))).
% 3.13/1.87 thf(fact_153_know__composition__neg__ine__k, axiom, (! [P:secrecy_specID,Key:secrecy_Keys,Q:secrecy_specID,PQ:secrecy_specID]: (((~ (((knowle1437066798e_know @ P) @ (secrecy_kKS @ Key)))) => ((~ (((knowle1437066798e_know @ Q) @ (secrecy_kKS @ Key)))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correctCompositionIn @ PQ) => (~ (((ine @ PQ) @ (secrecy_kE @ Key))))))))))).
% 3.13/1.87 thf(fact_154_LocalSecretsComposition__ine1__k, axiom, (! [K:secrecy_Keys,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ Q) @ (secrecy_kE @ K)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ Q)))) => ((ine @ P) @ (secrecy_kE @ K))))))))))).
% 3.13/1.87 thf(fact_155_LocalSecretsComposition__ine2__k, axiom, (! [K:secrecy_Keys,PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID]: (((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ PQ)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_kE @ K)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ K)) @ (localSecrets @ Q)))) => ((ine @ Q) @ (secrecy_kE @ K))))))))))).
% 3.13/1.87 thf(fact_156_LocalSecretsComposition__neg1__k, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Keys:secrecy_Keys]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((~ (((ine @ P) @ (secrecy_kE @ Keys)))) => ((~ (((ine @ Q) @ (secrecy_kE @ Keys)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ Keys)) @ (localSecrets @ PQ))))))))))))).
% 3.13/1.87 thf(fact_157_LocalSecretsComposition__exprChannel__k, axiom, (! [X:secrecy_chanID,Keys:secrecy_Keys,P:secrecy_specID,Q:secrecy_specID]: ((((exprChannel @ X) @ (secrecy_kE @ Keys)) => ((~ (((ine @ P) @ (secrecy_kE @ Keys)))) => ((~ (((ine @ Q) @ (secrecy_kE @ Keys)))) => ((~ ((((member @ secrecy_chanID) @ X) @ (ins @ P)))) & (~ ((((member @ secrecy_chanID) @ X) @ (ins @ Q))))))))))).
% 3.13/1.87 thf(fact_158_LocalSecretsComposition__neg, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((correctCompositionKS @ PQ) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (specKeysSecrets @ Q)))) => ((! [M4:secrecy_Keys]: (((Ks = (secrecy_kKS @ M4)) => ((~ (((ine @ P) @ (secrecy_kE @ M4)))) & (~ (((ine @ Q) @ (secrecy_kE @ M4)))))))) => ((! [M4:secrecy_Secrets]: (((Ks = (secrecy_sKS @ M4)) => ((~ (((ine @ P) @ (secrecy_sE @ M4)))) & (~ (((ine @ Q) @ (secrecy_sE @ M4)))))))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (((sup_sup @ (set @ secrecy_KS)) @ (localSecrets @ P)) @ (localSecrets @ Q))))) => (~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ PQ))))))))))))))).
% 3.13/1.87 thf(fact_159_LocalSecretsComposition__neg1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,Ks:secrecy_KS]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc965049635ionLoc @ PQ) => ((! [M4:secrecy_Keys]: (((Ks = (secrecy_kKS @ M4)) => ((~ (((ine @ P) @ (secrecy_kE @ M4)))) & (~ (((ine @ Q) @ (secrecy_kE @ M4)))))))) => ((! [M4:secrecy_Secrets]: (((Ks = (secrecy_sKS @ M4)) => ((~ (((ine @ P) @ (secrecy_sE @ M4)))) & (~ (((ine @ Q) @ (secrecy_sE @ M4)))))))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ P)))) => ((~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ Q)))) => (~ ((((member @ secrecy_KS) @ Ks) @ (localSecrets @ PQ))))))))))))).
% 3.13/1.87 thf(fact_160_sup__bot__left, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ X) = X))))))).
% 3.13/1.87 thf(fact_161_sup__bot__right, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A]: (((((sup_sup @ A) @ X) @ (bot_bot @ A)) = X))))))).
% 3.13/1.87 thf(fact_162_bot__eq__sup__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y3:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ X) @ Y3)) = ((X = (bot_bot @ A)) & (Y3 = (bot_bot @ A)))))))))).
% 3.13/1.87 thf(fact_163_sup__eq__bot__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [X:A,Y3:A]: ((((((sup_sup @ A) @ X) @ Y3) = (bot_bot @ A)) = ((X = (bot_bot @ A)) & (Y3 = (bot_bot @ A)))))))))).
% 3.13/1.87 thf(fact_164_sup__bot_Oright__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ A3) @ (bot_bot @ A)) = A3))))))).
% 3.13/1.87 thf(fact_165_sup__bot_Oneutr__eq__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B2:A]: ((((bot_bot @ A) = (((sup_sup @ A) @ A3) @ B2)) = ((A3 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 3.13/1.87 thf(fact_166_sup__bot_Oleft__neutral, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A]: (((((sup_sup @ A) @ (bot_bot @ A)) @ A3) = A3))))))).
% 3.13/1.87 thf(fact_167_sup__bot_Oeq__neutr__iff, axiom, (! [A:$tType]: (((bounde1808546759up_bot @ A) => (! [A3:A,B2:A]: ((((((sup_sup @ A) @ A3) @ B2) = (bot_bot @ A)) = ((A3 = (bot_bot @ A)) & (B2 = (bot_bot @ A)))))))))).
% 3.13/1.87 thf(fact_168_ineM__Un1, axiom, (! [P:secrecy_specID,A2:(set @ secrecy_chanID),E:secrecy_Expression,B:(set @ secrecy_chanID)]: (((((ineM @ P) @ A2) @ E) => (((ineM @ P) @ (((sup_sup @ (set @ secrecy_chanID)) @ A2) @ B)) @ E))))).
% 3.13/1.87 thf(fact_169_notSpecKeysSecretsExpr__def, axiom, (notSpe1586871396tsExpr = (^ [P2:secrecy_specID,E3:(list @ secrecy_Expression)]: (((! [X3:secrecy_Keys]: (((((mem @ secrecy_Expression) @ (secrecy_kE @ X3)) @ E3) => (~ ((((member @ secrecy_KS) @ (secrecy_kKS @ X3)) @ (specKeysSecrets @ P2))))))) & (! [Y5:secrecy_Secrets]: (((((mem @ secrecy_Expression) @ (secrecy_sE @ Y5)) @ E3) => (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ Y5)) @ (specKeysSecrets @ P2)))))))))))).
% 3.13/1.87 thf(fact_170_TBtheorem5a__empty, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E) | ((eout @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((loc @ PQ) = (bot_bot @ (set @ secrecy_chanID))) => ((eout @ PQ) @ E)))))))).
% 3.13/1.87 thf(fact_171_correctCompositionKS__subcomp4, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Secrets]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X)) => (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ C4)))))))).
% 3.13/1.87 thf(fact_172_TBtheorem2a, axiom, (! [PQ:secrecy_specID,E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: ((((eout @ PQ) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => (((eout @ P) @ E) | ((eout @ Q) @ E)))))))).
% 3.13/1.87 thf(fact_173_correctCompositionKS__subcomp2, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Secrets]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ C4)) => (? [X4:secrecy_specID]: (((((member @ secrecy_specID) @ X4) @ (subcomponents @ C4)) & (((member @ secrecy_Secrets) @ Xa) @ (specSecrets @ X4))))))))))).
% 3.13/1.87 thf(fact_174_TBtheorem5a__notP1, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((eout @ P) @ E) => ((~ (((eout @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch2) @ E) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E))))))))))).
% 3.13/1.87 thf(fact_175_TBtheorem5a__notP2, axiom, (! [Q:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ (((eout @ Q) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSet) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E))))))))))).
% 3.13/1.87 thf(fact_176_TBtheorem5a__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSetP) @ E) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetP) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetQ) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ (((eout @ PQ) @ E)))))))))))).
% 3.13/1.87 thf(fact_177_out__exprChannelSingle__Set, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((out_ex985543062Single @ P) @ Ch) @ E) => (((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E))))).
% 3.13/1.87 thf(fact_178_out__exprChannelSet__Single, axiom, (! [P:secrecy_specID,Ch:secrecy_chanID,E:secrecy_Expression]: (((((out_exprChannelSet @ P) @ (((insert @ secrecy_chanID) @ Ch) @ (bot_bot @ (set @ secrecy_chanID)))) @ E) => (((out_ex985543062Single @ P) @ Ch) @ E))))).
% 3.13/1.87 thf(fact_179_TBtheorem5b__notPQ, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,ChSetP:(set @ secrecy_chanID),E:secrecy_Expression,ChSetQ:(set @ secrecy_chanID),M2:(set @ secrecy_chanID)]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSetP) @ E) => ((((out_exprChannelSet @ Q) @ ChSetQ) @ E) => ((M2 = (((sup_sup @ (set @ secrecy_chanID)) @ ChSetP) @ ChSetQ)) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetP) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSetQ) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M2) @ E))))))))))))).
% 3.13/1.87 thf(fact_180_eout__know__nonKS__s, axiom, (! [M:secrecy_Secrets,A2:secrecy_specID]: (((~ ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ A2)))) => (((eout @ A2) @ (secrecy_sE @ M)) => (((knowle1667810483orrect @ A2) @ (secrecy_sKS @ M)) => ((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))))))).
% 3.13/1.87 thf(fact_181_eoutKnowCorrect__L1s, axiom, (! [C4:secrecy_specID,M:secrecy_Secrets]: ((((knowle1667810483orrect @ C4) @ (secrecy_sKS @ M)) => (((eout @ C4) @ (secrecy_sE @ M)) => ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_sKS @ M)))))))).
% 3.13/1.87 thf(fact_182_eoutM__eout, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression]: (((((eoutM @ P) @ M2) @ E) => ((eout @ P) @ E))))).
% 3.13/1.87 thf(fact_183_not__eout__eoutM, axiom, (! [P:secrecy_specID,E:secrecy_Expression,M2:(set @ secrecy_chanID)]: (((~ (((eout @ P) @ E))) => (~ ((((eoutM @ P) @ M2) @ E))))))).
% 3.13/1.87 thf(fact_184_TBtheorem2b, axiom, (! [PQ:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,P:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ PQ) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((eoutM @ P) @ M2) @ E) | (((eoutM @ Q) @ M2) @ E)))))))).
% 3.13/1.87 thf(fact_185_TBtheorem5b__notP2, axiom, (! [Q:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,P:secrecy_specID,ChSet:(set @ secrecy_chanID)]: (((~ ((((eoutM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((out_exprChannelSet @ P) @ ChSet) @ E) => ((! [X4:secrecy_chanID]: (((((member @ secrecy_chanID) @ X4) @ ChSet) => (((member @ secrecy_chanID) @ X4) @ (loc @ PQ))))) => (~ ((((eoutM @ PQ) @ M2) @ E))))))))))).
% 3.13/1.87 thf(fact_186_TBtheorem5b__notP1, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eoutM @ P) @ M2) @ E) => ((~ ((((eoutM @ Q) @ M2) @ E))) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((out_ex985543062Single @ P) @ Ch2) @ E) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))) => (~ ((((eoutM @ PQ) @ M2) @ E))))))))))).
% 3.13/1.87 thf(fact_187_eout__know__s, axiom, (! [C4:secrecy_specID,M:secrecy_Secrets]: ((((knowle1667810483orrect @ C4) @ (secrecy_sKS @ M)) = (((eout @ C4) @ (secrecy_sE @ M)) = ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_sKS @ M)))))))).
% 3.13/1.87 thf(fact_188_not__know__s__not__eout, axiom, (! [M:secrecy_Secrets,A2:secrecy_specID]: (((~ ((((member @ secrecy_Secrets) @ M) @ (specSecrets @ A2)))) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (((knowle1667810483orrect @ A2) @ (secrecy_sKS @ M)) => (~ (((eout @ A2) @ (secrecy_sE @ M)))))))))).
% 3.13/1.87 thf(fact_189_TBtheore54b__P, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: (((((eoutM @ P) @ M2) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ Q)) & (((exprChannel @ Ch2) @ E) & ((~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))) & (((member @ secrecy_chanID) @ Ch2) @ M2)))))) => (((eoutM @ PQ) @ M2) @ E)))))))).
% 3.13/1.87 thf(fact_190_TBtheorem5b__PQ, axiom, (! [P:secrecy_specID,M2:(set @ secrecy_chanID),E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: ((((((eoutM @ P) @ M2) @ E) | (((eoutM @ Q) @ M2) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (out @ Q))) & ((((member @ secrecy_chanID) @ Ch2) @ M2) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ))))))))) => (((eoutM @ PQ) @ M2) @ E)))))))).
% 3.13/1.87 thf(fact_191_TBtheorem45a__P, axiom, (! [P:secrecy_specID,E:secrecy_Expression,PQ:secrecy_specID,Q:secrecy_specID]: ((((eout @ P) @ E) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch2) @ (out @ P)) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E)))))))).
% 3.13/1.87 thf(fact_192_eout__def, axiom, (eout = (^ [SP:secrecy_specID,E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & ((exprChannel @ Ch3) @ E2)))))))).
% 3.13/1.87 thf(fact_193_eoutM__def, axiom, (eoutM = (^ [SP:secrecy_specID,M3:(set @ secrecy_chanID),E2:secrecy_Expression]: ((? [Ch3:secrecy_chanID]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & ((((member @ secrecy_chanID) @ Ch3) @ M3) & ((exprChannel @ Ch3) @ E2))))))))).
% 3.13/1.87 thf(fact_194_out__exprChannelSet__def, axiom, (out_exprChannelSet = (^ [SP:secrecy_specID,ChSet2:(set @ secrecy_chanID),E2:secrecy_Expression]: (((! [X3:secrecy_chanID]: (((((member @ secrecy_chanID) @ X3) @ ChSet2) => ((((member @ secrecy_chanID) @ X3) @ (out @ SP)) & ((exprChannel @ X3) @ E2))))) & (! [X3:secrecy_chanID]: ((((~ ((((member @ secrecy_chanID) @ X3) @ ChSet2))) & (((member @ secrecy_chanID) @ X3) @ (out @ SP))) => (~ (((exprChannel @ X3) @ E2))))))))))).
% 3.13/1.87 thf(fact_195_out__exprChannelSingle__def, axiom, (out_ex985543062Single = (^ [SP:secrecy_specID,Ch3:secrecy_chanID,E2:secrecy_Expression]: (((((member @ secrecy_chanID) @ Ch3) @ (out @ SP)) & (((exprChannel @ Ch3) @ E2) & (! [X3:secrecy_chanID,T:nat]: ((((((member @ secrecy_chanID) @ X3) @ (out @ SP)) & (X3 != Ch3)) => (~ (((exprChannel @ X3) @ E2)))))))))))).
% 3.13/1.87 thf(fact_196_correctCompositionOut__prop1, axiom, (! [PQ:secrecy_specID,P:secrecy_specID,Q:secrecy_specID,X:secrecy_chanID]: ((((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((((member @ secrecy_chanID) @ X) @ (out @ PQ)) => ((((member @ secrecy_chanID) @ X) @ (out @ P)) | (((member @ secrecy_chanID) @ X) @ (out @ Q))))))))).
% 3.13/1.87 thf(fact_197_TBtheorem5a__PQ, axiom, (! [P:secrecy_specID,E:secrecy_Expression,Q:secrecy_specID,PQ:secrecy_specID]: (((((eout @ P) @ E) | ((eout @ Q) @ E)) => (((subcomponents @ PQ) = (((insert @ secrecy_specID) @ P) @ (((insert @ secrecy_specID) @ Q) @ (bot_bot @ (set @ secrecy_specID))))) => ((correc990227761ionOut @ PQ) => ((? [Ch2:secrecy_chanID]: ((((((member @ secrecy_chanID) @ Ch2) @ (out @ P)) | (((member @ secrecy_chanID) @ Ch2) @ (out @ Q))) & (((exprChannel @ Ch2) @ E) & (~ ((((member @ secrecy_chanID) @ Ch2) @ (loc @ PQ)))))))) => ((eout @ PQ) @ E)))))))).
% 3.13/1.87 thf(fact_198_outStream__def, axiom, (outStream = (^ [X3:secrecy_specID]: (((^ [Y4:(set @ secrecy_chanID),Z:(set @ secrecy_chanID)]: ((Y4 = Z))) @ (out @ X3)))))).
% 3.13/1.87 thf(fact_199_eout__know__k, axiom, (! [C4:secrecy_specID,M:secrecy_Keys]: ((((knowle1667810483orrect @ C4) @ (secrecy_kKS @ M)) = (((eout @ C4) @ (secrecy_kE @ M)) = ((((member @ secrecy_Keys) @ M) @ (specKeys @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_kKS @ M)))))))).
% 3.13/1.87 thf(fact_200_correctCompositionKS__subcomp1, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Keys]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xa) @ (specKeys @ C4)) => (? [X4:secrecy_specID]: (((((member @ secrecy_specID) @ X4) @ (subcomponents @ C4)) & (((member @ secrecy_Keys) @ Xa) @ (specKeys @ X4))))))))))).
% 3.13/1.87 thf(fact_201_correctCompositionKS__subcomp3, axiom, (! [C4:secrecy_specID,X:secrecy_specID,Xa:secrecy_Keys]: (((correctCompositionKS @ C4) => ((((member @ secrecy_specID) @ X) @ (subcomponents @ C4)) => ((((member @ secrecy_Keys) @ Xa) @ (specKeys @ X)) => (((member @ secrecy_Keys) @ Xa) @ (specKeys @ C4)))))))).
% 3.13/1.87 thf(fact_202_eout__know__nonKS__k, axiom, (! [M:secrecy_Keys,A2:secrecy_specID]: (((~ ((((member @ secrecy_Keys) @ M) @ (specKeys @ A2)))) => (((eout @ A2) @ (secrecy_kE @ M)) => (((knowle1667810483orrect @ A2) @ (secrecy_kKS @ M)) => ((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))))))).
% 3.13/1.87 thf(fact_203_eoutKnowCorrect__L1k, axiom, (! [C4:secrecy_specID,M:secrecy_Keys]: ((((knowle1667810483orrect @ C4) @ (secrecy_kKS @ M)) => (((eout @ C4) @ (secrecy_kE @ M)) => ((((member @ secrecy_Keys) @ M) @ (specKeys @ C4)) | ((knowle1437066798e_know @ C4) @ (secrecy_kKS @ M)))))))).
% 3.13/1.87 thf(fact_204_not__know__k__not__eout, axiom, (! [M:secrecy_Keys,A2:secrecy_specID]: (((~ ((((member @ secrecy_Keys) @ M) @ (specKeys @ A2)))) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (((knowle1667810483orrect @ A2) @ (secrecy_kKS @ M)) => (~ (((eout @ A2) @ (secrecy_kE @ M)))))))))).
% 3.13/1.87 thf(fact_205_adv__not__know2, axiom, (! [P:secrecy_specID,A2:secrecy_specID,M:secrecy_Secrets]: (((((ord_less_eq @ (set @ secrecy_chanID)) @ (out @ P)) @ (ins @ A2)) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_sKS @ M)))) => (~ (((eout @ P) @ (secrecy_sE @ M))))))))).
% 3.13/1.87 thf(fact_206_adv__not__know1, axiom, (! [P:secrecy_specID,A2:secrecy_specID,M:secrecy_Keys]: (((((ord_less_eq @ (set @ secrecy_chanID)) @ (out @ P)) @ (ins @ A2)) => ((~ (((knowle1437066798e_know @ A2) @ (secrecy_kKS @ M)))) => (~ (((eout @ P) @ (secrecy_kE @ M))))))))).
% 3.13/1.87 thf(fact_207_order__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A]: ((((ord_less_eq @ A) @ X) @ X))))))).
% 3.13/1.87 thf(fact_208_subsetI, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((! [X4:A]: (((((member @ A) @ X4) @ A2) => (((member @ A) @ X4) @ B)))) => (((ord_less_eq @ (set @ A)) @ A2) @ B))))).
% 3.13/1.87 thf(fact_209_subset__antisym, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((ord_less_eq @ (set @ A)) @ B) @ A2) => (A2 = B)))))).
% 3.13/1.87 thf(fact_210_subset__empty, axiom, (! [A:$tType,A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ (bot_bot @ (set @ A))) = (A2 = (bot_bot @ (set @ A))))))).
% 3.13/1.87 thf(fact_211_empty__subsetI, axiom, (! [A:$tType,A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ (bot_bot @ (set @ A))) @ A2)))).
% 3.13/1.87 thf(fact_212_insert__subset, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((insert @ A) @ X) @ A2)) @ B) = ((((member @ A) @ X) @ B) & (((ord_less_eq @ (set @ A)) @ A2) @ B)))))).
% 3.13/1.87 thf(fact_213_Un__subset__iff, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C4:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ C4) = ((((ord_less_eq @ (set @ A)) @ A2) @ C4) & (((ord_less_eq @ (set @ A)) @ B) @ C4)))))).
% 3.13/1.87 thf(fact_214_singleton__insert__inj__eq_H, axiom, (! [A:$tType,A3:A,A2:(set @ A),B2:A]: ((((((insert @ A) @ A3) @ A2) = (((insert @ A) @ B2) @ (bot_bot @ (set @ A)))) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 3.13/1.87 thf(fact_215_singleton__insert__inj__eq, axiom, (! [A:$tType,B2:A,A3:A,A2:(set @ A)]: ((((((insert @ A) @ B2) @ (bot_bot @ (set @ A))) = (((insert @ A) @ A3) @ A2)) = ((A3 = B2) & (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ (bot_bot @ (set @ A))))))))).
% 3.13/1.87 thf(fact_216_subset__Un__eq, axiom, (! [A:$tType]: (((ord_less_eq @ (set @ A)) = (^ [A4:(set @ A),B5:(set @ A)]: (((((sup_sup @ (set @ A)) @ A4) @ B5) = B5))))))).
% 3.13/1.87 thf(fact_217_subset__UnE, axiom, (! [A:$tType,C4:(set @ A),A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ C4) @ (((sup_sup @ (set @ A)) @ A2) @ B)) => (~ ((! [A6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A6) @ A2) => (! [B6:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B6) @ B) => (C4 != (((sup_sup @ (set @ A)) @ A6) @ B6)))))))))))))).
% 3.13/1.87 thf(fact_218_Un__absorb2, axiom, (! [A:$tType,B:(set @ A),A2:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ B) @ A2) => ((((sup_sup @ (set @ A)) @ A2) @ B) = A2))))).
% 3.13/1.87 thf(fact_219_Un__absorb1, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((sup_sup @ (set @ A)) @ A2) @ B) = B))))).
% 3.13/1.87 thf(fact_220_Un__upper2, axiom, (! [A:$tType,B:(set @ A),A2:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ B) @ (((sup_sup @ (set @ A)) @ A2) @ B))))).
% 3.13/1.87 thf(fact_221_Un__upper1, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A)]: ((((ord_less_eq @ (set @ A)) @ A2) @ (((sup_sup @ (set @ A)) @ A2) @ B))))).
% 3.13/1.87 thf(fact_222_Un__least, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ C4) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ C4)))))).
% 3.13/1.87 thf(fact_223_Un__mono, axiom, (! [A:$tType,A2:(set @ A),C4:(set @ A),B:(set @ A),D3:(set @ A)]: (((((ord_less_eq @ (set @ A)) @ A2) @ C4) => ((((ord_less_eq @ (set @ A)) @ B) @ D3) => (((ord_less_eq @ (set @ A)) @ (((sup_sup @ (set @ A)) @ A2) @ B)) @ (((sup_sup @ (set @ A)) @ C4) @ D3))))))).
% 3.13/1.87 thf(fact_224_insert__mono, axiom, (! [A:$tType,C4:(set @ A),D3:(set @ A),A3:A]: (((((ord_less_eq @ (set @ A)) @ C4) @ D3) => (((ord_less_eq @ (set @ A)) @ (((insert @ A) @ A3) @ C4)) @ (((insert @ A) @ A3) @ D3)))))).
% 3.13/1.87 thf(fact_225_subset__insert, axiom, (! [A:$tType,X:A,A2:(set @ A),B:(set @ A)]: (((~ ((((member @ A) @ X) @ A2))) => ((((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ X) @ B)) = (((ord_less_eq @ (set @ A)) @ A2) @ B)))))).
% 3.13/1.87 thf(fact_226_subset__insertI, axiom, (! [A:$tType,B:(set @ A),A3:A]: ((((ord_less_eq @ (set @ A)) @ B) @ (((insert @ A) @ A3) @ B))))).
% 3.13/1.87 thf(fact_227_subset__insertI2, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),B2:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => (((ord_less_eq @ (set @ A)) @ A2) @ (((insert @ A) @ B2) @ B)))))).
% 3.13/1.87 thf(fact_228_le__funD, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => (! [F:(A > B4),G:(A > B4),X:A]: (((((ord_less_eq @ (A > B4)) @ F) @ G) => (((ord_less_eq @ B4) @ (F @ X)) @ (G @ X))))))))).
% 3.13/1.87 thf(fact_229_le__funE, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => (! [F:(A > B4),G:(A > B4),X:A]: (((((ord_less_eq @ (A > B4)) @ F) @ G) => (((ord_less_eq @ B4) @ (F @ X)) @ (G @ X))))))))).
% 3.13/1.87 thf(fact_230_le__funI, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => (! [F:(A > B4),G:(A > B4)]: (((! [X4:A]: ((((ord_less_eq @ B4) @ (F @ X4)) @ (G @ X4)))) => (((ord_less_eq @ (A > B4)) @ F) @ G)))))))).
% 3.13/1.87 thf(fact_231_le__fun__def, axiom, (! [B4:$tType,A:$tType]: (((ord @ B4) => ((ord_less_eq @ (A > B4)) = (^ [F3:(A > B4),G2:(A > B4)]: ((! [X3:A]: ((((ord_less_eq @ B4) @ (F3 @ X3)) @ (G2 @ X3))))))))))).
% 3.13/1.87 thf(fact_232_order__subst1, axiom, (! [A:$tType,B4:$tType]: ((((order @ B4) & (order @ A)) => (! [A3:A,F:(B4 > A),B2:B4,C:B4]: (((((ord_less_eq @ A) @ A3) @ (F @ B2)) => ((((ord_less_eq @ B4) @ B2) @ C) => ((! [X4:B4,Y:B4]: (((((ord_less_eq @ B4) @ X4) @ Y) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y))))) => (((ord_less_eq @ A) @ A3) @ (F @ C))))))))))).
% 3.13/1.87 thf(fact_233_order__subst2, axiom, (! [A:$tType,C3:$tType]: ((((order @ C3) & (order @ A)) => (! [A3:A,B2:A,F:(A > C3),C:C3]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ C3) @ (F @ B2)) @ C) => ((! [X4:A,Y:A]: (((((ord_less_eq @ A) @ X4) @ Y) => (((ord_less_eq @ C3) @ (F @ X4)) @ (F @ Y))))) => (((ord_less_eq @ C3) @ (F @ A3)) @ C)))))))))).
% 3.13/1.87 thf(fact_234_ord__eq__le__subst, axiom, (! [A:$tType,B4:$tType]: ((((ord @ B4) & (ord @ A)) => (! [A3:A,F:(B4 > A),B2:B4,C:B4]: (((A3 = (F @ B2)) => ((((ord_less_eq @ B4) @ B2) @ C) => ((! [X4:B4,Y:B4]: (((((ord_less_eq @ B4) @ X4) @ Y) => (((ord_less_eq @ A) @ (F @ X4)) @ (F @ Y))))) => (((ord_less_eq @ A) @ A3) @ (F @ C))))))))))).
% 3.13/1.87 thf(fact_235_ord__le__eq__subst, axiom, (! [A:$tType,B4:$tType]: ((((ord @ B4) & (ord @ A)) => (! [A3:A,B2:A,F:(A > B4),C:B4]: (((((ord_less_eq @ A) @ A3) @ B2) => (((F @ B2) = C) => ((! [X4:A,Y:A]: (((((ord_less_eq @ A) @ X4) @ Y) => (((ord_less_eq @ B4) @ (F @ X4)) @ (F @ Y))))) => (((ord_less_eq @ B4) @ (F @ A3)) @ C)))))))))).
% 3.13/1.87 thf(fact_236_eq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [X3:A,Y5:A]: (((((ord_less_eq @ A) @ X3) @ Y5) & (((ord_less_eq @ A) @ Y5) @ X3))))))))).
% 3.13/1.87 thf(fact_237_antisym, axiom, (! [A:$tType]: (((order @ A) => (! [X:A,Y3:A]: (((((ord_less_eq @ A) @ X) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ X) => (X = Y3))))))))).
% 3.13/1.87 thf(fact_238_linear, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y3:A]: (((((ord_less_eq @ A) @ X) @ Y3) | (((ord_less_eq @ A) @ Y3) @ X)))))))).
% 3.13/1.87 thf(fact_239_eq__refl, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y3:A]: (((X = Y3) => (((ord_less_eq @ A) @ X) @ Y3)))))))).
% 3.13/1.87 thf(fact_240_le__cases, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y3:A]: (((~ ((((ord_less_eq @ A) @ X) @ Y3))) => (((ord_less_eq @ A) @ Y3) @ X)))))))).
% 3.13/1.87 thf(fact_241_order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 3.13/1.87 thf(fact_242_le__cases3, axiom, (! [A:$tType]: (((linorder @ A) => (! [X:A,Y3:A,Z2:A]: ((((((ord_less_eq @ A) @ X) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ Z2)))) => (((((ord_less_eq @ A) @ Y3) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Z2)))) => (((((ord_less_eq @ A) @ X) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ Y3)))) => (((((ord_less_eq @ A) @ Z2) @ Y3) => (~ ((((ord_less_eq @ A) @ Y3) @ X)))) => (((((ord_less_eq @ A) @ Y3) @ Z2) => (~ ((((ord_less_eq @ A) @ Z2) @ X)))) => (~ (((((ord_less_eq @ A) @ Z2) @ X) => (~ ((((ord_less_eq @ A) @ X) @ Y3))))))))))))))))).
% 3.13/1.87 thf(fact_243_antisym__conv, axiom, (! [A:$tType]: (((order @ A) => (! [Y3:A,X:A]: (((((ord_less_eq @ A) @ Y3) @ X) => ((((ord_less_eq @ A) @ X) @ Y3) = (X = Y3))))))))).
% 3.13/1.87 thf(fact_244_order__class_Oorder_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ A5) @ B7) & (((ord_less_eq @ A) @ B7) @ A5))))))))).
% 3.13/1.87 thf(fact_245_ord__eq__le__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B2:A,C:A]: (((A3 = B2) => ((((ord_less_eq @ A) @ B2) @ C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 3.13/1.87 thf(fact_246_ord__le__eq__trans, axiom, (! [A:$tType]: (((ord @ A) => (! [A3:A,B2:A,C:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((B2 = C) => (((ord_less_eq @ A) @ A3) @ C))))))))).
% 3.13/1.87 thf(fact_247_order__class_Oorder_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A,B2:A]: (((((ord_less_eq @ A) @ A3) @ B2) => ((((ord_less_eq @ A) @ B2) @ A3) => (A3 = B2))))))))).
% 3.13/1.87 thf(fact_248_order__trans, axiom, (! [A:$tType]: (((preorder @ A) => (! [X:A,Y3:A,Z2:A]: (((((ord_less_eq @ A) @ X) @ Y3) => ((((ord_less_eq @ A) @ Y3) @ Z2) => (((ord_less_eq @ A) @ X) @ Z2))))))))).
% 3.13/1.87 thf(fact_249_dual__order_Orefl, axiom, (! [A:$tType]: (((order @ A) => (! [A3:A]: ((((ord_less_eq @ A) @ A3) @ A3))))))).
% 3.13/1.87 thf(fact_250_linorder__wlog, axiom, (! [A:$tType]: (((linorder @ A) => (! [P:(A > (A > $o)),A3:A,B2:A]: (((! [A7:A,B8:A]: (((((ord_less_eq @ A) @ A7) @ B8) => ((P @ A7) @ B8)))) => ((! [A7:A,B8:A]: ((((P @ B8) @ A7) => ((P @ A7) @ B8)))) => ((P @ A3) @ B2))))))))).
% 3.13/1.87 thf(fact_251_dual__order_Otrans, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A,C:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ C) @ B2) => (((ord_less_eq @ A) @ C) @ A3))))))))).
% 3.13/1.87 thf(fact_252_dual__order_Oeq__iff, axiom, (! [A:$tType]: (((order @ A) => ((^ [Y4:A,Z:A]: ((Y4 = Z))) = (^ [A5:A,B7:A]: (((((ord_less_eq @ A) @ B7) @ A5) & (((ord_less_eq @ A) @ A5) @ B7))))))))).
% 3.13/1.87 thf(fact_253_dual__order_Oantisym, axiom, (! [A:$tType]: (((order @ A) => (! [B2:A,A3:A]: (((((ord_less_eq @ A) @ B2) @ A3) => ((((ord_less_eq @ A) @ A3) @ B2) => (A3 = B2))))))))).
% 3.13/1.87 thf(fact_254_in__mono, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),X:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((member @ A) @ X) @ A2) => (((member @ A) @ X) @ B)))))).
% 3.13/1.87 thf(fact_255_subsetD, axiom, (! [A:$tType,A2:(set @ A),B:(set @ A),C:A]: (((((ord_less_eq @ (set @ A)) @ A2) @ B) => ((((member @ A) @ C) @ A2) => (((member @ A) @ C) @ B)))))).
% 3.13/1.87 thf(tcon_HOL_Obool___Lattices_Obounded__lattice, axiom, (bounded_lattice @ $o)).
% 3.13/1.87 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1, axiom, (! [A8:$tType]: ((bounded_lattice @ (set @ A8))))).
% 3.13/1.87 thf(tcon_fun___Lattices_Obounded__lattice_2, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounded_lattice @ (A8 > A9)))))).
% 3.13/1.87 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot, axiom, (! [A8:$tType,A9:$tType]: (((bounded_lattice @ A9) => (bounde1808546759up_bot @ (A8 > A9)))))).
% 3.13/1.87 thf(tcon_fun___Orderings_Opreorder, axiom, (! [A8:$tType,A9:$tType]: (((preorder @ A9) => (preorder @ (A8 > A9)))))).
% 3.13/1.87 thf(tcon_fun___Orderings_Oorder, axiom, (! [A8:$tType,A9:$tType]: (((order @ A9) => (order @ (A8 > A9)))))).
% 3.13/1.87 thf(tcon_fun___Orderings_Oord, axiom, (! [A8:$tType,A9:$tType]: (((ord @ A9) => (ord @ (A8 > A9)))))).
% 3.13/1.87 thf(tcon_fun___Orderings_Obot, axiom, (! [A8:$tType,A9:$tType]: (((bot @ A9) => (bot @ (A8 > A9)))))).
% 3.13/1.87 thf(tcon_Nat_Onat___Orderings_Opreorder_3, axiom, (preorder @ nat)).
% 3.13/1.87 thf(tcon_Nat_Onat___Orderings_Olinorder, axiom, (linorder @ nat)).
% 3.13/1.87 thf(tcon_Nat_Onat___Orderings_Oorder_4, axiom, (order @ nat)).
% 3.13/1.87 thf(tcon_Nat_Onat___Orderings_Oord_5, axiom, (ord @ nat)).
% 3.13/1.87 thf(tcon_Nat_Onat___Orderings_Obot_6, axiom, (bot @ nat)).
% 3.13/1.87 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7, axiom, (! [A8:$tType]: ((bounde1808546759up_bot @ (set @ A8))))).
% 3.13/1.87 thf(tcon_Set_Oset___Orderings_Opreorder_8, axiom, (! [A8:$tType]: ((preorder @ (set @ A8))))).
% 3.13/1.87 thf(tcon_Set_Oset___Orderings_Oorder_9, axiom, (! [A8:$tType]: ((order @ (set @ A8))))).
% 3.13/1.87 thf(tcon_Set_Oset___Orderings_Oord_10, axiom, (! [A8:$tType]: ((ord @ (set @ A8))))).
% 3.13/1.87 thf(tcon_Set_Oset___Orderings_Obot_11, axiom, (! [A8:$tType]: ((bot @ (set @ A8))))).
% 3.13/1.87 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12, axiom, (bounde1808546759up_bot @ $o)).
% 3.13/1.87 thf(tcon_HOL_Obool___Orderings_Opreorder_13, axiom, (preorder @ $o)).
% 3.13/1.87 thf(tcon_HOL_Obool___Orderings_Olinorder_14, axiom, (linorder @ $o)).
% 3.13/1.87 thf(tcon_HOL_Obool___Orderings_Oorder_15, axiom, (order @ $o)).
% 3.13/1.87 thf(tcon_HOL_Obool___Orderings_Oord_16, axiom, (ord @ $o)).
% 3.13/1.87 thf(tcon_HOL_Obool___Orderings_Obot_17, axiom, (bot @ $o)).
% 3.13/1.87 thf(conj_0, conjecture, (~ ((((member @ secrecy_KS) @ (secrecy_sKS @ secret)) @ (localSecrets @ pq))))).
% 3.13/1.87 % SZS output end ListOfTHF for /export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2DTF3672.p
% 3.13/1.87 ------------------------
% 3.28/1.90 ---- Cleaned THF ---
% 3.28/1.90 thf(ty_t_Secrecy__types_OExpression,type,
% 3.28/1.90 secrecy_Expression: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Secrecy__types_OSecrets,type,
% 3.28/1.90 secrecy_Secrets: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Secrecy__types_OspecID,type,
% 3.28/1.90 secrecy_specID: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Secrecy__types_OchanID,type,
% 3.28/1.90 secrecy_chanID: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Secrecy__types_OKeys,type,
% 3.28/1.90 secrecy_Keys: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Secrecy__types_OKS,type,
% 3.28/1.90 secrecy_KS: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_List_Olist,type,
% 3.28/1.90 list: $tType > $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Set_Oset,type,
% 3.28/1.90 set: $tType > $tType ).
% 3.28/1.90
% 3.28/1.90 thf(ty_t_Nat_Onat,type,
% 3.28/1.90 nat: $tType ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Lattices_Obounded__lattice,type,
% 3.28/1.90 bounded_lattice:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_HOL_Otype,type,
% 3.28/1.90 type:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Orderings_Obot,type,
% 3.28/1.90 bot:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Orderings_Oord,type,
% 3.28/1.90 ord:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Orderings_Oorder,type,
% 3.28/1.90 order:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Orderings_Olinorder,type,
% 3.28/1.90 linorder:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Orderings_Opreorder,type,
% 3.28/1.90 preorder:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_cl_Lattices_Obounded__semilattice__sup__bot,type,
% 3.28/1.90 bounde1808546759up_bot:
% 3.28/1.90 !>[A: $tType] : $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_CompLocalSecrets_OLocalSecrets,type,
% 3.28/1.90 localSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_OeoutKnowCorrect,type,
% 3.28/1.90 knowle1667810483orrect: secrecy_specID > secrecy_KS > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_KnowledgeKeysSecrets__Mirabelle__khazhniute_Oknow,type,
% 3.28/1.90 knowle1437066798e_know: secrecy_specID > secrecy_KS > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Lattices_Osup__class_Osup,type,
% 3.28/1.90 sup_sup:
% 3.28/1.90 !>[A: $tType] : ( A > A > A ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_ListExtras_Omem,type,
% 3.28/1.90 mem:
% 3.28/1.90 !>[A: $tType] : ( A > ( list @ A ) > $o ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Orderings_Obot__class_Obot,type,
% 3.28/1.90 bot_bot:
% 3.28/1.90 !>[A: $tType] : A ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Orderings_Oord__class_Oless__eq,type,
% 3.28/1.90 ord_less_eq:
% 3.28/1.90 !>[A: $tType] : ( A > A > $o ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OcorrectCompositionKS,type,
% 3.28/1.90 correctCompositionKS: secrecy_specID > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_Oeout,type,
% 3.28/1.90 eout: secrecy_specID > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OeoutM,type,
% 3.28/1.90 eoutM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OexprChannel,type,
% 3.28/1.90 exprChannel: secrecy_chanID > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_Oine,type,
% 3.28/1.90 ine: secrecy_specID > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OineM,type,
% 3.28/1.90 ineM: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_Oine__exprChannelSet,type,
% 3.28/1.90 ine_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_Oine__exprChannelSingle,type,
% 3.28/1.90 ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OnotSpecKeysSecretsExpr,type,
% 3.28/1.90 notSpe1586871396tsExpr: secrecy_specID > ( list @ secrecy_Expression ) > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_Oout__exprChannelSet,type,
% 3.28/1.90 out_exprChannelSet: secrecy_specID > ( set @ secrecy_chanID ) > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_Oout__exprChannelSingle,type,
% 3.28/1.90 out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OspecKeys,type,
% 3.28/1.90 specKeys: secrecy_specID > ( set @ secrecy_Keys ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OspecKeysSecrets,type,
% 3.28/1.90 specKeysSecrets: secrecy_specID > ( set @ secrecy_KS ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy_OspecSecrets,type,
% 3.28/1.90 specSecrets: secrecy_specID > ( set @ secrecy_Secrets ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OExpression_OkE,type,
% 3.28/1.90 secrecy_kE: secrecy_Keys > secrecy_Expression ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OExpression_OsE,type,
% 3.28/1.90 secrecy_sE: secrecy_Secrets > secrecy_Expression ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OKS2Expression,type,
% 3.28/1.90 secrec1016742679ession: secrecy_KS > secrecy_Expression ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OKS_Ocase__KS,type,
% 3.28/1.90 secrecy_case_KS:
% 3.28/1.90 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OKS_OkKS,type,
% 3.28/1.90 secrecy_kKS: secrecy_Keys > secrecy_KS ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OKS_Orec__KS,type,
% 3.28/1.90 secrecy_rec_KS:
% 3.28/1.90 !>[A: $tType] : ( ( secrecy_Keys > A ) > ( secrecy_Secrets > A ) > secrecy_KS > A ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Secrecy__types_OKS_OsKS,type,
% 3.28/1.90 secrecy_sKS: secrecy_Secrets > secrecy_KS ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Set_OCollect,type,
% 3.28/1.90 collect:
% 3.28/1.90 !>[A: $tType] : ( ( A > $o ) > ( set @ A ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Set_Oinsert,type,
% 3.28/1.90 insert:
% 3.28/1.90 !>[A: $tType] : ( A > ( set @ A ) > ( set @ A ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Set_Ois__empty,type,
% 3.28/1.90 is_empty:
% 3.28/1.90 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Set_Ois__singleton,type,
% 3.28/1.90 is_singleton:
% 3.28/1.90 !>[A: $tType] : ( ( set @ A ) > $o ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_Set_Othe__elem,type,
% 3.28/1.90 the_elem:
% 3.28/1.90 !>[A: $tType] : ( ( set @ A ) > A ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_OcorrectCompositionIn,type,
% 3.28/1.90 correctCompositionIn: secrecy_specID > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_OcorrectCompositionLoc,type,
% 3.28/1.90 correc965049635ionLoc: secrecy_specID > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_OcorrectCompositionOut,type,
% 3.28/1.90 correc990227761ionOut: secrecy_specID > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_OinStream,type,
% 3.28/1.90 inStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_Oins,type,
% 3.28/1.90 ins: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_Oloc,type,
% 3.28/1.90 loc: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_OlocStream,type,
% 3.28/1.90 locStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_Oout,type,
% 3.28/1.90 out: secrecy_specID > ( set @ secrecy_chanID ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_OoutStream,type,
% 3.28/1.90 outStream: secrecy_specID > ( set @ secrecy_chanID ) > $o ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_inout_Osubcomponents,type,
% 3.28/1.90 subcomponents: secrecy_specID > ( set @ secrecy_specID ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_c_member,type,
% 3.28/1.90 member:
% 3.28/1.90 !>[A: $tType] : ( A > ( set @ A ) > $o ) ).
% 3.28/1.90
% 3.28/1.90 thf(sy_v_P,type,
% 3.28/1.90 p: secrecy_specID ).
% 3.28/1.90
% 3.28/1.90 thf(sy_v_PQ,type,
% 3.28/1.90 pq: secrecy_specID ).
% 3.28/1.90
% 3.28/1.90 thf(sy_v_Q,type,
% 3.28/1.90 q: secrecy_specID ).
% 3.28/1.90
% 3.28/1.90 thf(sy_v_m,type,
% 3.28/1.90 m: secrecy_KS ).
% 3.28/1.90
% 3.28/1.90 thf(sy_v_secret____,type,
% 3.28/1.90 secret: secrecy_Secrets ).
% 3.28/1.90
% 3.28/1.90 thf(fact_0_cCompLoc,axiom,
% 3.28/1.90 correc965049635ionLoc @ pq ).
% 3.28/1.90
% 3.28/1.90 thf(fact_1_sg1a,axiom,
% 3.28/1.90 ~ ( ine @ p @ ( secrecy_sE @ secret ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_2_sg2a,axiom,
% 3.28/1.90 ~ ( ine @ q @ ( secrecy_sE @ secret ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_3_sg1b,axiom,
% 3.28/1.90 ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ p ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_4_sg2b,axiom,
% 3.28/1.90 ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ q ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_5_subPQ,axiom,
% 3.28/1.90 ( ( subcomponents @ pq )
% 3.28/1.90 = ( insert @ secrecy_specID @ p @ ( insert @ secrecy_specID @ q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_6_a2,axiom,
% 3.28/1.90 ( m
% 3.28/1.90 = ( secrecy_sKS @ secret ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_7_cCompI,axiom,
% 3.28/1.90 correctCompositionIn @ pq ).
% 3.28/1.90
% 3.28/1.90 thf(fact_8_sg3,axiom,
% 3.28/1.90 ~ ( ine @ pq @ ( secrecy_sE @ secret ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_9_KS_Oinject_I2_J,axiom,
% 3.28/1.90 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 3.28/1.90 ( ( ( secrecy_sKS @ X2 )
% 3.28/1.90 = ( secrecy_sKS @ Y2 ) )
% 3.28/1.90 = ( X2 = Y2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_10_sg1,axiom,
% 3.28/1.90 ~ ( knowle1437066798e_know @ p @ ( secrecy_sKS @ secret ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_11_sg2,axiom,
% 3.28/1.90 ~ ( knowle1437066798e_know @ q @ ( secrecy_sKS @ secret ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_12_know_Osimps_I2_J,axiom,
% 3.28/1.90 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 3.28/1.90 ( ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.28/1.90 = ( ( ine @ A2 @ ( secrecy_sE @ M ) )
% 3.28/1.90 | ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_13_KS_Osimps_I8_J,axiom,
% 3.28/1.90 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 3.28/1.90 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 3.28/1.90 = ( F2 @ X2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_14_KS_Osimps_I6_J,axiom,
% 3.28/1.90 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X2: secrecy_Secrets] :
% 3.28/1.90 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_sKS @ X2 ) )
% 3.28/1.90 = ( F2 @ X2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_15_LocalSecretsComposition__ine1__s,axiom,
% 3.28/1.90 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.90 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.28/1.90 => ( ine @ P @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_16_LocalSecretsComposition__ine2__s,axiom,
% 3.28/1.90 ! [S: secrecy_Secrets,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.90 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.28/1.90 => ( ine @ Q @ ( secrecy_sE @ S ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_17_LocalSecretsComposition__neg1__s,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,S: secrecy_Secrets] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.90 => ( ~ ( ine @ P @ ( secrecy_sE @ S ) )
% 3.28/1.90 => ( ~ ( ine @ Q @ ( secrecy_sE @ S ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ Q ) )
% 3.28/1.90 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ S ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_18_KS2Expression_Osimps_I2_J,axiom,
% 3.28/1.90 ! [M: secrecy_Secrets] :
% 3.28/1.90 ( ( secrec1016742679ession @ ( secrecy_sKS @ M ) )
% 3.28/1.90 = ( secrecy_sE @ M ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_19_LocalSecretsComposition1,axiom,
% 3.28/1.90 ! [Ls: secrecy_KS,P: secrecy_specID,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( member @ secrecy_KS @ Ls @ ( localSecrets @ P ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( member @ secrecy_KS @ Ls @ ( localSecrets @ PQ ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_20_not__know__s__not__ine,axiom,
% 3.28/1.90 ! [A2: secrecy_specID,M: secrecy_Secrets] :
% 3.28/1.90 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.28/1.90 => ~ ( ine @ A2 @ ( secrecy_sE @ M ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_21_notknowQ,axiom,
% 3.28/1.90 ~ ( knowle1437066798e_know @ q @ m ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_22_notknowP,axiom,
% 3.28/1.90 ~ ( knowle1437066798e_know @ p @ m ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_23_Expression_Oinject_I2_J,axiom,
% 3.28/1.90 ! [X2: secrecy_Secrets,Y2: secrecy_Secrets] :
% 3.28/1.90 ( ( ( secrecy_sE @ X2 )
% 3.28/1.90 = ( secrecy_sE @ Y2 ) )
% 3.28/1.90 = ( X2 = Y2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_24_know__composition__neg__ine__s,axiom,
% 3.28/1.90 ! [P: secrecy_specID,Secret: secrecy_Secrets,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_sKS @ Secret ) )
% 3.28/1.90 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_sKS @ Secret ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ~ ( ine @ PQ @ ( secrecy_sE @ Secret ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_25_TBtheorem1a,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( ine @ PQ @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ine @ P @ E )
% 3.28/1.90 | ( ine @ Q @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_26_TBtheorem3a,axiom,
% 3.28/1.90 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ~ ( ine @ P @ E )
% 3.28/1.90 => ( ~ ( ine @ Q @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ~ ( ine @ PQ @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_27_singletonI,axiom,
% 3.28/1.90 ! [A: $tType,A3: A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_28_insertCI,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 3.28/1.90 ( ( ~ ( member @ A @ A3 @ B )
% 3.28/1.90 => ( A3 = B2 ) )
% 3.28/1.90 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_29_insert__iff,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 3.28/1.90 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 3.28/1.90 = ( ( A3 = B2 )
% 3.28/1.90 | ( member @ A @ A3 @ A2 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_30_insert__absorb2,axiom,
% 3.28/1.90 ! [A: $tType,X: A,A2: set @ A] :
% 3.28/1.90 ( ( insert @ A @ X @ ( insert @ A @ X @ A2 ) )
% 3.28/1.90 = ( insert @ A @ X @ A2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_31_empty__iff,axiom,
% 3.28/1.90 ! [A: $tType,C: A] :
% 3.28/1.90 ~ ( member @ A @ C @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_32_all__not__in__conv,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( ! [X3: A] :
% 3.28/1.90 ~ ( member @ A @ X3 @ A2 ) )
% 3.28/1.90 = ( A2
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_33_Collect__empty__eq,axiom,
% 3.28/1.90 ! [A: $tType,P: A > $o] :
% 3.28/1.90 ( ( ( collect @ A @ P )
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 = ( ! [X3: A] :
% 3.28/1.90 ~ ( P @ X3 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_34_empty__Collect__eq,axiom,
% 3.28/1.90 ! [A: $tType,P: A > $o] :
% 3.28/1.90 ( ( ( bot_bot @ ( set @ A ) )
% 3.28/1.90 = ( collect @ A @ P ) )
% 3.28/1.90 = ( ! [X3: A] :
% 3.28/1.90 ~ ( P @ X3 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_35_ex__in__conv,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( ? [X3: A] : ( member @ A @ X3 @ A2 ) )
% 3.28/1.90 = ( A2
% 3.28/1.90 != ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_36_equals0I,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ! [Y: A] :
% 3.28/1.90 ~ ( member @ A @ Y @ A2 )
% 3.28/1.90 => ( A2
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_37_equals0D,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,A3: A] :
% 3.28/1.90 ( ( A2
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 => ~ ( member @ A @ A3 @ A2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_38_emptyE,axiom,
% 3.28/1.90 ! [A: $tType,A3: A] :
% 3.28/1.90 ~ ( member @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_39_mk__disjoint__insert,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,A2: set @ A] :
% 3.28/1.90 ( ( member @ A @ A3 @ A2 )
% 3.28/1.90 => ? [B3: set @ A] :
% 3.28/1.90 ( ( A2
% 3.28/1.90 = ( insert @ A @ A3 @ B3 ) )
% 3.28/1.90 & ~ ( member @ A @ A3 @ B3 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_40_insert__commute,axiom,
% 3.28/1.90 ! [A: $tType,X: A,Y3: A,A2: set @ A] :
% 3.28/1.90 ( ( insert @ A @ X @ ( insert @ A @ Y3 @ A2 ) )
% 3.28/1.90 = ( insert @ A @ Y3 @ ( insert @ A @ X @ A2 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_41_insert__eq__iff,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,A2: set @ A,B2: A,B: set @ A] :
% 3.28/1.90 ( ~ ( member @ A @ A3 @ A2 )
% 3.28/1.90 => ( ~ ( member @ A @ B2 @ B )
% 3.28/1.90 => ( ( ( insert @ A @ A3 @ A2 )
% 3.28/1.90 = ( insert @ A @ B2 @ B ) )
% 3.28/1.90 = ( ( ( A3 = B2 )
% 3.28/1.90 => ( A2 = B ) )
% 3.28/1.90 & ( ( A3 != B2 )
% 3.28/1.90 => ? [C2: set @ A] :
% 3.28/1.90 ( ( A2
% 3.28/1.90 = ( insert @ A @ B2 @ C2 ) )
% 3.28/1.90 & ~ ( member @ A @ B2 @ C2 )
% 3.28/1.90 & ( B
% 3.28/1.90 = ( insert @ A @ A3 @ C2 ) )
% 3.28/1.90 & ~ ( member @ A @ A3 @ C2 ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_42_insert__absorb,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,A2: set @ A] :
% 3.28/1.90 ( ( member @ A @ A3 @ A2 )
% 3.28/1.90 => ( ( insert @ A @ A3 @ A2 )
% 3.28/1.90 = A2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_43_insert__ident,axiom,
% 3.28/1.90 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.28/1.90 ( ~ ( member @ A @ X @ A2 )
% 3.28/1.90 => ( ~ ( member @ A @ X @ B )
% 3.28/1.90 => ( ( ( insert @ A @ X @ A2 )
% 3.28/1.90 = ( insert @ A @ X @ B ) )
% 3.28/1.90 = ( A2 = B ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_44_Set_Oset__insert,axiom,
% 3.28/1.90 ! [A: $tType,X: A,A2: set @ A] :
% 3.28/1.90 ( ( member @ A @ X @ A2 )
% 3.28/1.90 => ~ ! [B3: set @ A] :
% 3.28/1.90 ( ( A2
% 3.28/1.90 = ( insert @ A @ X @ B3 ) )
% 3.28/1.90 => ( member @ A @ X @ B3 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_45_mem__Collect__eq,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,P: A > $o] :
% 3.28/1.90 ( ( member @ A @ A3 @ ( collect @ A @ P ) )
% 3.28/1.90 = ( P @ A3 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_46_Collect__mem__eq,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( collect @ A
% 3.28/1.90 @ ^ [X3: A] : ( member @ A @ X3 @ A2 ) )
% 3.28/1.90 = A2 ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_47_Collect__cong,axiom,
% 3.28/1.90 ! [A: $tType,P: A > $o,Q: A > $o] :
% 3.28/1.90 ( ! [X4: A] :
% 3.28/1.90 ( ( P @ X4 )
% 3.28/1.90 = ( Q @ X4 ) )
% 3.28/1.90 => ( ( collect @ A @ P )
% 3.28/1.90 = ( collect @ A @ Q ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_48_ext,axiom,
% 3.28/1.90 ! [B4: $tType,A: $tType,F: A > B4,G: A > B4] :
% 3.28/1.90 ( ! [X4: A] :
% 3.28/1.90 ( ( F @ X4 )
% 3.28/1.90 = ( G @ X4 ) )
% 3.28/1.90 => ( F = G ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_49_insertI2,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B: set @ A,B2: A] :
% 3.28/1.90 ( ( member @ A @ A3 @ B )
% 3.28/1.90 => ( member @ A @ A3 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_50_insertI1,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B: set @ A] : ( member @ A @ A3 @ ( insert @ A @ A3 @ B ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_51_insertE,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B2: A,A2: set @ A] :
% 3.28/1.90 ( ( member @ A @ A3 @ ( insert @ A @ B2 @ A2 ) )
% 3.28/1.90 => ( ( A3 != B2 )
% 3.28/1.90 => ( member @ A @ A3 @ A2 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_52_singleton__inject,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B2: A] :
% 3.28/1.90 ( ( ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.90 => ( A3 = B2 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_53_insert__not__empty,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,A2: set @ A] :
% 3.28/1.90 ( ( insert @ A @ A3 @ A2 )
% 3.28/1.90 != ( bot_bot @ ( set @ A ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_54_doubleton__eq__iff,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B2: A,C: A,D: A] :
% 3.28/1.90 ( ( ( insert @ A @ A3 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.90 = ( insert @ A @ C @ ( insert @ A @ D @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.28/1.90 = ( ( ( A3 = C )
% 3.28/1.90 & ( B2 = D ) )
% 3.28/1.90 | ( ( A3 = D )
% 3.28/1.90 & ( B2 = C ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_55_singleton__iff,axiom,
% 3.28/1.90 ! [A: $tType,B2: A,A3: A] :
% 3.28/1.90 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.90 = ( B2 = A3 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_56_singletonD,axiom,
% 3.28/1.90 ! [A: $tType,B2: A,A3: A] :
% 3.28/1.90 ( ( member @ A @ B2 @ ( insert @ A @ A3 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.90 => ( B2 = A3 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_57_the__elem__eq,axiom,
% 3.28/1.90 ! [A: $tType,X: A] :
% 3.28/1.90 ( ( the_elem @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.90 = X ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_58_bot__apply,axiom,
% 3.28/1.90 ! [C3: $tType,D2: $tType] :
% 3.28/1.90 ( ( bot @ C3 )
% 3.28/1.90 => ( ( bot_bot @ ( D2 > C3 ) )
% 3.28/1.90 = ( ^ [X3: D2] : ( bot_bot @ C3 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_59_is__singletonI,axiom,
% 3.28/1.90 ! [A: $tType,X: A] : ( is_singleton @ A @ ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_60_TBtheorem4a__empty,axiom,
% 3.28/1.90 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ( ( ine @ P @ E )
% 3.28/1.90 | ( ine @ Q @ E ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ( loc @ PQ )
% 3.28/1.90 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.28/1.90 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_61_TBtheorem3b,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ~ ( ineM @ P @ M2 @ E )
% 3.28/1.90 => ( ~ ( ineM @ Q @ M2 @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_62_TBtheorem1b,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( ineM @ PQ @ M2 @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ineM @ P @ M2 @ E )
% 3.28/1.90 | ( ineM @ Q @ M2 @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_63_Set_Ois__empty__def,axiom,
% 3.28/1.90 ! [A: $tType] :
% 3.28/1.90 ( ( is_empty @ A )
% 3.28/1.90 = ( ^ [A4: set @ A] :
% 3.28/1.90 ( A4
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_64_correctCompositionIn__prop1,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ X @ ( ins @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.28/1.90 | ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_65_correctCompositionIn__L2,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 | ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_66_bot__set__def,axiom,
% 3.28/1.90 ! [A: $tType] :
% 3.28/1.90 ( ( bot_bot @ ( set @ A ) )
% 3.28/1.90 = ( collect @ A @ ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_67_ineM__ine,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.90 ( ( ineM @ P @ M2 @ E )
% 3.28/1.90 => ( ine @ P @ E ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_68_not__ine__ineM,axiom,
% 3.28/1.90 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 3.28/1.90 ( ~ ( ine @ P @ E )
% 3.28/1.90 => ~ ( ineM @ P @ M2 @ E ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_69_is__singleton__the__elem,axiom,
% 3.28/1.90 ! [A: $tType] :
% 3.28/1.90 ( ( is_singleton @ A )
% 3.28/1.90 = ( ^ [A4: set @ A] :
% 3.28/1.90 ( A4
% 3.28/1.90 = ( insert @ A @ ( the_elem @ A @ A4 ) @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_70_correctCompositionIn__L1,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_71_is__singletonI_H,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( A2
% 3.28/1.90 != ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 => ( ! [X4: A,Y: A] :
% 3.28/1.90 ( ( member @ A @ X4 @ A2 )
% 3.28/1.90 => ( ( member @ A @ Y @ A2 )
% 3.28/1.90 => ( X4 = Y ) ) )
% 3.28/1.90 => ( is_singleton @ A @ A2 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_72_bot__fun__def,axiom,
% 3.28/1.90 ! [B4: $tType,A: $tType] :
% 3.28/1.90 ( ( bot @ B4 )
% 3.28/1.90 => ( ( bot_bot @ ( A > B4 ) )
% 3.28/1.90 = ( ^ [X3: A] : ( bot_bot @ B4 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_73_is__singletonE,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( is_singleton @ A @ A2 )
% 3.28/1.90 => ~ ! [X4: A] :
% 3.28/1.90 ( A2
% 3.28/1.90 != ( insert @ A @ X4 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_74_is__singleton__def,axiom,
% 3.28/1.90 ! [A: $tType] :
% 3.28/1.90 ( ( is_singleton @ A )
% 3.28/1.90 = ( ^ [A4: set @ A] :
% 3.28/1.90 ? [X3: A] :
% 3.28/1.90 ( A4
% 3.28/1.90 = ( insert @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_75_subcomponents__loc,axiom,
% 3.28/1.90 ! [X: secrecy_specID] :
% 3.28/1.90 ( ( correc965049635ionLoc @ X )
% 3.28/1.90 => ( ( ( subcomponents @ X )
% 3.28/1.90 = ( bot_bot @ ( set @ secrecy_specID ) ) )
% 3.28/1.90 => ( ( loc @ X )
% 3.28/1.90 = ( bot_bot @ ( set @ secrecy_chanID ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_76_TBtheorem4b__notP1,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ( ineM @ P @ M2 @ E )
% 3.28/1.90 => ( ~ ( ineM @ Q @ M2 @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.90 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 3.28/1.90 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.28/1.90 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_77_TBtheorem4a__notP1,axiom,
% 3.28/1.90 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ( ine @ P @ E )
% 3.28/1.90 => ( ~ ( ine @ Q @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.90 ( ( ine_ex1303305700Single @ P @ Ch2 @ E )
% 3.28/1.90 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_78_TBtheorem4b__notP2,axiom,
% 3.28/1.90 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.28/1.90 ( ~ ( ineM @ Q @ M2 @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 3.28/1.90 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_79_TBtheorem4b__notPQ,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.28/1.90 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 3.28/1.90 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 3.28/1.90 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ~ ( ineM @ PQ @ M2 @ E ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_80_TBtheorem4a__notP2,axiom,
% 3.28/1.90 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.28/1.90 ( ~ ( ine @ Q @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 3.28/1.90 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_81_TBtheorem4a__notPQ,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( ine_exprChannelSet @ P @ ChSetP @ E )
% 3.28/1.90 => ( ( ine_exprChannelSet @ Q @ ChSetQ @ E )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 3.28/1.90 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 3.28/1.90 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ~ ( ine @ PQ @ E ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_82_ine__exprChannelSingle__Set,axiom,
% 3.28/1.90 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.90 ( ( ine_ex1303305700Single @ P @ Ch @ E )
% 3.28/1.90 => ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_83_ine__exprChannelSet__Single,axiom,
% 3.28/1.90 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.90 ( ( ine_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 3.28/1.90 => ( ine_ex1303305700Single @ P @ Ch @ E ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_84_ine__empty__exprChannelSet,axiom,
% 3.28/1.90 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.90 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.28/1.90 => ( ( ChSet
% 3.28/1.90 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.28/1.90 => ~ ( ine @ P @ E ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_85_ine__nonempty__exprChannelSet,axiom,
% 3.28/1.90 ! [P: secrecy_specID,ChSet: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.90 ( ( ine_exprChannelSet @ P @ ChSet @ E )
% 3.28/1.90 => ( ( ChSet
% 3.28/1.90 != ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.28/1.90 => ( ine @ P @ E ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_86_locStream__def,axiom,
% 3.28/1.90 ( locStream
% 3.28/1.90 = ( ^ [X3: secrecy_specID] :
% 3.28/1.90 ( ^ [Y4: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y4 = Z )
% 3.28/1.90 @ ( loc @ X3 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_87_inStream__def,axiom,
% 3.28/1.90 ( inStream
% 3.28/1.90 = ( ^ [X3: secrecy_specID] :
% 3.28/1.90 ( ^ [Y4: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y4 = Z )
% 3.28/1.90 @ ( ins @ X3 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_88_TBtheorem4b__PQ,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ( ( ineM @ P @ M2 @ E )
% 3.28/1.90 | ( ineM @ Q @ M2 @ E ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.90 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 3.28/1.90 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 3.28/1.90 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.28/1.90 & ( exprChannel @ Ch2 @ E )
% 3.28/1.90 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_89_TBtheorem4b__P,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( ineM @ P @ M2 @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) )
% 3.28/1.90 & ( exprChannel @ Ch2 @ E )
% 3.28/1.90 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 3.28/1.90 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 3.28/1.90 => ( ineM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_90_TBtheorem4a__PQ,axiom,
% 3.28/1.90 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ( ( ine @ P @ E )
% 3.28/1.90 | ( ine @ Q @ E ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.90 ( ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 3.28/1.90 | ( member @ secrecy_chanID @ Ch2 @ ( ins @ Q ) ) )
% 3.28/1.90 & ( exprChannel @ Ch2 @ E )
% 3.28/1.90 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_91_TBtheorem4a__P,axiom,
% 3.28/1.90 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( ine @ P @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch2 @ ( ins @ P ) )
% 3.28/1.90 & ( exprChannel @ Ch2 @ E )
% 3.28/1.90 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.90 => ( ine @ PQ @ E ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_92_ine__def,axiom,
% 3.28/1.90 ( ine
% 3.28/1.90 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.28/1.90 ? [Ch3: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 3.28/1.90 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_93_ine__ins__neg1,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M: secrecy_Expression,X: secrecy_chanID] :
% 3.28/1.90 ( ~ ( ine @ P @ M )
% 3.28/1.90 => ( ( exprChannel @ X @ M )
% 3.28/1.90 => ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_94_ineM__def,axiom,
% 3.28/1.90 ( ineM
% 3.28/1.90 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.28/1.90 ? [Ch3: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 3.28/1.90 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 3.28/1.90 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_95_ineM__L1,axiom,
% 3.28/1.90 ! [Ch: secrecy_chanID,M2: set @ secrecy_chanID,P: secrecy_specID,E: secrecy_Expression] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch @ M2 )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ E )
% 3.28/1.90 => ( ineM @ P @ M2 @ E ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_96_ine__exprChannelSet__def,axiom,
% 3.28/1.90 ( ine_exprChannelSet
% 3.28/1.90 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.28/1.90 ( ! [X3: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ X3 @ ( ins @ SP ) )
% 3.28/1.90 & ( exprChannel @ X3 @ E2 ) ) )
% 3.28/1.90 & ! [X3: secrecy_chanID] :
% 3.28/1.90 ( ( ~ ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 3.28/1.90 & ( member @ secrecy_chanID @ X3 @ ( ins @ SP ) ) )
% 3.28/1.90 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_97_ine__exprChannelSingle__def,axiom,
% 3.28/1.90 ( ine_ex1303305700Single
% 3.28/1.90 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch3 @ ( ins @ SP ) )
% 3.28/1.90 & ( exprChannel @ Ch3 @ E2 )
% 3.28/1.90 & ! [X3: secrecy_chanID,T: nat] :
% 3.28/1.90 ( ( ( member @ secrecy_chanID @ X3 @ ( ins @ SP ) )
% 3.28/1.90 & ( X3 != Ch3 ) )
% 3.28/1.90 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_98_LocalSecretsComposition__exprChannel__s,axiom,
% 3.28/1.90 ! [X: secrecy_chanID,Secrets: secrecy_Secrets,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.90 ( ( exprChannel @ X @ ( secrecy_sE @ Secrets ) )
% 3.28/1.90 => ( ~ ( ine @ P @ ( secrecy_sE @ Secrets ) )
% 3.28/1.90 => ( ~ ( ine @ Q @ ( secrecy_sE @ Secrets ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.28/1.90 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_99_correctCompositionInLoc__exprChannel,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ch: secrecy_chanID,M: secrecy_Expression] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ M )
% 3.28/1.90 => ( ! [X4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ X4 @ ( ins @ PQ ) )
% 3.28/1.90 => ~ ( exprChannel @ X4 @ M ) )
% 3.28/1.90 => ( member @ secrecy_chanID @ Ch @ ( loc @ PQ ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_100_TBlemma3b,axiom,
% 3.28/1.90 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID,Ch: secrecy_chanID] :
% 3.28/1.90 ( ~ ( ineM @ P @ M2 @ E )
% 3.28/1.90 => ( ~ ( ineM @ Q @ M2 @ E )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ M2 )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.28/1.90 => ~ ( exprChannel @ Ch @ E ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_101_Collect__empty__eq__bot,axiom,
% 3.28/1.90 ! [A: $tType,P: A > $o] :
% 3.28/1.90 ( ( ( collect @ A @ P )
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 = ( P
% 3.28/1.90 = ( bot_bot @ ( A > $o ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_102_bot__empty__eq,axiom,
% 3.28/1.90 ! [A: $tType] :
% 3.28/1.90 ( ( bot_bot @ ( A > $o ) )
% 3.28/1.90 = ( ^ [X3: A] : ( member @ A @ X3 @ ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_103_LocalSecretsComposition__neg__loc__s,axiom,
% 3.28/1.90 ! [Secret: secrecy_Secrets,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.28/1.90 ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ P ) )
% 3.28/1.90 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_104_correctCompositionKS__exprChannel__s__P,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_105_correctCompositionKS__exprChannel__s__Q,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_106_correctCompositionKS__negQ,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_107_correctCompositionKS__negP,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_108_correctCompositionKS__neg1,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.28/1.90 => ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_109_correctCompositionKS__PQ,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.28/1.90 | ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_110_know__composition2,axiom,
% 3.28/1.90 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.28/1.90 => ( ( knowle1437066798e_know @ Q @ M )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_111_know__composition1,axiom,
% 3.28/1.90 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.28/1.90 => ( ( knowle1437066798e_know @ P @ M )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_112_know__composition,axiom,
% 3.28/1.90 ! [M: secrecy_KS,P: secrecy_specID,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.90 ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ M @ ( specKeysSecrets @ Q ) )
% 3.28/1.90 => ( ( ( knowle1437066798e_know @ P @ M )
% 3.28/1.90 | ( knowle1437066798e_know @ Q @ M ) )
% 3.28/1.90 => ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( knowle1437066798e_know @ PQ @ M ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_113_correctCompositionKS__exprChannel__s__Qex,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ? [Ch4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_114_correctCompositionKS__exprChannel__s__Pex,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Secret: secrecy_Secrets,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_sE @ Secret ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Secret ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ? [Ch4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch4 @ ( secrecy_sE @ Secret ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_115_LocalSecretsComposition__neg__s,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Secrets] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ P ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( specKeysSecrets @ Q ) )
% 3.28/1.90 => ( ~ ( ine @ P @ ( secrecy_sE @ M ) )
% 3.28/1.90 => ( ~ ( ine @ Q @ ( secrecy_sE @ M ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.28/1.90 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_116_correctCompositionKS__exprChannel__k__Qex,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ? [Ch4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_117_correctCompositionKS__exprChannel__k__Pex,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ? [Ch4: secrecy_chanID] :
% 3.28/1.90 ( ( member @ secrecy_chanID @ Ch4 @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch4 @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_118_correctCompositionKS__exprChannel__k__Q,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ Q ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_119_correctCompositionKS__exprChannel__k__P,axiom,
% 3.28/1.90 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Key: secrecy_Keys,Ch: secrecy_chanID] :
% 3.28/1.90 ( ( ( subcomponents @ PQ )
% 3.28/1.90 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.90 => ( ( correctCompositionKS @ PQ )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ PQ ) )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ P ) )
% 3.28/1.90 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.28/1.90 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ PQ ) )
% 3.28/1.90 => ( ( correctCompositionIn @ PQ )
% 3.28/1.90 => ( ( member @ secrecy_chanID @ Ch @ ( ins @ PQ ) )
% 3.28/1.90 & ( exprChannel @ Ch @ ( secrecy_kE @ Key ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_120_Un__iff,axiom,
% 3.28/1.90 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 3.28/1.90 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.90 = ( ( member @ A @ C @ A2 )
% 3.28/1.90 | ( member @ A @ C @ B ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_121_UnCI,axiom,
% 3.28/1.90 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 3.28/1.90 ( ( ~ ( member @ A @ C @ B )
% 3.28/1.90 => ( member @ A @ C @ A2 ) )
% 3.28/1.90 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_122_KS_Oinject_I1_J,axiom,
% 3.28/1.90 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.28/1.90 ( ( ( secrecy_kKS @ X1 )
% 3.28/1.90 = ( secrecy_kKS @ Y1 ) )
% 3.28/1.90 = ( X1 = Y1 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_123_Expression_Oinject_I1_J,axiom,
% 3.28/1.90 ! [X1: secrecy_Keys,Y1: secrecy_Keys] :
% 3.28/1.90 ( ( ( secrecy_kE @ X1 )
% 3.28/1.90 = ( secrecy_kE @ Y1 ) )
% 3.28/1.90 = ( X1 = Y1 ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_124_Un__empty,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.28/1.90 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 = ( ( A2
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 & ( B
% 3.28/1.90 = ( bot_bot @ ( set @ A ) ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_125_Un__insert__left,axiom,
% 3.28/1.90 ! [A: $tType,A3: A,B: set @ A,C4: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ ( insert @ A @ A3 @ B ) @ C4 )
% 3.28/1.90 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_126_Un__insert__right,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,A3: A,B: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ A2 @ ( insert @ A @ A3 @ B ) )
% 3.28/1.90 = ( insert @ A @ A3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_127_not__know__k__not__ine,axiom,
% 3.28/1.90 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 3.28/1.90 ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.28/1.90 => ~ ( ine @ A2 @ ( secrecy_kE @ M ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_128_Un__empty__right,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.28/1.90 = A2 ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_129_Un__empty__left,axiom,
% 3.28/1.90 ! [A: $tType,B: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ B )
% 3.28/1.90 = B ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_130_KS2Expression_Osimps_I1_J,axiom,
% 3.28/1.90 ! [M: secrecy_Keys] :
% 3.28/1.90 ( ( secrec1016742679ession @ ( secrecy_kKS @ M ) )
% 3.28/1.90 = ( secrecy_kE @ M ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_131_Un__left__commute,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) )
% 3.28/1.90 = ( sup_sup @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ C4 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_132_Un__left__absorb,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.90 = ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_133_Un__commute,axiom,
% 3.28/1.90 ! [A: $tType] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) )
% 3.28/1.90 = ( ^ [A4: set @ A,B5: set @ A] : ( sup_sup @ ( set @ A ) @ B5 @ A4 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_134_Un__absorb,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ A2 @ A2 )
% 3.28/1.90 = A2 ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_135_Un__assoc,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.28/1.90 ( ( sup_sup @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 3.28/1.90 = ( sup_sup @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_136_ball__Un,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 3.28/1.90 ( ( ! [X3: A] :
% 3.28/1.90 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.90 => ( P @ X3 ) ) )
% 3.28/1.90 = ( ! [X3: A] :
% 3.28/1.90 ( ( member @ A @ X3 @ A2 )
% 3.28/1.90 => ( P @ X3 ) )
% 3.28/1.90 & ! [X3: A] :
% 3.28/1.90 ( ( member @ A @ X3 @ B )
% 3.28/1.90 => ( P @ X3 ) ) ) ) ).
% 3.28/1.90
% 3.28/1.90 thf(fact_137_bex__Un,axiom,
% 3.28/1.90 ! [A: $tType,A2: set @ A,B: set @ A,P: A > $o] :
% 3.28/1.90 ( ( ? [X3: A] :
% 3.28/1.90 ( ( member @ A @ X3 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.90 & ( P @ X3 ) ) )
% 3.28/1.90 = ( ? [X3: A] :
% 3.28/1.90 ( ( member @ A @ X3 @ A2 )
% 3.28/1.90 & ( P @ X3 ) )
% 3.28/1.90 | ? [X3: A] :
% 3.28/1.90 ( ( member @ A @ X3 @ B )
% 3.28/1.91 & ( P @ X3 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_138_UnI2,axiom,
% 3.28/1.91 ! [A: $tType,C: A,B: set @ A,A2: set @ A] :
% 3.28/1.91 ( ( member @ A @ C @ B )
% 3.28/1.91 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_139_UnI1,axiom,
% 3.28/1.91 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( member @ A @ C @ A2 )
% 3.28/1.91 => ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_140_UnE,axiom,
% 3.28/1.91 ! [A: $tType,C: A,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( member @ A @ C @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.91 => ( ~ ( member @ A @ C @ A2 )
% 3.28/1.91 => ( member @ A @ C @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_141_KS_Oexhaust,axiom,
% 3.28/1.91 ! [Y3: secrecy_KS] :
% 3.28/1.91 ( ! [X12: secrecy_Keys] :
% 3.28/1.91 ( Y3
% 3.28/1.91 != ( secrecy_kKS @ X12 ) )
% 3.28/1.91 => ~ ! [X22: secrecy_Secrets] :
% 3.28/1.91 ( Y3
% 3.28/1.91 != ( secrecy_sKS @ X22 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_142_KS_Oinduct,axiom,
% 3.28/1.91 ! [P: secrecy_KS > $o,KS: secrecy_KS] :
% 3.28/1.91 ( ! [X4: secrecy_Keys] : ( P @ ( secrecy_kKS @ X4 ) )
% 3.28/1.91 => ( ! [X4: secrecy_Secrets] : ( P @ ( secrecy_sKS @ X4 ) )
% 3.28/1.91 => ( P @ KS ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_143_KS_Odistinct_I1_J,axiom,
% 3.28/1.91 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 3.28/1.91 ( ( secrecy_kKS @ X1 )
% 3.28/1.91 != ( secrecy_sKS @ X2 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_144_Expression_Odistinct_I1_J,axiom,
% 3.28/1.91 ! [X1: secrecy_Keys,X2: secrecy_Secrets] :
% 3.28/1.91 ( ( secrecy_kE @ X1 )
% 3.28/1.91 != ( secrecy_sE @ X2 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_145_KS_Osimps_I5_J,axiom,
% 3.28/1.91 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 3.28/1.91 ( ( secrecy_case_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 3.28/1.91 = ( F1 @ X1 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_146_know_Osimps_I1_J,axiom,
% 3.28/1.91 ! [A2: secrecy_specID,M: secrecy_Keys] :
% 3.28/1.91 ( ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 = ( ( ine @ A2 @ ( secrecy_kE @ M ) )
% 3.28/1.91 | ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ A2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_147_KS_Osimps_I7_J,axiom,
% 3.28/1.91 ! [A: $tType,F1: secrecy_Keys > A,F2: secrecy_Secrets > A,X1: secrecy_Keys] :
% 3.28/1.91 ( ( secrecy_rec_KS @ A @ F1 @ F2 @ ( secrecy_kKS @ X1 ) )
% 3.28/1.91 = ( F1 @ X1 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_148_insert__is__Un,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( insert @ A )
% 3.28/1.91 = ( ^ [A5: A] : ( sup_sup @ ( set @ A ) @ ( insert @ A @ A5 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_149_Un__singleton__iff,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 3.28/1.91 ( ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 = ( ( ( A2
% 3.28/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.91 & ( B
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.28/1.91 | ( ( A2
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 & ( B
% 3.28/1.91 = ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 | ( ( A2
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 & ( B
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_150_singleton__Un__iff,axiom,
% 3.28/1.91 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) )
% 3.28/1.91 = ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.91 = ( ( ( A2
% 3.28/1.91 = ( bot_bot @ ( set @ A ) ) )
% 3.28/1.91 & ( B
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) )
% 3.28/1.91 | ( ( A2
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 & ( B
% 3.28/1.91 = ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 | ( ( A2
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 & ( B
% 3.28/1.91 = ( insert @ A @ X @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_151_LocalSecretsComposition__neg__loc__k,axiom,
% 3.28/1.91 ! [Key: secrecy_Keys,P: secrecy_specID,Ch: secrecy_chanID] :
% 3.28/1.91 ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( localSecrets @ P ) )
% 3.28/1.91 => ( ( exprChannel @ Ch @ ( secrecy_kE @ Key ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Key ) @ ( specKeysSecrets @ P ) )
% 3.28/1.91 => ~ ( member @ secrecy_chanID @ Ch @ ( loc @ P ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_152_LocalSecretsComposition__neg__k,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,M: secrecy_Keys] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.91 => ( ( correctCompositionKS @ PQ )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ P ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( specKeysSecrets @ Q ) )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_kE @ M ) )
% 3.28/1.91 => ( ~ ( ine @ Q @ ( secrecy_kE @ M ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.28/1.91 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ M ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_153_know__composition__neg__ine__k,axiom,
% 3.28/1.91 ! [P: secrecy_specID,Key: secrecy_Keys,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.91 ( ~ ( knowle1437066798e_know @ P @ ( secrecy_kKS @ Key ) )
% 3.28/1.91 => ( ~ ( knowle1437066798e_know @ Q @ ( secrecy_kKS @ Key ) )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correctCompositionIn @ PQ )
% 3.28/1.91 => ~ ( ine @ PQ @ ( secrecy_kE @ Key ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_154_LocalSecretsComposition__ine1__k,axiom,
% 3.28/1.91 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.91 => ( ~ ( ine @ Q @ ( secrecy_kE @ K ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.28/1.91 => ( ine @ P @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_155_LocalSecretsComposition__ine2__k,axiom,
% 3.28/1.91 ! [K: secrecy_Keys,PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ PQ ) )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_kE @ K ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ P ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ K ) @ ( localSecrets @ Q ) )
% 3.28/1.91 => ( ine @ Q @ ( secrecy_kE @ K ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_156_LocalSecretsComposition__neg1__k,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Keys: secrecy_Keys] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.28/1.91 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ P ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ Q ) )
% 3.28/1.91 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ Keys ) @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_157_LocalSecretsComposition__exprChannel__k,axiom,
% 3.28/1.91 ! [X: secrecy_chanID,Keys: secrecy_Keys,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( exprChannel @ X @ ( secrecy_kE @ Keys ) )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_kE @ Keys ) )
% 3.28/1.91 => ( ~ ( ine @ Q @ ( secrecy_kE @ Keys ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_chanID @ X @ ( ins @ P ) )
% 3.28/1.91 & ~ ( member @ secrecy_chanID @ X @ ( ins @ Q ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_158_LocalSecretsComposition__neg,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.91 => ( ( correctCompositionKS @ PQ )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ P ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ Ks @ ( specKeysSecrets @ Q ) )
% 3.28/1.91 => ( ! [M4: secrecy_Keys] :
% 3.28/1.91 ( ( Ks
% 3.28/1.91 = ( secrecy_kKS @ M4 ) )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.28/1.91 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.28/1.91 => ( ! [M4: secrecy_Secrets] :
% 3.28/1.91 ( ( Ks
% 3.28/1.91 = ( secrecy_sKS @ M4 ) )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.28/1.91 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ Ks @ ( sup_sup @ ( set @ secrecy_KS ) @ ( localSecrets @ P ) @ ( localSecrets @ Q ) ) )
% 3.28/1.91 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_159_LocalSecretsComposition__neg1,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,Ks: secrecy_KS] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc965049635ionLoc @ PQ )
% 3.28/1.91 => ( ! [M4: secrecy_Keys] :
% 3.28/1.91 ( ( Ks
% 3.28/1.91 = ( secrecy_kKS @ M4 ) )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_kE @ M4 ) )
% 3.28/1.91 & ~ ( ine @ Q @ ( secrecy_kE @ M4 ) ) ) )
% 3.28/1.91 => ( ! [M4: secrecy_Secrets] :
% 3.28/1.91 ( ( Ks
% 3.28/1.91 = ( secrecy_sKS @ M4 ) )
% 3.28/1.91 => ( ~ ( ine @ P @ ( secrecy_sE @ M4 ) )
% 3.28/1.91 & ~ ( ine @ Q @ ( secrecy_sE @ M4 ) ) ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ P ) )
% 3.28/1.91 => ( ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ Q ) )
% 3.28/1.91 => ~ ( member @ secrecy_KS @ Ks @ ( localSecrets @ PQ ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_160_sup__bot__left,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [X: A] :
% 3.28/1.91 ( ( sup_sup @ A @ ( bot_bot @ A ) @ X )
% 3.28/1.91 = X ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_161_sup__bot__right,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [X: A] :
% 3.28/1.91 ( ( sup_sup @ A @ X @ ( bot_bot @ A ) )
% 3.28/1.91 = X ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_162_bot__eq__sup__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [X: A,Y3: A] :
% 3.28/1.91 ( ( ( bot_bot @ A )
% 3.28/1.91 = ( sup_sup @ A @ X @ Y3 ) )
% 3.28/1.91 = ( ( X
% 3.28/1.91 = ( bot_bot @ A ) )
% 3.28/1.91 & ( Y3
% 3.28/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_163_sup__eq__bot__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [X: A,Y3: A] :
% 3.28/1.91 ( ( ( sup_sup @ A @ X @ Y3 )
% 3.28/1.91 = ( bot_bot @ A ) )
% 3.28/1.91 = ( ( X
% 3.28/1.91 = ( bot_bot @ A ) )
% 3.28/1.91 & ( Y3
% 3.28/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_164_sup__bot_Oright__neutral,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [A3: A] :
% 3.28/1.91 ( ( sup_sup @ A @ A3 @ ( bot_bot @ A ) )
% 3.28/1.91 = A3 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_165_sup__bot_Oneutr__eq__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [A3: A,B2: A] :
% 3.28/1.91 ( ( ( bot_bot @ A )
% 3.28/1.91 = ( sup_sup @ A @ A3 @ B2 ) )
% 3.28/1.91 = ( ( A3
% 3.28/1.91 = ( bot_bot @ A ) )
% 3.28/1.91 & ( B2
% 3.28/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_166_sup__bot_Oleft__neutral,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [A3: A] :
% 3.28/1.91 ( ( sup_sup @ A @ ( bot_bot @ A ) @ A3 )
% 3.28/1.91 = A3 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_167_sup__bot_Oeq__neutr__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( bounde1808546759up_bot @ A )
% 3.28/1.91 => ! [A3: A,B2: A] :
% 3.28/1.91 ( ( ( sup_sup @ A @ A3 @ B2 )
% 3.28/1.91 = ( bot_bot @ A ) )
% 3.28/1.91 = ( ( A3
% 3.28/1.91 = ( bot_bot @ A ) )
% 3.28/1.91 & ( B2
% 3.28/1.91 = ( bot_bot @ A ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_168_ineM__Un1,axiom,
% 3.28/1.91 ! [P: secrecy_specID,A2: set @ secrecy_chanID,E: secrecy_Expression,B: set @ secrecy_chanID] :
% 3.28/1.91 ( ( ineM @ P @ A2 @ E )
% 3.28/1.91 => ( ineM @ P @ ( sup_sup @ ( set @ secrecy_chanID ) @ A2 @ B ) @ E ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_169_notSpecKeysSecretsExpr__def,axiom,
% 3.28/1.91 ( notSpe1586871396tsExpr
% 3.28/1.91 = ( ^ [P2: secrecy_specID,E3: list @ secrecy_Expression] :
% 3.28/1.91 ( ! [X3: secrecy_Keys] :
% 3.28/1.91 ( ( mem @ secrecy_Expression @ ( secrecy_kE @ X3 ) @ E3 )
% 3.28/1.91 => ~ ( member @ secrecy_KS @ ( secrecy_kKS @ X3 ) @ ( specKeysSecrets @ P2 ) ) )
% 3.28/1.91 & ! [Y5: secrecy_Secrets] :
% 3.28/1.91 ( ( mem @ secrecy_Expression @ ( secrecy_sE @ Y5 ) @ E3 )
% 3.28/1.91 => ~ ( member @ secrecy_KS @ ( secrecy_sKS @ Y5 ) @ ( specKeysSecrets @ P2 ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_170_TBtheorem5a__empty,axiom,
% 3.28/1.91 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.91 ( ( ( eout @ P @ E )
% 3.28/1.91 | ( eout @ Q @ E ) )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( ( loc @ PQ )
% 3.28/1.91 = ( bot_bot @ ( set @ secrecy_chanID ) ) )
% 3.28/1.91 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_171_correctCompositionKS__subcomp4,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.28/1.91 ( ( correctCompositionKS @ C4 )
% 3.28/1.91 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.28/1.91 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X ) )
% 3.28/1.91 => ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_172_TBtheorem2a,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( eout @ PQ @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( eout @ P @ E )
% 3.28/1.91 | ( eout @ Q @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_173_correctCompositionKS__subcomp2,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Secrets] :
% 3.28/1.91 ( ( correctCompositionKS @ C4 )
% 3.28/1.91 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.28/1.91 => ( ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ C4 ) )
% 3.28/1.91 => ? [X4: secrecy_specID] :
% 3.28/1.91 ( ( member @ secrecy_specID @ X4 @ ( subcomponents @ C4 ) )
% 3.28/1.91 & ( member @ secrecy_Secrets @ Xa @ ( specSecrets @ X4 ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_174_TBtheorem5a__notP1,axiom,
% 3.28/1.91 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.91 ( ( eout @ P @ E )
% 3.28/1.91 => ( ~ ( eout @ Q @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.91 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 3.28/1.91 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_175_TBtheorem5a__notP2,axiom,
% 3.28/1.91 ! [Q: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.28/1.91 ( ~ ( eout @ Q @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.28/1.91 => ( ! [X4: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 3.28/1.91 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_176_TBtheorem5a__notPQ,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.28/1.91 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.28/1.91 => ( ! [X4: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 3.28/1.91 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ( ! [X4: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 3.28/1.91 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ~ ( eout @ PQ @ E ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_177_out__exprChannelSingle__Set,axiom,
% 3.28/1.91 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.91 ( ( out_ex985543062Single @ P @ Ch @ E )
% 3.28/1.91 => ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_178_out__exprChannelSet__Single,axiom,
% 3.28/1.91 ! [P: secrecy_specID,Ch: secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.91 ( ( out_exprChannelSet @ P @ ( insert @ secrecy_chanID @ Ch @ ( bot_bot @ ( set @ secrecy_chanID ) ) ) @ E )
% 3.28/1.91 => ( out_ex985543062Single @ P @ Ch @ E ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_179_TBtheorem5b__notPQ,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,ChSetP: set @ secrecy_chanID,E: secrecy_Expression,ChSetQ: set @ secrecy_chanID,M2: set @ secrecy_chanID] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( out_exprChannelSet @ P @ ChSetP @ E )
% 3.28/1.91 => ( ( out_exprChannelSet @ Q @ ChSetQ @ E )
% 3.28/1.91 => ( ( M2
% 3.28/1.91 = ( sup_sup @ ( set @ secrecy_chanID ) @ ChSetP @ ChSetQ ) )
% 3.28/1.91 => ( ! [X4: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X4 @ ChSetP )
% 3.28/1.91 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ( ! [X4: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X4 @ ChSetQ )
% 3.28/1.91 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_180_eout__know__nonKS__s,axiom,
% 3.28/1.91 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 3.28/1.91 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 3.28/1.91 => ( ( eout @ A2 @ ( secrecy_sE @ M ) )
% 3.28/1.91 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 3.28/1.91 => ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_181_eoutKnowCorrect__L1s,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 3.28/1.91 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 3.28/1.91 => ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 3.28/1.91 => ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 3.28/1.91 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_182_eoutM__eout,axiom,
% 3.28/1.91 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression] :
% 3.28/1.91 ( ( eoutM @ P @ M2 @ E )
% 3.28/1.91 => ( eout @ P @ E ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_183_not__eout__eoutM,axiom,
% 3.28/1.91 ! [P: secrecy_specID,E: secrecy_Expression,M2: set @ secrecy_chanID] :
% 3.28/1.91 ( ~ ( eout @ P @ E )
% 3.28/1.91 => ~ ( eoutM @ P @ M2 @ E ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_184_TBtheorem2b,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,P: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( eoutM @ PQ @ M2 @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( eoutM @ P @ M2 @ E )
% 3.28/1.91 | ( eoutM @ Q @ M2 @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_185_TBtheorem5b__notP2,axiom,
% 3.28/1.91 ! [Q: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,P: secrecy_specID,ChSet: set @ secrecy_chanID] :
% 3.28/1.91 ( ~ ( eoutM @ Q @ M2 @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( out_exprChannelSet @ P @ ChSet @ E )
% 3.28/1.91 => ( ! [X4: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X4 @ ChSet )
% 3.28/1.91 => ( member @ secrecy_chanID @ X4 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_186_TBtheorem5b__notP1,axiom,
% 3.28/1.91 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.91 ( ( eoutM @ P @ M2 @ E )
% 3.28/1.91 => ( ~ ( eoutM @ Q @ M2 @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.91 ( ( out_ex985543062Single @ P @ Ch2 @ E )
% 3.28/1.91 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.28/1.91 & ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ~ ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_187_eout__know__s,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,M: secrecy_Secrets] :
% 3.28/1.91 ( ( knowle1667810483orrect @ C4 @ ( secrecy_sKS @ M ) )
% 3.28/1.91 = ( ( eout @ C4 @ ( secrecy_sE @ M ) )
% 3.28/1.91 = ( ( member @ secrecy_Secrets @ M @ ( specSecrets @ C4 ) )
% 3.28/1.91 | ( knowle1437066798e_know @ C4 @ ( secrecy_sKS @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_188_not__know__s__not__eout,axiom,
% 3.28/1.91 ! [M: secrecy_Secrets,A2: secrecy_specID] :
% 3.28/1.91 ( ~ ( member @ secrecy_Secrets @ M @ ( specSecrets @ A2 ) )
% 3.28/1.91 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.28/1.91 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_sKS @ M ) )
% 3.28/1.91 => ~ ( eout @ A2 @ ( secrecy_sE @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_189_TBtheore54b__P,axiom,
% 3.28/1.91 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( eoutM @ P @ M2 @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) )
% 3.28/1.91 & ( exprChannel @ Ch2 @ E )
% 3.28/1.91 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) )
% 3.28/1.91 & ( member @ secrecy_chanID @ Ch2 @ M2 ) )
% 3.28/1.91 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_190_TBtheorem5b__PQ,axiom,
% 3.28/1.91 ! [P: secrecy_specID,M2: set @ secrecy_chanID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.91 ( ( ( eoutM @ P @ M2 @ E )
% 3.28/1.91 | ( eoutM @ Q @ M2 @ E ) )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.91 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 3.28/1.91 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 3.28/1.91 & ( member @ secrecy_chanID @ Ch2 @ M2 )
% 3.28/1.91 & ( exprChannel @ Ch2 @ E )
% 3.28/1.91 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ( eoutM @ PQ @ M2 @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_191_TBtheorem45a__P,axiom,
% 3.28/1.91 ! [P: secrecy_specID,E: secrecy_Expression,PQ: secrecy_specID,Q: secrecy_specID] :
% 3.28/1.91 ( ( eout @ P @ E )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 3.28/1.91 & ( exprChannel @ Ch2 @ E )
% 3.28/1.91 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_192_eout__def,axiom,
% 3.28/1.91 ( eout
% 3.28/1.91 = ( ^ [SP: secrecy_specID,E2: secrecy_Expression] :
% 3.28/1.91 ? [Ch3: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 3.28/1.91 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_193_eoutM__def,axiom,
% 3.28/1.91 ( eoutM
% 3.28/1.91 = ( ^ [SP: secrecy_specID,M3: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.28/1.91 ? [Ch3: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 3.28/1.91 & ( member @ secrecy_chanID @ Ch3 @ M3 )
% 3.28/1.91 & ( exprChannel @ Ch3 @ E2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_194_out__exprChannelSet__def,axiom,
% 3.28/1.91 ( out_exprChannelSet
% 3.28/1.91 = ( ^ [SP: secrecy_specID,ChSet2: set @ secrecy_chanID,E2: secrecy_Expression] :
% 3.28/1.91 ( ! [X3: secrecy_chanID] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 3.28/1.91 => ( ( member @ secrecy_chanID @ X3 @ ( out @ SP ) )
% 3.28/1.91 & ( exprChannel @ X3 @ E2 ) ) )
% 3.28/1.91 & ! [X3: secrecy_chanID] :
% 3.28/1.91 ( ( ~ ( member @ secrecy_chanID @ X3 @ ChSet2 )
% 3.28/1.91 & ( member @ secrecy_chanID @ X3 @ ( out @ SP ) ) )
% 3.28/1.91 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_195_out__exprChannelSingle__def,axiom,
% 3.28/1.91 ( out_ex985543062Single
% 3.28/1.91 = ( ^ [SP: secrecy_specID,Ch3: secrecy_chanID,E2: secrecy_Expression] :
% 3.28/1.91 ( ( member @ secrecy_chanID @ Ch3 @ ( out @ SP ) )
% 3.28/1.91 & ( exprChannel @ Ch3 @ E2 )
% 3.28/1.91 & ! [X3: secrecy_chanID,T: nat] :
% 3.28/1.91 ( ( ( member @ secrecy_chanID @ X3 @ ( out @ SP ) )
% 3.28/1.91 & ( X3 != Ch3 ) )
% 3.28/1.91 => ~ ( exprChannel @ X3 @ E2 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_196_correctCompositionOut__prop1,axiom,
% 3.28/1.91 ! [PQ: secrecy_specID,P: secrecy_specID,Q: secrecy_specID,X: secrecy_chanID] :
% 3.28/1.91 ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ( member @ secrecy_chanID @ X @ ( out @ PQ ) )
% 3.28/1.91 => ( ( member @ secrecy_chanID @ X @ ( out @ P ) )
% 3.28/1.91 | ( member @ secrecy_chanID @ X @ ( out @ Q ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_197_TBtheorem5a__PQ,axiom,
% 3.28/1.91 ! [P: secrecy_specID,E: secrecy_Expression,Q: secrecy_specID,PQ: secrecy_specID] :
% 3.28/1.91 ( ( ( eout @ P @ E )
% 3.28/1.91 | ( eout @ Q @ E ) )
% 3.28/1.91 => ( ( ( subcomponents @ PQ )
% 3.28/1.91 = ( insert @ secrecy_specID @ P @ ( insert @ secrecy_specID @ Q @ ( bot_bot @ ( set @ secrecy_specID ) ) ) ) )
% 3.28/1.91 => ( ( correc990227761ionOut @ PQ )
% 3.28/1.91 => ( ? [Ch2: secrecy_chanID] :
% 3.28/1.91 ( ( ( member @ secrecy_chanID @ Ch2 @ ( out @ P ) )
% 3.28/1.91 | ( member @ secrecy_chanID @ Ch2 @ ( out @ Q ) ) )
% 3.28/1.91 & ( exprChannel @ Ch2 @ E )
% 3.28/1.91 & ~ ( member @ secrecy_chanID @ Ch2 @ ( loc @ PQ ) ) )
% 3.28/1.91 => ( eout @ PQ @ E ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_198_outStream__def,axiom,
% 3.28/1.91 ( outStream
% 3.28/1.91 = ( ^ [X3: secrecy_specID] :
% 3.28/1.91 ( ^ [Y4: set @ secrecy_chanID,Z: set @ secrecy_chanID] : ( Y4 = Z )
% 3.28/1.91 @ ( out @ X3 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_199_eout__know__k,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 3.28/1.91 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 = ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 3.28/1.91 = ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 3.28/1.91 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_200_correctCompositionKS__subcomp1,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.28/1.91 ( ( correctCompositionKS @ C4 )
% 3.28/1.91 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.28/1.91 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) )
% 3.28/1.91 => ? [X4: secrecy_specID] :
% 3.28/1.91 ( ( member @ secrecy_specID @ X4 @ ( subcomponents @ C4 ) )
% 3.28/1.91 & ( member @ secrecy_Keys @ Xa @ ( specKeys @ X4 ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_201_correctCompositionKS__subcomp3,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,X: secrecy_specID,Xa: secrecy_Keys] :
% 3.28/1.91 ( ( correctCompositionKS @ C4 )
% 3.28/1.91 => ( ( member @ secrecy_specID @ X @ ( subcomponents @ C4 ) )
% 3.28/1.91 => ( ( member @ secrecy_Keys @ Xa @ ( specKeys @ X ) )
% 3.28/1.91 => ( member @ secrecy_Keys @ Xa @ ( specKeys @ C4 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_202_eout__know__nonKS__k,axiom,
% 3.28/1.91 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 3.28/1.91 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 3.28/1.91 => ( ( eout @ A2 @ ( secrecy_kE @ M ) )
% 3.28/1.91 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 => ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_203_eoutKnowCorrect__L1k,axiom,
% 3.28/1.91 ! [C4: secrecy_specID,M: secrecy_Keys] :
% 3.28/1.91 ( ( knowle1667810483orrect @ C4 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 => ( ( eout @ C4 @ ( secrecy_kE @ M ) )
% 3.28/1.91 => ( ( member @ secrecy_Keys @ M @ ( specKeys @ C4 ) )
% 3.28/1.91 | ( knowle1437066798e_know @ C4 @ ( secrecy_kKS @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_204_not__know__k__not__eout,axiom,
% 3.28/1.91 ! [M: secrecy_Keys,A2: secrecy_specID] :
% 3.28/1.91 ( ~ ( member @ secrecy_Keys @ M @ ( specKeys @ A2 ) )
% 3.28/1.91 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 => ( ( knowle1667810483orrect @ A2 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 => ~ ( eout @ A2 @ ( secrecy_kE @ M ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_205_adv__not__know2,axiom,
% 3.28/1.91 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Secrets] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 3.28/1.91 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_sKS @ M ) )
% 3.28/1.91 => ~ ( eout @ P @ ( secrecy_sE @ M ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_206_adv__not__know1,axiom,
% 3.28/1.91 ! [P: secrecy_specID,A2: secrecy_specID,M: secrecy_Keys] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ secrecy_chanID ) @ ( out @ P ) @ ( ins @ A2 ) )
% 3.28/1.91 => ( ~ ( knowle1437066798e_know @ A2 @ ( secrecy_kKS @ M ) )
% 3.28/1.91 => ~ ( eout @ P @ ( secrecy_kE @ M ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_207_order__refl,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( preorder @ A )
% 3.28/1.91 => ! [X: A] : ( ord_less_eq @ A @ X @ X ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_208_subsetI,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ! [X4: A] :
% 3.28/1.91 ( ( member @ A @ X4 @ A2 )
% 3.28/1.91 => ( member @ A @ X4 @ B ) )
% 3.28/1.91 => ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_209_subset__antisym,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 => ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 3.28/1.91 => ( A2 = B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_210_subset__empty,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( bot_bot @ ( set @ A ) ) )
% 3.28/1.91 = ( A2
% 3.28/1.91 = ( bot_bot @ ( set @ A ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_211_empty__subsetI,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ ( bot_bot @ ( set @ A ) ) @ A2 ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_212_insert__subset,axiom,
% 3.28/1.91 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ X @ A2 ) @ B )
% 3.28/1.91 = ( ( member @ A @ X @ B )
% 3.28/1.91 & ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_213_Un__subset__iff,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A,C4: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 )
% 3.28/1.91 = ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 3.28/1.91 & ( ord_less_eq @ ( set @ A ) @ B @ C4 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_214_singleton__insert__inj__eq_H,axiom,
% 3.28/1.91 ! [A: $tType,A3: A,A2: set @ A,B2: A] :
% 3.28/1.91 ( ( ( insert @ A @ A3 @ A2 )
% 3.28/1.91 = ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) )
% 3.28/1.91 = ( ( A3 = B2 )
% 3.28/1.91 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_215_singleton__insert__inj__eq,axiom,
% 3.28/1.91 ! [A: $tType,B2: A,A3: A,A2: set @ A] :
% 3.28/1.91 ( ( ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) )
% 3.28/1.91 = ( insert @ A @ A3 @ A2 ) )
% 3.28/1.91 = ( ( A3 = B2 )
% 3.28/1.91 & ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ ( bot_bot @ ( set @ A ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_216_subset__Un__eq,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) )
% 3.28/1.91 = ( ^ [A4: set @ A,B5: set @ A] :
% 3.28/1.91 ( ( sup_sup @ ( set @ A ) @ A4 @ B5 )
% 3.28/1.91 = B5 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_217_subset__UnE,axiom,
% 3.28/1.91 ! [A: $tType,C4: set @ A,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ C4 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) )
% 3.28/1.91 => ~ ! [A6: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A6 @ A2 )
% 3.28/1.91 => ! [B6: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ B6 @ B )
% 3.28/1.91 => ( C4
% 3.28/1.91 != ( sup_sup @ ( set @ A ) @ A6 @ B6 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_218_Un__absorb2,axiom,
% 3.28/1.91 ! [A: $tType,B: set @ A,A2: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ B @ A2 )
% 3.28/1.91 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 = A2 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_219_Un__absorb1,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 => ( ( sup_sup @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 = B ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_220_Un__upper2,axiom,
% 3.28/1.91 ! [A: $tType,B: set @ A,A2: set @ A] : ( ord_less_eq @ ( set @ A ) @ B @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_221_Un__upper1,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A] : ( ord_less_eq @ ( set @ A ) @ A2 @ ( sup_sup @ ( set @ A ) @ A2 @ B ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_222_Un__least,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 3.28/1.91 => ( ( ord_less_eq @ ( set @ A ) @ B @ C4 )
% 3.28/1.91 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ C4 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_223_Un__mono,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,C4: set @ A,B: set @ A,D3: set @ A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ C4 )
% 3.28/1.91 => ( ( ord_less_eq @ ( set @ A ) @ B @ D3 )
% 3.28/1.91 => ( ord_less_eq @ ( set @ A ) @ ( sup_sup @ ( set @ A ) @ A2 @ B ) @ ( sup_sup @ ( set @ A ) @ C4 @ D3 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_224_insert__mono,axiom,
% 3.28/1.91 ! [A: $tType,C4: set @ A,D3: set @ A,A3: A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ C4 @ D3 )
% 3.28/1.91 => ( ord_less_eq @ ( set @ A ) @ ( insert @ A @ A3 @ C4 ) @ ( insert @ A @ A3 @ D3 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_225_subset__insert,axiom,
% 3.28/1.91 ! [A: $tType,X: A,A2: set @ A,B: set @ A] :
% 3.28/1.91 ( ~ ( member @ A @ X @ A2 )
% 3.28/1.91 => ( ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ X @ B ) )
% 3.28/1.91 = ( ord_less_eq @ ( set @ A ) @ A2 @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_226_subset__insertI,axiom,
% 3.28/1.91 ! [A: $tType,B: set @ A,A3: A] : ( ord_less_eq @ ( set @ A ) @ B @ ( insert @ A @ A3 @ B ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_227_subset__insertI2,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A,B2: A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 => ( ord_less_eq @ ( set @ A ) @ A2 @ ( insert @ A @ B2 @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_228_le__funD,axiom,
% 3.28/1.91 ! [B4: $tType,A: $tType] :
% 3.28/1.91 ( ( ord @ B4 )
% 3.28/1.91 => ! [F: A > B4,G: A > B4,X: A] :
% 3.28/1.91 ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 3.28/1.91 => ( ord_less_eq @ B4 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_229_le__funE,axiom,
% 3.28/1.91 ! [B4: $tType,A: $tType] :
% 3.28/1.91 ( ( ord @ B4 )
% 3.28/1.91 => ! [F: A > B4,G: A > B4,X: A] :
% 3.28/1.91 ( ( ord_less_eq @ ( A > B4 ) @ F @ G )
% 3.28/1.91 => ( ord_less_eq @ B4 @ ( F @ X ) @ ( G @ X ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_230_le__funI,axiom,
% 3.28/1.91 ! [B4: $tType,A: $tType] :
% 3.28/1.91 ( ( ord @ B4 )
% 3.28/1.91 => ! [F: A > B4,G: A > B4] :
% 3.28/1.91 ( ! [X4: A] : ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( G @ X4 ) )
% 3.28/1.91 => ( ord_less_eq @ ( A > B4 ) @ F @ G ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_231_le__fun__def,axiom,
% 3.28/1.91 ! [B4: $tType,A: $tType] :
% 3.28/1.91 ( ( ord @ B4 )
% 3.28/1.91 => ( ( ord_less_eq @ ( A > B4 ) )
% 3.28/1.91 = ( ^ [F3: A > B4,G2: A > B4] :
% 3.28/1.91 ! [X3: A] : ( ord_less_eq @ B4 @ ( F3 @ X3 ) @ ( G2 @ X3 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_232_order__subst1,axiom,
% 3.28/1.91 ! [A: $tType,B4: $tType] :
% 3.28/1.91 ( ( ( order @ B4 )
% 3.28/1.91 & ( order @ A ) )
% 3.28/1.91 => ! [A3: A,F: B4 > A,B2: B4,C: B4] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A3 @ ( F @ B2 ) )
% 3.28/1.91 => ( ( ord_less_eq @ B4 @ B2 @ C )
% 3.28/1.91 => ( ! [X4: B4,Y: B4] :
% 3.28/1.91 ( ( ord_less_eq @ B4 @ X4 @ Y )
% 3.28/1.91 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y ) ) )
% 3.28/1.91 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_233_order__subst2,axiom,
% 3.28/1.91 ! [A: $tType,C3: $tType] :
% 3.28/1.91 ( ( ( order @ C3 )
% 3.28/1.91 & ( order @ A ) )
% 3.28/1.91 => ! [A3: A,B2: A,F: A > C3,C: C3] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.28/1.91 => ( ( ord_less_eq @ C3 @ ( F @ B2 ) @ C )
% 3.28/1.91 => ( ! [X4: A,Y: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ X4 @ Y )
% 3.28/1.91 => ( ord_less_eq @ C3 @ ( F @ X4 ) @ ( F @ Y ) ) )
% 3.28/1.91 => ( ord_less_eq @ C3 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_234_ord__eq__le__subst,axiom,
% 3.28/1.91 ! [A: $tType,B4: $tType] :
% 3.28/1.91 ( ( ( ord @ B4 )
% 3.28/1.91 & ( ord @ A ) )
% 3.28/1.91 => ! [A3: A,F: B4 > A,B2: B4,C: B4] :
% 3.28/1.91 ( ( A3
% 3.28/1.91 = ( F @ B2 ) )
% 3.28/1.91 => ( ( ord_less_eq @ B4 @ B2 @ C )
% 3.28/1.91 => ( ! [X4: B4,Y: B4] :
% 3.28/1.91 ( ( ord_less_eq @ B4 @ X4 @ Y )
% 3.28/1.91 => ( ord_less_eq @ A @ ( F @ X4 ) @ ( F @ Y ) ) )
% 3.28/1.91 => ( ord_less_eq @ A @ A3 @ ( F @ C ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_235_ord__le__eq__subst,axiom,
% 3.28/1.91 ! [A: $tType,B4: $tType] :
% 3.28/1.91 ( ( ( ord @ B4 )
% 3.28/1.91 & ( ord @ A ) )
% 3.28/1.91 => ! [A3: A,B2: A,F: A > B4,C: B4] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.28/1.91 => ( ( ( F @ B2 )
% 3.28/1.91 = C )
% 3.28/1.91 => ( ! [X4: A,Y: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ X4 @ Y )
% 3.28/1.91 => ( ord_less_eq @ B4 @ ( F @ X4 ) @ ( F @ Y ) ) )
% 3.28/1.91 => ( ord_less_eq @ B4 @ ( F @ A3 ) @ C ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_236_eq__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.28/1.91 = ( ^ [X3: A,Y5: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ X3 @ Y5 )
% 3.28/1.91 & ( ord_less_eq @ A @ Y5 @ X3 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_237_antisym,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [X: A,Y3: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ X @ Y3 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ Y3 @ X )
% 3.28/1.91 => ( X = Y3 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_238_linear,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( linorder @ A )
% 3.28/1.91 => ! [X: A,Y3: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ X @ Y3 )
% 3.28/1.91 | ( ord_less_eq @ A @ Y3 @ X ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_239_eq__refl,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( preorder @ A )
% 3.28/1.91 => ! [X: A,Y3: A] :
% 3.28/1.91 ( ( X = Y3 )
% 3.28/1.91 => ( ord_less_eq @ A @ X @ Y3 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_240_le__cases,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( linorder @ A )
% 3.28/1.91 => ! [X: A,Y3: A] :
% 3.28/1.91 ( ~ ( ord_less_eq @ A @ X @ Y3 )
% 3.28/1.91 => ( ord_less_eq @ A @ Y3 @ X ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_241_order_Otrans,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [A3: A,B2: A,C: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.28/1.91 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_242_le__cases3,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( linorder @ A )
% 3.28/1.91 => ! [X: A,Y3: A,Z2: A] :
% 3.28/1.91 ( ( ( ord_less_eq @ A @ X @ Y3 )
% 3.28/1.91 => ~ ( ord_less_eq @ A @ Y3 @ Z2 ) )
% 3.28/1.91 => ( ( ( ord_less_eq @ A @ Y3 @ X )
% 3.28/1.91 => ~ ( ord_less_eq @ A @ X @ Z2 ) )
% 3.28/1.91 => ( ( ( ord_less_eq @ A @ X @ Z2 )
% 3.28/1.91 => ~ ( ord_less_eq @ A @ Z2 @ Y3 ) )
% 3.28/1.91 => ( ( ( ord_less_eq @ A @ Z2 @ Y3 )
% 3.28/1.91 => ~ ( ord_less_eq @ A @ Y3 @ X ) )
% 3.28/1.91 => ( ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 3.28/1.91 => ~ ( ord_less_eq @ A @ Z2 @ X ) )
% 3.28/1.91 => ~ ( ( ord_less_eq @ A @ Z2 @ X )
% 3.28/1.91 => ~ ( ord_less_eq @ A @ X @ Y3 ) ) ) ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_243_antisym__conv,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [Y3: A,X: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ Y3 @ X )
% 3.28/1.91 => ( ( ord_less_eq @ A @ X @ Y3 )
% 3.28/1.91 = ( X = Y3 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_244_order__class_Oorder_Oeq__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.28/1.91 = ( ^ [A5: A,B7: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A5 @ B7 )
% 3.28/1.91 & ( ord_less_eq @ A @ B7 @ A5 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_245_ord__eq__le__trans,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( ord @ A )
% 3.28/1.91 => ! [A3: A,B2: A,C: A] :
% 3.28/1.91 ( ( A3 = B2 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ B2 @ C )
% 3.28/1.91 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_246_ord__le__eq__trans,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( ord @ A )
% 3.28/1.91 => ! [A3: A,B2: A,C: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.28/1.91 => ( ( B2 = C )
% 3.28/1.91 => ( ord_less_eq @ A @ A3 @ C ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_247_order__class_Oorder_Oantisym,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [A3: A,B2: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.28/1.91 => ( A3 = B2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_248_order__trans,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( preorder @ A )
% 3.28/1.91 => ! [X: A,Y3: A,Z2: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ X @ Y3 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ Y3 @ Z2 )
% 3.28/1.91 => ( ord_less_eq @ A @ X @ Z2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_249_dual__order_Orefl,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [A3: A] : ( ord_less_eq @ A @ A3 @ A3 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_250_linorder__wlog,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( linorder @ A )
% 3.28/1.91 => ! [P: A > A > $o,A3: A,B2: A] :
% 3.28/1.91 ( ! [A7: A,B8: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ A7 @ B8 )
% 3.28/1.91 => ( P @ A7 @ B8 ) )
% 3.28/1.91 => ( ! [A7: A,B8: A] :
% 3.28/1.91 ( ( P @ B8 @ A7 )
% 3.28/1.91 => ( P @ A7 @ B8 ) )
% 3.28/1.91 => ( P @ A3 @ B2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_251_dual__order_Otrans,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [B2: A,A3: A,C: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ C @ B2 )
% 3.28/1.91 => ( ord_less_eq @ A @ C @ A3 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_252_dual__order_Oeq__iff,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ( ( ^ [Y4: A,Z: A] : ( Y4 = Z ) )
% 3.28/1.91 = ( ^ [A5: A,B7: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ B7 @ A5 )
% 3.28/1.91 & ( ord_less_eq @ A @ A5 @ B7 ) ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_253_dual__order_Oantisym,axiom,
% 3.28/1.91 ! [A: $tType] :
% 3.28/1.91 ( ( order @ A )
% 3.28/1.91 => ! [B2: A,A3: A] :
% 3.28/1.91 ( ( ord_less_eq @ A @ B2 @ A3 )
% 3.28/1.91 => ( ( ord_less_eq @ A @ A3 @ B2 )
% 3.28/1.91 => ( A3 = B2 ) ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_254_in__mono,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A,X: A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 => ( ( member @ A @ X @ A2 )
% 3.28/1.91 => ( member @ A @ X @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(fact_255_subsetD,axiom,
% 3.28/1.91 ! [A: $tType,A2: set @ A,B: set @ A,C: A] :
% 3.28/1.91 ( ( ord_less_eq @ ( set @ A ) @ A2 @ B )
% 3.28/1.91 => ( ( member @ A @ C @ A2 )
% 3.28/1.91 => ( member @ A @ C @ B ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Lattices_Obounded__lattice,axiom,
% 3.28/1.91 bounded_lattice @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Set_Oset___Lattices_Obounded__lattice_1,axiom,
% 3.28/1.91 ! [A8: $tType] : ( bounded_lattice @ ( set @ A8 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_fun___Lattices_Obounded__lattice_2,axiom,
% 3.28/1.91 ! [A8: $tType,A9: $tType] :
% 3.28/1.91 ( ( bounded_lattice @ A9 )
% 3.28/1.91 => ( bounded_lattice @ ( A8 > A9 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_fun___Lattices_Obounded__semilattice__sup__bot,axiom,
% 3.28/1.91 ! [A8: $tType,A9: $tType] :
% 3.28/1.91 ( ( bounded_lattice @ A9 )
% 3.28/1.91 => ( bounde1808546759up_bot @ ( A8 > A9 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_fun___Orderings_Opreorder,axiom,
% 3.28/1.91 ! [A8: $tType,A9: $tType] :
% 3.28/1.91 ( ( preorder @ A9 )
% 3.28/1.91 => ( preorder @ ( A8 > A9 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_fun___Orderings_Oorder,axiom,
% 3.28/1.91 ! [A8: $tType,A9: $tType] :
% 3.28/1.91 ( ( order @ A9 )
% 3.28/1.91 => ( order @ ( A8 > A9 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_fun___Orderings_Oord,axiom,
% 3.28/1.91 ! [A8: $tType,A9: $tType] :
% 3.28/1.91 ( ( ord @ A9 )
% 3.28/1.91 => ( ord @ ( A8 > A9 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_fun___Orderings_Obot,axiom,
% 3.28/1.91 ! [A8: $tType,A9: $tType] :
% 3.28/1.91 ( ( bot @ A9 )
% 3.28/1.91 => ( bot @ ( A8 > A9 ) ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Nat_Onat___Orderings_Opreorder_3,axiom,
% 3.28/1.91 preorder @ nat ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Nat_Onat___Orderings_Olinorder,axiom,
% 3.28/1.91 linorder @ nat ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Nat_Onat___Orderings_Oorder_4,axiom,
% 3.28/1.91 order @ nat ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Nat_Onat___Orderings_Oord_5,axiom,
% 3.28/1.91 ord @ nat ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Nat_Onat___Orderings_Obot_6,axiom,
% 3.28/1.91 bot @ nat ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Set_Oset___Lattices_Obounded__semilattice__sup__bot_7,axiom,
% 3.28/1.91 ! [A8: $tType] : ( bounde1808546759up_bot @ ( set @ A8 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Set_Oset___Orderings_Opreorder_8,axiom,
% 3.28/1.91 ! [A8: $tType] : ( preorder @ ( set @ A8 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Set_Oset___Orderings_Oorder_9,axiom,
% 3.28/1.91 ! [A8: $tType] : ( order @ ( set @ A8 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Set_Oset___Orderings_Oord_10,axiom,
% 3.28/1.91 ! [A8: $tType] : ( ord @ ( set @ A8 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_Set_Oset___Orderings_Obot_11,axiom,
% 3.28/1.91 ! [A8: $tType] : ( bot @ ( set @ A8 ) ) ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Lattices_Obounded__semilattice__sup__bot_12,axiom,
% 3.28/1.91 bounde1808546759up_bot @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Orderings_Opreorder_13,axiom,
% 3.28/1.91 preorder @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Orderings_Olinorder_14,axiom,
% 3.28/1.91 linorder @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Orderings_Oorder_15,axiom,
% 3.28/1.91 order @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Orderings_Oord_16,axiom,
% 3.28/1.91 ord @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(tcon_HOL_Obool___Orderings_Obot_17,axiom,
% 3.28/1.91 bot @ $o ).
% 3.28/1.91
% 3.28/1.91 thf(conj_0,conjecture,
% 3.28/1.91 ~ ( member @ secrecy_KS @ ( secrecy_sKS @ secret ) @ ( localSecrets @ pq ) ) ).
% 3.28/1.91 ------------------------
% 3.28/1.93 % (3779)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/183Mi)
% 3.28/1.93 % (3781)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/27Mi)
% 3.28/1.94 % (3782)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/2Mi)
% 3.28/1.94 % (3785)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/18Mi)
% 3.28/1.94 % (3783)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/2Mi)
% 3.28/1.94 % (3784)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/275Mi)
% 3.28/1.94 % (3782)Instruction limit reached!
% 3.28/1.94 % (3782)------------------------------
% 3.28/1.94 % (3782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.94 % (3782)Termination reason: Unknown
% 3.28/1.94 % (3783)Instruction limit reached!
% 3.28/1.94 % (3783)------------------------------
% 3.28/1.94 % (3783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.94 % (3783)Termination reason: Unknown
% 3.28/1.94 % (3783)Termination phase: shuffling
% 3.28/1.94
% 3.28/1.94 % (3783)Memory used [KB]: 1407
% 3.28/1.94 % (3783)Time elapsed: 0.003 s
% 3.28/1.94 % (3783)Instructions burned: 3 (million)
% 3.28/1.94 % (3783)------------------------------
% 3.28/1.94 % (3783)------------------------------
% 3.28/1.94 % (3782)Termination phase: shuffling
% 3.28/1.94
% 3.28/1.94 % (3782)Memory used [KB]: 1407
% 3.28/1.94 % (3782)Time elapsed: 0.003 s
% 3.28/1.94 % (3782)Instructions burned: 3 (million)
% 3.28/1.94 % (3781)Instruction limit reached!
% 3.28/1.94 % (3781)------------------------------
% 3.28/1.94 % (3781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.94 % (3782)------------------------------
% 3.28/1.94 % (3782)------------------------------
% 3.28/1.94 % (3781)Termination reason: Unknown
% 3.28/1.94 % (3781)Termination phase: shuffling
% 3.28/1.94
% 3.28/1.94 % (3781)Memory used [KB]: 1918
% 3.28/1.94 % (3781)Time elapsed: 0.011 s
% 3.28/1.94 % (3781)Instructions burned: 28 (million)
% 3.28/1.94 % (3781)------------------------------
% 3.28/1.94 % (3781)------------------------------
% 3.28/1.94 % (3780)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/4Mi)
% 3.28/1.94 % (3780)Instruction limit reached!
% 3.28/1.94 % (3780)------------------------------
% 3.28/1.94 % (3780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.94 % (3780)Termination reason: Unknown
% 3.28/1.94 % (3780)Termination phase: shuffling
% 3.28/1.94
% 3.28/1.94 % (3780)Memory used [KB]: 1407
% 3.28/1.94 % (3780)Time elapsed: 0.003 s
% 3.28/1.94 % (3780)Instructions burned: 7 (million)
% 3.28/1.94 % (3780)------------------------------
% 3.28/1.94 % (3780)------------------------------
% 3.28/1.95 % (3785)Instruction limit reached!
% 3.28/1.95 % (3785)------------------------------
% 3.28/1.95 % (3785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.95 % (3785)Termination reason: Unknown
% 3.28/1.95 % (3785)Termination phase: shuffling
% 3.28/1.95
% 3.28/1.95 % (3785)Memory used [KB]: 1663
% 3.28/1.95 % (3785)Time elapsed: 0.011 s
% 3.28/1.95 % (3785)Instructions burned: 18 (million)
% 3.28/1.95 % (3785)------------------------------
% 3.28/1.95 % (3785)------------------------------
% 3.28/1.95 % (3789)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/3Mi)
% 3.28/1.95 % (3789)Instruction limit reached!
% 3.28/1.95 % (3789)------------------------------
% 3.28/1.95 % (3789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.95 % (3789)Termination reason: Unknown
% 3.28/1.95 % (3789)Termination phase: shuffling
% 3.28/1.95
% 3.28/1.95 % (3789)Memory used [KB]: 1407
% 3.28/1.95 % (3789)Time elapsed: 0.002 s
% 3.28/1.95 % (3789)Instructions burned: 3 (million)
% 3.28/1.95 % (3789)------------------------------
% 3.28/1.95 % (3789)------------------------------
% 3.28/1.96 % (3786)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/3Mi)
% 3.28/1.96 % (3787)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/37Mi)
% 3.28/1.96 % (3788)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/15Mi)
% 3.28/1.96 % (3786)Instruction limit reached!
% 3.28/1.96 % (3786)------------------------------
% 3.28/1.96 % (3786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.96 % (3786)Termination reason: Unknown
% 3.28/1.96 % (3786)Termination phase: shuffling
% 3.28/1.96
% 3.28/1.96 % (3786)Memory used [KB]: 1407
% 3.28/1.96 % (3786)Time elapsed: 0.003 s
% 3.28/1.96 % (3786)Instructions burned: 3 (million)
% 3.28/1.96 % (3786)------------------------------
% 3.28/1.96 % (3786)------------------------------
% 3.28/1.96 % (3791)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/7Mi)
% 3.28/1.97 % (3791)Instruction limit reached!
% 3.28/1.97 % (3791)------------------------------
% 3.28/1.97 % (3791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.97 % (3791)Termination reason: Unknown
% 3.28/1.97 % (3791)Termination phase: shuffling
% 3.28/1.97
% 3.28/1.97 % (3791)Memory used [KB]: 1535
% 3.28/1.97 % (3791)Time elapsed: 0.004 s
% 3.28/1.97 % (3791)Instructions burned: 9 (million)
% 3.28/1.97 % (3791)------------------------------
% 3.28/1.97 % (3791)------------------------------
% 3.28/1.97 % (3790)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/1041Mi)
% 3.28/1.97 % (3788)Instruction limit reached!
% 3.28/1.97 % (3788)------------------------------
% 3.28/1.97 % (3788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.97 % (3788)Termination reason: Unknown
% 3.28/1.97 % (3788)Termination phase: shuffling
% 3.28/1.97
% 3.28/1.97 % (3788)Memory used [KB]: 1663
% 3.28/1.97 % (3788)Time elapsed: 0.011 s
% 3.28/1.97 % (3788)Instructions burned: 16 (million)
% 3.28/1.97 % (3788)------------------------------
% 3.28/1.97 % (3788)------------------------------
% 3.28/1.97 % (3793)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/3Mi)
% 3.28/1.98 % (3787)Instruction limit reached!
% 3.28/1.98 % (3787)------------------------------
% 3.28/1.98 % (3787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.98 % (3787)Termination reason: Unknown
% 3.28/1.98 % (3787)Termination phase: shuffling
% 3.28/1.98
% 3.28/1.98 % (3787)Memory used [KB]: 2046
% 3.28/1.98 % (3787)Time elapsed: 0.021 s
% 3.28/1.98 % (3787)Instructions burned: 38 (million)
% 3.28/1.98 % (3787)------------------------------
% 3.28/1.98 % (3787)------------------------------
% 3.28/1.98 % (3793)Instruction limit reached!
% 3.28/1.98 % (3793)------------------------------
% 3.28/1.98 % (3793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.98 % (3793)Termination reason: Unknown
% 3.28/1.98 % (3793)Termination phase: shuffling
% 3.28/1.98
% 3.28/1.98 % (3793)Memory used [KB]: 1407
% 3.28/1.98 % (3793)Time elapsed: 0.003 s
% 3.28/1.98 % (3793)Instructions burned: 5 (million)
% 3.28/1.98 % (3793)------------------------------
% 3.28/1.98 % (3793)------------------------------
% 3.28/1.98 % (3784)Refutation not found, incomplete strategy
% 3.28/1.98 % (3784)------------------------------
% 3.28/1.98 % (3784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.98 % (3784)Termination reason: Refutation not found, incomplete strategy
% 3.28/1.98
% 3.28/1.98
% 3.28/1.98 % (3784)Memory used [KB]: 6652
% 3.28/1.98 % (3784)Time elapsed: 0.043 s
% 3.28/1.98 % (3784)Instructions burned: 73 (million)
% 3.28/1.98 % (3784)------------------------------
% 3.28/1.98 % (3784)------------------------------
% 3.28/1.98 % (3792)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/16Mi)
% 3.28/1.99 % (3795)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/7Mi)
% 3.28/1.99 % (3794)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/3Mi)
% 3.28/1.99 % (3792)Instruction limit reached!
% 3.28/1.99 % (3792)------------------------------
% 3.28/1.99 % (3792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.99 % (3792)Termination reason: Unknown
% 3.28/1.99 % (3792)Termination phase: shuffling
% 3.28/1.99
% 3.28/1.99 % (3792)Memory used [KB]: 1663
% 3.28/1.99 % (3792)Time elapsed: 0.011 s
% 3.28/1.99 % (3792)Instructions burned: 17 (million)
% 3.28/1.99 % (3792)------------------------------
% 3.28/1.99 % (3792)------------------------------
% 3.28/1.99 % (3794)Instruction limit reached!
% 3.28/1.99 % (3794)------------------------------
% 3.28/1.99 % (3794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.99 % (3794)Termination reason: Unknown
% 3.28/1.99 % (3794)Termination phase: shuffling
% 3.28/1.99
% 3.28/1.99 % (3794)Memory used [KB]: 1407
% 3.28/1.99 % (3794)Time elapsed: 0.003 s
% 3.28/1.99 % (3794)Instructions burned: 3 (million)
% 3.28/1.99 % (3794)------------------------------
% 3.28/1.99 % (3794)------------------------------
% 3.28/1.99 % (3795)Instruction limit reached!
% 3.28/1.99 % (3795)------------------------------
% 3.28/1.99 % (3795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.99 % (3795)Termination reason: Unknown
% 3.28/1.99 % (3795)Termination phase: shuffling
% 3.28/1.99
% 3.28/1.99 % (3795)Memory used [KB]: 1535
% 3.28/1.99 % (3795)Time elapsed: 0.005 s
% 3.28/1.99 % (3795)Instructions burned: 8 (million)
% 3.28/1.99 % (3795)------------------------------
% 3.28/1.99 % (3795)------------------------------
% 3.28/1.99 % (3779)Instruction limit reached!
% 3.28/1.99 % (3779)------------------------------
% 3.28/1.99 % (3779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/1.99 % (3779)Termination reason: Unknown
% 3.28/1.99 % (3779)Termination phase: Saturation
% 3.28/1.99
% 3.28/1.99 % (3779)Memory used [KB]: 6908
% 3.28/1.99 % (3779)Time elapsed: 0.053 s
% 3.28/1.99 % (3779)Instructions burned: 183 (million)
% 3.28/1.99 % (3779)------------------------------
% 3.28/1.99 % (3779)------------------------------
% 3.28/2.00 % (3797)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/4Mi)
% 3.28/2.00 % (3800)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/6Mi)
% 3.28/2.00 % (3797)Instruction limit reached!
% 3.28/2.00 % (3797)------------------------------
% 3.28/2.00 % (3797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/2.00 % (3797)Termination reason: Unknown
% 3.28/2.00 % (3797)Termination phase: shuffling
% 3.28/2.00
% 3.28/2.00 % (3797)Memory used [KB]: 1407
% 3.28/2.00 % (3797)Time elapsed: 0.005 s
% 3.28/2.00 % (3797)Instructions burned: 5 (million)
% 3.28/2.00 % (3797)------------------------------
% 3.28/2.00 % (3797)------------------------------
% 3.28/2.00 % (3800)Instruction limit reached!
% 3.28/2.00 % (3800)------------------------------
% 3.28/2.00 % (3800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/2.00 % (3800)Termination reason: Unknown
% 3.28/2.00 % (3800)Termination phase: shuffling
% 3.28/2.00
% 3.28/2.00 % (3800)Memory used [KB]: 1407
% 3.28/2.00 % (3800)Time elapsed: 0.003 s
% 3.28/2.00 % (3800)Instructions burned: 6 (million)
% 3.28/2.00 % (3800)------------------------------
% 3.28/2.00 % (3800)------------------------------
% 3.28/2.01 % (3799)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/710Mi)
% 3.28/2.01 % (3796)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/3Mi)
% 3.28/2.01 % (3798)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/18Mi)
% 3.28/2.01 % (3796)Instruction limit reached!
% 3.28/2.01 % (3796)------------------------------
% 3.28/2.01 % (3796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.28/2.01 % (3796)Termination reason: Unknown
% 3.28/2.01 % (3796)Termination phase: shuffling
% 3.28/2.01
% 3.28/2.01 % (3796)Memory used [KB]: 1407
% 3.28/2.01 % (3796)Time elapsed: 0.004 s
% 3.28/2.01 % (3796)Instructions burned: 4 (million)
% 3.28/2.01 % (3796)------------------------------
% 3.28/2.01 % (3796)------------------------------
% 3.28/2.01 % (3801)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/902Mi)
% 3.28/2.01 % (3802)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/21Mi)
% 3.84/2.02 % (3798)Instruction limit reached!
% 3.84/2.02 % (3798)------------------------------
% 3.84/2.02 % (3798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.02 % (3798)Termination reason: Unknown
% 3.84/2.02 % (3798)Termination phase: shuffling
% 3.84/2.02
% 3.84/2.02 % (3798)Memory used [KB]: 1663
% 3.84/2.02 % (3798)Time elapsed: 0.012 s
% 3.84/2.02 % (3798)Instructions burned: 19 (million)
% 3.84/2.02 % (3798)------------------------------
% 3.84/2.02 % (3798)------------------------------
% 3.84/2.02 % (3802)Instruction limit reached!
% 3.84/2.02 % (3802)------------------------------
% 3.84/2.02 % (3802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.02 % (3802)Termination reason: Unknown
% 3.84/2.02 % (3802)Termination phase: shuffling
% 3.84/2.02
% 3.84/2.02 % (3802)Memory used [KB]: 1663
% 3.84/2.02 % (3802)Time elapsed: 0.009 s
% 3.84/2.02 % (3802)Instructions burned: 23 (million)
% 3.84/2.02 % (3802)------------------------------
% 3.84/2.02 % (3802)------------------------------
% 3.84/2.02 % (3803)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/5Mi)
% 3.84/2.02 % (3803)Instruction limit reached!
% 3.84/2.02 % (3803)------------------------------
% 3.84/2.02 % (3803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.02 % (3803)Termination reason: Unknown
% 3.84/2.02 % (3803)Termination phase: shuffling
% 3.84/2.02
% 3.84/2.02 % (3803)Memory used [KB]: 1407
% 3.84/2.02 % (3803)Time elapsed: 0.005 s
% 3.84/2.02 % (3803)Instructions burned: 6 (million)
% 3.84/2.02 % (3803)------------------------------
% 3.84/2.02 % (3803)------------------------------
% 3.84/2.03 % (3805)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/377Mi)
% 3.84/2.03 % (3804)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3672 for (2999ds/6Mi)
% 3.84/2.03 % (3804)Instruction limit reached!
% 3.84/2.03 % (3804)------------------------------
% 3.84/2.03 % (3804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.03 % (3804)Termination reason: Unknown
% 3.84/2.03 % (3804)Termination phase: shuffling
% 3.84/2.03
% 3.84/2.03 % (3804)Memory used [KB]: 1407
% 3.84/2.03 % (3804)Time elapsed: 0.005 s
% 3.84/2.03 % (3804)Instructions burned: 7 (million)
% 3.84/2.03 % (3804)------------------------------
% 3.84/2.03 % (3804)------------------------------
% 3.84/2.03 % (3807)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/19Mi)
% 3.84/2.04 % (3806)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/779Mi)
% 3.84/2.04 % (3807)Instruction limit reached!
% 3.84/2.04 % (3807)------------------------------
% 3.84/2.04 % (3807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.04 % (3807)Termination reason: Unknown
% 3.84/2.04 % (3807)Termination phase: shuffling
% 3.84/2.04
% 3.84/2.04 % (3807)Memory used [KB]: 1663
% 3.84/2.04 % (3807)Time elapsed: 0.007 s
% 3.84/2.04 % (3807)Instructions burned: 21 (million)
% 3.84/2.04 % (3807)------------------------------
% 3.84/2.04 % (3807)------------------------------
% 3.84/2.05 % (3809)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/17Mi)
% 3.84/2.05 % (3808)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/879Mi)
% 3.84/2.05 % (3809)Instruction limit reached!
% 3.84/2.05 % (3809)------------------------------
% 3.84/2.05 % (3809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.05 % (3809)Termination reason: Unknown
% 3.84/2.05 % (3809)Termination phase: shuffling
% 3.84/2.05
% 3.84/2.05 % (3809)Memory used [KB]: 1663
% 3.84/2.05 % (3809)Time elapsed: 0.007 s
% 3.84/2.05 % (3809)Instructions burned: 17 (million)
% 3.84/2.05 % (3809)------------------------------
% 3.84/2.05 % (3809)------------------------------
% 3.84/2.06 % (3810)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/3Mi)
% 3.84/2.07 % (3810)Instruction limit reached!
% 3.84/2.07 % (3810)------------------------------
% 3.84/2.07 % (3810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.07 % (3810)Termination reason: Unknown
% 3.84/2.07 % (3810)Termination phase: shuffling
% 3.84/2.07
% 3.84/2.07 % (3810)Memory used [KB]: 1407
% 3.84/2.07 % (3810)Time elapsed: 0.003 s
% 3.84/2.07 % (3810)Instructions burned: 5 (million)
% 3.84/2.07 % (3810)------------------------------
% 3.84/2.07 % (3810)------------------------------
% 3.84/2.08 % (3811)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/30Mi)
% 3.84/2.09 % (3811)Instruction limit reached!
% 3.84/2.09 % (3811)------------------------------
% 3.84/2.09 % (3811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 3.84/2.09 % (3811)Termination reason: Unknown
% 3.84/2.09 % (3811)Termination phase: shuffling
% 3.84/2.09
% 3.84/2.09 % (3811)Memory used [KB]: 1918
% 3.84/2.09 % (3811)Time elapsed: 0.012 s
% 3.84/2.09 % (3811)Instructions burned: 31 (million)
% 3.84/2.09 % (3811)------------------------------
% 3.84/2.09 % (3811)------------------------------
% 3.84/2.10 % (3812)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_3672 for (2998ds/127Mi)
% 4.31/2.13 % (3812)Instruction limit reached!
% 4.31/2.13 % (3812)------------------------------
% 4.31/2.13 % (3812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.31/2.13 % (3812)Termination reason: Unknown
% 4.31/2.13 % (3812)Termination phase: Property scanning
% 4.31/2.13
% 4.31/2.13 % (3812)Memory used [KB]: 2302
% 4.31/2.13 % (3812)Time elapsed: 0.037 s
% 4.31/2.13 % (3812)Instructions burned: 127 (million)
% 4.31/2.13 % (3812)------------------------------
% 4.31/2.13 % (3812)------------------------------
% 4.31/2.13 % (3805)Instruction limit reached!
% 4.31/2.13 % (3805)------------------------------
% 4.31/2.13 % (3805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.31/2.13 % (3805)Termination reason: Unknown
% 4.31/2.13 % (3805)Termination phase: Saturation
% 4.31/2.13
% 4.31/2.13 % (3805)Memory used [KB]: 7803
% 4.31/2.13 % (3805)Time elapsed: 0.107 s
% 4.31/2.13 % (3805)Instructions burned: 377 (million)
% 4.31/2.13 % (3805)------------------------------
% 4.31/2.13 % (3805)------------------------------
% 4.31/2.14 % (3813)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_3672 for (2997ds/100Mi)
% 4.31/2.15 % (3814)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_3672 for (2997ds/3Mi)
% 4.31/2.15 % (3814)Instruction limit reached!
% 4.31/2.15 % (3814)------------------------------
% 4.31/2.15 % (3814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.31/2.15 % (3814)Termination reason: Unknown
% 4.31/2.15 % (3814)Termination phase: shuffling
% 4.31/2.15
% 4.31/2.15 % (3814)Memory used [KB]: 1407
% 4.31/2.15 % (3814)Time elapsed: 0.003 s
% 4.31/2.15 % (3814)Instructions burned: 3 (million)
% 4.31/2.15 % (3814)------------------------------
% 4.31/2.15 % (3814)------------------------------
% 4.31/2.17 % (3813)Instruction limit reached!
% 4.31/2.17 % (3813)------------------------------
% 4.31/2.17 % (3813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.31/2.17 % (3813)Termination reason: Unknown
% 4.31/2.17 % (3813)Termination phase: Property scanning
% 4.31/2.17
% 4.31/2.17 % (3813)Memory used [KB]: 2302
% 4.31/2.17 % (3813)Time elapsed: 0.028 s
% 4.31/2.17 % (3813)Instructions burned: 100 (million)
% 4.31/2.17 % (3813)------------------------------
% 4.31/2.17 % (3813)------------------------------
% 4.31/2.17 % (3815)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_3672 for (2997ds/20Mi)
% 4.31/2.18 % (3816)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_3672 for (2997ds/86Mi)
% 4.31/2.18 % (3815)Instruction limit reached!
% 4.31/2.18 % (3815)------------------------------
% 4.31/2.18 % (3815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.31/2.18 % (3815)Termination reason: Unknown
% 4.31/2.18 % (3815)Termination phase: shuffling
% 4.31/2.18
% 4.31/2.18 % (3815)Memory used [KB]: 1663
% 4.31/2.18 % (3815)Time elapsed: 0.013 s
% 4.31/2.18 % (3815)Instructions burned: 21 (million)
% 4.31/2.18 % (3815)------------------------------
% 4.31/2.18 % (3815)------------------------------
% 4.80/2.20 % (3817)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_3672 for (2997ds/107Mi)
% 4.80/2.20 % (3816)Instruction limit reached!
% 4.80/2.20 % (3816)------------------------------
% 4.80/2.20 % (3816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.20 % (3816)Termination reason: Unknown
% 4.80/2.20 % (3816)Termination phase: Function definition elimination
% 4.80/2.20
% 4.80/2.20 % (3816)Memory used [KB]: 2302
% 4.80/2.20 % (3816)Time elapsed: 0.027 s
% 4.80/2.20 % (3816)Instructions burned: 89 (million)
% 4.80/2.20 % (3816)------------------------------
% 4.80/2.20 % (3816)------------------------------
% 4.80/2.21 % (3818)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_3672 for (2997ds/39Mi)
% 4.80/2.22 % (3818)Instruction limit reached!
% 4.80/2.22 % (3818)------------------------------
% 4.80/2.22 % (3818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.22 % (3818)Termination reason: Unknown
% 4.80/2.22 % (3818)Termination phase: shuffling
% 4.80/2.22
% 4.80/2.22 % (3818)Memory used [KB]: 2046
% 4.80/2.22 % (3818)Time elapsed: 0.012 s
% 4.80/2.22 % (3818)Instructions burned: 39 (million)
% 4.80/2.22 % (3818)------------------------------
% 4.80/2.22 % (3818)------------------------------
% 4.80/2.23 % (3819)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_3672 for (2996ds/448Mi)
% 4.80/2.26 % (3817)Instruction limit reached!
% 4.80/2.26 % (3817)------------------------------
% 4.80/2.26 % (3817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.26 % (3817)Termination reason: Unknown
% 4.80/2.26 % (3817)Termination phase: Property scanning
% 4.80/2.26
% 4.80/2.26 % (3817)Memory used [KB]: 2302
% 4.80/2.26 % (3817)Time elapsed: 0.060 s
% 4.80/2.26 % (3817)Instructions burned: 107 (million)
% 4.80/2.26 % (3817)------------------------------
% 4.80/2.26 % (3817)------------------------------
% 4.80/2.27 % (3820)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_3672 for (2996ds/46Mi)
% 4.80/2.28 % (3820)Instruction limit reached!
% 4.80/2.28 % (3820)------------------------------
% 4.80/2.28 % (3820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.80/2.28 % (3820)Termination reason: Unknown
% 4.80/2.28 % (3820)Termination phase: Property scanning
% 4.80/2.28
% 4.80/2.28 % (3820)Memory used [KB]: 1918
% 4.80/2.28 % (3820)Time elapsed: 0.016 s
% 4.80/2.28 % (3820)Instructions burned: 46 (million)
% 4.80/2.28 % (3820)------------------------------
% 4.80/2.28 % (3820)------------------------------
% 4.80/2.29 % (3821)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_3672 for (2996ds/98Mi)
% 5.26/2.31 % (3801)Instruction limit reached!
% 5.26/2.31 % (3801)------------------------------
% 5.26/2.31 % (3801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.31 % (3801)Termination reason: Unknown
% 5.26/2.31 % (3801)Termination phase: Saturation
% 5.26/2.31
% 5.26/2.31 % (3801)Memory used [KB]: 8059
% 5.26/2.31 % (3801)Time elapsed: 0.300 s
% 5.26/2.31 % (3801)Instructions burned: 902 (million)
% 5.26/2.31 % (3801)------------------------------
% 5.26/2.31 % (3801)------------------------------
% 5.26/2.32 % (3822)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_3672 for (2996ds/507Mi)
% 5.26/2.32 % (3821)Instruction limit reached!
% 5.26/2.32 % (3821)------------------------------
% 5.26/2.32 % (3821)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.32 % (3821)Termination reason: Unknown
% 5.26/2.32 % (3821)Termination phase: Property scanning
% 5.26/2.32
% 5.26/2.32 % (3821)Memory used [KB]: 2302
% 5.26/2.32 % (3821)Time elapsed: 0.028 s
% 5.26/2.32 % (3821)Instructions burned: 99 (million)
% 5.26/2.32 % (3821)------------------------------
% 5.26/2.32 % (3821)------------------------------
% 5.26/2.33 % (3823)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_3672 for (2996ds/149Mi)
% 5.26/2.36 % (3819)Instruction limit reached!
% 5.26/2.36 % (3819)------------------------------
% 5.26/2.36 % (3819)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.36 % (3819)Termination reason: Unknown
% 5.26/2.36 % (3819)Termination phase: Saturation
% 5.26/2.36
% 5.26/2.36 % (3819)Memory used [KB]: 7931
% 5.26/2.36 % (3819)Time elapsed: 0.129 s
% 5.26/2.36 % (3819)Instructions burned: 450 (million)
% 5.26/2.36 % (3819)------------------------------
% 5.26/2.36 % (3819)------------------------------
% 5.26/2.37 % (3799)Instruction limit reached!
% 5.26/2.37 % (3799)------------------------------
% 5.26/2.37 % (3799)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.37 % (3799)Termination reason: Unknown
% 5.26/2.37 % (3799)Termination phase: Saturation
% 5.26/2.37
% 5.26/2.37 % (3799)Memory used [KB]: 8187
% 5.26/2.37 % (3799)Time elapsed: 0.362 s
% 5.26/2.37 % (3799)Instructions burned: 711 (million)
% 5.26/2.37 % (3799)------------------------------
% 5.26/2.37 % (3799)------------------------------
% 5.26/2.37 % (3824)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_3672 for (2995ds/39Mi)
% 5.26/2.37 % (3823)Instruction limit reached!
% 5.26/2.37 % (3823)------------------------------
% 5.26/2.37 % (3823)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.37 % (3823)Termination reason: Unknown
% 5.26/2.37 % (3823)Termination phase: Saturation
% 5.26/2.37
% 5.26/2.37 % (3823)Memory used [KB]: 6780
% 5.26/2.37 % (3823)Time elapsed: 0.043 s
% 5.26/2.37 % (3823)Instructions burned: 149 (million)
% 5.26/2.37 % (3823)------------------------------
% 5.26/2.37 % (3823)------------------------------
% 5.26/2.38 % (3825)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_3672 for (2995ds/6Mi)
% 5.26/2.38 % (3825)Instruction limit reached!
% 5.26/2.38 % (3825)------------------------------
% 5.26/2.38 % (3825)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.38 % (3825)Termination reason: Unknown
% 5.26/2.38 % (3825)Termination phase: shuffling
% 5.26/2.38
% 5.26/2.38 % (3825)Memory used [KB]: 1407
% 5.26/2.38 % (3825)Time elapsed: 0.003 s
% 5.26/2.38 % (3825)Instructions burned: 6 (million)
% 5.26/2.38 % (3825)------------------------------
% 5.26/2.38 % (3825)------------------------------
% 5.26/2.38 % (3826)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_3672 for (2995ds/1087Mi)
% 5.26/2.38 % (3824)Instruction limit reached!
% 5.26/2.38 % (3824)------------------------------
% 5.26/2.38 % (3824)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.26/2.38 % (3824)Termination reason: Unknown
% 5.26/2.38 % (3824)Termination phase: Property scanning
% 5.26/2.38
% 5.26/2.38 % (3824)Memory used [KB]: 1918
% 5.26/2.38 % (3824)Time elapsed: 0.014 s
% 5.26/2.38 % (3824)Instructions burned: 41 (million)
% 5.26/2.38 % (3824)------------------------------
% 5.26/2.38 % (3824)------------------------------
% 5.26/2.39 % (3827)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_3672 for (2995ds/47Mi)
% 5.26/2.39 % (3828)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_3672 for (2995ds/44Mi)
% 5.71/2.40 % (3827)Instruction limit reached!
% 5.71/2.40 % (3827)------------------------------
% 5.71/2.40 % (3827)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.40 % (3827)Termination reason: Unknown
% 5.71/2.40 % (3827)Termination phase: Preprocessing 1
% 5.71/2.40
% 5.71/2.40 % (3827)Memory used [KB]: 1918
% 5.71/2.40 % (3827)Time elapsed: 0.016 s
% 5.71/2.40 % (3827)Instructions burned: 48 (million)
% 5.71/2.40 % (3827)------------------------------
% 5.71/2.40 % (3827)------------------------------
% 5.71/2.41 % (3828)Instruction limit reached!
% 5.71/2.41 % (3828)------------------------------
% 5.71/2.41 % (3828)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.41 % (3828)Termination reason: Unknown
% 5.71/2.41 % (3828)Termination phase: shuffling
% 5.71/2.41
% 5.71/2.41 % (3828)Memory used [KB]: 2174
% 5.71/2.41 % (3828)Time elapsed: 0.014 s
% 5.71/2.41 % (3828)Instructions burned: 46 (million)
% 5.71/2.41 % (3828)------------------------------
% 5.71/2.41 % (3828)------------------------------
% 5.71/2.41 % (3829)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_3672 for (2995ds/432Mi)
% 5.71/2.42 % (3830)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/62Mi)
% 5.71/2.43 % (3830)Instruction limit reached!
% 5.71/2.43 % (3830)------------------------------
% 5.71/2.43 % (3830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.43 % (3830)Termination reason: Unknown
% 5.71/2.43 % (3830)Termination phase: Property scanning
% 5.71/2.43
% 5.71/2.43 % (3830)Memory used [KB]: 2302
% 5.71/2.43 % (3830)Time elapsed: 0.018 s
% 5.71/2.43 % (3830)Instructions burned: 63 (million)
% 5.71/2.43 % (3830)------------------------------
% 5.71/2.43 % (3830)------------------------------
% 5.71/2.44 % (3831)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/31Mi)
% 5.71/2.45 % (3831)Instruction limit reached!
% 5.71/2.45 % (3831)------------------------------
% 5.71/2.45 % (3831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.45 % (3831)Termination reason: Unknown
% 5.71/2.45 % (3831)Termination phase: Property scanning
% 5.71/2.45
% 5.71/2.45 % (3831)Memory used [KB]: 1918
% 5.71/2.45 % (3831)Time elapsed: 0.012 s
% 5.71/2.45 % (3831)Instructions burned: 33 (million)
% 5.71/2.45 % (3831)------------------------------
% 5.71/2.45 % (3831)------------------------------
% 5.71/2.46 % (3806)Instruction limit reached!
% 5.71/2.46 % (3806)------------------------------
% 5.71/2.46 % (3806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.46 % (3806)Termination reason: Unknown
% 5.71/2.46 % (3806)Termination phase: Saturation
% 5.71/2.46
% 5.71/2.46 % (3806)Memory used [KB]: 8187
% 5.71/2.46 % (3806)Time elapsed: 0.420 s
% 5.71/2.46 % (3806)Instructions burned: 779 (million)
% 5.71/2.46 % (3806)------------------------------
% 5.71/2.46 % (3806)------------------------------
% 5.71/2.46 % (3832)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/96Mi)
% 5.71/2.47 % (3822)Instruction limit reached!
% 5.71/2.47 % (3822)------------------------------
% 5.71/2.47 % (3822)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.47 % (3822)Termination reason: Unknown
% 5.71/2.47 % (3822)Termination phase: Saturation
% 5.71/2.47
% 5.71/2.47 % (3822)Memory used [KB]: 8187
% 5.71/2.47 % (3822)Time elapsed: 0.176 s
% 5.71/2.47 % (3822)Instructions burned: 507 (million)
% 5.71/2.47 % (3822)------------------------------
% 5.71/2.47 % (3822)------------------------------
% 5.71/2.47 % (3833)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/453Mi)
% 5.71/2.48 % (3808)Instruction limit reached!
% 5.71/2.48 % (3808)------------------------------
% 5.71/2.48 % (3808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.48 % (3808)Termination reason: Unknown
% 5.71/2.48 % (3808)Termination phase: Saturation
% 5.71/2.48
% 5.71/2.48 % (3808)Memory used [KB]: 7803
% 5.71/2.48 % (3808)Time elapsed: 0.431 s
% 5.71/2.48 % (3808)Instructions burned: 880 (million)
% 5.71/2.48 % (3808)------------------------------
% 5.71/2.48 % (3808)------------------------------
% 5.71/2.48 % (3834)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/71Mi)
% 5.71/2.49 % (3835)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/83Mi)
% 5.71/2.49 % (3832)Instruction limit reached!
% 5.71/2.49 % (3832)------------------------------
% 5.71/2.49 % (3832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.71/2.49 % (3832)Termination reason: Unknown
% 5.71/2.49 % (3832)Termination phase: Property scanning
% 5.71/2.49
% 5.71/2.49 % (3832)Memory used [KB]: 2302
% 5.71/2.49 % (3832)Time elapsed: 0.029 s
% 5.71/2.49 % (3832)Instructions burned: 99 (million)
% 5.71/2.49 % (3832)------------------------------
% 5.71/2.49 % (3832)------------------------------
% 6.99/2.50 % (3836)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/11Mi)
% 6.99/2.50 % (3834)Instruction limit reached!
% 6.99/2.50 % (3834)------------------------------
% 6.99/2.50 % (3834)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.50 % (3834)Termination reason: Unknown
% 6.99/2.50 % (3834)Termination phase: Property scanning
% 6.99/2.50
% 6.99/2.50 % (3834)Memory used [KB]: 2302
% 6.99/2.50 % (3834)Time elapsed: 0.022 s
% 6.99/2.50 % (3834)Instructions burned: 71 (million)
% 6.99/2.50 % (3834)------------------------------
% 6.99/2.50 % (3834)------------------------------
% 6.99/2.51 % (3836)Instruction limit reached!
% 6.99/2.51 % (3836)------------------------------
% 6.99/2.51 % (3836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.51 % (3836)Termination reason: Unknown
% 6.99/2.51 % (3836)Termination phase: shuffling
% 6.99/2.51
% 6.99/2.51 % (3836)Memory used [KB]: 1663
% 6.99/2.51 % (3836)Time elapsed: 0.005 s
% 6.99/2.51 % (3836)Instructions burned: 14 (million)
% 6.99/2.51 % (3836)------------------------------
% 6.99/2.51 % (3836)------------------------------
% 6.99/2.51 % (3837)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/41Mi)
% 6.99/2.51 % (3835)Instruction limit reached!
% 6.99/2.51 % (3835)------------------------------
% 6.99/2.51 % (3835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.51 % (3835)Termination reason: Unknown
% 6.99/2.51 % (3835)Termination phase: Property scanning
% 6.99/2.51
% 6.99/2.51 % (3835)Memory used [KB]: 2046
% 6.99/2.51 % (3835)Time elapsed: 0.025 s
% 6.99/2.51 % (3835)Instructions burned: 83 (million)
% 6.99/2.51 % (3835)------------------------------
% 6.99/2.51 % (3835)------------------------------
% 6.99/2.51 % (3838)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_3672 for (2994ds/6Mi)
% 6.99/2.52 % (3838)Instruction limit reached!
% 6.99/2.52 % (3838)------------------------------
% 6.99/2.52 % (3838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.52 % (3838)Termination reason: Unknown
% 6.99/2.52 % (3838)Termination phase: shuffling
% 6.99/2.52
% 6.99/2.52 % (3838)Memory used [KB]: 1407
% 6.99/2.52 % (3838)Time elapsed: 0.003 s
% 6.99/2.52 % (3838)Instructions burned: 6 (million)
% 6.99/2.52 % (3838)------------------------------
% 6.99/2.52 % (3838)------------------------------
% 6.99/2.52 % (3790)Instruction limit reached!
% 6.99/2.52 % (3790)------------------------------
% 6.99/2.52 % (3790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.52 % (3790)Termination reason: Unknown
% 6.99/2.52 % (3790)Termination phase: Saturation
% 6.99/2.52
% 6.99/2.52 % (3790)Memory used [KB]: 9850
% 6.99/2.52 % (3790)Time elapsed: 0.558 s
% 6.99/2.52 % (3790)Instructions burned: 1042 (million)
% 6.99/2.52 % (3790)------------------------------
% 6.99/2.52 % (3790)------------------------------
% 6.99/2.52 % (3837)Instruction limit reached!
% 6.99/2.52 % (3837)------------------------------
% 6.99/2.52 % (3837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.52 % (3837)Termination reason: Unknown
% 6.99/2.52 % (3837)Termination phase: shuffling
% 6.99/2.52
% 6.99/2.52 % (3837)Memory used [KB]: 2174
% 6.99/2.52 % (3837)Time elapsed: 0.012 s
% 6.99/2.52 % (3837)Instructions burned: 41 (million)
% 6.99/2.52 % (3837)------------------------------
% 6.99/2.52 % (3837)------------------------------
% 6.99/2.52 % (3839)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/150Mi)
% 6.99/2.53 % (3840)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/343Mi)
% 6.99/2.53 % (3841)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/109Mi)
% 6.99/2.54 % (3829)Instruction limit reached!
% 6.99/2.54 % (3829)------------------------------
% 6.99/2.54 % (3829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.54 % (3829)Termination reason: Unknown
% 6.99/2.54 % (3829)Termination phase: Saturation
% 6.99/2.54
% 6.99/2.54 % (3829)Memory used [KB]: 3709
% 6.99/2.54 % (3829)Time elapsed: 0.126 s
% 6.99/2.54 % (3829)Instructions burned: 433 (million)
% 6.99/2.54 % (3829)------------------------------
% 6.99/2.54 % (3829)------------------------------
% 6.99/2.54 % (3842)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/253Mi)
% 6.99/2.56 % (3843)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/140Mi)
% 6.99/2.56 % (3841)Instruction limit reached!
% 6.99/2.56 % (3841)------------------------------
% 6.99/2.56 % (3841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.56 % (3841)Termination reason: Unknown
% 6.99/2.56 % (3841)Termination phase: Property scanning
% 6.99/2.56
% 6.99/2.56 % (3841)Memory used [KB]: 2302
% 6.99/2.56 % (3841)Time elapsed: 0.032 s
% 6.99/2.56 % (3841)Instructions burned: 109 (million)
% 6.99/2.56 % (3841)------------------------------
% 6.99/2.56 % (3841)------------------------------
% 6.99/2.57 % (3844)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/614Mi)
% 6.99/2.59 % (3839)Instruction limit reached!
% 6.99/2.59 % (3839)------------------------------
% 6.99/2.59 % (3839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.99/2.59 % (3839)Termination reason: Unknown
% 6.99/2.59 % (3839)Termination phase: Saturation
% 6.99/2.59
% 6.99/2.59 % (3839)Memory used [KB]: 6908
% 6.99/2.59 % (3839)Time elapsed: 0.070 s
% 6.99/2.59 % (3839)Instructions burned: 151 (million)
% 6.99/2.59 % (3839)------------------------------
% 6.99/2.59 % (3839)------------------------------
% 7.38/2.61 % (3845)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_3672 for (2993ds/202Mi)
% 7.38/2.62 % (3842)Instruction limit reached!
% 7.38/2.62 % (3842)------------------------------
% 7.38/2.62 % (3842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.62 % (3842)Termination reason: Unknown
% 7.38/2.62 % (3842)Termination phase: Saturation
% 7.38/2.62
% 7.38/2.62 % (3842)Memory used [KB]: 7419
% 7.38/2.62 % (3842)Time elapsed: 0.075 s
% 7.38/2.62 % (3842)Instructions burned: 253 (million)
% 7.38/2.62 % (3842)------------------------------
% 7.38/2.62 % (3842)------------------------------
% 7.38/2.63 % (3846)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_3672 for (2992ds/339Mi)
% 7.38/2.63 % (3833)Instruction limit reached!
% 7.38/2.63 % (3833)------------------------------
% 7.38/2.63 % (3833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.63 % (3833)Termination reason: Unknown
% 7.38/2.63 % (3833)Termination phase: Saturation
% 7.38/2.63
% 7.38/2.63 % (3833)Memory used [KB]: 7803
% 7.38/2.63 % (3833)Time elapsed: 0.157 s
% 7.38/2.63 % (3833)Instructions burned: 455 (million)
% 7.38/2.63 % (3833)------------------------------
% 7.38/2.63 % (3833)------------------------------
% 7.38/2.63 % (3840)Instruction limit reached!
% 7.38/2.63 % (3840)------------------------------
% 7.38/2.63 % (3840)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.63 % (3840)Termination reason: Unknown
% 7.38/2.63 % (3840)Termination phase: Saturation
% 7.38/2.63
% 7.38/2.63 % (3840)Memory used [KB]: 7419
% 7.38/2.63 % (3840)Time elapsed: 0.106 s
% 7.38/2.63 % (3840)Instructions burned: 346 (million)
% 7.38/2.63 % (3840)------------------------------
% 7.38/2.63 % (3840)------------------------------
% 7.38/2.63 % (3843)Instruction limit reached!
% 7.38/2.63 % (3843)------------------------------
% 7.38/2.63 % (3843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.63 % (3843)Termination reason: Unknown
% 7.38/2.63 % (3843)Termination phase: Saturation
% 7.38/2.63
% 7.38/2.63 % (3843)Memory used [KB]: 6780
% 7.38/2.63 % (3843)Time elapsed: 0.078 s
% 7.38/2.63 % (3843)Instructions burned: 140 (million)
% 7.38/2.63 % (3843)------------------------------
% 7.38/2.63 % (3843)------------------------------
% 7.38/2.64 % (3847)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=283:si=on:rtra=on_0 on DTF2THF_3672 for (2992ds/283Mi)
% 7.38/2.64 % (3848)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_3672 for (2992ds/134Mi)
% 7.38/2.65 % (3849)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_3672 for (2992ds/298Mi)
% 7.38/2.66 % (3845)Refutation not found, incomplete strategy
% 7.38/2.66 % (3845)------------------------------
% 7.38/2.66 % (3845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.66 % (3845)Termination reason: Refutation not found, incomplete strategy
% 7.38/2.66
% 7.38/2.66
% 7.38/2.66 % (3845)Memory used [KB]: 6652
% 7.38/2.66 % (3845)Time elapsed: 0.047 s
% 7.38/2.66 % (3845)Instructions burned: 83 (million)
% 7.38/2.66 % (3845)------------------------------
% 7.38/2.66 % (3845)------------------------------
% 7.38/2.68 % (3848)Instruction limit reached!
% 7.38/2.68 % (3848)------------------------------
% 7.38/2.68 % (3848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.38/2.68 % (3848)Termination reason: Unknown
% 7.38/2.68 % (3848)Termination phase: Property scanning
% 7.38/2.68
% 7.38/2.68 % (3848)Memory used [KB]: 2302
% 7.38/2.68 % (3848)Time elapsed: 0.037 s
% 7.38/2.68 % (3848)Instructions burned: 134 (million)
% 7.38/2.68 % (3848)------------------------------
% 7.38/2.68 % (3848)------------------------------
% 7.38/2.68 % (3850)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_3672 for (2992ds/192Mi)
% 7.38/2.69 % (3851)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_3672 for (2992ds/258Mi)
% 7.96/2.72 % (3846)Instruction limit reached!
% 7.96/2.72 % (3846)------------------------------
% 7.96/2.72 % (3846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.72 % (3846)Termination reason: Unknown
% 7.96/2.72 % (3846)Termination phase: Saturation
% 7.96/2.72
% 7.96/2.72 % (3846)Memory used [KB]: 7291
% 7.96/2.72 % (3846)Time elapsed: 0.097 s
% 7.96/2.72 % (3846)Instructions burned: 340 (million)
% 7.96/2.72 % (3846)------------------------------
% 7.96/2.72 % (3846)------------------------------
% 7.96/2.73 % (3852)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/90Mi)
% 7.96/2.74 % (3844)Instruction limit reached!
% 7.96/2.74 % (3844)------------------------------
% 7.96/2.74 % (3844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.74 % (3844)Termination reason: Unknown
% 7.96/2.74 % (3844)Termination phase: Saturation
% 7.96/2.74
% 7.96/2.74 % (3844)Memory used [KB]: 8443
% 7.96/2.74 % (3844)Time elapsed: 0.171 s
% 7.96/2.74 % (3844)Instructions burned: 614 (million)
% 7.96/2.74 % (3844)------------------------------
% 7.96/2.74 % (3844)------------------------------
% 7.96/2.75 % (3847)Instruction limit reached!
% 7.96/2.75 % (3847)------------------------------
% 7.96/2.75 % (3847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.75 % (3847)Termination reason: Unknown
% 7.96/2.75 % (3847)Termination phase: Saturation
% 7.96/2.75
% 7.96/2.75 % (3847)Memory used [KB]: 7547
% 7.96/2.75 % (3847)Time elapsed: 0.118 s
% 7.96/2.75 % (3847)Instructions burned: 283 (million)
% 7.96/2.75 % (3847)------------------------------
% 7.96/2.75 % (3847)------------------------------
% 7.96/2.75 % (3853)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/231Mi)
% 7.96/2.76 % (3854)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/458Mi)
% 7.96/2.76 % (3826)Instruction limit reached!
% 7.96/2.76 % (3826)------------------------------
% 7.96/2.76 % (3826)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.76 % (3826)Termination reason: Unknown
% 7.96/2.76 % (3826)Termination phase: Saturation
% 7.96/2.76
% 7.96/2.76 % (3826)Memory used [KB]: 8315
% 7.96/2.76 % (3826)Time elapsed: 0.401 s
% 7.96/2.76 % (3826)Instructions burned: 1089 (million)
% 7.96/2.76 % (3826)------------------------------
% 7.96/2.76 % (3826)------------------------------
% 7.96/2.76 % (3851)Instruction limit reached!
% 7.96/2.76 % (3851)------------------------------
% 7.96/2.76 % (3851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.76 % (3851)Termination reason: Unknown
% 7.96/2.76 % (3851)Termination phase: Saturation
% 7.96/2.76
% 7.96/2.76 % (3851)Memory used [KB]: 7419
% 7.96/2.76 % (3851)Time elapsed: 0.075 s
% 7.96/2.76 % (3851)Instructions burned: 259 (million)
% 7.96/2.76 % (3851)------------------------------
% 7.96/2.76 % (3851)------------------------------
% 7.96/2.76 % (3852)Instruction limit reached!
% 7.96/2.76 % (3852)------------------------------
% 7.96/2.76 % (3852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.76 % (3852)Termination reason: Unknown
% 7.96/2.76 % (3852)Termination phase: Property scanning
% 7.96/2.76
% 7.96/2.76 % (3852)Memory used [KB]: 2302
% 7.96/2.76 % (3852)Time elapsed: 0.028 s
% 7.96/2.76 % (3852)Instructions burned: 93 (million)
% 7.96/2.76 % (3852)------------------------------
% 7.96/2.76 % (3852)------------------------------
% 7.96/2.77 % (3855)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/31Mi)
% 7.96/2.77 % (3856)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/297Mi)
% 7.96/2.77 % (3857)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/987Mi)
% 7.96/2.78 % (3855)Instruction limit reached!
% 7.96/2.78 % (3855)------------------------------
% 7.96/2.78 % (3855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.78 % (3855)Termination reason: Unknown
% 7.96/2.78 % (3855)Termination phase: Property scanning
% 7.96/2.78
% 7.96/2.78 % (3855)Memory used [KB]: 1918
% 7.96/2.78 % (3855)Time elapsed: 0.012 s
% 7.96/2.78 % (3855)Instructions burned: 33 (million)
% 7.96/2.78 % (3855)------------------------------
% 7.96/2.78 % (3855)------------------------------
% 7.96/2.79 % (3850)Instruction limit reached!
% 7.96/2.79 % (3850)------------------------------
% 7.96/2.79 % (3850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.96/2.79 % (3850)Termination reason: Unknown
% 7.96/2.79 % (3850)Termination phase: Saturation
% 7.96/2.79
% 7.96/2.79 % (3850)Memory used [KB]: 3070
% 7.96/2.79 % (3850)Time elapsed: 0.104 s
% 7.96/2.79 % (3850)Instructions burned: 192 (million)
% 7.96/2.79 % (3850)------------------------------
% 7.96/2.79 % (3850)------------------------------
% 7.96/2.79 % (3858)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/182Mi)
% 8.99/2.80 % (3849)Instruction limit reached!
% 8.99/2.80 % (3849)------------------------------
% 8.99/2.80 % (3849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.80 % (3849)Termination reason: Unknown
% 8.99/2.80 % (3849)Termination phase: Saturation
% 8.99/2.80
% 8.99/2.80 % (3849)Memory used [KB]: 7419
% 8.99/2.80 % (3849)Time elapsed: 0.146 s
% 8.99/2.80 % (3849)Instructions burned: 300 (million)
% 8.99/2.80 % (3849)------------------------------
% 8.99/2.80 % (3849)------------------------------
% 8.99/2.81 % (3859)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/182Mi)
% 8.99/2.81 % (3860)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/154Mi)
% 8.99/2.81 % (3853)Instruction limit reached!
% 8.99/2.81 % (3853)------------------------------
% 8.99/2.81 % (3853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.81 % (3853)Termination reason: Unknown
% 8.99/2.81 % (3853)Termination phase: Saturation
% 8.99/2.81
% 8.99/2.81 % (3853)Memory used [KB]: 7164
% 8.99/2.81 % (3853)Time elapsed: 0.060 s
% 8.99/2.81 % (3853)Instructions burned: 231 (million)
% 8.99/2.81 % (3853)------------------------------
% 8.99/2.81 % (3853)------------------------------
% 8.99/2.82 % (3861)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_3672 for (2991ds/79Mi)
% 8.99/2.84 % (3858)Instruction limit reached!
% 8.99/2.84 % (3858)------------------------------
% 8.99/2.84 % (3858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.84 % (3858)Termination reason: Unknown
% 8.99/2.84 % (3858)Termination phase: Saturation
% 8.99/2.84
% 8.99/2.84 % (3858)Memory used [KB]: 6908
% 8.99/2.84 % (3858)Time elapsed: 0.051 s
% 8.99/2.84 % (3858)Instructions burned: 182 (million)
% 8.99/2.84 % (3858)------------------------------
% 8.99/2.84 % (3858)------------------------------
% 8.99/2.84 % (3861)Instruction limit reached!
% 8.99/2.84 % (3861)------------------------------
% 8.99/2.84 % (3861)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.84 % (3861)Termination reason: Unknown
% 8.99/2.85 % (3861)Termination phase: Property scanning
% 8.99/2.85
% 8.99/2.85 % (3861)Memory used [KB]: 2302
% 8.99/2.85 % (3861)Time elapsed: 0.025 s
% 8.99/2.85 % (3861)Instructions burned: 82 (million)
% 8.99/2.85 % (3861)------------------------------
% 8.99/2.85 % (3861)------------------------------
% 8.99/2.85 % (3860)Instruction limit reached!
% 8.99/2.85 % (3860)------------------------------
% 8.99/2.85 % (3860)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.85 % (3860)Termination reason: Unknown
% 8.99/2.85 % (3860)Termination phase: Property scanning
% 8.99/2.85
% 8.99/2.85 % (3860)Memory used [KB]: 2430
% 8.99/2.85 % (3860)Time elapsed: 0.041 s
% 8.99/2.85 % (3860)Instructions burned: 156 (million)
% 8.99/2.85 % (3860)------------------------------
% 8.99/2.85 % (3860)------------------------------
% 8.99/2.85 % (3862)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/216Mi)
% 8.99/2.85 % (3856)Instruction limit reached!
% 8.99/2.85 % (3856)------------------------------
% 8.99/2.85 % (3856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.85 % (3856)Termination reason: Unknown
% 8.99/2.85 % (3856)Termination phase: Saturation
% 8.99/2.85
% 8.99/2.85 % (3856)Memory used [KB]: 7419
% 8.99/2.85 % (3856)Time elapsed: 0.084 s
% 8.99/2.85 % (3856)Instructions burned: 298 (million)
% 8.99/2.85 % (3856)------------------------------
% 8.99/2.85 % (3856)------------------------------
% 8.99/2.85 % (3863)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/114Mi)
% 8.99/2.86 % (3864)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/922Mi)
% 8.99/2.86 % (3865)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/182Mi)
% 8.99/2.89 % (3863)Instruction limit reached!
% 8.99/2.89 % (3863)------------------------------
% 8.99/2.89 % (3863)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.99/2.89 % (3863)Termination reason: Unknown
% 8.99/2.89 % (3863)Termination phase: Property scanning
% 8.99/2.89
% 8.99/2.89 % (3863)Memory used [KB]: 2302
% 8.99/2.89 % (3863)Time elapsed: 0.033 s
% 8.99/2.89 % (3863)Instructions burned: 115 (million)
% 8.99/2.89 % (3863)------------------------------
% 8.99/2.89 % (3863)------------------------------
% 9.50/2.90 % (3867)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/164Mi)
% 9.50/2.91 % (3859)Instruction limit reached!
% 9.50/2.91 % (3859)------------------------------
% 9.50/2.91 % (3859)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.91 % (3859)Termination reason: Unknown
% 9.50/2.91 % (3859)Termination phase: Saturation
% 9.50/2.91
% 9.50/2.91 % (3859)Memory used [KB]: 7164
% 9.50/2.91 % (3859)Time elapsed: 0.122 s
% 9.50/2.91 % (3859)Instructions burned: 183 (million)
% 9.50/2.91 % (3859)------------------------------
% 9.50/2.91 % (3859)------------------------------
% 9.50/2.91 % (3862)Instruction limit reached!
% 9.50/2.91 % (3862)------------------------------
% 9.50/2.91 % (3862)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.91 % (3862)Termination reason: Unknown
% 9.50/2.91 % (3862)Termination phase: Saturation
% 9.50/2.91
% 9.50/2.91 % (3862)Memory used [KB]: 7164
% 9.50/2.91 % (3862)Time elapsed: 0.059 s
% 9.50/2.91 % (3862)Instructions burned: 218 (million)
% 9.50/2.91 % (3862)------------------------------
% 9.50/2.91 % (3862)------------------------------
% 9.50/2.91 % (3865)Instruction limit reached!
% 9.50/2.91 % (3865)------------------------------
% 9.50/2.91 % (3865)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.91 % (3865)Termination reason: Unknown
% 9.50/2.91 % (3865)Termination phase: Saturation
% 9.50/2.91
% 9.50/2.91 % (3865)Memory used [KB]: 6908
% 9.50/2.91 % (3865)Time elapsed: 0.048 s
% 9.50/2.91 % (3865)Instructions burned: 184 (million)
% 9.50/2.91 % (3865)------------------------------
% 9.50/2.91 % (3865)------------------------------
% 9.50/2.92 % (3868)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/50Mi)
% 9.50/2.92 % (3870)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_3672 for (2989ds/1021Mi)
% 9.50/2.92 % (3869)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_3672 for (2990ds/368Mi)
% 9.50/2.93 % (3868)Instruction limit reached!
% 9.50/2.93 % (3868)------------------------------
% 9.50/2.93 % (3868)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.93 % (3868)Termination reason: Unknown
% 9.50/2.93 % (3868)Termination phase: Property scanning
% 9.50/2.93
% 9.50/2.93 % (3868)Memory used [KB]: 2302
% 9.50/2.93 % (3868)Time elapsed: 0.015 s
% 9.50/2.93 % (3868)Instructions burned: 51 (million)
% 9.50/2.93 % (3868)------------------------------
% 9.50/2.93 % (3868)------------------------------
% 9.50/2.94 % (3867)Instruction limit reached!
% 9.50/2.94 % (3867)------------------------------
% 9.50/2.94 % (3867)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.94 % (3867)Termination reason: Unknown
% 9.50/2.94 % (3867)Termination phase: Saturation
% 9.50/2.94
% 9.50/2.94 % (3867)Memory used [KB]: 2302
% 9.50/2.94 % (3867)Time elapsed: 0.045 s
% 9.50/2.94 % (3867)Instructions burned: 167 (million)
% 9.50/2.94 % (3867)------------------------------
% 9.50/2.94 % (3867)------------------------------
% 9.50/2.95 % (3871)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_3672 for (2989ds/267Mi)
% 9.50/2.95 % (3872)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_3672 for (2989ds/204Mi)
% 9.50/2.97 % (3854)Instruction limit reached!
% 9.50/2.97 % (3854)------------------------------
% 9.50/2.97 % (3854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/2.97 % (3854)Termination reason: Unknown
% 9.50/2.97 % (3854)Termination phase: Saturation
% 9.50/2.97
% 9.50/2.97 % (3854)Memory used [KB]: 8187
% 9.50/2.97 % (3854)Time elapsed: 0.215 s
% 9.50/2.97 % (3854)Instructions burned: 459 (million)
% 9.50/2.97 % (3854)------------------------------
% 9.50/2.97 % (3854)------------------------------
% 9.50/2.99 % (3873)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3672 for (2989ds/26Mi)
% 9.50/3.00 % (3873)Instruction limit reached!
% 9.50/3.00 % (3873)------------------------------
% 9.50/3.00 % (3873)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/3.00 % (3873)Termination reason: Unknown
% 9.50/3.00 % (3873)Termination phase: shuffling
% 9.50/3.00
% 9.50/3.00 % (3873)Memory used [KB]: 1791
% 9.50/3.00 % (3873)Time elapsed: 0.015 s
% 9.50/3.00 % (3873)Instructions burned: 26 (million)
% 9.50/3.00 % (3873)------------------------------
% 9.50/3.00 % (3873)------------------------------
% 9.50/3.01 % (3872)Instruction limit reached!
% 9.50/3.01 % (3872)------------------------------
% 9.50/3.01 % (3872)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.50/3.01 % (3872)Termination reason: Unknown
% 9.50/3.01 % (3872)Termination phase: Saturation
% 9.50/3.01
% 9.50/3.01 % (3872)Memory used [KB]: 7036
% 9.50/3.01 % (3872)Time elapsed: 0.058 s
% 9.50/3.01 % (3872)Instructions burned: 205 (million)
% 9.50/3.01 % (3872)------------------------------
% 9.50/3.01 % (3872)------------------------------
% 9.50/3.02 % (3875)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_3672 for (2989ds/4436Mi)
% 10.79/3.02 % (3874)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_3672 for (2989ds/53Mi)
% 10.79/3.04 % (3871)Instruction limit reached!
% 10.79/3.04 % (3871)------------------------------
% 10.79/3.04 % (3871)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.79/3.04 % (3871)Termination reason: Unknown
% 10.79/3.04 % (3871)Termination phase: Saturation
% 10.79/3.04
% 10.79/3.04 % (3871)Memory used [KB]: 7419
% 10.79/3.04 % (3871)Time elapsed: 0.081 s
% 10.79/3.04 % (3871)Instructions burned: 267 (million)
% 10.79/3.04 % (3871)------------------------------
% 10.79/3.04 % (3871)------------------------------
% 10.79/3.05 % (3874)Instruction limit reached!
% 10.79/3.05 % (3874)------------------------------
% 10.79/3.05 % (3874)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.79/3.05 % (3874)Termination reason: Unknown
% 10.79/3.05 % (3874)Termination phase: Property scanning
% 10.79/3.05
% 10.79/3.05 % (3874)Memory used [KB]: 2174
% 10.79/3.05 % (3874)Time elapsed: 0.028 s
% 10.79/3.05 % (3874)Instructions burned: 53 (million)
% 10.79/3.05 % (3874)------------------------------
% 10.79/3.05 % (3874)------------------------------
% 10.79/3.06 % (3876)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_3672 for (2988ds/1539Mi)
% 10.79/3.06 % (3877)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_3672 for (2988ds/408Mi)
% 10.79/3.07 % (3857)Instruction limit reached!
% 10.79/3.07 % (3857)------------------------------
% 10.79/3.07 % (3857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.79/3.07 % (3857)Termination reason: Unknown
% 10.79/3.07 % (3857)Termination phase: Saturation
% 10.79/3.07
% 10.79/3.07 % (3857)Memory used [KB]: 9722
% 10.79/3.07 % (3857)Time elapsed: 0.299 s
% 10.79/3.07 % (3857)Instructions burned: 988 (million)
% 10.79/3.07 % (3857)------------------------------
% 10.79/3.07 % (3857)------------------------------
% 10.79/3.08 % (3878)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_3672 for (2988ds/5205Mi)
% 10.79/3.12 % (3869)Instruction limit reached!
% 10.79/3.12 % (3869)------------------------------
% 10.79/3.12 % (3869)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.79/3.12 % (3869)Termination reason: Unknown
% 10.79/3.12 % (3869)Termination phase: Saturation
% 10.79/3.12
% 10.79/3.12 % (3869)Memory used [KB]: 7547
% 10.79/3.12 % (3869)Time elapsed: 0.195 s
% 10.79/3.12 % (3869)Instructions burned: 369 (million)
% 10.79/3.12 % (3869)------------------------------
% 10.79/3.12 % (3869)------------------------------
% 11.27/3.13 % (3879)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_3672 for (2987ds/1913Mi)
% 11.27/3.14 % (3864)Instruction limit reached!
% 11.27/3.14 % (3864)------------------------------
% 11.27/3.14 % (3864)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.27/3.14 % (3864)Termination reason: Unknown
% 11.27/3.14 % (3864)Termination phase: Saturation
% 11.27/3.14
% 11.27/3.14 % (3864)Memory used [KB]: 7675
% 11.27/3.14 % (3864)Time elapsed: 0.307 s
% 11.27/3.14 % (3864)Instructions burned: 923 (million)
% 11.27/3.14 % (3864)------------------------------
% 11.27/3.14 % (3864)------------------------------
% 11.27/3.15 % (3880)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_3672 for (2987ds/4350Mi)
% 11.27/3.17 % (3880)Refutation not found, incomplete strategy
% 11.27/3.17 % (3880)------------------------------
% 11.27/3.17 % (3880)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.27/3.17 % (3880)Termination reason: Refutation not found, incomplete strategy
% 11.27/3.17
% 11.27/3.17
% 11.27/3.17 % (3880)Memory used [KB]: 6396
% 11.27/3.17 % (3880)Time elapsed: 0.019 s
% 11.27/3.17 % (3880)Instructions burned: 53 (million)
% 11.27/3.17 % (3880)------------------------------
% 11.27/3.17 % (3880)------------------------------
% 11.27/3.18 % (3881)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3672 for (2987ds/68Mi)
% 11.27/3.20 % (3877)Instruction limit reached!
% 11.27/3.20 % (3877)------------------------------
% 11.27/3.20 % (3877)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.27/3.20 % (3877)Termination reason: Unknown
% 11.27/3.20 % (3877)Termination phase: Saturation
% 11.27/3.20
% 11.27/3.20 % (3877)Memory used [KB]: 8187
% 11.27/3.20 % (3877)Time elapsed: 0.138 s
% 11.41/3.20 % (3877)Instructions burned: 409 (million)
% 11.41/3.20 % (3877)------------------------------
% 11.41/3.20 % (3877)------------------------------
% 11.41/3.20 % (3881)Instruction limit reached!
% 11.41/3.20 % (3881)------------------------------
% 11.41/3.20 % (3881)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.41/3.20 % (3881)Termination reason: Unknown
% 11.41/3.20 % (3881)Termination phase: Preprocessing 3
% 11.41/3.20
% 11.41/3.20 % (3881)Memory used [KB]: 2174
% 11.41/3.20 % (3881)Time elapsed: 0.023 s
% 11.41/3.20 % (3881)Instructions burned: 70 (million)
% 11.41/3.20 % (3881)------------------------------
% 11.41/3.20 % (3881)------------------------------
% 11.41/3.21 % (3883)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_3672 for (2987ds/31Mi)
% 11.41/3.21 % (3882)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_3672 for (2987ds/358Mi)
% 11.41/3.22 % (3870)Instruction limit reached!
% 11.41/3.22 % (3870)------------------------------
% 11.41/3.22 % (3870)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.41/3.22 % (3870)Termination reason: Unknown
% 11.41/3.22 % (3870)Termination phase: Saturation
% 11.41/3.22
% 11.41/3.22 % (3870)Memory used [KB]: 9338
% 11.41/3.22 % (3870)Time elapsed: 0.303 s
% 11.41/3.22 % (3870)Instructions burned: 1023 (million)
% 11.41/3.22 % (3870)------------------------------
% 11.41/3.22 % (3870)------------------------------
% 11.41/3.22 % (3883)Instruction limit reached!
% 11.41/3.22 % (3883)------------------------------
% 11.41/3.22 % (3883)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.41/3.22 % (3883)Termination reason: Unknown
% 11.41/3.22 % (3883)Termination phase: Property scanning
% 11.41/3.22
% 11.41/3.22 % (3883)Memory used [KB]: 1918
% 11.41/3.22 % (3883)Time elapsed: 0.012 s
% 11.41/3.22 % (3883)Instructions burned: 32 (million)
% 11.41/3.22 % (3883)------------------------------
% 11.41/3.22 % (3883)------------------------------
% 11.41/3.23 % (3884)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_3672 for (2986ds/279Mi)
% 11.41/3.23 % (3885)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_3672 for (2986ds/258Mi)
% 11.41/3.28 % (3884)Refutation not found, incomplete strategy
% 11.41/3.28 % (3884)------------------------------
% 11.41/3.28 % (3884)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.41/3.28 % (3884)Termination reason: Refutation not found, incomplete strategy
% 11.41/3.28
% 11.41/3.28
% 11.41/3.28 % (3884)Memory used [KB]: 7291
% 11.41/3.28 % (3884)Time elapsed: 0.052 s
% 11.41/3.28 % (3884)Instructions burned: 183 (million)
% 11.41/3.28 % (3884)------------------------------
% 11.41/3.28 % (3884)------------------------------
% 11.41/3.29 % (3886)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_3672 for (2986ds/26Mi)
% 11.70/3.30 % (3886)Instruction limit reached!
% 11.70/3.30 % (3886)------------------------------
% 11.70/3.30 % (3886)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.30 % (3886)Termination reason: Unknown
% 11.70/3.30 % (3886)Termination phase: shuffling
% 11.70/3.30
% 11.70/3.30 % (3886)Memory used [KB]: 1918
% 11.70/3.30 % (3886)Time elapsed: 0.009 s
% 11.70/3.30 % (3886)Instructions burned: 27 (million)
% 11.70/3.30 % (3886)------------------------------
% 11.70/3.30 % (3886)------------------------------
% 11.70/3.31 % (3885)Instruction limit reached!
% 11.70/3.31 % (3885)------------------------------
% 11.70/3.31 % (3885)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.31 % (3885)Termination reason: Unknown
% 11.70/3.31 % (3885)Termination phase: Saturation
% 11.70/3.31
% 11.70/3.31 % (3885)Memory used [KB]: 7419
% 11.70/3.31 % (3885)Time elapsed: 0.080 s
% 11.70/3.31 % (3885)Instructions burned: 258 (million)
% 11.70/3.31 % (3885)------------------------------
% 11.70/3.31 % (3885)------------------------------
% 11.70/3.31 % (3887)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_3672 for (2986ds/995Mi)
% 11.70/3.32 % (3888)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_3672 for (2986ds/373Mi)
% 11.70/3.38 % (3882)Instruction limit reached!
% 11.70/3.38 % (3882)------------------------------
% 11.70/3.38 % (3882)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.70/3.38 % (3882)Termination reason: Unknown
% 11.70/3.38 % (3882)Termination phase: Saturation
% 11.70/3.38
% 11.70/3.38 % (3882)Memory used [KB]: 7547
% 11.70/3.38 % (3882)Time elapsed: 0.169 s
% 11.70/3.38 % (3882)Instructions burned: 359 (million)
% 11.70/3.38 % (3882)------------------------------
% 11.70/3.38 % (3882)------------------------------
% 11.70/3.39 % (3889)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_3672 for (2985ds/253Mi)
% 11.99/3.42 % (3888)Instruction limit reached!
% 11.99/3.42 % (3888)------------------------------
% 11.99/3.42 % (3888)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.99/3.42 % (3888)Termination reason: Unknown
% 11.99/3.42 % (3888)Termination phase: Saturation
% 11.99/3.42
% 11.99/3.42 % (3888)Memory used [KB]: 8059
% 11.99/3.42 % (3888)Time elapsed: 0.106 s
% 11.99/3.42 % (3888)Instructions burned: 374 (million)
% 11.99/3.42 % (3888)------------------------------
% 11.99/3.42 % (3888)------------------------------
% 11.99/3.43 % (3890)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_3672 for (2984ds/832Mi)
% 11.99/3.46 % (3889)Instruction limit reached!
% 11.99/3.46 % (3889)------------------------------
% 11.99/3.46 % (3889)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.99/3.46 % (3889)Termination reason: Unknown
% 11.99/3.46 % (3889)Termination phase: Saturation
% 11.99/3.46
% 11.99/3.46 % (3889)Memory used [KB]: 7419
% 11.99/3.46 % (3889)Time elapsed: 0.068 s
% 11.99/3.46 % (3889)Instructions burned: 254 (million)
% 11.99/3.46 % (3889)------------------------------
% 11.99/3.46 % (3889)------------------------------
% 11.99/3.47 % (3891)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_3672 for (2984ds/668Mi)
% 12.18/3.57 % (3887)Instruction limit reached!
% 12.18/3.57 % (3887)------------------------------
% 12.18/3.57 % (3887)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.18/3.57 % (3887)Termination reason: Unknown
% 12.18/3.57 % (3887)Termination phase: Saturation
% 12.18/3.57
% 12.18/3.57 % (3887)Memory used [KB]: 7803
% 12.18/3.57 % (3887)Time elapsed: 0.266 s
% 12.18/3.57 % (3887)Instructions burned: 996 (million)
% 12.18/3.57 % (3887)------------------------------
% 12.18/3.57 % (3887)------------------------------
% 12.18/3.59 % (3892)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=40:si=on:rtra=on_0 on DTF2THF_3672 for (2983ds/40Mi)
% 12.46/3.60 % (3892)Instruction limit reached!
% 12.46/3.60 % (3892)------------------------------
% 12.46/3.60 % (3892)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.60 % (3892)Termination reason: Unknown
% 12.46/3.60 % (3892)Termination phase: shuffling
% 12.46/3.60
% 12.46/3.60 % (3892)Memory used [KB]: 2174
% 12.46/3.60 % (3892)Time elapsed: 0.013 s
% 12.46/3.60 % (3892)Instructions burned: 42 (million)
% 12.46/3.60 % (3892)------------------------------
% 12.46/3.60 % (3892)------------------------------
% 12.46/3.61 % (3893)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_3672 for (2983ds/294Mi)
% 12.46/3.64 % (3893)Refutation not found, incomplete strategy
% 12.46/3.64 % (3893)------------------------------
% 12.46/3.64 % (3893)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.64 % (3893)Termination reason: Refutation not found, incomplete strategy
% 12.46/3.64
% 12.46/3.64
% 12.46/3.64 % (3893)Memory used [KB]: 6780
% 12.46/3.64 % (3893)Time elapsed: 0.031 s
% 12.46/3.64 % (3893)Instructions burned: 113 (million)
% 12.46/3.64 % (3893)------------------------------
% 12.46/3.64 % (3893)------------------------------
% 12.46/3.64 % (3891)Instruction limit reached!
% 12.46/3.64 % (3891)------------------------------
% 12.46/3.64 % (3891)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.64 % (3891)Termination reason: Unknown
% 12.46/3.64 % (3891)Termination phase: Saturation
% 12.46/3.64
% 12.46/3.64 % (3891)Memory used [KB]: 12153
% 12.46/3.64 % (3891)Time elapsed: 0.179 s
% 12.46/3.64 % (3891)Instructions burned: 668 (million)
% 12.46/3.64 % (3891)------------------------------
% 12.46/3.64 % (3891)------------------------------
% 12.46/3.65 % (3894)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_3672 for (2982ds/187Mi)
% 12.46/3.65 % (3895)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_3672 for (2982ds/371Mi)
% 12.46/3.69 % (3890)Instruction limit reached!
% 12.46/3.69 % (3890)------------------------------
% 12.46/3.69 % (3890)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.46/3.69 % (3890)Termination reason: Unknown
% 12.46/3.69 % (3890)Termination phase: Saturation
% 12.46/3.69
% 12.46/3.69 % (3890)Memory used [KB]: 8187
% 12.46/3.69 % (3890)Time elapsed: 0.254 s
% 12.46/3.69 % (3890)Instructions burned: 832 (million)
% 12.46/3.69 % (3890)------------------------------
% 12.46/3.69 % (3890)------------------------------
% 12.98/3.70 % (3896)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_3672 for (2982ds/1827Mi)
% 12.98/3.70 % (3894)Instruction limit reached!
% 12.98/3.70 % (3894)------------------------------
% 12.98/3.70 % (3894)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.70 % (3894)Termination reason: Unknown
% 12.98/3.70 % (3894)Termination phase: Saturation
% 12.98/3.70
% 12.98/3.70 % (3894)Memory used [KB]: 7164
% 12.98/3.70 % (3894)Time elapsed: 0.053 s
% 12.98/3.70 % (3894)Instructions burned: 187 (million)
% 12.98/3.70 % (3894)------------------------------
% 12.98/3.70 % (3894)------------------------------
% 12.98/3.71 % (3897)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_3672 for (2982ds/70Mi)
% 12.98/3.73 % (3897)Instruction limit reached!
% 12.98/3.73 % (3897)------------------------------
% 12.98/3.73 % (3897)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.73 % (3897)Termination reason: Unknown
% 12.98/3.73 % (3897)Termination phase: Property scanning
% 12.98/3.73
% 12.98/3.73 % (3897)Memory used [KB]: 2302
% 12.98/3.73 % (3897)Time elapsed: 0.020 s
% 12.98/3.73 % (3897)Instructions burned: 71 (million)
% 12.98/3.73 % (3897)------------------------------
% 12.98/3.73 % (3897)------------------------------
% 12.98/3.74 % (3898)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_3672 for (2981ds/316Mi)
% 12.98/3.77 % (3895)Refutation not found, non-redundant clauses discarded% (3895)------------------------------
% 12.98/3.77 % (3895)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.98/3.77 % (3895)Termination reason: Refutation not found, non-redundant clauses discarded
% 12.98/3.77
% 12.98/3.77 % (3895)Memory used [KB]: 7036
% 12.98/3.77 % (3895)Time elapsed: 0.116 s
% 12.98/3.77 % (3895)Instructions burned: 364 (million)
% 12.98/3.77 % (3895)------------------------------
% 12.98/3.77 % (3895)------------------------------
% 12.98/3.78 % (3899)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_3672 for (2981ds/932Mi)
% 13.19/3.80 % (3879)Instruction limit reached!
% 13.19/3.80 % (3879)------------------------------
% 13.19/3.80 % (3879)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.80 % (3879)Termination reason: Unknown
% 13.19/3.80 % (3879)Termination phase: Saturation
% 13.19/3.80
% 13.19/3.80 % (3879)Memory used [KB]: 5373
% 13.19/3.80 % (3879)Time elapsed: 0.672 s
% 13.19/3.80 % (3879)Instructions burned: 1914 (million)
% 13.19/3.80 % (3879)------------------------------
% 13.19/3.80 % (3879)------------------------------
% 13.19/3.81 % (3898)Refutation not found, incomplete strategy
% 13.19/3.81 % (3898)------------------------------
% 13.19/3.81 % (3898)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.81 % (3898)Termination reason: Refutation not found, incomplete strategy
% 13.19/3.81
% 13.19/3.81
% 13.19/3.81 % (3898)Memory used [KB]: 7547
% 13.19/3.81 % (3898)Time elapsed: 0.070 s
% 13.19/3.81 % (3898)Instructions burned: 258 (million)
% 13.19/3.81 % (3898)------------------------------
% 13.19/3.81 % (3898)------------------------------
% 13.19/3.81 % (3900)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_3672 for (2981ds/4714Mi)
% 13.19/3.82 % (3901)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_3672 for (2981ds/8250Mi)
% 13.19/3.86 % (3876)Instruction limit reached!
% 13.19/3.86 % (3876)------------------------------
% 13.19/3.86 % (3876)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.86 % (3876)Termination reason: Unknown
% 13.19/3.86 % (3876)Termination phase: Saturation
% 13.19/3.86
% 13.19/3.86 % (3876)Memory used [KB]: 11001
% 13.19/3.86 % (3876)Time elapsed: 0.805 s
% 13.19/3.86 % (3876)Instructions burned: 1540 (million)
% 13.19/3.86 % (3876)------------------------------
% 13.19/3.86 % (3876)------------------------------
% 13.19/3.87 % (3902)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_3672 for (2980ds/770Mi)
% 13.19/3.88 % (3900)Refutation not found, incomplete strategy
% 13.19/3.88 % (3900)------------------------------
% 13.19/3.88 % (3900)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.88 % (3900)Termination reason: Refutation not found, incomplete strategy
% 13.19/3.88
% 13.19/3.88
% 13.19/3.88 % (3900)Memory used [KB]: 7675
% 13.19/3.88 % (3900)Time elapsed: 0.073 s
% 13.19/3.88 % (3900)Instructions burned: 275 (million)
% 13.19/3.88 % (3900)------------------------------
% 13.19/3.88 % (3900)------------------------------
% 13.19/3.89 % (3902)Refutation not found, incomplete strategy
% 13.19/3.89 % (3902)------------------------------
% 13.19/3.89 % (3902)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.19/3.89 % (3902)Termination reason: Refutation not found, incomplete strategy
% 13.19/3.89
% 13.19/3.89
% 13.19/3.89 % (3902)Memory used [KB]: 6396
% 13.19/3.89 % (3902)Time elapsed: 0.039 s
% 13.19/3.89 % (3902)Instructions burned: 54 (million)
% 13.19/3.89 % (3902)------------------------------
% 13.19/3.89 % (3902)------------------------------
% 13.19/3.89 % (3903)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_3672 for (2980ds/794Mi)
% 14.88/3.90 % (3904)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_3672 for (2980ds/464Mi)
% 17.76/4.04 % (3904)Instruction limit reached!
% 17.76/4.04 % (3904)------------------------------
% 17.76/4.04 % (3904)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 17.76/4.04 % (3904)Termination reason: Unknown
% 17.76/4.04 % (3904)Termination phase: Saturation
% 17.76/4.04
% 17.76/4.04 % (3904)Memory used [KB]: 7547
% 17.76/4.04 % (3904)Time elapsed: 0.132 s
% 17.76/4.04 % (3904)Instructions burned: 464 (million)
% 17.76/4.04 % (3904)------------------------------
% 17.76/4.04 % (3904)------------------------------
% 17.76/4.05 % (3905)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_3672 for (2978ds/1376Mi)
% 18.46/4.13 % (3903)Instruction limit reached!
% 18.46/4.13 % (3903)------------------------------
% 18.46/4.13 % (3903)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.46/4.13 % (3903)Termination reason: Unknown
% 18.46/4.13 % (3903)Termination phase: Saturation
% 18.46/4.13
% 18.46/4.13 % (3903)Memory used [KB]: 5245
% 18.46/4.13 % (3903)Time elapsed: 0.232 s
% 18.46/4.13 % (3903)Instructions burned: 794 (million)
% 18.46/4.13 % (3903)------------------------------
% 18.46/4.13 % (3903)------------------------------
% 18.46/4.14 % (3906)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_3672 for (2977ds/906Mi)
% 18.84/4.26 % (3896)Instruction limit reached!
% 18.84/4.26 % (3896)------------------------------
% 18.84/4.26 % (3896)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.84/4.27 % (3896)Termination reason: Unknown
% 18.84/4.27 % (3896)Termination phase: Saturation
% 18.84/4.27
% 18.84/4.27 % (3896)Memory used [KB]: 9978
% 18.84/4.27 % (3896)Time elapsed: 0.569 s
% 18.84/4.27 % (3896)Instructions burned: 1828 (million)
% 18.84/4.27 % (3896)------------------------------
% 18.84/4.27 % (3896)------------------------------
% 18.84/4.28 % (3907)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_3672 for (2976ds/434Mi)
% 18.84/4.28 % (3899)Instruction limit reached!
% 18.84/4.28 % (3899)------------------------------
% 18.84/4.28 % (3899)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.84/4.28 % (3899)Termination reason: Unknown
% 18.84/4.28 % (3899)Termination phase: Saturation
% 18.84/4.28
% 18.84/4.28 % (3899)Memory used [KB]: 9850
% 18.84/4.28 % (3899)Time elapsed: 0.526 s
% 18.84/4.28 % (3899)Instructions burned: 935 (million)
% 18.84/4.28 % (3899)------------------------------
% 18.84/4.28 % (3899)------------------------------
% 18.84/4.29 % (3908)lrs+10_5:4_cnfonf=conj_eager:fe=axiom:hflw=5:hfsq=on:hfsqc=10:hfsql=off:hud=10:plsq=on:sgt=5:spb=goal_then_units:ss=axioms:i=865:si=on:rtra=on_0 on DTF2THF_3672 for (2976ds/865Mi)
% 19.32/4.39 % (3875)Instruction limit reached!
% 19.32/4.39 % (3875)------------------------------
% 19.32/4.39 % (3875)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.32/4.39 % (3875)Termination reason: Unknown
% 19.32/4.39 % (3875)Termination phase: Saturation
% 19.32/4.39
% 19.32/4.39 % (3875)Memory used [KB]: 10746
% 19.32/4.39 % (3875)Time elapsed: 1.375 s
% 19.32/4.39 % (3875)Instructions burned: 4437 (million)
% 19.32/4.39 % (3875)------------------------------
% 19.32/4.39 % (3875)------------------------------
% 19.62/4.40 % (3909)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=593:si=on:rtra=on_0 on DTF2THF_3672 for (2975ds/593Mi)
% 19.62/4.42 % (3907)Instruction limit reached!
% 19.62/4.42 % (3907)------------------------------
% 19.62/4.42 % (3907)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.62/4.42 % (3907)Termination reason: Unknown
% 19.62/4.42 % (3907)Termination phase: Saturation
% 19.62/4.42
% 19.62/4.42 % (3907)Memory used [KB]: 7419
% 19.62/4.42 % (3907)Time elapsed: 0.146 s
% 19.62/4.42 % (3907)Instructions burned: 437 (million)
% 19.62/4.42 % (3907)------------------------------
% 19.62/4.42 % (3907)------------------------------
% 19.62/4.43 % (3910)dis+10_1:1_sd=2:sgt=20:slsq=on:ss=axioms:st=6.0:i=443:si=on:rtra=on_0 on DTF2THF_3672 for (2974ds/443Mi)
% 19.62/4.43 % (3906)Instruction limit reached!
% 19.62/4.43 % (3906)------------------------------
% 19.62/4.43 % (3906)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.62/4.43 % (3906)Termination reason: Unknown
% 19.62/4.43 % (3906)Termination phase: Saturation
% 19.62/4.43
% 19.62/4.43 % (3906)Memory used [KB]: 12153
% 19.62/4.43 % (3906)Time elapsed: 0.296 s
% 19.62/4.43 % (3906)Instructions burned: 907 (million)
% 19.62/4.43 % (3906)------------------------------
% 19.62/4.43 % (3906)------------------------------
% 19.62/4.44 % (3911)dis+10_1:1_atotf=0.1:cbe=off:sd=3:ss=axioms:st=2.0:i=594:si=on:rtra=on_0 on DTF2THF_3672 for (2974ds/594Mi)
% 20.27/4.54 % (3908)Instruction limit reached!
% 20.27/4.54 % (3908)------------------------------
% 20.27/4.54 % (3908)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.54 % (3908)Termination reason: Unknown
% 20.27/4.54 % (3908)Termination phase: Saturation
% 20.27/4.54
% 20.27/4.54 % (3908)Memory used [KB]: 8059
% 20.27/4.54 % (3908)Time elapsed: 0.250 s
% 20.27/4.54 % (3908)Instructions burned: 865 (million)
% 20.27/4.54 % (3908)------------------------------
% 20.27/4.54 % (3908)------------------------------
% 20.27/4.55 % (3912)ott+10_1:1024_anc=none:bd=off:e2e=on:fde=none:fsr=off:hud=10:ixr=off:nm=4:nwc=5.0:spb=goal:i=327:si=on:rtra=on_0 on DTF2THF_3672 for (2973ds/327Mi)
% 20.27/4.55 % (3910)Instruction limit reached!
% 20.27/4.55 % (3910)------------------------------
% 20.27/4.55 % (3910)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.55 % (3910)Termination reason: Unknown
% 20.27/4.55 % (3910)Termination phase: Saturation
% 20.27/4.55
% 20.27/4.55 % (3910)Memory used [KB]: 7803
% 20.27/4.55 % (3910)Time elapsed: 0.124 s
% 20.27/4.55 % (3910)Instructions burned: 443 (million)
% 20.27/4.55 % (3910)------------------------------
% 20.27/4.55 % (3910)------------------------------
% 20.27/4.56 % (3913)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=5411:si=on:rtra=on_0 on DTF2THF_3672 for (2973ds/5411Mi)
% 20.27/4.56 % (3909)Instruction limit reached!
% 20.27/4.56 % (3909)------------------------------
% 20.27/4.56 % (3909)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.56 % (3909)Termination reason: Unknown
% 20.27/4.56 % (3909)Termination phase: Saturation
% 20.27/4.56
% 20.27/4.56 % (3909)Memory used [KB]: 7931
% 20.27/4.56 % (3909)Time elapsed: 0.164 s
% 20.27/4.56 % (3909)Instructions burned: 594 (million)
% 20.27/4.56 % (3909)------------------------------
% 20.27/4.56 % (3909)------------------------------
% 20.27/4.57 % (3914)lrs+10_1:20_au=on:c=on:cbe=off:cnfonf=lazy_gen:ins=1:plsq=on:plsqc=1:plsqr=46,31:sac=on:i=1762:si=on:rtra=on_0 on DTF2THF_3672 for (2973ds/1762Mi)
% 20.27/4.58 % (3913)Refutation not found, incomplete strategy
% 20.27/4.58 % (3913)------------------------------
% 20.27/4.58 % (3913)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.58 % (3913)Termination reason: Refutation not found, incomplete strategy
% 20.27/4.58
% 20.27/4.58
% 20.27/4.58 % (3913)Memory used [KB]: 6652
% 20.27/4.58 % (3913)Time elapsed: 0.023 s
% 20.27/4.58 % (3913)Instructions burned: 73 (million)
% 20.27/4.59 % (3913)------------------------------
% 20.27/4.59 % (3913)------------------------------
% 20.27/4.59 % (3878)Instruction limit reached!
% 20.27/4.59 % (3878)------------------------------
% 20.27/4.59 % (3878)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.27/4.59 % (3878)Termination reason: Unknown
% 20.27/4.59 % (3878)Termination phase: Saturation
% 20.27/4.59
% 20.27/4.59 % (3878)Memory used [KB]: 15223
% 20.27/4.59 % (3878)Time elapsed: 1.512 s
% 20.27/4.59 % (3878)Instructions burned: 5208 (million)
% 20.27/4.59 % (3878)------------------------------
% 20.27/4.59 % (3878)------------------------------
% 20.27/4.60 % (3915)dis+1003_1:64_cha=on:cnfonf=lazy_gen:hud=9:nwc=8.0:prag=on:i=96:si=on:rtra=on_0 on DTF2THF_3672 for (2973ds/96Mi)
% 21.08/4.60 % (3916)lrs+21_1:1_hud=5:kws=inv_frequency:nm=16:nwc=2.0:prag=on:sos=on:ss=axioms:i=503:si=on:rtra=on_0 on DTF2THF_3672 for (2973ds/503Mi)
% 21.08/4.62 % (3911)Instruction limit reached!
% 21.08/4.62 % (3911)------------------------------
% 21.08/4.62 % (3911)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.62 % (3911)Termination reason: Unknown
% 21.08/4.62 % (3911)Termination phase: Saturation
% 21.08/4.62
% 21.08/4.62 % (3911)Memory used [KB]: 7803
% 21.08/4.62 % (3911)Time elapsed: 0.179 s
% 21.08/4.62 % (3911)Instructions burned: 595 (million)
% 21.08/4.62 % (3911)------------------------------
% 21.08/4.62 % (3911)------------------------------
% 21.08/4.62 % (3915)Instruction limit reached!
% 21.08/4.62 % (3915)------------------------------
% 21.08/4.62 % (3915)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.62 % (3915)Termination reason: Unknown
% 21.08/4.62 % (3915)Termination phase: Property scanning
% 21.08/4.62
% 21.08/4.62 % (3915)Memory used [KB]: 2302
% 21.08/4.62 % (3915)Time elapsed: 0.027 s
% 21.08/4.62 % (3915)Instructions burned: 97 (million)
% 21.08/4.62 % (3915)------------------------------
% 21.08/4.62 % (3915)------------------------------
% 21.08/4.63 % (3917)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_3672 for (2972ds/90Mi)
% 21.08/4.63 % (3918)lrs+10_1:64_hud=5:plsq=on:plsqr=2011171,524288:i=593:si=on:rtra=on_0 on DTF2THF_3672 for (2972ds/593Mi)
% 21.08/4.63 % (3916)Refutation not found, incomplete strategy
% 21.08/4.63 % (3916)------------------------------
% 21.08/4.63 % (3916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.63 % (3916)Termination reason: Refutation not found, incomplete strategy
% 21.08/4.63
% 21.08/4.63
% 21.08/4.63 % (3916)Memory used [KB]: 6908
% 21.08/4.63 % (3916)Time elapsed: 0.034 s
% 21.08/4.63 % (3916)Instructions burned: 108 (million)
% 21.08/4.63 % (3916)------------------------------
% 21.08/4.63 % (3916)------------------------------
% 21.08/4.64 % (3919)dis-1002_1:1_alpa=false:apa=on:au=on:bd=off:cnfonf=off:e2e=on:er=filter:fde=unused:plsq=on:plsqr=9699663,1048576:s2a=on:sos=on:sp=unary_first:i=1512:si=on:rtra=on_0 on DTF2THF_3672 for (2972ds/1512Mi)
% 21.08/4.65 % (3912)Instruction limit reached!
% 21.08/4.65 % (3912)------------------------------
% 21.08/4.65 % (3912)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.65 % (3912)Termination reason: Unknown
% 21.08/4.65 % (3912)Termination phase: Saturation
% 21.08/4.65
% 21.08/4.65 % (3912)Memory used [KB]: 7419
% 21.08/4.65 % (3912)Time elapsed: 0.098 s
% 21.08/4.65 % (3912)Instructions burned: 327 (million)
% 21.08/4.65 % (3912)------------------------------
% 21.08/4.65 % (3912)------------------------------
% 21.08/4.65 % (3917)Instruction limit reached!
% 21.08/4.65 % (3917)------------------------------
% 21.08/4.65 % (3917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.65 % (3917)Termination reason: Unknown
% 21.08/4.65 % (3917)Termination phase: Function definition elimination
% 21.08/4.65
% 21.08/4.65 % (3917)Memory used [KB]: 2302
% 21.08/4.65 % (3917)Time elapsed: 0.027 s
% 21.08/4.65 % (3917)Instructions burned: 90 (million)
% 21.08/4.65 % (3917)------------------------------
% 21.08/4.65 % (3917)------------------------------
% 21.08/4.66 % (3905)Instruction limit reached!
% 21.08/4.66 % (3905)------------------------------
% 21.08/4.66 % (3905)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.08/4.66 % (3905)Termination reason: Unknown
% 21.08/4.66 % (3905)Termination phase: Saturation
% 21.08/4.66
% 21.08/4.66 % (3905)Memory used [KB]: 14200
% 21.08/4.66 % (3905)Time elapsed: 0.606 s
% 21.08/4.66 % (3905)Instructions burned: 1377 (million)
% 21.08/4.66 % (3905)------------------------------
% 21.08/4.66 % (3905)------------------------------
% 21.08/4.66 % (3920)lrs+1002_1:128_cbe=off:cnfonf=lazy_not_gen_be_off:ins=1:i=569:si=on:rtra=on_0 on DTF2THF_3672 for (2972ds/569Mi)
% 21.08/4.66 % (3921)ott+1002_1:1_bd=off:cnfonf=off:e2e=on:fd=off:fe=axiom:hud=5:prag=on:sos=on:i=501:si=on:rtra=on_0 on DTF2THF_3672 for (2972ds/501Mi)
% 21.08/4.68 % (3922)lrs+1010_1:3_cnfonf=conj_eager:fsr=off:prag=on:sd=4:sgt=10:ss=axioms:i=562:si=on:rtra=on_0 on DTF2THF_3672 for (2972ds/562Mi)
% 22.20/4.80 % (3918)Instruction limit reached!
% 22.20/4.80 % (3918)------------------------------
% 22.20/4.80 % (3918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.20/4.80 % (3918)Termination reason: Unknown
% 22.20/4.80 % (3918)Termination phase: Saturation
% 22.20/4.80
% 22.20/4.80 % (3918)Memory used [KB]: 8699
% 22.20/4.80 % (3918)Time elapsed: 0.166 s
% 22.20/4.80 % (3918)Instructions burned: 595 (million)
% 22.20/4.80 % (3918)------------------------------
% 22.20/4.80 % (3918)------------------------------
% 22.30/4.81 % (3923)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3672 for (2971ds/406Mi)
% 22.30/4.81 % (3921)Instruction limit reached!
% 22.30/4.81 % (3921)------------------------------
% 22.30/4.81 % (3921)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.81 % (3921)Termination reason: Unknown
% 22.30/4.81 % (3921)Termination phase: Saturation
% 22.30/4.81
% 22.30/4.81 % (3921)Memory used [KB]: 8187
% 22.30/4.81 % (3921)Time elapsed: 0.149 s
% 22.30/4.81 % (3921)Instructions burned: 503 (million)
% 22.30/4.81 % (3921)------------------------------
% 22.30/4.81 % (3921)------------------------------
% 22.30/4.81 % (3920)Instruction limit reached!
% 22.30/4.81 % (3920)------------------------------
% 22.30/4.81 % (3920)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.30/4.81 % (3920)Termination reason: Unknown
% 22.30/4.81 % (3920)Termination phase: Saturation
% 22.30/4.81
% 22.30/4.81 % (3920)Memory used [KB]: 7803
% 22.30/4.81 % (3920)Time elapsed: 0.155 s
% 22.30/4.81 % (3920)Instructions burned: 570 (million)
% 22.30/4.81 % (3920)------------------------------
% 22.30/4.81 % (3920)------------------------------
% 22.30/4.82 % (3924)dis+1004_1:128_au=on:cbe=off:e2e=on:sac=on:i=582:si=on:rtra=on_0 on DTF2THF_3672 for (2971ds/582Mi)
% 22.30/4.82 % (3925)lrs+2_1:1_au=on:bd=off:bsr=unit_only:sd=2:sgt=32:sos=all:ss=axioms:i=456:si=on:rtra=on_0 on DTF2THF_3672 for (2971ds/456Mi)
% 22.90/4.92 % (3922)Instruction limit reached!
% 22.90/4.92 % (3922)------------------------------
% 22.90/4.92 % (3922)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.92 % (3922)Termination reason: Unknown
% 22.90/4.92 % (3922)Termination phase: Saturation
% 22.90/4.92
% 22.90/4.92 % (3922)Memory used [KB]: 7547
% 22.90/4.92 % (3922)Time elapsed: 0.244 s
% 22.90/4.92 % (3922)Instructions burned: 562 (million)
% 22.90/4.92 % (3922)------------------------------
% 22.90/4.92 % (3922)------------------------------
% 22.90/4.93 % (3926)lrs+1010_1:1_au=on:cbe=off:cnfonf=conj_eager:tgt=ground:i=393:si=on:rtra=on_0 on DTF2THF_3672 for (2970ds/393Mi)
% 22.90/4.95 % (3925)Instruction limit reached!
% 22.90/4.95 % (3925)------------------------------
% 22.90/4.95 % (3925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.95 % (3925)Termination reason: Unknown
% 22.90/4.95 % (3925)Termination phase: Saturation
% 22.90/4.95
% 22.90/4.95 % (3925)Memory used [KB]: 7803
% 22.90/4.95 % (3925)Time elapsed: 0.133 s
% 22.90/4.95 % (3925)Instructions burned: 456 (million)
% 22.90/4.95 % (3925)------------------------------
% 22.90/4.95 % (3925)------------------------------
% 22.90/4.96 % (3927)lrs+1010_1:6_au=on:cnfonf=conj_eager:nwc=10.0:pe=on:prag=on:s2a=on:ss=axioms:st=1.5:i=1335:si=on:rtra=on_0 on DTF2THF_3672 for (2969ds/1335Mi)
% 22.90/4.98 % (3924)Instruction limit reached!
% 22.90/4.98 % (3924)------------------------------
% 22.90/4.98 % (3924)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.90/4.98 % (3924)Termination reason: Unknown
% 22.90/4.98 % (3924)Termination phase: Saturation
% 22.90/4.98
% 22.90/4.98 % (3924)Memory used [KB]: 8827
% 22.90/4.98 % (3924)Time elapsed: 0.163 s
% 22.90/4.98 % (3924)Instructions burned: 584 (million)
% 22.90/4.98 % (3924)------------------------------
% 22.90/4.98 % (3924)------------------------------
% 22.90/4.99 % (3928)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=3373:si=on:rtra=on_0 on DTF2THF_3672 for (2969ds/3373Mi)
% 24.75/5.03 % (3923)Instruction limit reached!
% 24.75/5.03 % (3923)------------------------------
% 24.75/5.03 % (3923)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/5.03 % (3923)Termination reason: Unknown
% 24.75/5.03 % (3923)Termination phase: Saturation
% 24.75/5.03
% 24.75/5.03 % (3923)Memory used [KB]: 7675
% 24.75/5.03 % (3923)Time elapsed: 0.221 s
% 24.75/5.03 % (3923)Instructions burned: 407 (million)
% 24.75/5.03 % (3923)------------------------------
% 24.75/5.03 % (3923)------------------------------
% 24.75/5.04 % (3929)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3672 for (2968ds/474Mi)
% 24.75/5.07 % (3926)Instruction limit reached!
% 24.75/5.07 % (3926)------------------------------
% 24.75/5.07 % (3926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/5.07 % (3926)Termination reason: Unknown
% 24.75/5.07 % (3926)Termination phase: Saturation
% 24.75/5.07
% 24.75/5.07 % (3926)Memory used [KB]: 7419
% 24.75/5.07 % (3926)Time elapsed: 0.128 s
% 24.75/5.07 % (3926)Instructions burned: 394 (million)
% 24.75/5.07 % (3926)------------------------------
% 24.75/5.07 % (3926)------------------------------
% 24.75/5.08 % (3914)Instruction limit reached!
% 24.75/5.08 % (3914)------------------------------
% 24.75/5.08 % (3914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/5.08 % (3914)Termination reason: Unknown
% 24.75/5.08 % (3914)Termination phase: Saturation
% 24.75/5.08
% 24.75/5.08 % (3914)Memory used [KB]: 10234
% 24.75/5.08 % (3914)Time elapsed: 0.507 s
% 24.75/5.08 % (3914)Instructions burned: 1763 (million)
% 24.75/5.08 % (3914)------------------------------
% 24.75/5.08 % (3914)------------------------------
% 24.75/5.08 % (3930)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3672 for (2968ds/157Mi)
% 24.75/5.10 % (3931)dis+1010_1:1_amm=off:cs=on:kws=precedence:nwc=10.0:piset=all:s2a=on:sac=on:sp=unary_frequency:spb=goal:ss=axioms:st=3.0:i=590:si=on:rtra=on_0 on DTF2THF_3672 for (2968ds/590Mi)
% 24.75/5.11 % (3919)Instruction limit reached!
% 24.75/5.11 % (3919)------------------------------
% 24.75/5.11 % (3919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 24.75/5.11 % (3919)Termination reason: Unknown
% 24.75/5.11 % (3919)Termination phase: Saturation
% 24.75/5.11
% 24.75/5.11 % (3919)Memory used [KB]: 8571
% 24.75/5.11 % (3919)Time elapsed: 0.473 s
% 24.75/5.11 % (3919)Instructions burned: 1514 (million)
% 24.75/5.11 % (3919)------------------------------
% 24.75/5.11 % (3919)------------------------------
% 25.35/5.12 % (3932)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=104:si=on:rtra=on_0 on DTF2THF_3672 for (2968ds/104Mi)
% 25.35/5.14 % (3930)Instruction limit reached!
% 25.35/5.14 % (3930)------------------------------
% 25.35/5.14 % (3930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.35/5.14 % (3930)Termination reason: Unknown
% 25.35/5.14 % (3930)Termination phase: Property scanning
% 25.35/5.14
% 25.35/5.14 % (3930)Memory used [KB]: 2430
% 25.35/5.14 % (3930)Time elapsed: 0.059 s
% 25.35/5.14 % (3930)Instructions burned: 157 (million)
% 25.35/5.14 % (3930)------------------------------
% 25.35/5.14 % (3930)------------------------------
% 25.35/5.15 % (3932)Instruction limit reached!
% 25.35/5.15 % (3932)------------------------------
% 25.35/5.15 % (3932)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.35/5.15 % (3932)Termination reason: Unknown
% 25.35/5.15 % (3932)Termination phase: Property scanning
% 25.35/5.15
% 25.35/5.15 % (3932)Memory used [KB]: 2302
% 25.35/5.15 % (3932)Time elapsed: 0.031 s
% 25.35/5.15 % (3932)Instructions burned: 105 (million)
% 25.35/5.15 % (3932)------------------------------
% 25.35/5.15 % (3932)------------------------------
% 25.35/5.15 % (3933)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=414:si=on:rtra=on_0 on DTF2THF_3672 for (2967ds/414Mi)
% 25.35/5.16 % (3934)dis+10_1:1_av=off:bsd=on:bsr=unit_only:fd=off:hud=8:nm=16:prag=on:i=715:si=on:rtra=on_0 on DTF2THF_3672 for (2967ds/715Mi)
% 25.35/5.18 % (3929)Instruction limit reached!
% 25.35/5.18 % (3929)------------------------------
% 25.35/5.18 % (3929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.35/5.18 % (3929)Termination reason: Unknown
% 25.35/5.18 % (3929)Termination phase: Saturation
% 25.35/5.18
% 25.35/5.18 % (3929)Memory used [KB]: 8059
% 25.35/5.18 % (3929)Time elapsed: 0.137 s
% 25.35/5.18 % (3929)Instructions burned: 476 (million)
% 25.35/5.18 % (3929)------------------------------
% 25.35/5.18 % (3929)------------------------------
% 25.35/5.19 % (3935)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=961:si=on:rtra=on_0 on DTF2THF_3672 for (2967ds/961Mi)
% 25.85/5.27 % (3933)Instruction limit reached!
% 25.85/5.27 % (3933)------------------------------
% 25.85/5.27 % (3933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.85/5.27 % (3933)Termination reason: Unknown
% 25.85/5.27 % (3933)Termination phase: Saturation
% 25.85/5.27
% 25.85/5.27 % (3933)Memory used [KB]: 7675
% 25.85/5.27 % (3933)Time elapsed: 0.137 s
% 25.85/5.27 % (3933)Instructions burned: 414 (million)
% 25.85/5.27 % (3933)------------------------------
% 25.85/5.27 % (3933)------------------------------
% 25.85/5.27 % (3931)Instruction limit reached!
% 25.85/5.27 % (3931)------------------------------
% 25.85/5.27 % (3931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.85/5.27 % (3931)Termination reason: Unknown
% 25.85/5.27 % (3931)Termination phase: Saturation
% 25.85/5.27
% 25.85/5.27 % (3931)Memory used [KB]: 7931
% 25.85/5.27 % (3931)Time elapsed: 0.175 s
% 25.85/5.27 % (3931)Instructions burned: 591 (million)
% 25.85/5.27 % (3931)------------------------------
% 25.85/5.27 % (3931)------------------------------
% 25.85/5.28 % (3936)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=1213:si=on:rtra=on_0 on DTF2THF_3672 for (2966ds/1213Mi)
% 25.85/5.28 % (3937)lrs+1002_1:12_bd=off:hud=1:ntd=on:piset=equals:prag=on:i=1979:si=on:rtra=on_0 on DTF2THF_3672 for (2966ds/1979Mi)
% 26.46/5.35 % (3927)Instruction limit reached!
% 26.46/5.35 % (3927)------------------------------
% 26.46/5.35 % (3927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.46/5.35 % (3927)Termination reason: Unknown
% 26.46/5.35 % (3927)Termination phase: Saturation
% 26.46/5.35
% 26.46/5.35 % (3927)Memory used [KB]: 8955
% 26.46/5.35 % (3927)Time elapsed: 0.386 s
% 26.46/5.35 % (3927)Instructions burned: 1338 (million)
% 26.46/5.35 % (3927)------------------------------
% 26.46/5.35 % (3927)------------------------------
% 26.46/5.36 % (3938)dis+1002_1:1_amm=off:au=on:bsd=on:cbe=off:cnfonf=lazy_gen:sp=unary_frequency:i=481:si=on:rtra=on_0 on DTF2THF_3672 for (2965ds/481Mi)
% 26.46/5.37 % (3934)Instruction limit reached!
% 26.46/5.37 % (3934)------------------------------
% 26.46/5.37 % (3934)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.46/5.37 % (3934)Termination reason: Unknown
% 26.46/5.37 % (3934)Termination phase: Saturation
% 26.46/5.37
% 26.46/5.37 % (3934)Memory used [KB]: 4733
% 26.46/5.37 % (3934)Time elapsed: 0.203 s
% 26.46/5.37 % (3934)Instructions burned: 716 (million)
% 26.46/5.37 % (3934)------------------------------
% 26.46/5.37 % (3934)------------------------------
% 26.46/5.38 % (3939)dis+10_8:1_apa=on:cnfonf=off:e2e=on:plsq=on:plsqc=1:plsqr=32,1:ss=axioms:i=783:si=on:rtra=on_0 on DTF2THF_3672 for (2965ds/783Mi)
% 26.92/5.46 % (3935)Instruction limit reached!
% 26.92/5.46 % (3935)------------------------------
% 26.92/5.46 % (3935)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.92/5.46 % (3935)Termination reason: Unknown
% 26.92/5.46 % (3935)Termination phase: Saturation
% 26.92/5.46
% 26.92/5.46 % (3935)Memory used [KB]: 9210
% 26.92/5.46 % (3935)Time elapsed: 0.273 s
% 26.92/5.46 % (3935)Instructions burned: 961 (million)
% 26.92/5.46 % (3935)------------------------------
% 26.92/5.46 % (3935)------------------------------
% 26.92/5.47 % (3940)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=432:si=on:rtra=on_0 on DTF2THF_3672 for (2964ds/432Mi)
% 27.41/5.50 % (3938)Instruction limit reached!
% 27.41/5.50 % (3938)------------------------------
% 27.41/5.50 % (3938)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.41/5.50 % (3938)Termination reason: Unknown
% 27.41/5.50 % (3938)Termination phase: Saturation
% 27.41/5.50
% 27.41/5.50 % (3938)Memory used [KB]: 8059
% 27.41/5.50 % (3938)Time elapsed: 0.142 s
% 27.41/5.50 % (3938)Instructions burned: 483 (million)
% 27.41/5.50 % (3938)------------------------------
% 27.41/5.50 % (3938)------------------------------
% 27.41/5.51 % (3941)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=1670:si=on:rtra=on_0 on DTF2THF_3672 for (2964ds/1670Mi)
% 27.76/5.60 % (3940)Instruction limit reached!
% 27.76/5.60 % (3940)------------------------------
% 27.76/5.60 % (3940)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.76/5.60 % (3940)Termination reason: Unknown
% 27.76/5.60 % (3940)Termination phase: Saturation
% 27.76/5.60
% 27.76/5.60 % (3940)Memory used [KB]: 7675
% 27.76/5.60 % (3940)Time elapsed: 0.134 s
% 27.76/5.60 % (3940)Instructions burned: 435 (million)
% 27.76/5.60 % (3940)------------------------------
% 27.76/5.60 % (3940)------------------------------
% 27.76/5.61 % (3942)dis+2_1:1_au=on:hfaw=0:hfsq=on:sp=weighted_frequency:i=90:si=on:rtra=on_0 on DTF2THF_3672 for (2963ds/90Mi)
% 27.76/5.61 % (3939)Instruction limit reached!
% 27.76/5.61 % (3939)------------------------------
% 27.76/5.61 % (3939)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.76/5.61 % (3939)Termination reason: Unknown
% 27.76/5.61 % (3939)Termination phase: Saturation
% 27.76/5.61
% 27.76/5.61 % (3939)Memory used [KB]: 7931
% 27.76/5.61 % (3939)Time elapsed: 0.240 s
% 27.76/5.61 % (3939)Instructions burned: 783 (million)
% 27.76/5.61 % (3939)------------------------------
% 27.76/5.61 % (3939)------------------------------
% 27.76/5.62 % (3943)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3672 for (2962ds/346Mi)
% 27.76/5.64 % (3942)Instruction limit reached!
% 27.76/5.64 % (3942)------------------------------
% 27.76/5.64 % (3942)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.76/5.64 % (3942)Termination reason: Unknown
% 27.76/5.64 % (3942)Termination phase: Property scanning
% 27.76/5.64
% 27.76/5.64 % (3942)Memory used [KB]: 2302
% 27.76/5.64 % (3942)Time elapsed: 0.028 s
% 27.76/5.64 % (3942)Instructions burned: 93 (million)
% 27.76/5.64 % (3942)------------------------------
% 27.76/5.64 % (3942)------------------------------
% 27.76/5.64 % (3936)Instruction limit reached!
% 27.76/5.64 % (3936)------------------------------
% 27.76/5.64 % (3936)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.76/5.64 % (3936)Termination reason: Unknown
% 27.76/5.64 % (3936)Termination phase: Saturation
% 27.76/5.64
% 27.76/5.64 % (3936)Memory used [KB]: 7931
% 27.76/5.64 % (3936)Time elapsed: 0.362 s
% 27.76/5.64 % (3936)Instructions burned: 1216 (million)
% 27.76/5.64 % (3936)------------------------------
% 27.76/5.64 % (3936)------------------------------
% 27.76/5.65 % (3944)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=401:si=on:rtra=on_0 on DTF2THF_3672 for (2962ds/401Mi)
% 27.76/5.65 % (3945)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=6454:si=on:rtra=on_0 on DTF2THF_3672 for (2962ds/6454Mi)
% 28.75/5.72 % (3943)Instruction limit reached!
% 28.75/5.72 % (3943)------------------------------
% 28.75/5.72 % (3943)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.72 % (3943)Termination reason: Unknown
% 28.75/5.72 % (3943)Termination phase: Saturation
% 28.75/5.72
% 28.75/5.72 % (3943)Memory used [KB]: 7675
% 28.75/5.72 % (3943)Time elapsed: 0.098 s
% 28.75/5.72 % (3943)Instructions burned: 348 (million)
% 28.75/5.72 % (3943)------------------------------
% 28.75/5.72 % (3943)------------------------------
% 28.75/5.73 % (3946)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:kws=arity:prag=on:i=283:si=on:rtra=on_0 on DTF2THF_3672 for (2961ds/283Mi)
% 28.75/5.75 % (3944)Instruction limit reached!
% 28.75/5.75 % (3944)------------------------------
% 28.75/5.75 % (3944)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.75 % (3944)Termination reason: Unknown
% 28.75/5.75 % (3944)Termination phase: Saturation
% 28.75/5.75
% 28.75/5.75 % (3944)Memory used [KB]: 7419
% 28.75/5.75 % (3944)Time elapsed: 0.107 s
% 28.75/5.75 % (3944)Instructions burned: 404 (million)
% 28.75/5.75 % (3944)------------------------------
% 28.75/5.75 % (3944)------------------------------
% 28.75/5.76 % (3947)ott+10_1:1_aac=none:apa=on:au=on:cnfonf=off:ntd=on:nwc=12.0:sos=on:i=865:si=on:rtra=on_0 on DTF2THF_3672 for (2961ds/865Mi)
% 28.75/5.78 % (3937)Instruction limit reached!
% 28.75/5.78 % (3937)------------------------------
% 28.75/5.78 % (3937)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 28.75/5.78 % (3937)Termination reason: Unknown
% 28.75/5.78 % (3937)Termination phase: Saturation
% 28.75/5.78
% 28.75/5.78 % (3937)Memory used [KB]: 9210
% 28.75/5.78 % (3937)Time elapsed: 0.497 s
% 28.75/5.78 % (3937)Instructions burned: 1979 (million)
% 28.75/5.78 % (3937)------------------------------
% 28.75/5.78 % (3937)------------------------------
% 28.75/5.79 % (3948)lrs+1002_3:4_au=on:av=off:cnfonf=off:fd=off:fsr=off:ins=2:sd=1:sos=on:ss=axioms:i=4528:si=on:rtra=on_0 on DTF2THF_3672 for (2961ds/4528Mi)
% 29.68/5.80 % (3948)Refutation not found, incomplete strategy
% 29.68/5.80 % (3948)------------------------------
% 29.68/5.80 % (3948)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.68/5.80 % (3948)Termination reason: Refutation not found, incomplete strategy
% 29.68/5.80
% 29.68/5.80
% 29.68/5.80 % (3948)Memory used [KB]: 1918
% 29.68/5.80 % (3948)Time elapsed: 0.018 s
% 29.68/5.80 % (3948)Instructions burned: 55 (million)
% 29.68/5.80 % (3948)------------------------------
% 29.68/5.80 % (3948)------------------------------
% 29.68/5.81 % (3946)Instruction limit reached!
% 29.68/5.81 % (3946)------------------------------
% 29.68/5.81 % (3946)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.68/5.81 % (3946)Termination reason: Unknown
% 29.68/5.81 % (3946)Termination phase: Saturation
% 29.68/5.81
% 29.68/5.81 % (3946)Memory used [KB]: 7419
% 29.68/5.81 % (3946)Time elapsed: 0.080 s
% 29.68/5.81 % (3946)Instructions burned: 286 (million)
% 29.68/5.81 % (3946)------------------------------
% 29.68/5.81 % (3946)------------------------------
% 29.68/5.81 % (3949)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=1001:si=on:rtra=on_0 on DTF2THF_3672 for (2961ds/1001Mi)
% 29.68/5.82 % (3950)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=102:si=on:rtra=on_0 on DTF2THF_3672 for (2961ds/102Mi)
% 29.68/5.85 % (3950)Instruction limit reached!
% 29.68/5.85 % (3950)------------------------------
% 29.68/5.85 % (3950)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 29.68/5.85 % (3950)Termination reason: Unknown
% 29.68/5.85 % (3950)Termination phase: Property scanning
% 29.68/5.85
% 29.68/5.85 % (3950)Memory used [KB]: 2302
% 29.68/5.85 % (3950)Time elapsed: 0.028 s
% 29.68/5.85 % (3950)Instructions burned: 102 (million)
% 29.68/5.85 % (3950)------------------------------
% 29.68/5.85 % (3950)------------------------------
% 29.68/5.86 % (3951)ott+1010_3:1_nm=20:s2a=on:s2at=3.0:sp=const_frequency:i=952:si=on:rtra=on_0 on DTF2THF_3672 for (2960ds/952Mi)
% 30.03/5.97 % (3941)Instruction limit reached!
% 30.03/5.97 % (3941)------------------------------
% 30.03/5.97 % (3941)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.03/5.97 % (3941)Termination reason: Unknown
% 30.03/5.97 % (3941)Termination phase: Saturation
% 30.03/5.97
% 30.03/5.97 % (3941)Memory used [KB]: 9083
% 30.03/5.97 % (3941)Time elapsed: 0.465 s
% 30.03/5.97 % (3941)Instructions burned: 1673 (million)
% 30.03/5.97 % (3941)------------------------------
% 30.03/5.97 % (3941)------------------------------
% 30.03/5.98 % (3952)lrs+1010_1:1024_add=large:c=on:cbe=off:cnfonf=lazy_gen:fde=none:nm=30:piset=and:sac=on:uhcvi=on:i=578:si=on:rtra=on_0 on DTF2THF_3672 for (2959ds/578Mi)
% 30.03/6.03 % (3928)Instruction limit reached!
% 30.03/6.03 % (3928)------------------------------
% 30.03/6.03 % (3928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.03/6.03 % (3928)Termination reason: Unknown
% 30.03/6.03 % (3928)Termination phase: Saturation
% 30.03/6.03
% 30.03/6.03 % (3928)Memory used [KB]: 12665
% 30.03/6.03 % (3928)Time elapsed: 1.034 s
% 30.03/6.03 % (3928)Instructions burned: 3375 (million)
% 30.03/6.03 % (3928)------------------------------
% 30.03/6.03 % (3928)------------------------------
% 30.03/6.03 % (3947)Instruction limit reached!
% 30.03/6.03 % (3947)------------------------------
% 30.03/6.03 % (3947)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 30.03/6.03 % (3947)Termination reason: Unknown
% 30.03/6.03 % (3947)Termination phase: Saturation
% 30.03/6.03
% 30.03/6.03 % (3947)Memory used [KB]: 9083
% 30.03/6.03 % (3947)Time elapsed: 0.269 s
% 30.03/6.03 % (3947)Instructions burned: 867 (million)
% 30.03/6.03 % (3947)------------------------------
% 30.03/6.03 % (3947)------------------------------
% 31.81/6.04 % (3953)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_3672 for (2958ds/643Mi)
% 31.81/6.04 % (3954)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_3672 for (2958ds/865Mi)
% 31.81/6.10 % (3949)Instruction limit reached!
% 31.81/6.10 % (3949)------------------------------
% 31.81/6.10 % (3949)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.81/6.10 % (3949)Termination reason: Unknown
% 31.81/6.10 % (3949)Termination phase: Saturation
% 31.81/6.10
% 31.81/6.10 % (3949)Memory used [KB]: 9210
% 31.81/6.10 % (3949)Time elapsed: 0.284 s
% 31.81/6.10 % (3949)Instructions burned: 1001 (million)
% 31.81/6.10 % (3949)------------------------------
% 31.81/6.10 % (3949)------------------------------
% 31.81/6.11 % (3955)lrs+10_1:1_au=on:erd=off:s2a=on:s2at=3.0:sos=all:i=1174:si=on:rtra=on_0 on DTF2THF_3672 for (2958ds/1174Mi)
% 31.81/6.11 % (3951)Instruction limit reached!
% 31.81/6.11 % (3951)------------------------------
% 31.81/6.11 % (3951)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 31.81/6.11 % (3951)Termination reason: Unknown
% 31.81/6.11 % (3951)Termination phase: Saturation
% 31.81/6.11
% 31.81/6.11 % (3951)Memory used [KB]: 9210
% 31.81/6.11 % (3951)Time elapsed: 0.258 s
% 31.81/6.11 % (3951)Instructions burned: 952 (million)
% 31.81/6.11 % (3951)------------------------------
% 31.81/6.11 % (3951)------------------------------
% 31.81/6.12 % (3956)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=644:si=on:rtra=on_0 on DTF2THF_3672 for (2958ds/644Mi)
% 32.34/6.15 % (3952)Instruction limit reached!
% 32.34/6.15 % (3952)------------------------------
% 32.34/6.15 % (3952)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.34/6.15 % (3952)Termination reason: Unknown
% 32.34/6.15 % (3952)Termination phase: Saturation
% 32.34/6.15
% 32.34/6.15 % (3952)Memory used [KB]: 8315
% 32.34/6.15 % (3952)Time elapsed: 0.170 s
% 32.34/6.15 % (3952)Instructions burned: 579 (million)
% 32.34/6.15 % (3952)------------------------------
% 32.34/6.15 % (3952)------------------------------
% 32.34/6.16 % (3957)lrs+10_1:1_alpa=true:au=on:cs=on:tgt=ground:i=1201:si=on:rtra=on_0 on DTF2THF_3672 for (2957ds/1201Mi)
% 32.50/6.21 % (3953)Instruction limit reached!
% 32.50/6.21 % (3953)------------------------------
% 32.50/6.21 % (3953)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.50/6.21 % (3953)Termination reason: Unknown
% 32.50/6.21 % (3953)Termination phase: Saturation
% 32.50/6.21
% 32.50/6.21 % (3953)Memory used [KB]: 8571
% 32.50/6.21 % (3953)Time elapsed: 0.174 s
% 32.50/6.21 % (3953)Instructions burned: 643 (million)
% 32.50/6.21 % (3953)------------------------------
% 32.50/6.21 % (3953)------------------------------
% 32.50/6.22 % (3958)lrs+1666_1:64_cnfonf=lazy_simp:hud=5:plsq=on:plsql=on:plsqr=152565,524288:tnu=2:i=1046:si=on:rtra=on_0 on DTF2THF_3672 for (2957ds/1046Mi)
% 32.88/6.32 % (3956)Instruction limit reached!
% 32.88/6.32 % (3956)------------------------------
% 32.88/6.32 % (3956)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.88/6.32 % (3956)Termination reason: Unknown
% 32.88/6.32 % (3956)Termination phase: Saturation
% 32.88/6.32
% 32.88/6.32 % (3956)Memory used [KB]: 8955
% 32.88/6.32 % (3956)Time elapsed: 0.199 s
% 32.88/6.32 % (3956)Instructions burned: 644 (million)
% 32.88/6.32 % (3956)------------------------------
% 32.88/6.32 % (3956)------------------------------
% 32.88/6.33 % (3959)lrs+1010_1:1_c=on:cnfonf=lazy_simp:fsr=off:hud=5:kws=arity:nm=32:plsq=on:plsqc=1:plsqr=642,29:prag=on:i=222:si=on:rtra=on_0 on DTF2THF_3672 for (2955ds/222Mi)
% 32.88/6.36 % (3954)Instruction limit reached!
% 32.88/6.36 % (3954)------------------------------
% 32.88/6.36 % (3954)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.88/6.36 % (3954)Termination reason: Unknown
% 32.88/6.36 % (3954)Termination phase: Saturation
% 32.88/6.36
% 32.88/6.36 % (3954)Memory used [KB]: 8699
% 32.88/6.36 % (3954)Time elapsed: 0.324 s
% 32.88/6.36 % (3954)Instructions burned: 865 (million)
% 32.88/6.36 % (3954)------------------------------
% 32.88/6.36 % (3954)------------------------------
% 32.88/6.37 % (3960)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_3672 for (2955ds/68Mi)
% 32.88/6.39 % (3959)Instruction limit reached!
% 32.88/6.39 % (3959)------------------------------
% 32.88/6.39 % (3959)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.88/6.39 % (3959)Termination reason: Unknown
% 32.88/6.39 % (3959)Termination phase: Saturation
% 32.88/6.39
% 32.88/6.39 % (3959)Memory used [KB]: 7164
% 32.88/6.39 % (3959)Time elapsed: 0.058 s
% 32.88/6.39 % (3959)Instructions burned: 223 (million)
% 32.88/6.39 % (3959)------------------------------
% 32.88/6.39 % (3959)------------------------------
% 32.88/6.39 % (3960)Instruction limit reached!
% 32.88/6.39 % (3960)------------------------------
% 32.88/6.39 % (3960)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 32.88/6.39 % (3960)Termination reason: Unknown
% 32.88/6.39 % (3960)Termination phase: Preprocessing 3
% 32.88/6.39
% 32.88/6.39 % (3960)Memory used [KB]: 2174
% 32.88/6.39 % (3960)Time elapsed: 0.022 s
% 32.88/6.39 % (3960)Instructions burned: 69 (million)
% 32.88/6.39 % (3960)------------------------------
% 32.88/6.39 % (3960)------------------------------
% 33.72/6.40 % (3961)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_3672 for (2955ds/454Mi)
% 33.72/6.40 % (3962)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_3672 for (2955ds/360Mi)
% 33.72/6.46 % (3955)Instruction limit reached!
% 33.72/6.46 % (3955)------------------------------
% 33.72/6.46 % (3955)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 33.72/6.46 % (3955)Termination reason: Unknown
% 33.72/6.46 % (3955)Termination phase: Saturation
% 33.72/6.46
% 33.72/6.46 % (3955)Memory used [KB]: 9466
% 33.72/6.46 % (3955)Time elapsed: 0.350 s
% 33.72/6.46 % (3955)Instructions burned: 1176 (million)
% 33.72/6.46 % (3955)------------------------------
% 33.72/6.46 % (3955)------------------------------
% 33.72/6.47 % (3963)lrs+1002_1:16_amm=sco:cnfonf=lazy_pi_sigma_gen:fe=off:nm=60:piset=all_but_not_eq:plsq=on:plsqc=1:plsqr=2,1:rawr=on:sp=occurrence:ss=included:st=-1.0:i=157:si=on:rtra=on_0 on DTF2THF_3672 for (2954ds/157Mi)
% 34.28/6.50 % (3962)Instruction limit reached!
% 34.28/6.50 % (3962)------------------------------
% 34.28/6.50 % (3962)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.28/6.50 % (3962)Termination reason: Unknown
% 34.28/6.50 % (3962)Termination phase: Saturation
% 34.28/6.50
% 34.28/6.50 % (3962)Memory used [KB]: 7547
% 34.28/6.50 % (3962)Time elapsed: 0.096 s
% 34.28/6.50 % (3962)Instructions burned: 362 (million)
% 34.28/6.50 % (3962)------------------------------
% 34.28/6.50 % (3962)------------------------------
% 34.28/6.51 % (3963)Instruction limit reached!
% 34.28/6.51 % (3963)------------------------------
% 34.28/6.51 % (3963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.28/6.51 % (3963)Termination reason: Unknown
% 34.28/6.51 % (3963)Termination phase: Property scanning
% 34.28/6.51
% 34.28/6.51 % (3963)Memory used [KB]: 2430
% 34.28/6.51 % (3963)Time elapsed: 0.042 s
% 34.28/6.51 % (3963)Instructions burned: 158 (million)
% 34.28/6.51 % (3963)------------------------------
% 34.28/6.51 % (3963)------------------------------
% 34.28/6.51 % (3964)ott+1004_1:24_anc=none:cbe=off:cnfonf=lazy_not_gen:fe=off:piset=not:prag=on:rp=on:i=5061:si=on:rtra=on_0 on DTF2THF_3672 for (2954ds/5061Mi)
% 34.28/6.51 % (3958)Instruction limit reached!
% 34.28/6.51 % (3958)------------------------------
% 34.28/6.51 % (3958)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.28/6.51 % (3958)Termination reason: Unknown
% 34.28/6.51 % (3958)Termination phase: Saturation
% 34.28/6.51
% 34.28/6.51 % (3958)Memory used [KB]: 8059
% 34.28/6.51 % (3958)Time elapsed: 0.295 s
% 34.28/6.51 % (3958)Instructions burned: 1046 (million)
% 34.28/6.51 % (3958)------------------------------
% 34.28/6.51 % (3958)------------------------------
% 34.28/6.52 % (3965)lrs+1002_1:8_av=off:fd=off:hud=5:tnu=1:i=2401:si=on:rtra=on_0 on DTF2THF_3672 for (2954ds/2401Mi)
% 34.28/6.52 % (3961)Instruction limit reached!
% 34.28/6.52 % (3961)------------------------------
% 34.28/6.52 % (3961)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.28/6.52 % (3961)Termination reason: Unknown
% 34.28/6.52 % (3961)Termination phase: Saturation
% 34.28/6.52
% 34.28/6.52 % (3961)Memory used [KB]: 12409
% 34.28/6.52 % (3961)Time elapsed: 0.126 s
% 34.28/6.52 % (3961)Instructions burned: 454 (million)
% 34.28/6.52 % (3961)------------------------------
% 34.28/6.52 % (3961)------------------------------
% 34.28/6.52 % (3966)dis+10_1:1_av=off:e2e=on:nm=4:s2a=on:i=5798:si=on:rtra=on_0 on DTF2THF_3672 for (2954ds/5798Mi)
% 34.28/6.53 % (3967)dis+10_1:1_au=on:cnfonf=lazy_gen:ixr=off:plsq=on:plsqc=1:plsqr=32,1:i=346:si=on:rtra=on_0 on DTF2THF_3672 for (2954ds/346Mi)
% 34.28/6.56 % (3957)Instruction limit reached!
% 34.28/6.56 % (3957)------------------------------
% 34.28/6.56 % (3957)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 34.28/6.56 % (3957)Termination reason: Unknown
% 34.28/6.56 % (3957)Termination phase: Saturation
% 34.28/6.56
% 34.28/6.56 % (3957)Memory used [KB]: 9850
% 34.28/6.56 % (3957)Time elapsed: 0.404 s
% 34.28/6.56 % (3957)Instructions burned: 1204 (million)
% 34.28/6.56 % (3957)------------------------------
% 34.28/6.56 % (3957)------------------------------
% 34.28/6.57 % (3968)lrs+1002_1:1_av=off:bd=off:bet=on:e2e=on:fde=unused:fe=off:plsq=on:prag=on:sos=on:i=1321:si=on:rtra=on_0 on DTF2THF_3672 for (2953ds/1321Mi)
% 35.47/6.62 % (3968)Refutation not found, incomplete strategy
% 35.47/6.62 % (3968)------------------------------
% 35.47/6.62 % (3968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.47/6.62 % (3968)Termination reason: Refutation not found, incomplete strategy
% 35.47/6.62
% 35.47/6.62
% 35.47/6.62 % (3968)Memory used [KB]: 2942
% 35.47/6.62 % (3968)Time elapsed: 0.049 s
% 35.47/6.62 % (3968)Instructions burned: 163 (million)
% 35.47/6.62 % (3968)------------------------------
% 35.47/6.62 % (3968)------------------------------
% 35.47/6.63 % (3967)Instruction limit reached!
% 35.47/6.63 % (3967)------------------------------
% 35.47/6.63 % (3967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 35.47/6.63 % (3967)Termination reason: Unknown
% 35.47/6.63 % (3967)Termination phase: Saturation
% 35.47/6.63
% 35.47/6.63 % (3967)Memory used [KB]: 7675
% 35.47/6.63 % (3967)Time elapsed: 0.098 s
% 35.47/6.63 % (3967)Instructions burned: 347 (million)
% 35.47/6.63 % (3967)------------------------------
% 35.47/6.63 % (3967)------------------------------
% 35.47/6.63 % (3969)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:i=1312:si=on:rtra=on_0 on DTF2THF_3672 for (2953ds/1312Mi)
% 35.47/6.64 % (3970)ott+2_8:1_add=large:c=on:cnfonf=off:e2e=on:er=filter:hud=5:plsq=on:plsqr=1,1:ss=axioms:i=672:si=on:rtra=on_0 on DTF2THF_3672 for (2952ds/672Mi)
% 36.05/6.85 % (3970)Instruction limit reached!
% 36.05/6.85 % (3970)------------------------------
% 36.05/6.85 % (3970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.05/6.85 % (3970)Termination reason: Unknown
% 36.05/6.85 % (3970)Termination phase: Saturation
% 36.05/6.85
% 36.05/6.85 % (3970)Memory used [KB]: 8187
% 36.05/6.85 % (3970)Time elapsed: 0.233 s
% 36.05/6.85 % (3970)Instructions burned: 674 (million)
% 36.05/6.85 % (3970)------------------------------
% 36.05/6.85 % (3970)------------------------------
% 36.05/6.86 % (3971)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=1897:si=on:rtra=on_0 on DTF2THF_3672 for (2950ds/1897Mi)
% 36.48/6.99 % (3901)Instruction limit reached!
% 36.48/6.99 % (3901)------------------------------
% 36.48/6.99 % (3901)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 36.48/6.99 % (3901)Termination reason: Unknown
% 36.48/6.99 % (3901)Termination phase: Saturation
% 36.48/6.99
% 36.48/6.99 % (3901)Memory used [KB]: 13560
% 36.48/6.99 % (3901)Time elapsed: 3.184 s
% 36.48/6.99 % (3901)Instructions burned: 8252 (million)
% 36.48/6.99 % (3901)------------------------------
% 36.48/6.99 % (3901)------------------------------
% 36.48/7.00 % (3972)lrs+10_1:40_av=off:fde=unused:ntd=on:plsq=on:plsqc=2:plsqr=411915,1048576:sp=unary_frequency:tgt=full:i=1202:si=on:rtra=on_0 on DTF2THF_3672 for (2949ds/1202Mi)
% 38.71/7.04 % (3969)Instruction limit reached!
% 38.71/7.04 % (3969)------------------------------
% 38.71/7.04 % (3969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.71/7.04 % (3969)Termination reason: Unknown
% 38.71/7.04 % (3969)Termination phase: Saturation
% 38.71/7.04
% 38.71/7.04 % (3969)Memory used [KB]: 9722
% 38.71/7.04 % (3969)Time elapsed: 0.416 s
% 38.71/7.04 % (3969)Instructions burned: 1313 (million)
% 38.71/7.04 % (3969)------------------------------
% 38.71/7.04 % (3969)------------------------------
% 38.71/7.05 % (3973)dis+21_1:1_au=on:cnfonf=lazy_pi_sigma_gen:hfsq=on:hfsqc=40:hfsqr=8,1:ntd=on:sos=on:sp=occurrence:ss=axioms:i=1493:si=on:rtra=on_0 on DTF2THF_3672 for (2948ds/1493Mi)
% 38.71/7.10 % (3973)Refutation not found, incomplete strategy
% 38.71/7.10 % (3973)------------------------------
% 38.71/7.10 % (3973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.71/7.10 % (3973)Termination reason: Refutation not found, incomplete strategy
% 38.71/7.10
% 38.71/7.10
% 38.71/7.10 % (3973)Memory used [KB]: 7036
% 38.71/7.10 % (3973)Time elapsed: 0.051 s
% 38.71/7.10 % (3973)Instructions burned: 185 (million)
% 38.71/7.10 % (3973)------------------------------
% 38.71/7.10 % (3973)------------------------------
% 38.71/7.11 % (3965)Instruction limit reached!
% 38.71/7.11 % (3965)------------------------------
% 38.71/7.11 % (3965)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 38.71/7.11 % (3965)Termination reason: Unknown
% 38.71/7.11 % (3965)Termination phase: Saturation
% 38.71/7.11
% 38.71/7.11 % (3965)Memory used [KB]: 5628
% 38.71/7.11 % (3965)Time elapsed: 0.596 s
% 38.71/7.11 % (3965)Instructions burned: 2401 (million)
% 38.71/7.11 % (3965)------------------------------
% 38.71/7.11 % (3965)------------------------------
% 38.71/7.11 % (3974)dis+1010_3:1_av=off:fde=unused:hud=10:nwc=10.0:s2a=on:ss=axioms:i=7679:si=on:rtra=on_0 on DTF2THF_3672 for (2948ds/7679Mi)
% 39.44/7.12 % (3975)lrs+2_1:1024_anc=all:cnfonf=off:cs=on:e2e=on:nm=20:s2at=1.5:slsq=on:slsqr=1,2:spb=goal:i=340:si=on:rtra=on_0 on DTF2THF_3672 for (2947ds/340Mi)
% 39.85/7.22 % (3975)Instruction limit reached!
% 39.85/7.22 % (3975)------------------------------
% 39.85/7.22 % (3975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 39.85/7.22 % (3975)Termination reason: Unknown
% 39.85/7.22 % (3975)Termination phase: Saturation
% 39.85/7.22
% 39.85/7.22 % (3975)Memory used [KB]: 7291
% 39.85/7.22 % (3975)Time elapsed: 0.095 s
% 39.85/7.22 % (3975)Instructions burned: 343 (million)
% 39.85/7.22 % (3975)------------------------------
% 39.85/7.22 % (3975)------------------------------
% 39.85/7.23 % (3976)dis+1002_1:1_acc=model:au=on:nwc=5.0:sd=5:ss=axioms:st=2.5:i=3672:si=on:rtra=on_0 on DTF2THF_3672 for (2946ds/3672Mi)
% 40.45/7.35 % (3945)Instruction limit reached!
% 40.45/7.35 % (3945)------------------------------
% 40.45/7.35 % (3945)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.45/7.35 % (3945)Termination reason: Unknown
% 40.45/7.35 % (3945)Termination phase: Saturation
% 40.45/7.35
% 40.45/7.35 % (3945)Memory used [KB]: 8059
% 40.45/7.35 % (3945)Time elapsed: 1.699 s
% 40.45/7.35 % (3945)Instructions burned: 6454 (million)
% 40.45/7.35 % (3945)------------------------------
% 40.45/7.35 % (3945)------------------------------
% 40.45/7.35 % (3972)Instruction limit reached!
% 40.45/7.35 % (3972)------------------------------
% 40.45/7.35 % (3972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.45/7.35 % (3972)Termination reason: Unknown
% 40.45/7.35 % (3972)Termination phase: Saturation
% 40.45/7.35
% 40.45/7.35 % (3972)Memory used [KB]: 4221
% 40.45/7.35 % (3972)Time elapsed: 0.382 s
% 40.45/7.35 % (3972)Instructions burned: 1202 (million)
% 40.45/7.35 % (3972)------------------------------
% 40.45/7.35 % (3972)------------------------------
% 40.45/7.36 % (3977)dis-1002_3:1_acc=model:bd=off:bsd=on:bsdmm=1:cnfonf=lazy_not_be_gen:fd=off:fe=off:ntd=on:nwc=10.0:piset=equals:plsq=on:plsqc=1:plsqr=32,1:sp=const_max:uhcvi=on:i=1535:si=on:rtra=on_0 on DTF2THF_3672 for (2945ds/1535Mi)
% 40.45/7.36 % (3978)dis+10_16:1_hud=1:plsq=on:plsqc=1:plsqr=32,1:prag=on:sd=1:sgt=64:ss=axioms:i=4637:si=on:rtra=on_0 on DTF2THF_3672 for (2945ds/4637Mi)
% 40.87/7.44 % (3971)Instruction limit reached!
% 40.87/7.44 % (3971)------------------------------
% 40.87/7.44 % (3971)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 40.87/7.44 % (3971)Termination reason: Unknown
% 40.87/7.44 % (3971)Termination phase: Saturation
% 40.87/7.44
% 40.87/7.44 % (3971)Memory used [KB]: 9210
% 40.87/7.44 % (3971)Time elapsed: 0.601 s
% 40.87/7.44 % (3971)Instructions burned: 1899 (million)
% 40.87/7.44 % (3971)------------------------------
% 40.87/7.44 % (3971)------------------------------
% 40.87/7.45 % (3979)lrs+10_1:1_fde=unused:prag=on:sd=2:sgt=32:ss=axioms:i=3174:si=on:rtra=on_0 on DTF2THF_3672 for (2944ds/3174Mi)
% 41.52/7.79 % (3977)Instruction limit reached!
% 41.52/7.79 % (3977)------------------------------
% 41.52/7.79 % (3977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 41.52/7.79 % (3977)Termination reason: Unknown
% 41.52/7.79 % (3977)Termination phase: Saturation
% 41.52/7.79
% 41.52/7.79 % (3977)Memory used [KB]: 11129
% 41.52/7.79 % (3977)Time elapsed: 0.434 s
% 41.52/7.79 % (3977)Instructions burned: 1536 (million)
% 41.52/7.79 % (3977)------------------------------
% 41.52/7.79 % (3977)------------------------------
% 42.16/7.80 % (3980)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3672 for (2941ds/307Mi)
% 42.16/7.80 % (3964)Instruction limit reached!
% 42.16/7.80 % (3964)------------------------------
% 42.16/7.80 % (3964)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.16/7.80 % (3964)Termination reason: Unknown
% 42.16/7.80 % (3964)Termination phase: Saturation
% 42.16/7.80
% 42.16/7.80 % (3964)Memory used [KB]: 9850
% 42.16/7.80 % (3964)Time elapsed: 1.297 s
% 42.16/7.80 % (3964)Instructions burned: 5065 (million)
% 42.16/7.80 % (3964)------------------------------
% 42.16/7.80 % (3964)------------------------------
% 42.16/7.81 % (3981)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=3619:si=on:rtra=on_0 on DTF2THF_3672 for (2941ds/3619Mi)
% 42.16/7.88 % (3980)Instruction limit reached!
% 42.16/7.88 % (3980)------------------------------
% 42.16/7.88 % (3980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 42.16/7.88 % (3980)Termination reason: Unknown
% 42.16/7.88 % (3980)Termination phase: Saturation
% 42.16/7.88
% 42.16/7.88 % (3980)Memory used [KB]: 7419
% 42.16/7.88 % (3980)Time elapsed: 0.082 s
% 42.16/7.88 % (3980)Instructions burned: 309 (million)
% 42.16/7.88 % (3980)------------------------------
% 42.16/7.88 % (3980)------------------------------
% 42.16/7.89 % (3982)lrs+1002_1:1_au=on:cbe=off:fde=none:ins=1:sp=const_max:i=2325:si=on:rtra=on_0 on DTF2THF_3672 for (2940ds/2325Mi)
% 47.67/8.30 % (3976)Instruction limit reached!
% 47.67/8.30 % (3976)------------------------------
% 47.67/8.30 % (3976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 47.67/8.30 % (3976)Termination reason: Unknown
% 47.67/8.30 % (3976)Termination phase: Saturation
% 47.67/8.30
% 47.67/8.30 % (3976)Memory used [KB]: 12281
% 47.67/8.30 % (3976)Time elapsed: 1.078 s
% 47.67/8.30 % (3976)Instructions burned: 3673 (million)
% 47.67/8.30 % (3976)------------------------------
% 47.67/8.30 % (3976)------------------------------
% 47.67/8.31 % (3983)dis+1002_1:1_au=on:sac=on:sd=5:slsq=on:slsqr=1,4:ss=axioms:st=2.0:i=2341:si=on:rtra=on_0 on DTF2THF_3672 for (2936ds/2341Mi)
% 48.28/8.42 % (3979)Instruction limit reached!
% 48.28/8.42 % (3979)------------------------------
% 48.28/8.42 % (3979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 48.28/8.42 % (3979)Termination reason: Unknown
% 48.28/8.42 % (3979)Termination phase: Saturation
% 48.28/8.42
% 48.28/8.42 % (3979)Memory used [KB]: 9338
% 48.28/8.42 % (3979)Time elapsed: 0.973 s
% 48.28/8.42 % (3979)Instructions burned: 3174 (million)
% 48.28/8.42 % (3979)------------------------------
% 48.28/8.42 % (3979)------------------------------
% 48.28/8.43 % (3984)lrs+1010_1:16_apa=on:bsd=on:cnfonf=off:hud=10:sac=on:sos=on:ss=axioms:i=7257:si=on:rtra=on_0 on DTF2THF_3672 for (2934ds/7257Mi)
% 49.31/8.61 % (3982)Instruction limit reached!
% 49.31/8.61 % (3982)------------------------------
% 49.31/8.61 % (3982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 49.31/8.61 % (3982)Termination reason: Unknown
% 49.31/8.61 % (3982)Termination phase: Saturation
% 49.31/8.61
% 49.31/8.61 % (3982)Memory used [KB]: 10874
% 49.31/8.61 % (3982)Time elapsed: 0.721 s
% 49.31/8.61 % (3982)Instructions burned: 2328 (million)
% 49.31/8.61 % (3982)------------------------------
% 49.31/8.61 % (3982)------------------------------
% 49.31/8.62 % (3985)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=3710:si=on:rtra=on_0 on DTF2THF_3672 for (2933ds/3710Mi)
% 50.14/8.80 % (3978)Instruction limit reached!
% 50.14/8.80 % (3978)------------------------------
% 50.14/8.80 % (3978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.14/8.80 % (3978)Termination reason: Unknown
% 50.14/8.80 % (3978)Termination phase: Saturation
% 50.14/8.80
% 50.14/8.80 % (3978)Memory used [KB]: 10106
% 50.14/8.80 % (3978)Time elapsed: 1.434 s
% 50.14/8.80 % (3978)Instructions burned: 4639 (million)
% 50.14/8.80 % (3978)------------------------------
% 50.14/8.80 % (3978)------------------------------
% 50.14/8.81 % (3986)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=326:si=on:rtra=on_0 on DTF2THF_3672 for (2931ds/326Mi)
% 50.14/8.86 % (3981)Instruction limit reached!
% 50.14/8.86 % (3981)------------------------------
% 50.14/8.86 % (3981)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.14/8.86 % (3981)Termination reason: Unknown
% 50.14/8.86 % (3981)Termination phase: Saturation
% 50.14/8.86
% 50.14/8.86 % (3981)Memory used [KB]: 10234
% 50.14/8.86 % (3981)Time elapsed: 1.044 s
% 50.14/8.86 % (3981)Instructions burned: 3619 (million)
% 50.14/8.86 % (3981)------------------------------
% 50.14/8.86 % (3981)------------------------------
% 50.14/8.87 % (3987)lrs+1010_1:64_au=on:c=on:e2e=on:flr=on:hfsq=on:hfsql=off:hfsqr=4,1:ins=1:ntd=on:sp=occurrence:i=1100:si=on:rtra=on_0 on DTF2THF_3672 for (2930ds/1100Mi)
% 50.42/8.91 % (3986)Instruction limit reached!
% 50.42/8.91 % (3986)------------------------------
% 50.42/8.91 % (3986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 50.42/8.91 % (3986)Termination reason: Unknown
% 50.42/8.91 % (3986)Termination phase: Saturation
% 50.42/8.91
% 50.42/8.91 % (3986)Memory used [KB]: 7547
% 50.42/8.91 % (3986)Time elapsed: 0.102 s
% 50.42/8.91 % (3986)Instructions burned: 327 (million)
% 50.42/8.91 % (3986)------------------------------
% 50.42/8.91 % (3986)------------------------------
% 50.42/8.92 % (3988)lrs+10_1:1_au=on:cnfonf=off:fde=unused:kws=precedence:tgt=full:i=406:si=on:rtra=on_0 on DTF2THF_3672 for (2930ds/406Mi)
% 52.67/9.02 % (3983)Instruction limit reached!
% 52.67/9.02 % (3983)------------------------------
% 52.67/9.02 % (3983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.67/9.02 % (3983)Termination reason: Unknown
% 52.67/9.02 % (3983)Termination phase: Saturation
% 52.67/9.02
% 52.67/9.02 % (3983)Memory used [KB]: 11001
% 52.67/9.02 % (3983)Time elapsed: 0.704 s
% 52.67/9.02 % (3983)Instructions burned: 2341 (million)
% 52.67/9.02 % (3983)------------------------------
% 52.67/9.02 % (3983)------------------------------
% 52.67/9.03 % (3989)dis+1010_1:1_aac=none:bd=preordered:e2e=on:fde=none:fe=axiom:nm=16:nwc=10.0:prag=on:i=1871:si=on:rtra=on_0 on DTF2THF_3672 for (2928ds/1871Mi)
% 52.67/9.04 % (3988)Instruction limit reached!
% 52.67/9.04 % (3988)------------------------------
% 52.67/9.04 % (3988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 52.67/9.04 % (3988)Termination reason: Unknown
% 52.67/9.04 % (3988)Termination phase: Saturation
% 52.67/9.04
% 52.67/9.04 % (3988)Memory used [KB]: 7675
% 52.67/9.04 % (3988)Time elapsed: 0.125 s
% 52.67/9.04 % (3988)Instructions burned: 409 (million)
% 52.67/9.04 % (3988)------------------------------
% 52.67/9.04 % (3988)------------------------------
% 52.67/9.05 % (3990)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1194:si=on:rtra=on_0 on DTF2THF_3672 for (2928ds/1194Mi)
% 53.22/9.19 % (3987)Instruction limit reached!
% 53.22/9.19 % (3987)------------------------------
% 53.22/9.19 % (3987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 53.22/9.19 % (3987)Termination reason: Unknown
% 53.22/9.19 % (3987)Termination phase: Saturation
% 53.22/9.19
% 53.22/9.19 % (3987)Memory used [KB]: 10746
% 53.22/9.19 % (3987)Time elapsed: 0.328 s
% 53.22/9.19 % (3987)Instructions burned: 1100 (million)
% 53.22/9.19 % (3987)------------------------------
% 53.22/9.19 % (3987)------------------------------
% 53.64/9.20 % (3991)dis+10_1:1024_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=32,1:spb=goal_then_units:i=474:si=on:rtra=on_0 on DTF2THF_3672 for (2927ds/474Mi)
% 54.04/9.34 % (3991)Instruction limit reached!
% 54.04/9.34 % (3991)------------------------------
% 54.04/9.34 % (3991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.04/9.34 % (3991)Termination reason: Unknown
% 54.04/9.34 % (3991)Termination phase: Saturation
% 54.04/9.34
% 54.04/9.34 % (3991)Memory used [KB]: 8059
% 54.04/9.34 % (3991)Time elapsed: 0.139 s
% 54.04/9.34 % (3991)Instructions burned: 476 (million)
% 54.04/9.34 % (3991)------------------------------
% 54.04/9.34 % (3991)------------------------------
% 54.04/9.35 % (3992)dis+1010_1:1_au=on:cnfonf=lazy_gen:ins=3:plsq=on:plsqc=1:plsqr=15142123,262144:sp=reverse_arity:i=3115:si=on:rtra=on_0 on DTF2THF_3672 for (2925ds/3115Mi)
% 54.57/9.41 % (3990)Instruction limit reached!
% 54.57/9.41 % (3990)------------------------------
% 54.57/9.41 % (3990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 54.57/9.41 % (3990)Termination reason: Unknown
% 54.57/9.41 % (3990)Termination phase: Saturation
% 54.57/9.41
% 54.57/9.41 % (3990)Memory used [KB]: 10106
% 54.57/9.41 % (3990)Time elapsed: 0.358 s
% 54.57/9.41 % (3990)Instructions burned: 1195 (million)
% 54.57/9.41 % (3990)------------------------------
% 54.57/9.41 % (3990)------------------------------
% 54.57/9.42 % (3993)dis+10_1:1024_kws=precedence:prag=on:rawr=on:sos=all:sp=unary_first:i=831:si=on:rtra=on_0 on DTF2THF_3672 for (2925ds/831Mi)
% 55.34/9.54 % (3974)Instruction limit reached!
% 55.34/9.54 % (3974)------------------------------
% 55.34/9.54 % (3974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.34/9.54 % (3974)Termination reason: Unknown
% 55.34/9.54 % (3974)Termination phase: Saturation
% 55.34/9.54
% 55.34/9.54 % (3974)Memory used [KB]: 12920
% 55.34/9.54 % (3974)Time elapsed: 2.424 s
% 55.34/9.54 % (3974)Instructions burned: 7681 (million)
% 55.34/9.54 % (3974)------------------------------
% 55.34/9.54 % (3974)------------------------------
% 55.34/9.55 % (3994)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_3672 for (2923ds/1188Mi)
% 55.69/9.61 % (3989)Instruction limit reached!
% 55.69/9.61 % (3989)------------------------------
% 55.69/9.61 % (3989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.61 % (3989)Termination reason: Unknown
% 55.69/9.61 % (3989)Termination phase: Saturation
% 55.69/9.61
% 55.69/9.61 % (3989)Memory used [KB]: 10618
% 55.69/9.61 % (3989)Time elapsed: 0.583 s
% 55.69/9.61 % (3989)Instructions burned: 1874 (million)
% 55.69/9.61 % (3989)------------------------------
% 55.69/9.61 % (3989)------------------------------
% 55.69/9.62 % (3995)ott+1010_1:20_cnfonf=lazy_pi_sigma_gen:fe=axiom:plsq=on:plsqc=2:plsqr=32,1:sac=on:sos=all:i=2868:si=on:rtra=on_0 on DTF2THF_3672 for (2923ds/2868Mi)
% 55.69/9.66 % (3993)Instruction limit reached!
% 55.69/9.66 % (3993)------------------------------
% 55.69/9.66 % (3993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.66 % (3993)Termination reason: Unknown
% 55.69/9.66 % (3993)Termination phase: Saturation
% 55.69/9.66
% 55.69/9.66 % (3993)Memory used [KB]: 8827
% 55.69/9.66 % (3993)Time elapsed: 0.247 s
% 55.69/9.66 % (3993)Instructions burned: 834 (million)
% 55.69/9.66 % (3993)------------------------------
% 55.69/9.66 % (3993)------------------------------
% 55.69/9.67 % (3966)Instruction limit reached!
% 55.69/9.67 % (3966)------------------------------
% 55.69/9.67 % (3966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.67 % (3966)Termination reason: Unknown
% 55.69/9.67 % (3966)Termination phase: Saturation
% 55.69/9.67
% 55.69/9.67 % (3966)Memory used [KB]: 11641
% 55.69/9.67 % (3966)Time elapsed: 3.152 s
% 55.69/9.67 % (3966)Instructions burned: 5800 (million)
% 55.69/9.67 % (3966)------------------------------
% 55.69/9.67 % (3966)------------------------------
% 55.69/9.67 % (3996)dis+10_1:4_atotf=0.1:avsq=on:bsr=unit_only:e2e=on:sd=1:sp=const_max:ss=axioms:i=1516:si=on:rtra=on_0 on DTF2THF_3672 for (2922ds/1516Mi)
% 55.69/9.68 % (3997)lrs+1002_1:20_afp=1000:au=on:bsd=on:cnfonf=lazy_not_gen_be_off:sos=all:sp=const_max:i=2321:si=on:rtra=on_0 on DTF2THF_3672 for (2922ds/2321Mi)
% 55.69/9.69 % (3995)Refutation not found, incomplete strategy
% 55.69/9.69 % (3995)------------------------------
% 55.69/9.69 % (3995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 55.69/9.69 % (3995)Termination reason: Refutation not found, incomplete strategy
% 55.69/9.69
% 55.69/9.69
% 55.69/9.69 % (3995)Memory used [KB]: 7675
% 55.69/9.69 % (3995)Time elapsed: 0.075 s
% 55.69/9.69 % (3995)Instructions burned: 276 (million)
% 55.69/9.69 % (3995)------------------------------
% 55.69/9.69 % (3995)------------------------------
% 56.91/9.70 % (3998)dis+1010_1:1_au=on:bd=off:bsd=on:ixr=off:sp=const_max:i=2812:si=on:rtra=on_0 on DTF2THF_3672 for (2922ds/2812Mi)
% 56.91/9.72 % (3985)Instruction limit reached!
% 56.91/9.72 % (3985)------------------------------
% 56.91/9.72 % (3985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.91/9.72 % (3985)Termination reason: Unknown
% 56.91/9.72 % (3985)Termination phase: Saturation
% 56.91/9.72
% 56.91/9.72 % (3985)Memory used [KB]: 15607
% 56.91/9.72 % (3985)Time elapsed: 1.098 s
% 56.91/9.72 % (3985)Instructions burned: 3713 (million)
% 56.91/9.72 % (3985)------------------------------
% 56.91/9.72 % (3985)------------------------------
% 56.91/9.73 % (3999)dis+1002_8:1_bd=off:sd=1:sgt=16:ss=axioms:i=4604:si=on:rtra=on_0 on DTF2THF_3672 for (2922ds/4604Mi)
% 56.91/9.76 % (3997)Refutation not found, incomplete strategy
% 56.91/9.76 % (3997)------------------------------
% 56.91/9.76 % (3997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 56.91/9.76 % (3997)Termination reason: Refutation not found, incomplete strategy
% 56.91/9.76
% 56.91/9.76
% 56.91/9.76 % (3997)Memory used [KB]: 7803
% 56.91/9.76 % (3997)Time elapsed: 0.075 s
% 56.91/9.76 % (3997)Instructions burned: 281 (million)
% 56.91/9.76 % (3997)------------------------------
% 56.91/9.76 % (3997)------------------------------
% 56.91/9.77 % (4000)ott+1002_1:4_c=on:chr=on:cnfonf=lazy_not_be_gen:hud=10:nm=10:piset=all_but_not_eq:rp=on:spb=goal:uhcvi=on:i=2678:si=on:rtra=on_0 on DTF2THF_3672 for (2921ds/2678Mi)
% 57.23/9.99 % (3994)Instruction limit reached!
% 57.23/9.99 % (3994)------------------------------
% 57.23/9.99 % (3994)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 57.23/9.99 % (3994)Termination reason: Unknown
% 57.23/9.99 % (3994)Termination phase: Saturation
% 57.23/9.99
% 57.23/9.99 % (3994)Memory used [KB]: 9466
% 57.23/9.99 % (3994)Time elapsed: 0.443 s
% 57.23/9.99 % (3994)Instructions burned: 1189 (million)
% 57.23/9.99 % (3994)------------------------------
% 57.23/9.99 % (3994)------------------------------
% 57.23/10.00 % (4001)dis+1010_1:4_avsq=on:avsqr=16,1:bet=on:cbe=off:cnfonf=lazy_not_be_gen:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=643:si=on:rtra=on_0 on DTF2THF_3672 for (2919ds/643Mi)
% 59.76/10.12 % (3996)Instruction limit reached!
% 59.76/10.12 % (3996)------------------------------
% 59.76/10.12 % (3996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 59.76/10.12 % (3996)Termination reason: Unknown
% 59.76/10.12 % (3996)Termination phase: Saturation
% 59.76/10.12
% 59.76/10.12 % (3996)Memory used [KB]: 8827
% 59.76/10.12 % (3996)Time elapsed: 0.449 s
% 59.76/10.12 % (3996)Instructions burned: 1518 (million)
% 59.76/10.12 % (3996)------------------------------
% 59.76/10.12 % (3996)------------------------------
% 60.49/10.13 % (4002)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=458:si=on:rtra=on_0 on DTF2THF_3672 for (2918ds/458Mi)
% 60.88/10.24 % (3992)Instruction limit reached!
% 60.88/10.24 % (3992)------------------------------
% 60.88/10.24 % (3992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.88/10.24 % (3992)Termination reason: Unknown
% 60.88/10.24 % (3992)Termination phase: Saturation
% 60.88/10.24
% 60.88/10.24 % (3992)Memory used [KB]: 12792
% 60.88/10.24 % (3992)Time elapsed: 0.886 s
% 60.88/10.24 % (3992)Instructions burned: 3117 (million)
% 60.88/10.24 % (3992)------------------------------
% 60.88/10.24 % (3992)------------------------------
% 60.88/10.25 % (4003)lrs+1010_1:1_anc=all_dependent:apa=on:au=on:bd=off:c=on:cnfonf=off:ntd=on:i=2546:si=on:rtra=on_0 on DTF2THF_3672 for (2916ds/2546Mi)
% 60.88/10.26 % (4002)Instruction limit reached!
% 60.88/10.26 % (4002)------------------------------
% 60.88/10.26 % (4002)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.88/10.26 % (4002)Termination reason: Unknown
% 60.88/10.26 % (4002)Termination phase: Saturation
% 60.88/10.26
% 60.88/10.26 % (4002)Memory used [KB]: 7547
% 60.88/10.26 % (4002)Time elapsed: 0.126 s
% 60.88/10.26 % (4002)Instructions burned: 460 (million)
% 60.88/10.26 % (4002)------------------------------
% 60.88/10.26 % (4002)------------------------------
% 60.88/10.26 % (4001)Instruction limit reached!
% 60.88/10.26 % (4001)------------------------------
% 60.88/10.26 % (4001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 60.88/10.26 % (4001)Termination reason: Unknown
% 60.88/10.26 % (4001)Termination phase: Saturation
% 60.88/10.26
% 60.88/10.26 % (4001)Memory used [KB]: 7931
% 60.88/10.26 % (4001)Time elapsed: 0.265 s
% 60.88/10.26 % (4001)Instructions burned: 645 (million)
% 60.88/10.26 % (4001)------------------------------
% 60.88/10.26 % (4001)------------------------------
% 60.88/10.27 % (4004)dis+21_1:1_acc=model:au=on:cnfonf=lazy_gen:ins=2:plsq=on:plsqc=1:plsqr=32,1:i=1432:si=on:rtra=on_0 on DTF2THF_3672 for (2916ds/1432Mi)
% 60.88/10.28 % (4005)dis+1002_1:1_cnfonf=lazy_not_gen:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=386:si=on:rtra=on_0 on DTF2THF_3672 for (2916ds/386Mi)
% 61.94/10.42 % (4005)Instruction limit reached!
% 61.94/10.42 % (4005)------------------------------
% 61.94/10.42 % (4005)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 61.94/10.42 % (4005)Termination reason: Unknown
% 61.94/10.42 % (4005)Termination phase: Saturation
% 61.94/10.42
% 61.94/10.42 % (4005)Memory used [KB]: 7675
% 61.94/10.42 % (4005)Time elapsed: 0.136 s
% 61.94/10.42 % (4005)Instructions burned: 388 (million)
% 61.94/10.42 % (4005)------------------------------
% 61.94/10.42 % (4005)------------------------------
% 61.94/10.43 % (4006)dis+1002_1:1_cnfonf=lazy_simp:hud=5:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=360:si=on:rtra=on_0 on DTF2THF_3672 for (2914ds/360Mi)
% 62.49/10.55 % (3998)Instruction limit reached!
% 62.49/10.55 % (3998)------------------------------
% 62.49/10.55 % (3998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.49/10.55 % (3998)Termination reason: Unknown
% 62.49/10.55 % (3998)Termination phase: Saturation
% 62.49/10.55
% 62.49/10.55 % (3998)Memory used [KB]: 11897
% 62.49/10.55 % (3998)Time elapsed: 0.851 s
% 62.49/10.55 % (3998)Instructions burned: 2813 (million)
% 62.49/10.55 % (3998)------------------------------
% 62.49/10.55 % (3998)------------------------------
% 62.49/10.56 % (3984)Instruction limit reached!
% 62.49/10.56 % (3984)------------------------------
% 62.49/10.56 % (3984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.49/10.56 % (3984)Termination reason: Unknown
% 62.49/10.56 % (3984)Termination phase: Saturation
% 62.49/10.56
% 62.49/10.56 % (3984)Memory used [KB]: 14456
% 62.49/10.56 % (3984)Time elapsed: 2.133 s
% 62.49/10.56 % (3984)Instructions burned: 7260 (million)
% 62.49/10.56 % (3984)------------------------------
% 62.49/10.56 % (3984)------------------------------
% 62.49/10.56 % (4007)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=5446:si=on:rtra=on_0 on DTF2THF_3672 for (2913ds/5446Mi)
% 62.49/10.57 % (4008)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=2573:si=on:rtra=on_0 on DTF2THF_3672 for (2913ds/2573Mi)
% 62.49/10.58 % (4006)Instruction limit reached!
% 62.49/10.58 % (4006)------------------------------
% 62.49/10.58 % (4006)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.49/10.58 % (4006)Termination reason: Unknown
% 62.49/10.58 % (4006)Termination phase: Saturation
% 62.49/10.58
% 62.49/10.58 % (4006)Memory used [KB]: 7419
% 62.49/10.58 % (4006)Time elapsed: 0.150 s
% 62.49/10.58 % (4006)Instructions burned: 361 (million)
% 62.49/10.58 % (4006)------------------------------
% 62.49/10.58 % (4006)------------------------------
% 62.49/10.58 % (4004)Instruction limit reached!
% 62.49/10.58 % (4004)------------------------------
% 62.49/10.58 % (4004)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 62.49/10.58 % (4004)Termination reason: Unknown
% 62.49/10.58 % (4004)Termination phase: Saturation
% 62.49/10.58
% 62.49/10.58 % (4004)Memory used [KB]: 11129
% 62.49/10.58 % (4004)Time elapsed: 0.319 s
% 62.49/10.58 % (4004)Instructions burned: 1433 (million)
% 62.49/10.58 % (4004)------------------------------
% 62.49/10.58 % (4004)------------------------------
% 62.49/10.59 % (4009)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=2655:si=on:rtra=on_0 on DTF2THF_3672 for (2913ds/2655Mi)
% 62.49/10.59 % (4010)dis+1002_16:1_apa=on:au=on:av=off:cnfonf=off:e2e=on:nm=0:nwc=10.0:i=2781:si=on:rtra=on_0 on DTF2THF_3672 for (2913ds/2781Mi)
% 63.33/10.65 % (4000)Instruction limit reached!
% 63.33/10.65 % (4000)------------------------------
% 63.33/10.65 % (4000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.33/10.65 % (4000)Termination reason: Unknown
% 63.33/10.65 % (4000)Termination phase: Saturation
% 63.33/10.65
% 63.33/10.65 % (4000)Memory used [KB]: 8571
% 63.33/10.65 % (4000)Time elapsed: 0.878 s
% 63.33/10.65 % (4000)Instructions burned: 2680 (million)
% 63.33/10.65 % (4000)------------------------------
% 63.33/10.65 % (4000)------------------------------
% 63.33/10.66 % (4011)lrs+1010_1:10_au=on:bd=off:cnfonf=lazy_pi_sigma_gen:sp=occurrence:i=307:si=on:rtra=on_0 on DTF2THF_3672 for (2912ds/307Mi)
% 63.49/10.74 % (4011)Instruction limit reached!
% 63.49/10.74 % (4011)------------------------------
% 63.49/10.74 % (4011)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 63.49/10.74 % (4011)Termination reason: Unknown
% 63.49/10.74 % (4011)Termination phase: Saturation
% 63.49/10.74
% 63.49/10.74 % (4011)Memory used [KB]: 7419
% 63.49/10.74 % (4011)Time elapsed: 0.084 s
% 63.49/10.74 % (4011)Instructions burned: 309 (million)
% 63.49/10.74 % (4011)------------------------------
% 63.49/10.74 % (4011)------------------------------
% 63.49/10.75 % (4012)lrs+1010_1:1_avsq=on:avsqr=1,16:kws=inv_arity:nwc=5.0:sd=1:ss=axioms:i=1548:si=on:rtra=on_0 on DTF2THF_3672 for (2911ds/1548Mi)
% 66.63/11.07 % (4003)Instruction limit reached!
% 66.63/11.07 % (4003)------------------------------
% 66.63/11.07 % (4003)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.63/11.07 % (4003)Termination reason: Unknown
% 66.63/11.07 % (4003)Termination phase: Saturation
% 66.63/11.07
% 66.63/11.07 % (4003)Memory used [KB]: 11129
% 66.63/11.07 % (4003)Time elapsed: 0.827 s
% 66.63/11.07 % (4003)Instructions burned: 2547 (million)
% 66.63/11.07 % (4003)------------------------------
% 66.63/11.07 % (4003)------------------------------
% 66.63/11.08 % (4013)lrs+10_1:3_alpa=true:hud=3:ins=1:ntd=on:plsq=on:plsqc=1:plsqr=32,1:prag=on:s2a=on:s2agt=10:i=5214:si=on:rtra=on_0 on DTF2THF_3672 for (2908ds/5214Mi)
% 66.63/11.10 % (3999)Instruction limit reached!
% 66.63/11.10 % (3999)------------------------------
% 66.63/11.10 % (3999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 66.63/11.10 % (3999)Termination reason: Unknown
% 66.63/11.10 % (3999)Termination phase: Saturation
% 66.63/11.10
% 66.63/11.10 % (3999)Memory used [KB]: 10874
% 66.63/11.10 % (3999)Time elapsed: 1.371 s
% 66.63/11.10 % (3999)Instructions burned: 4606 (million)
% 66.63/11.10 % (3999)------------------------------
% 66.63/11.10 % (3999)------------------------------
% 66.63/11.11 % (4014)dis+21_1:1_aac=none:bsr=on:nwc=3.0:s2a=on:i=3201:si=on:rtra=on_0 on DTF2THF_3672 for (2908ds/3201Mi)
% 67.71/11.25 % (4012)Instruction limit reached!
% 67.71/11.25 % (4012)------------------------------
% 67.71/11.25 % (4012)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 67.71/11.25 % (4012)Termination reason: Unknown
% 67.71/11.25 % (4012)Termination phase: Saturation
% 67.71/11.25
% 67.71/11.25 % (4012)Memory used [KB]: 9850
% 67.71/11.25 % (4012)Time elapsed: 0.488 s
% 67.71/11.25 % (4012)Instructions burned: 1549 (million)
% 67.71/11.25 % (4012)------------------------------
% 67.71/11.25 % (4012)------------------------------
% 67.71/11.26 % (4015)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=454:si=on:rtra=on_0 on DTF2THF_3672 for (2906ds/454Mi)
% 68.18/11.32 % (4008)Instruction limit reached!
% 68.18/11.32 % (4008)------------------------------
% 68.18/11.32 % (4008)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.18/11.32 % (4008)Termination reason: Unknown
% 68.18/11.32 % (4008)Termination phase: Saturation
% 68.18/11.32
% 68.18/11.32 % (4008)Memory used [KB]: 12665
% 68.18/11.32 % (4008)Time elapsed: 0.755 s
% 68.18/11.32 % (4008)Instructions burned: 2573 (million)
% 68.18/11.32 % (4008)------------------------------
% 68.18/11.32 % (4008)------------------------------
% 68.18/11.34 % (4016)lrs+1002_1:32_au=on:ins=2:nm=16:ntd=on:piset=all_but_not_eq:sp=occurrence:i=3049:si=on:rtra=on_0 on DTF2THF_3672 for (2905ds/3049Mi)
% 68.18/11.37 % (4015)Instruction limit reached!
% 68.18/11.37 % (4015)------------------------------
% 68.18/11.37 % (4015)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.18/11.37 % (4015)Termination reason: Unknown
% 68.18/11.37 % (4015)Termination phase: Saturation
% 68.18/11.37
% 68.18/11.37 % (4015)Memory used [KB]: 12025
% 68.18/11.37 % (4015)Time elapsed: 0.118 s
% 68.18/11.37 % (4015)Instructions burned: 455 (million)
% 68.18/11.37 % (4015)------------------------------
% 68.18/11.37 % (4015)------------------------------
% 68.18/11.38 % (4017)lrs+1010_1:1_bd=preordered:cnfonf=off:e2e=on:kws=inv_precedence:lwlo=on:sd=2:ss=axioms:i=7311:si=on:rtra=on_0 on DTF2THF_3672 for (2905ds/7311Mi)
% 68.65/11.43 % (4009)Instruction limit reached!
% 68.65/11.43 % (4009)------------------------------
% 68.65/11.43 % (4009)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.65/11.43 % (4009)Termination reason: Unknown
% 68.65/11.43 % (4009)Termination phase: Saturation
% 68.65/11.43
% 68.65/11.43 % (4009)Memory used [KB]: 16630
% 68.65/11.43 % (4009)Time elapsed: 0.843 s
% 68.65/11.43 % (4009)Instructions burned: 2655 (million)
% 68.65/11.43 % (4009)------------------------------
% 68.65/11.43 % (4009)------------------------------
% 68.65/11.44 % (4018)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=6804:si=on:rtra=on_0 on DTF2THF_3672 for (2904ds/6804Mi)
% 68.65/11.45 % (4010)Instruction limit reached!
% 68.65/11.45 % (4010)------------------------------
% 68.65/11.45 % (4010)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 68.65/11.45 % (4010)Termination reason: Unknown
% 68.65/11.45 % (4010)Termination phase: Saturation
% 68.65/11.45
% 68.65/11.45 % (4010)Memory used [KB]: 5117
% 68.65/11.45 % (4010)Time elapsed: 0.858 s
% 68.65/11.45 % (4010)Instructions burned: 2783 (million)
% 68.65/11.45 % (4010)------------------------------
% 68.65/11.45 % (4010)------------------------------
% 68.65/11.46 % (4019)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1683:si=on:rtra=on_0 on DTF2THF_3672 for (2904ds/1683Mi)
% 69.25/11.99 % (4019)Instruction limit reached!
% 69.25/11.99 % (4019)------------------------------
% 69.25/11.99 % (4019)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 69.25/11.99 % (4019)Termination reason: Unknown
% 69.25/11.99 % (4019)Termination phase: Saturation
% 69.25/11.99
% 69.25/11.99 % (4019)Memory used [KB]: 9466
% 69.25/11.99 % (4019)Time elapsed: 0.554 s
% 69.25/11.99 % (4019)Instructions burned: 1684 (million)
% 69.25/11.99 % (4019)------------------------------
% 69.25/11.99 % (4019)------------------------------
% 69.25/12.00 % (4020)lrs+10_8:1_au=on:av=off:bd=off:cs=on:e2e=on:hfsq=on:hfsqc=50:hfsql=off:nm=0:i=4688:si=on:rtra=on_0 on DTF2THF_3672 for (2899ds/4688Mi)
% 73.58/12.05 % (4014)Instruction limit reached!
% 73.58/12.05 % (4014)------------------------------
% 73.58/12.05 % (4014)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.58/12.05 % (4014)Termination reason: Unknown
% 73.58/12.05 % (4014)Termination phase: Saturation
% 73.58/12.05
% 73.58/12.05 % (4014)Memory used [KB]: 13048
% 73.58/12.05 % (4014)Time elapsed: 0.949 s
% 73.58/12.06 % (4014)Instructions burned: 3202 (million)
% 73.58/12.06 % (4014)------------------------------
% 73.58/12.06 % (4014)------------------------------
% 73.58/12.07 % (4021)dis-1_1:1_amm=off:au=on:cbe=off:spb=intro:i=2207:si=on:rtra=on_0 on DTF2THF_3672 for (2898ds/2207Mi)
% 73.58/12.09 % (4016)Instruction limit reached!
% 73.58/12.09 % (4016)------------------------------
% 73.58/12.09 % (4016)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 73.58/12.09 % (4016)Termination reason: Unknown
% 73.58/12.09 % (4016)Termination phase: Saturation
% 73.58/12.09
% 73.58/12.09 % (4016)Memory used [KB]: 10234
% 73.58/12.09 % (4016)Time elapsed: 0.753 s
% 73.58/12.09 % (4016)Instructions burned: 3052 (million)
% 73.58/12.09 % (4016)------------------------------
% 73.58/12.09 % (4016)------------------------------
% 73.58/12.10 % (4022)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=8216:si=on:rtra=on_0 on DTF2THF_3672 for (2898ds/8216Mi)
% 75.69/12.40 % (4007)Instruction limit reached!
% 75.69/12.40 % (4007)------------------------------
% 75.69/12.40 % (4007)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 75.69/12.40 % (4007)Termination reason: Unknown
% 75.69/12.40 % (4007)Termination phase: Saturation
% 75.69/12.40
% 75.69/12.40 % (4007)Memory used [KB]: 16630
% 75.69/12.40 % (4007)Time elapsed: 1.837 s
% 75.69/12.40 % (4007)Instructions burned: 5446 (million)
% 75.69/12.40 % (4007)------------------------------
% 75.69/12.40 % (4007)------------------------------
% 75.69/12.41 % (4023)lrs+1010_1:1_atotf=0.5:au=on:cbe=off:cnfonf=lazy_not_be_gen:fe=off:nwc=5.0:spb=units:i=430:si=on:rtra=on_0 on DTF2THF_3672 for (2895ds/430Mi)
% 76.10/12.53 % (4023)Instruction limit reached!
% 76.10/12.53 % (4023)------------------------------
% 76.10/12.53 % (4023)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.10/12.53 % (4023)Termination reason: Unknown
% 76.10/12.53 % (4023)Termination phase: Saturation
% 76.10/12.53
% 76.10/12.53 % (4023)Memory used [KB]: 7419
% 76.10/12.53 % (4023)Time elapsed: 0.119 s
% 76.10/12.53 % (4023)Instructions burned: 430 (million)
% 76.10/12.53 % (4023)------------------------------
% 76.10/12.53 % (4023)------------------------------
% 76.10/12.54 % (4024)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=2012:si=on:rtra=on_0 on DTF2THF_3672 for (2893ds/2012Mi)
% 76.62/12.63 % (4013)Instruction limit reached!
% 76.62/12.63 % (4013)------------------------------
% 76.62/12.63 % (4013)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.62/12.63 % (4013)Termination reason: Unknown
% 76.62/12.63 % (4013)Termination phase: Saturation
% 76.62/12.63
% 76.62/12.63 % (4013)Memory used [KB]: 17526
% 76.62/12.63 % (4013)Time elapsed: 1.546 s
% 76.62/12.63 % (4013)Instructions burned: 5216 (million)
% 76.62/12.63 % (4013)------------------------------
% 76.62/12.63 % (4013)------------------------------
% 76.62/12.64 % (4025)ott+1010_1:32_apa=on:atotf=0.3:au=on:c=on:cnfonf=off:fe=off:fsr=off:nm=6:piset=or:sac=on:sos=on:i=631:si=on:rtra=on_0 on DTF2THF_3672 for (2892ds/631Mi)
% 76.96/12.73 % (4021)Instruction limit reached!
% 76.96/12.73 % (4021)------------------------------
% 76.96/12.73 % (4021)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 76.96/12.73 % (4021)Termination reason: Unknown
% 76.96/12.73 % (4021)Termination phase: Saturation
% 76.96/12.73
% 76.96/12.73 % (4021)Memory used [KB]: 11385
% 76.96/12.73 % (4021)Time elapsed: 0.686 s
% 76.96/12.73 % (4021)Instructions burned: 2207 (million)
% 76.96/12.73 % (4021)------------------------------
% 76.96/12.73 % (4021)------------------------------
% 76.96/12.74 % (4026)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=8785:si=on:rtra=on_0 on DTF2THF_3672 for (2891ds/8785Mi)
% 77.94/12.83 % (4025)Instruction limit reached!
% 77.94/12.83 % (4025)------------------------------
% 77.94/12.83 % (4025)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 77.94/12.83 % (4025)Termination reason: Unknown
% 77.94/12.83 % (4025)Termination phase: Saturation
% 77.94/12.83
% 77.94/12.83 % (4025)Memory used [KB]: 9083
% 77.94/12.83 % (4025)Time elapsed: 0.197 s
% 77.94/12.83 % (4025)Instructions burned: 633 (million)
% 77.94/12.83 % (4025)------------------------------
% 77.94/12.83 % (4025)------------------------------
% 77.94/12.84 % (4027)lrs-1002_1:128_abs=on:bd=preordered:cbe=off:e2e=on:fde=unused:fe=off:tgt=full:i=739:si=on:rtra=on_0 on DTF2THF_3672 for (2890ds/739Mi)
% 80.57/13.07 % (4027)Instruction limit reached!
% 80.57/13.07 % (4027)------------------------------
% 80.57/13.07 % (4027)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 80.57/13.07 % (4027)Termination reason: Unknown
% 80.57/13.07 % (4027)Termination phase: Saturation
% 80.57/13.07
% 80.57/13.07 % (4027)Memory used [KB]: 7931
% 80.57/13.07 % (4027)Time elapsed: 0.228 s
% 80.57/13.07 % (4027)Instructions burned: 740 (million)
% 80.57/13.07 % (4027)------------------------------
% 80.57/13.07 % (4027)------------------------------
% 80.57/13.08 % (4028)dis+1002_1:1024_fe=off:hud=5:prag=on:i=5473:si=on:rtra=on_0 on DTF2THF_3672 for (2888ds/5473Mi)
% 81.24/13.14 % (4024)Instruction limit reached!
% 81.24/13.14 % (4024)------------------------------
% 81.24/13.14 % (4024)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.24/13.14 % (4024)Termination reason: Unknown
% 81.24/13.14 % (4024)Termination phase: Saturation
% 81.24/13.14
% 81.24/13.14 % (4024)Memory used [KB]: 18805
% 81.24/13.14 % (4024)Time elapsed: 0.600 s
% 81.24/13.14 % (4024)Instructions burned: 2013 (million)
% 81.24/13.14 % (4024)------------------------------
% 81.24/13.14 % (4024)------------------------------
% 81.24/13.15 % (4029)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=43570:si=on:rtra=on_0 on DTF2THF_3672 for (2887ds/43570Mi)
% 81.24/13.17 % (4029)Refutation not found, incomplete strategy
% 81.24/13.17 % (4029)------------------------------
% 81.24/13.17 % (4029)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 81.24/13.17 % (4029)Termination reason: Refutation not found, incomplete strategy
% 81.24/13.17
% 81.24/13.17
% 81.24/13.17 % (4029)Memory used [KB]: 6652
% 81.24/13.17 % (4029)Time elapsed: 0.024 s
% 81.24/13.17 % (4029)Instructions burned: 72 (million)
% 81.24/13.17 % (4029)------------------------------
% 81.24/13.17 % (4029)------------------------------
% 81.24/13.18 % (4030)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=8382:si=on:rtra=on_0 on DTF2THF_3672 for (2887ds/8382Mi)
% 82.24/13.33 % (4020)Instruction limit reached!
% 82.24/13.33 % (4020)------------------------------
% 82.24/13.33 % (4020)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.24/13.33 % (4020)Termination reason: Unknown
% 82.24/13.33 % (4020)Termination phase: Saturation
% 82.24/13.33
% 82.24/13.33 % (4020)Memory used [KB]: 14839
% 82.24/13.33 % (4020)Time elapsed: 1.331 s
% 82.24/13.33 % (4020)Instructions burned: 4689 (million)
% 82.24/13.33 % (4020)------------------------------
% 82.24/13.33 % (4020)------------------------------
% 82.24/13.34 % (4031)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=407:si=on:rtra=on_0 on DTF2THF_3672 for (2885ds/407Mi)
% 82.24/13.36 % (4018)Instruction limit reached!
% 82.24/13.36 % (4018)------------------------------
% 82.24/13.36 % (4018)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.24/13.36 % (4018)Termination reason: Unknown
% 82.24/13.36 % (4018)Termination phase: Saturation
% 82.24/13.36
% 82.24/13.36 % (4018)Memory used [KB]: 10874
% 82.24/13.36 % (4018)Time elapsed: 1.941 s
% 82.24/13.36 % (4018)Instructions burned: 6805 (million)
% 82.24/13.36 % (4018)------------------------------
% 82.24/13.36 % (4018)------------------------------
% 82.24/13.37 % (4032)lrs+10_1:50_cbe=off:cnfonf=lazy_pi_sigma_gen:fe=off:hud=5:plsq=on:plsqr=1,32:sos=all:i=2971:si=on:rtra=on_0 on DTF2THF_3672 for (2885ds/2971Mi)
% 82.66/13.44 % (4032)Refutation not found, incomplete strategy
% 82.66/13.44 % (4032)------------------------------
% 82.66/13.44 % (4032)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.66/13.44 % (4032)Termination reason: Refutation not found, incomplete strategy
% 82.66/13.44
% 82.66/13.44
% 82.66/13.44 % (4032)Memory used [KB]: 7675
% 82.66/13.44 % (4032)Time elapsed: 0.075 s
% 82.66/13.44 % (4032)Instructions burned: 277 (million)
% 82.66/13.44 % (4032)------------------------------
% 82.66/13.44 % (4032)------------------------------
% 82.66/13.45 % (4033)lrs+1002_1:1_aac=none:bd=off:e2e=on:fde=none:fe=off:piset=or:prag=on:rawr=on:sos=on:updr=off:i=9822:si=on:rtra=on_0 on DTF2THF_3672 for (2884ds/9822Mi)
% 82.66/13.46 % (4031)Instruction limit reached!
% 82.66/13.46 % (4031)------------------------------
% 82.66/13.46 % (4031)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 82.66/13.46 % (4031)Termination reason: Unknown
% 82.66/13.46 % (4031)Termination phase: Saturation
% 82.66/13.46
% 82.66/13.46 % (4031)Memory used [KB]: 7803
% 82.66/13.46 % (4031)Time elapsed: 0.114 s
% 82.66/13.46 % (4031)Instructions burned: 409 (million)
% 82.66/13.46 % (4031)------------------------------
% 82.66/13.46 % (4031)------------------------------
% 82.66/13.47 % (4034)dis+10_5:1_av=off:ntd=on:s2a=on:s2at=3.0:sgt=16:sp=unary_frequency:ss=axioms:i=8425:si=on:rtra=on_0 on DTF2THF_3672 for (2884ds/8425Mi)
% 83.16/13.50 % (4033)Refutation not found, incomplete strategy
% 83.16/13.50 % (4033)------------------------------
% 83.16/13.50 % (4033)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.16/13.50 % (4033)Termination reason: Refutation not found, incomplete strategy
% 83.16/13.50
% 83.16/13.50
% 83.16/13.50 % (4033)Memory used [KB]: 7419
% 83.16/13.50 % (4033)Time elapsed: 0.048 s
% 83.16/13.50 % (4033)Instructions burned: 160 (million)
% 83.16/13.50 % (4033)------------------------------
% 83.16/13.50 % (4033)------------------------------
% 83.16/13.51 % (4035)lrs+30_1:1_aac=none:au=on:cbe=off:cs=on:nm=2:rawr=on:sos=on:i=3107:si=on:rtra=on_0 on DTF2THF_3672 for (2884ds/3107Mi)
% 83.52/13.64 % (4017)Instruction limit reached!
% 83.52/13.64 % (4017)------------------------------
% 83.52/13.64 % (4017)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.52/13.64 % (4017)Termination reason: Unknown
% 83.52/13.64 % (4017)Termination phase: Saturation
% 83.52/13.64
% 83.52/13.64 % (4017)Memory used [KB]: 13048
% 83.52/13.64 % (4017)Time elapsed: 2.269 s
% 83.52/13.64 % (4017)Instructions burned: 7314 (million)
% 83.52/13.64 % (4017)------------------------------
% 83.52/13.64 % (4017)------------------------------
% 83.52/13.65 % (4036)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=7967:si=on:rtra=on_0 on DTF2THF_3672 for (2882ds/7967Mi)
% 83.77/13.73 % (4036)Refutation not found, incomplete strategy
% 83.77/13.73 % (4036)------------------------------
% 83.77/13.73 % (4036)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 83.77/13.73 % (4036)Termination reason: Refutation not found, incomplete strategy
% 83.77/13.73
% 83.77/13.73
% 83.77/13.73 % (4036)Memory used [KB]: 7675
% 83.77/13.73 % (4036)Time elapsed: 0.075 s
% 83.77/13.73 % (4036)Instructions burned: 277 (million)
% 83.77/13.73 % (4036)------------------------------
% 83.77/13.73 % (4036)------------------------------
% 83.77/13.74 % (4037)lrs+1010_10:959_abs=on:acc=on:bd=off:ccuc=small_ones:cha=on:cnfonf=lazy_simp:fd=preordered:fe=off:hud=3:ile=on:kws=inv_frequency:nm=2:piset=and:sd=5:sp=frequency:spb=goal_then_units:ss=axioms:st=4.5:i=3629:si=on:rtra=on_0 on DTF2THF_3672 for (2881ds/3629Mi)
% 90.26/14.44 % (4035)Instruction limit reached!
% 90.26/14.44 % (4035)------------------------------
% 90.26/14.44 % (4035)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.26/14.44 % (4035)Termination reason: Unknown
% 90.26/14.44 % (4035)Termination phase: Saturation
% 90.26/14.44
% 90.26/14.44 % (4035)Memory used [KB]: 16247
% 90.26/14.44 % (4035)Time elapsed: 0.928 s
% 90.26/14.44 % (4035)Instructions burned: 3109 (million)
% 90.26/14.44 % (4035)------------------------------
% 90.26/14.44 % (4035)------------------------------
% 90.26/14.45 % (4038)lrs+1010_1:1024_au=on:fe=axiom:lwlo=on:nm=0:ntd=on:nwc=10.0:spb=non_intro:uhcvi=on:i=939:si=on:rtra=on_0 on DTF2THF_3672 for (2874ds/939Mi)
% 90.91/14.55 % (4022)Instruction limit reached!
% 90.91/14.55 % (4022)------------------------------
% 90.91/14.55 % (4022)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 90.91/14.55 % (4022)Termination reason: Unknown
% 90.91/14.55 % (4022)Termination phase: Saturation
% 90.91/14.55
% 90.91/14.55 % (4022)Memory used [KB]: 10746
% 90.91/14.55 % (4022)Time elapsed: 2.472 s
% 90.91/14.55 % (4022)Instructions burned: 8217 (million)
% 90.91/14.55 % (4022)------------------------------
% 90.91/14.55 % (4022)------------------------------
% 90.91/14.56 % (4039)dis+1666_14:1_cnfonf=lazy_gen:fe=off:hud=10:piset=all_but_not_eq:prag=on:sp=const_max:i=1188:si=on:rtra=on_0 on DTF2THF_3672 for (2873ds/1188Mi)
% 91.50/14.64 % (4037)Instruction limit reached!
% 91.50/14.64 % (4037)------------------------------
% 91.50/14.64 % (4037)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.50/14.64 % (4037)Termination reason: Unknown
% 91.50/14.64 % (4037)Termination phase: Saturation
% 91.50/14.64
% 91.50/14.64 % (4037)Memory used [KB]: 8699
% 91.50/14.64 % (4037)Time elapsed: 0.888 s
% 91.50/14.64 % (4037)Instructions burned: 3633 (million)
% 91.50/14.64 % (4037)------------------------------
% 91.50/14.64 % (4037)------------------------------
% 91.50/14.65 % (4040)dis+21_3:2_avsq=on:cbe=off:e2e=on:flr=on:ile=on:nwc=5.0:piset=or:rawr=on:sp=occurrence:i=3205:si=on:rtra=on_0 on DTF2THF_3672 for (2872ds/3205Mi)
% 91.94/14.70 % (4038)Instruction limit reached!
% 91.94/14.70 % (4038)------------------------------
% 91.94/14.70 % (4038)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.94/14.70 % (4038)Termination reason: Unknown
% 91.94/14.70 % (4038)Termination phase: Saturation
% 91.94/14.70
% 91.94/14.70 % (4038)Memory used [KB]: 9210
% 91.94/14.70 % (4038)Time elapsed: 0.257 s
% 91.94/14.70 % (4038)Instructions burned: 941 (million)
% 91.94/14.70 % (4038)------------------------------
% 91.94/14.70 % (4038)------------------------------
% 91.94/14.71 % (4041)lrs+1010_1:1_cnfonf=off:ntd=on:nwc=3.0:s2a=on:sp=const_frequency:i=865:si=on:rtra=on_0 on DTF2THF_3672 for (2872ds/865Mi)
% 91.94/14.73 % (4028)Instruction limit reached!
% 91.94/14.73 % (4028)------------------------------
% 91.94/14.73 % (4028)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 91.94/14.73 % (4028)Termination reason: Unknown
% 91.94/14.73 % (4028)Termination phase: Saturation
% 91.94/14.73
% 91.94/14.73 % (4028)Memory used [KB]: 10746
% 91.94/14.73 % (4028)Time elapsed: 1.649 s
% 91.94/14.73 % (4028)Instructions burned: 5474 (million)
% 91.94/14.73 % (4028)------------------------------
% 91.94/14.73 % (4028)------------------------------
% 91.94/14.74 % (4042)ott+1002_1:1_au=on:bd=off:cbe=off:cha=on:cnfonf=lazy_pi_sigma_gen:fd=off:fe=off:ntd=on:sp=const_frequency:i=7469:si=on:rtra=on_0 on DTF2THF_3672 for (2871ds/7469Mi)
% 92.85/14.91 % (4039)Instruction limit reached!
% 92.85/14.91 % (4039)------------------------------
% 92.85/14.91 % (4039)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.85/14.91 % (4039)Termination reason: Unknown
% 92.85/14.91 % (4039)Termination phase: Saturation
% 92.85/14.91
% 92.85/14.91 % (4039)Memory used [KB]: 9594
% 92.85/14.92 % (4039)Time elapsed: 0.355 s
% 92.85/14.92 % (4039)Instructions burned: 1188 (million)
% 92.85/14.92 % (4039)------------------------------
% 92.85/14.92 % (4039)------------------------------
% 92.85/14.93 % (4043)dis+10_1:10_bd=preordered:e2e=on:fde=none:fe=axiom:hud=3:kws=precedence:nwc=3.0:prag=on:sp=const_max:tgt=full:i=4165:si=on:rtra=on_0 on DTF2THF_3672 for (2870ds/4165Mi)
% 92.85/14.97 % (4041)Instruction limit reached!
% 92.85/14.97 % (4041)------------------------------
% 92.85/14.97 % (4041)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 92.85/14.97 % (4041)Termination reason: Unknown
% 92.85/14.97 % (4041)Termination phase: Saturation
% 92.85/14.97
% 92.85/14.97 % (4041)Memory used [KB]: 8571
% 92.85/14.97 % (4041)Time elapsed: 0.259 s
% 92.85/14.97 % (4041)Instructions burned: 867 (million)
% 92.85/14.97 % (4041)------------------------------
% 92.85/14.97 % (4041)------------------------------
% 92.85/14.98 % (4044)dis+1010_1:1_au=on:avsq=on:cnfonf=lazy_simp:fsr=off:ntd=on:nwc=10.0:sp=reverse_frequency:ss=axioms:st=1.5:i=13468:si=on:rtra=on_0 on DTF2THF_3672 for (2869ds/13468Mi)
% 95.24/15.12 % (4034)First to succeed.
% 95.24/15.12 % (4034)Refutation found. Thanks to Tanya!
% 95.24/15.12 % SZS status Theorem for DTF2THF_3672
% 95.24/15.12 % SZS output start Proof for DTF2THF_3672
% 95.24/15.12 thf(type_def_5, type, secrecy_specID: $tType).
% 95.24/15.12 thf(type_def_6, type, secrecy_KS: $tType).
% 95.24/15.12 thf(type_def_7, type, set: ($tType) > $tType).
% 95.24/15.12 thf(type_def_9, type, list: ($tType) > $tType).
% 95.24/15.12 thf(type_def_10, type, secrecy_Expression: $tType).
% 95.24/15.12 thf(type_def_11, type, secrecy_chanID: $tType).
% 95.24/15.12 thf(type_def_12, type, secrecy_Keys: $tType).
% 95.24/15.12 thf(type_def_13, type, secrecy_Secrets: $tType).
% 95.24/15.12 thf(type_def_14, type, nat: $tType).
% 95.24/15.12 thf(func_def_0, type, secrecy_Expression: $tType).
% 95.24/15.12 thf(func_def_1, type, secrecy_Secrets: $tType).
% 95.24/15.12 thf(func_def_2, type, secrecy_specID: $tType).
% 95.24/15.12 thf(func_def_3, type, secrecy_chanID: $tType).
% 95.24/15.12 thf(func_def_4, type, secrecy_Keys: $tType).
% 95.24/15.12 thf(func_def_5, type, secrecy_KS: $tType).
% 95.24/15.12 thf(func_def_6, type, list: ($tType) > $tType).
% 95.24/15.12 thf(func_def_7, type, set: ($tType) > $tType).
% 95.24/15.12 thf(func_def_8, type, nat: $tType).
% 95.24/15.12 thf(func_def_9, type, bounded_lattice: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_10, type, type: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_11, type, bot: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_12, type, ord: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_13, type, order: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_14, type, linorder: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_15, type, preorder: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_16, type, bounde1808546759up_bot: !>[X0: $tType]:($o)).
% 95.24/15.12 thf(func_def_17, type, localSecrets: secrecy_specID > set @ secrecy_KS).
% 95.24/15.12 thf(func_def_18, type, knowle1667810483orrect: secrecy_specID > secrecy_KS > $o).
% 95.24/15.12 thf(func_def_19, type, knowle1437066798e_know: secrecy_specID > secrecy_KS > $o).
% 95.24/15.12 thf(func_def_20, type, sup_sup: !>[X0: $tType]:(X0 > X0 > X0)).
% 95.24/15.12 thf(func_def_21, type, mem: !>[X0: $tType]:(X0 > list @ X0 > $o)).
% 95.24/15.12 thf(func_def_22, type, bot_bot: !>[X0: $tType]:(X0)).
% 95.24/15.12 thf(func_def_23, type, ord_less_eq: !>[X0: $tType]:(X0 > X0 > $o)).
% 95.24/15.12 thf(func_def_24, type, correctCompositionKS: secrecy_specID > $o).
% 95.24/15.12 thf(func_def_25, type, eout: secrecy_specID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_26, type, eoutM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_27, type, exprChannel: secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_28, type, ine: secrecy_specID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_29, type, ineM: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_30, type, ine_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_31, type, ine_ex1303305700Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_32, type, notSpe1586871396tsExpr: secrecy_specID > list @ secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_33, type, out_exprChannelSet: secrecy_specID > set @ secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_34, type, out_ex985543062Single: secrecy_specID > secrecy_chanID > secrecy_Expression > $o).
% 95.24/15.12 thf(func_def_35, type, specKeys: secrecy_specID > set @ secrecy_Keys).
% 95.24/15.12 thf(func_def_36, type, specKeysSecrets: secrecy_specID > set @ secrecy_KS).
% 95.24/15.12 thf(func_def_37, type, specSecrets: secrecy_specID > set @ secrecy_Secrets).
% 95.24/15.12 thf(func_def_38, type, secrecy_kE: secrecy_Keys > secrecy_Expression).
% 95.24/15.12 thf(func_def_39, type, secrecy_sE: secrecy_Secrets > secrecy_Expression).
% 95.24/15.12 thf(func_def_40, type, secrec1016742679ession: secrecy_KS > secrecy_Expression).
% 95.24/15.12 thf(func_def_41, type, secrecy_case_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 95.24/15.12 thf(func_def_42, type, secrecy_kKS: secrecy_Keys > secrecy_KS).
% 95.24/15.12 thf(func_def_43, type, secrecy_rec_KS: !>[X0: $tType]:((secrecy_Keys > X0) > (secrecy_Secrets > X0) > secrecy_KS > X0)).
% 95.24/15.12 thf(func_def_44, type, secrecy_sKS: secrecy_Secrets > secrecy_KS).
% 95.24/15.12 thf(func_def_45, type, collect: !>[X0: $tType]:((X0 > $o) > set @ X0)).
% 95.24/15.12 thf(func_def_46, type, insert: !>[X0: $tType]:(X0 > set @ X0 > set @ X0)).
% 95.24/15.12 thf(func_def_47, type, is_empty: !>[X0: $tType]:(set @ X0 > $o)).
% 95.24/15.12 thf(func_def_48, type, is_singleton: !>[X0: $tType]:(set @ X0 > $o)).
% 95.24/15.12 thf(func_def_49, type, the_elem: !>[X0: $tType]:(set @ X0 > X0)).
% 95.24/15.12 thf(func_def_50, type, correctCompositionIn: secrecy_specID > $o).
% 95.24/15.12 thf(func_def_51, type, correc965049635ionLoc: secrecy_specID > $o).
% 95.24/15.12 thf(func_def_52, type, correc990227761ionOut: secrecy_specID > $o).
% 95.24/15.12 thf(func_def_53, type, inStream: secrecy_specID > set @ secrecy_chanID > $o).
% 95.24/15.12 thf(func_def_54, type, ins: secrecy_specID > set @ secrecy_chanID).
% 95.24/15.12 thf(func_def_55, type, loc: secrecy_specID > set @ secrecy_chanID).
% 95.24/15.12 thf(func_def_56, type, locStream: secrecy_specID > set @ secrecy_chanID > $o).
% 95.24/15.12 thf(func_def_57, type, out: secrecy_specID > set @ secrecy_chanID).
% 95.24/15.12 thf(func_def_58, type, outStream: secrecy_specID > set @ secrecy_chanID > $o).
% 95.24/15.12 thf(func_def_59, type, subcomponents: secrecy_specID > set @ secrecy_specID).
% 95.24/15.12 thf(func_def_60, type, member: !>[X0: $tType]:(X0 > set @ X0 > $o)).
% 95.24/15.12 thf(func_def_61, type, p: secrecy_specID).
% 95.24/15.12 thf(func_def_62, type, pq: secrecy_specID).
% 95.24/15.12 thf(func_def_63, type, q: secrecy_specID).
% 95.24/15.12 thf(func_def_64, type, m: secrecy_KS).
% 95.24/15.12 thf(func_def_65, type, secret: secrecy_Secrets).
% 95.24/15.12 thf(func_def_81, type, sK0: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 95.24/15.12 thf(func_def_82, type, sK1: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 95.24/15.12 thf(func_def_83, type, sK2: secrecy_KS > secrecy_Secrets).
% 95.24/15.12 thf(func_def_84, type, sK3: secrecy_KS > secrecy_Keys).
% 95.24/15.12 thf(func_def_85, type, sK4: !>[X0: $tType]:(set @ X0 > X0)).
% 95.24/15.12 thf(func_def_86, type, sK5: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 95.24/15.12 thf(func_def_87, type, sK6: (secrecy_KS > $o) > secrecy_Secrets).
% 95.24/15.12 thf(func_def_88, type, sK7: (secrecy_KS > $o) > secrecy_Keys).
% 95.24/15.12 thf(func_def_89, type, sK8: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 95.24/15.12 thf(func_def_90, type, sK9: !>[X0: $tType]:(set @ X0 > set @ X0 > set @ X0 > set @ X0)).
% 95.24/15.12 thf(func_def_91, type, sK10: !>[X0: $tType]:(set @ X0 > set @ X0 > X0)).
% 95.24/15.12 thf(func_def_92, type, sK11: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 95.24/15.12 thf(func_def_93, type, sK12: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 95.24/15.12 thf(func_def_94, type, sK13: !>[X0: $tType]:(set @ X0 > X0 > set @ X0)).
% 95.24/15.12 thf(func_def_95, type, sK14: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Keys).
% 95.24/15.12 thf(func_def_96, type, sK15: secrecy_KS > secrecy_specID > secrecy_specID > secrecy_Secrets).
% 95.24/15.12 thf(func_def_97, type, sK16: secrecy_Expression > secrecy_specID > secrecy_chanID).
% 95.24/15.12 thf(func_def_98, type, sK17: secrecy_Secrets > secrecy_specID > secrecy_chanID).
% 95.24/15.12 thf(func_def_99, type, sK18: secrecy_Keys > secrecy_specID > secrecy_chanID).
% 95.24/15.12 thf(func_def_100, type, sK19: !>[X0: $tType, X1: $tType]:((X1 > X0) > (X1 > X0) > X1)).
% 95.24/15.12 thf(func_def_101, type, ph20: !>[X0: $tType]:(X0)).
% 95.24/15.12 thf(f7265,plain,(
% 95.24/15.12 $false),
% 95.24/15.12 inference(subsumption_resolution,[status(thm)],[f7264,f1140])).
% 95.24/15.12 thf(f1140,plain,(
% 95.24/15.12 ((ine @ q @ (secrecy_sE @ secret)) != $true)),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f796])).
% 95.24/15.12 thf(f796,plain,(
% 95.24/15.12 ((ine @ q @ (secrecy_sE @ secret)) != $true)),
% 95.24/15.12 inference(flattening,[status(thm)],[f413])).
% 95.24/15.12 thf(f413,plain,(
% 95.24/15.12 ~((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f412])).
% 95.24/15.12 thf(f412,plain,(
% 95.24/15.12 ~(ine @ q @ (secrecy_sE @ secret))),
% 95.24/15.12 inference(rectify,[status(thm)],[f3])).
% 95.24/15.12 thf(f3,axiom,(
% 95.24/15.12 ~(ine @ q @ (secrecy_sE @ secret))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_2_sg2a)).
% 95.24/15.12 thf(f7264,plain,(
% 95.24/15.12 ((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 95.24/15.12 inference(subsumption_resolution,[status(thm)],[f7263,f1153])).
% 95.24/15.12 thf(f1153,plain,(
% 95.24/15.12 ((correc965049635ionLoc @ pq) = $true)),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f757])).
% 95.24/15.12 thf(f757,plain,(
% 95.24/15.12 ((correc965049635ionLoc @ pq) = $true)),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f756])).
% 95.24/15.12 thf(f756,plain,(
% 95.24/15.12 (correc965049635ionLoc @ pq)),
% 95.24/15.12 inference(rectify,[status(thm)],[f1])).
% 95.24/15.12 thf(f1,axiom,(
% 95.24/15.12 (correc965049635ionLoc @ pq)),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_0_cCompLoc)).
% 95.24/15.12 thf(f7263,plain,(
% 95.24/15.12 ((correc965049635ionLoc @ pq) != $true) | ((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 95.24/15.12 inference(subsumption_resolution,[status(thm)],[f7262,f1130])).
% 95.24/15.12 thf(f1130,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) != $true)),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f795])).
% 95.24/15.12 thf(f795,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) != $true)),
% 95.24/15.12 inference(flattening,[status(thm)],[f555])).
% 95.24/15.12 thf(f555,plain,(
% 95.24/15.12 ~((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f554])).
% 95.24/15.12 thf(f554,plain,(
% 95.24/15.12 ~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 95.24/15.12 inference(rectify,[status(thm)],[f5])).
% 95.24/15.12 thf(f5,axiom,(
% 95.24/15.12 ~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_4_sg2b)).
% 95.24/15.12 thf(f7262,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 95.24/15.12 inference(subsumption_resolution,[status(thm)],[f7261,f1119])).
% 95.24/15.12 thf(f1119,plain,(
% 95.24/15.12 ((ine @ p @ (secrecy_sE @ secret)) != $true)),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f797])).
% 95.24/15.12 thf(f797,plain,(
% 95.24/15.12 ((ine @ p @ (secrecy_sE @ secret)) != $true)),
% 95.24/15.12 inference(flattening,[status(thm)],[f289])).
% 95.24/15.12 thf(f289,plain,(
% 95.24/15.12 ~((ine @ p @ (secrecy_sE @ secret)) = $true)),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f288])).
% 95.24/15.12 thf(f288,plain,(
% 95.24/15.12 ~(ine @ p @ (secrecy_sE @ secret))),
% 95.24/15.12 inference(rectify,[status(thm)],[f2])).
% 95.24/15.12 thf(f2,axiom,(
% 95.24/15.12 ~(ine @ p @ (secrecy_sE @ secret))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_1_sg1a)).
% 95.24/15.12 thf(f7261,plain,(
% 95.24/15.12 ((ine @ p @ (secrecy_sE @ secret)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((ine @ q @ (secrecy_sE @ secret)) = $true) | ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 95.24/15.12 inference(subsumption_resolution,[status(thm)],[f7250,f1125])).
% 95.24/15.12 thf(f1125,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) != $true)),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f792])).
% 95.24/15.12 thf(f792,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) != $true)),
% 95.24/15.12 inference(flattening,[status(thm)],[f779])).
% 95.24/15.12 thf(f779,plain,(
% 95.24/15.12 ~((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) = $true)),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f778])).
% 95.24/15.12 thf(f778,plain,(
% 95.24/15.12 ~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p))),
% 95.24/15.12 inference(rectify,[status(thm)],[f4])).
% 95.24/15.12 thf(f4,axiom,(
% 95.24/15.12 ~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_3_sg1b)).
% 95.24/15.12 thf(f7250,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) = $true) | ((ine @ p @ (secrecy_sE @ secret)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true) | ((ine @ q @ (secrecy_sE @ secret)) = $true)),
% 95.24/15.12 inference(trivial_inequality_removal,[status(thm)],[f7242])).
% 95.24/15.12 thf(f7242,plain,(
% 95.24/15.12 ((subcomponents @ pq) != (subcomponents @ pq)) | ((ine @ q @ (secrecy_sE @ secret)) = $true) | ((correc965049635ionLoc @ pq) != $true) | ((ine @ p @ (secrecy_sE @ secret)) = $true) | ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ p)) = $true) | ($true != $true) | ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ q)) = $true)),
% 95.24/15.12 inference(superposition,[status(thm)],[f1467,f1108])).
% 95.24/15.12 thf(f1108,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq)) = $true)),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f790])).
% 95.24/15.12 thf(f790,plain,(
% 95.24/15.12 ((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq)) = $true)),
% 95.24/15.12 inference(flattening,[status(thm)],[f461])).
% 95.24/15.12 thf(f461,plain,(
% 95.24/15.12 ~~((member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq)) = $true)),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f460])).
% 95.24/15.12 thf(f460,plain,(
% 95.24/15.12 ~~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq))),
% 95.24/15.12 inference(rectify,[status(thm)],[f282])).
% 95.24/15.12 thf(f282,negated_conjecture,(
% 95.24/15.12 ~~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq))),
% 95.24/15.12 inference(negated_conjecture,[status(cth)],[f281])).
% 95.24/15.12 thf(f281,conjecture,(
% 95.24/15.12 ~(member @ secrecy_KS @ (secrecy_sKS @ secret) @ (localSecrets @ pq))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',conj_0)).
% 95.24/15.12 thf(f1467,plain,(
% 95.24/15.12 ( ! [X0 : secrecy_specID,X1 : secrecy_Secrets] : (($true != (member @ secrecy_KS @ (secrecy_sKS @ X1) @ (localSecrets @ X0))) | ((ine @ p @ (secrecy_sE @ X1)) = $true) | ((correc965049635ionLoc @ X0) != $true) | ((member @ secrecy_KS @ (secrecy_sKS @ X1) @ (localSecrets @ q)) = $true) | ((ine @ q @ (secrecy_sE @ X1)) = $true) | ((member @ secrecy_KS @ (secrecy_sKS @ X1) @ (localSecrets @ p)) = $true) | ((subcomponents @ pq) != (subcomponents @ X0))) )),
% 95.24/15.12 inference(superposition,[status(thm)],[f1046,f1080])).
% 95.24/15.12 thf(f1080,plain,(
% 95.24/15.12 ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f6])).
% 95.24/15.12 thf(f6,axiom,(
% 95.24/15.12 ((subcomponents @ pq) = (insert @ secrecy_specID @ p @ (insert @ secrecy_specID @ q @ bot_bot @ set @ secrecy_specID)))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_5_subPQ)).
% 95.24/15.12 thf(f1046,plain,(
% 95.24/15.12 ( ! [X2 : secrecy_specID,X3 : secrecy_Secrets,X0 : secrecy_specID,X1 : secrecy_specID] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) != (subcomponents @ X0)) | ($true = (ine @ X2 @ (secrecy_sE @ X3))) | ((correc965049635ionLoc @ X0) != $true) | ((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X1)) = $true) | ($true != (member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X0))) | ((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) = $true) | ((ine @ X1 @ (secrecy_sE @ X3)) = $true)) )),
% 95.24/15.12 inference(cnf_transformation,[status(thm)],[f889])).
% 95.24/15.12 thf(f889,plain,(
% 95.24/15.12 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_Secrets] : (($true != (member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X0))) | ((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X1)) = $true) | ((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) = $true) | ((ine @ X1 @ (secrecy_sE @ X3)) = $true) | ($true = (ine @ X2 @ (secrecy_sE @ X3))) | ((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) != (subcomponents @ X0)) | ((correc965049635ionLoc @ X0) != $true))),
% 95.24/15.12 inference(flattening,[status(thm)],[f888])).
% 95.24/15.12 thf(f888,plain,(
% 95.24/15.12 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_Secrets] : ((((((($true != (member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X0))) | ((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) = $true)) | ((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X1)) = $true)) | ($true = (ine @ X2 @ (secrecy_sE @ X3)))) | ((ine @ X1 @ (secrecy_sE @ X3)) = $true)) | ((correc965049635ionLoc @ X0) != $true)) | ((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) != (subcomponents @ X0)))),
% 95.24/15.12 inference(ennf_transformation,[status(thm)],[f818])).
% 95.24/15.12 thf(f818,plain,(
% 95.24/15.12 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_Secrets] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) = (subcomponents @ X0)) => (((correc965049635ionLoc @ X0) = $true) => (((ine @ X1 @ (secrecy_sE @ X3)) != $true) => (($true != (ine @ X2 @ (secrecy_sE @ X3))) => (((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X1)) != $true) => (((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) != $true) => ($true != (member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X0)))))))))),
% 95.24/15.12 inference(flattening,[status(thm)],[f485])).
% 95.24/15.12 thf(f485,plain,(
% 95.24/15.12 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_Secrets] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) = (subcomponents @ X0)) => (((correc965049635ionLoc @ X0) = $true) => (~((ine @ X1 @ (secrecy_sE @ X3)) = $true) => (~($true = (ine @ X2 @ (secrecy_sE @ X3))) => (~((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X1)) = $true) => (~((member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) = $true) => ~($true = (member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X0)))))))))),
% 95.24/15.12 inference(fool_elimination,[status(thm)],[f484])).
% 95.24/15.12 thf(f484,plain,(
% 95.24/15.12 ! [X0 : secrecy_specID,X1 : secrecy_specID,X2 : secrecy_specID,X3 : secrecy_Secrets] : (((insert @ secrecy_specID @ X1 @ (insert @ secrecy_specID @ X2 @ bot_bot @ set @ secrecy_specID)) = (subcomponents @ X0)) => ((correc965049635ionLoc @ X0) => (~(ine @ X1 @ (secrecy_sE @ X3)) => (~(ine @ X2 @ (secrecy_sE @ X3)) => (~(member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X1)) => (~(member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X2)) => ~(member @ secrecy_KS @ (secrecy_sKS @ X3) @ (localSecrets @ X0))))))))),
% 95.24/15.12 inference(rectify,[status(thm)],[f18])).
% 95.24/15.12 thf(f18,axiom,(
% 95.24/15.12 ! [X8 : secrecy_specID,X9 : secrecy_specID,X10 : secrecy_specID,X7 : secrecy_Secrets] : (((subcomponents @ X8) = (insert @ secrecy_specID @ X9 @ (insert @ secrecy_specID @ X10 @ bot_bot @ set @ secrecy_specID))) => ((correc965049635ionLoc @ X8) => (~(ine @ X9 @ (secrecy_sE @ X7)) => (~(ine @ X10 @ (secrecy_sE @ X7)) => (~(member @ secrecy_KS @ (secrecy_sKS @ X7) @ (localSecrets @ X9)) => (~(member @ secrecy_KS @ (secrecy_sKS @ X7) @ (localSecrets @ X10)) => ~(member @ secrecy_KS @ (secrecy_sKS @ X7) @ (localSecrets @ X8))))))))),
% 95.24/15.12 file('/export/starexec/sandbox/tmp/tmp.LC406oXMJp/DTF2THF_3672.p',fact_17_LocalSecretsComposition__neg1__s)).
% 95.24/15.12 % SZS output end Proof for DTF2THF_3672
% 95.24/15.12 % (4034)------------------------------
% 95.24/15.12 % (4034)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 95.24/15.12 % (4034)Termination reason: Refutation
% 95.24/15.12
% 95.24/15.12 % (4034)Memory used [KB]: 8059
% 95.24/15.12 % (4034)Time elapsed: 1.649 s
% 95.24/15.12 % (4034)Instructions burned: 5442 (million)
% 95.24/15.12 % (4034)------------------------------
% 95.24/15.12 % (4034)------------------------------
% 95.24/15.12 % (3778)Success in time 13.198 s
%------------------------------------------------------------------------------